the [possible] fallacy of Lorentz contractions

roosh

Mods apologies if this is in breach of the rules. I've posted this in a thread in the Philosophy section, but it pertains to relativity, so I would be interested in getting some feedback on it.



Abstract
The basic premise that I'll try to put forward is that the idea, or the necessity, of Lorentz contractions, namely length contraction and time dilation (hopefully I'm using the terms correctly here), arise from a potentially erroneous assumption arising from the misapplication of the principle of Galilean invariance, which appears to lead to reference frames (in relativity) being treated as being at absolute rest - from the perspective of an observer at rest in that reference frame.

For the purpose of the discussion it may be helpful to try and put ourselves in the shoes of Lorentz, Einstein, et al to consider the assumptions they were working from and to see how they may have reasoned as they did.

Time dilation
In "the fundamentals of physics" by Halliday, Resnick, and Walker the authors use a variation on the light clock thought experiment (Chapter 39.4 - p1257) , which is effectively no different, but just formalised slightly differently; which may or may make it more helpful as an explanatory - again there is no special significance other than it just happens to be the one I've read.

The thought experiment
A mirror is fixed to the ceiling of the vehicle, and observer O - at rest in this system - holds a laser a distance d below the mirror. At some instant, the laser emits a pulse of light directed towards the mirror (event 1), and at some later time, after reflecting from the mirror, the pulse arrives back at the laser (event 2). Observer O carries a clock C [let's assume it's a light clock]*, and uses it to measure the time interval between these two events.

Because the light pulse has a speed c, the time it takes the pulse to travel from O to the mirror and back to O (the laser) is:

Distance traveled/speed

= 2d/c.


From there it goes on to describe the perspective of an observer on the platform, as per the Einsteinian thought experiment; with the observer on the platform observing a longer path length for the light. From there, gamma (is that the Lorentz factor?) is derived using the Pythagorean theorem.


As mentioned this is effectively the light clock on the train thought experiment, just formulated slightly differently


The issue
The [main] issu, as I see it, is with the treatment of the observer on the train, or more pointedly the treatment of the path length of the photon [in the clock or from the laser] - the treatment of the observer on the platform is debatable as well, but with regard to arriving at the conclusion of Lorentz contractions it is less so.

As we can see from the thought experiment, the path length of the photon is given as twice the distance from the laser to the mirror; this is no different from the light clock thought experiment where the path length is given as twice the distance between mirrors; the measurement is labelled above as 2d.

The issue, however, is that this assumes that the observer on the train, the train itself, the light clock and the laser are all at absolute rest; because anything other than absolute rest would result in a longer path length for the photon. Unless, of course, length contraction and time dilation could be invoked, but if Einstein were to have done so, he would have been guilty, surely, of assuming the conclusion. If we follow the path of reasoning though, I think we can see where the ideas arose from.

Galilean Invariance
According to the principle of Galilean invariance - again, hopefully I'm using these terms correctly - for an observer at rest in an inertial reference frame, there is no experiment that they can conduct to determine if they are at absolute rest, or if they are in motion. This in itself is not being questioned - not saying that it should go unquestioned, it's just not the remit of this particular point - it is however the apparent assumption that seems to follow from this that is being questioned.

Firstly, it is probably worth stating the obvious, that just because an observer cannot determine if they are in motion, they are not free to label themselves as being at rest; it simply means that they cannot tell either way.

One of the assumptions that seems to follow from the idea of galilean invariance, is that a clock at rest in one inertial reference frame will tick at the same rate as a clock at rest in an inertial reference frame moving relative to it. This, however, is a non-sequitor. There may be no experiment yet (that I'm aware of) which will enable an observer to determine if their clock is ticking slower or faster (than that of another observer moving relative to them) - although the [thought] experiment involving the light clocks, if it materialised, probably would.

To frame it in terms of the galilean thought experiment, of the observer on the ship (that is accurate isn't it), they would not be able to tell if their clock is ticking faster, slower, or at the same rate as though they were at rest, because they would have nothing to compare it to [on the ship that is]. It may have been the relative lack of understanding of the phenomenon of light that made it difficult to see the issue with assuming that a clock will tick at the same rate whether at rest, or in motion, but given the advances in that area, and our relatively better understanding, it should be a little clearer.

Absolute rest
It is probably worth stating again, that the assumption, that the path length of a photon [in a light clock, or from a laser pulse, at rest relative to the train] is given as twice the distance between the mirrors (or from the laser to the mirror), arises from treating the reference frame of the train as being at absolute rest. This, however, is not necessarily a justified assumption. From the perspective of the observer on the train, as with the observer on the platform, there are two conclusions they can come to, either they are at [absolute] rest, or they are in motion. If the observer on the train is at absolute rest then the path length of the photon will be 2d; if they are in motion, then it won't be - without assuming the conclusion of contraction.

At this point an obvious issue arises; just as the observer on the train cannot determine if they are in motion, neither can the observer on the platform. So how do they determine the path length of the photon? It is probably worth mentioning another obvious scenario here, and that is that both observers are in motion, which could of course be the case, if the earth is actually orbiting the sun; but we don't really need to speculate that here. There is an assumption in real world experiments which makes this decision.

Thought experiments vs real experiments
There is a disconnect between thought experiments and real world experiments, that has certain implications for our consideration of the aforementioned phenomena. That disconnect centres around clocks and in particular the definition of "the second".

"The second" is defined in terms of the oscillations of a caesium atomic, at rest relative to the earth. By defining the second thusly, the assumed rest frame for a clock is therefore relative to the earth, such that any clock or observer moving relative to this must be assumed to be in motion.

This fact also materially affects the assumption that the speed of light is the same for all observers regardless of their motion relative to the source, because the speed of light is defined in terms of a clock (and therefore an observer) at rest relative to the earth. This means that we implicitly assume that the earth is the rest frame, and that motion relative to the earth is deemed to be "in motion"

Lorentz factor
When we consider this fact we can see that the need for Lorentz contractions are negated, because a clock at rest relative to the earth will tick at a certain rate, any clock moving relative to that will tick at a different rate because the photon will have to travel a longer path length between mirrors. This holds true whether the earth is at absolute rest or in motion.

Incidentally, it will tick at a different rate by a factor of gamma. Length contraction and time dilation only need to be invoked, however, if we start with the assumption that a clock moving relative to the earth will tick at the same rate, even in the frame at which it is at rest - as hopefully will be coming clear, that isn't a justified assumption.


The speed of light
The definition of "the second" also has a material effect on the definition of the speed of light, and therefore the assumption that the speed of light is the same for all observers, regardless of their motion relative to the source. The reason being that the speed of light is, by definition [of "the second"], deemed to be relative to an observer, or clock at rest relative to the earth.


Unfortunately I don't know the ins and outs of the MMX or the KTX, or indeed I don't have the mathematical ability to calculate it, but I would imagine that these assumptions would probably affect the calculated path length for the light inside and interferometer, as well as the expected interference fringe of the converging light waves. I'm not sure if you'd expect a fringe shift, but regardless, it would probably affect the calcultions of what that shift should be (if any).

The results of the Hafele-Keating experiment can I would imagine, be explained if the earth is, as believed, rotating, such that flying in the direction of rotation would increase the path length and flying in the opposite direction would decrease it, resulting in net "loss of time" and net "gain in time" respectively.


As for the decay of muon, the assumption that a clock at rest relative to the muon will tick at the same rate as though it were at rest is, as has hopefully been shown, not a justified assumption



If it seems as though the explanation here "switches frames", it should be pointed out that in practice, by the definition of "the second", the rest frame is implicitly assumed to be relative to the earth, so that the relative motion of observers can be taken to be with respect to the earth.




Unfortunately, I will be away for about a week and a half, so probably won't get the opportunity to reply until then, but I would be greatly interested in any feedback.

Maximus Alexander

Now, I might be misunderstanding you, but if I am on a train and I walk from one end of the carriage to the other it will take me the same amount of time and I will expend the same amount of energy regardless of whether the train is sitting in the station or travelling at 1000 kph. As such, I can't see where you draw your conclusion that the light is travelling a longer path on the train in motion.

Morbert

roosh wrote: »

The issue
The [main] issu, as I see it, is with the treatment of the observer on the train, or more pointedly the treatment of the path length of the photon [in the clock or from the laser] - the treatment of the observer on the platform is debatable as well, but with regard to arriving at the conclusion of Lorentz contractions it is less so.

As we can see from the thought experiment, the path length of the photon is given as twice the distance from the laser to the mirror; this is no different from the light clock thought experiment where the path length is given as twice the distance between mirrors; the measurement is labelled above as 2d.

The issue, however, is that this assumes that the observer on the train, the train itself, the light clock and the laser are all at absolute rest; because anything other than absolute rest would result in a longer path length for the photon. Unless, of course, length contraction and time dilation could be invoked, but if Einstein were to have done so, he would have been guilty, surely, of assuming the conclusion. If we follow the path of reasoning though, I think we can see where the ideas arose from.

The observer on the train does not have to assume they are at absolute rest. Instead, they say they are at rest relative to the train/apparatus. That is all they assume.

You don't even need relativity to see that this is the case. If you bounce a tennis ball off the ceiling, it will travel straight up and straight down, relative to the train.

roosh

LeighH wrote: »

Now, I might be misunderstanding you, but if I am on a train and I walk from one end of the carriage to the other it will take me the same amount of time and I will expend the same amount of energy regardless of whether the train is sitting in the station or travelling at 1000 kph. As such, I can't see where you draw your conclusion that the light is travelling a longer path on the train in motion.

You might use the same amount of energy, and it may take you the same amount of time to walk the length of the carriage, but the train will use additional energy with you on board, and in the time it takes you to walk the length of the carriage, the train will also have traveled a certain distance - if it is in motion. To [probably] misapply the term, you are entangled with the system of the train, such that you are piggybacking off it; so you will have traveled a longer distance than the length of the carriage, if the train is in motion; even if you only travel the length of the carriage relative to the carriage itself. You could remain at rest relative to the carriage and still travel a longer distance than the distance you travel relative to the carriage.

For example, if you get on the Dublin train in Cork and take your seat, such that you remain at rest relative to the carriage for the duration of the journey, you will still have traveled the distance between Cork and Dublin despite not traveling any distance relative to the carriage.

roosh

Morbert wrote: »

The observer on the train does not have to assume they are at absolute rest. Instead, they say they are at rest relative to the train/apparatus. That is all they assume.

You don't even need relativity to see that this is the case. If you bounce a tennis ball off the ceiling, it will travel straight up and straight down, relative to the train.

I think it is most easily explained by considering the two possibilities of being either at absolute rest, or in motion. If we imagine a clock as being at absolute rest, then the path length of the photon, from the midpoint of one mirror, to the corresponding midpoint of the other, will be 2d.

If we then imagine that, from that position of absolute rest, the clock moves in any direction (at precisely the moment the photon is "leaving" the midpoint of one of the mirrors); then, in order for the photon to hit the midpoint of the other mirror, it must travel a longer distance because the other mirror will have moved from it's original position. The change in path length can be calculated using the Pythagorean theorem, which will give the Lorentz factor without the necessity for invoking length contraction and/or time dilation.

The photon will still travel a distance of 2d relative to the train, but because the train and the apparatus are also in motion, the photon will travel a longer actual distance; indeed, in order to travel a distance of 2d relative to the train, it has to travel a longer distance.


This doesn't involve switching reference frames either; an observer at rest on the train can reason that only a position of absolute rest will result in a path length of 2d, while anything other than absolute rest will result in a longer path length of the photon, while maintaining a distance of 2d relative to the carriage.

Maximus Alexander

roosh wrote: »

I think it is most easily explained by considering the two possibilities of being either at absolute rest, or in motion. If we imagine a clock as being at absolute rest, then the path length of the photon, from the midpoint of one mirror, to the corresponding midpoint of the other, will be 2d.

What is absolute rest? Can you give an example of something that is at absolute rest? Or how you would be able to tell that it was?

Morbert

roosh wrote: »

I think it is most easily explained by considering the two possibilities of being either at absolute rest, or in motion. If we imagine a clock as being at absolute rest, then the path length of the photon, from the midpoint of one mirror, to the corresponding midpoint of the other, will be 2d.

If we then imagine that, from that position of absolute rest, the clock moves in any direction (at precisely the moment the photon is "leaving" the midpoint of one of the mirrors); then, in order for the photon to hit the midpoint of the other mirror, it must travel a longer distance because the other mirror will have moved from it's original position. The change in path length can be calculated using the Pythagorean theorem, which will give the Lorentz factor without the necessity for invoking length contraction and/or time dilation.

The photon will still travel a distance of 2d relative to the train, but because the train and the apparatus are also in motion, the photon will travel a longer actual distance; indeed, in order to travel a distance of 2d relative to the train, it has to travel a longer distance.

This doesn't involve switching reference frames either; an observer at rest on the train can reason that only a position of absolute rest will result in a path length of 2d, while anything other than absolute rest will result in a longer path length of the photon, while maintaining a distance of 2d relative to the carriage.

There are two problems with the above:

1) The exact same reasoning can be used if we assume the train is at rest and the ground is moving. The above does not deterimines the train is moving, but arbitrarily assumes it without evidence.

2) The speed of light is the same for all observers. If both measure the speed of light to be c, then the only way a photon can travel a greater distance is if it is given more time to do so.

firefly08

Roosh, it's funny that you posted this now, since a few days ago I posted a question about more or less exactly the same issue regarding the period of the light clock! One of the intriguing things for me was that no-one could prove that the observer who goes with the moving clock does not actually experience the clock slowing down. That seemed to me to be an assumption. However, I'm beginning to come around...

The heart of the issue seems to be the question: when the reflected photon arrives at the second mirror, where will it appear to have come from? Relativity says that the light will appear to have originated exactly where the first mirror is now. Whereas logic seems to tell us that the light should appear to have come from where the first mirror was at the time that the reflection took place.

Analogies involving tennis balls and such are not really helpful - if I am moving horizontally, and I launch a tennis ball vertically, then the ball will "keep up" with me so to speak, such that I will not perceive the ball to be moving horizontally, but a stationary observer (relative to whom I am moving horizontally) will see the ball moving in both directions. But this can be explained by classical mechanics: the ball has horizontal momentum, which it received from me. (In practice, if I'm outdoors, friction with the air will actually slow the ball down, and it will not come down to quite the same place, but that can be safely ignored)

But why should the light "keep up" with my reference frame? That is the difficult part for me. Let's imagine the light emanating in a sphere from the point where it reflects off the first mirror. If the centre of that sphere does not move, but the mirrors do, then the light has longer to travel by virtue of the movement of the second mirror (relative to the centre of this sphere). That accounts for the slower clock period. But here is the problem; there is an implicit reference frame in this interpretation, relative to which the centre of the sphere of light does not move. This cannot be the reference frame of the observer on the ground, since we know the earth is moving through space. Where, then, is that reference frame? Relativity says there is none, therefore the light cannot appear to come from a point relative to which the observer is moving. Another way of putting it is: measurement of the speed of light in any direction will always indicate that the observer is stationary.

Unfortunately, that last axiom is not something I can verify for myself. I have to take someone else's word for it that this has been observed by experimentation. This indicates that time dilation is something which cannot be reasoned out by though experiment.

roosh

LeighH wrote: »

What is absolute rest? Can you give an example of something that is at absolute rest? Or how you would be able to tell that it was?

The point isn't to demonstrate that anything is at absolute rest, so providing an example of something that is, isn't required. Incidentally, any scenario where the actual path length of a photon in a light clock is twice the distance between the mirrors, that would be absolute rest.

The Galilean principle of invariance says that no experiment can be carried out to determine if an observer is in motion or at rest. This quite clearly distinguishes between absolute rest and motion; because there are plenty of experiments an observer could carry out to determine if they are at rest relative to their frame of reference.

To that end we only need to reason between the two scenarios of being at absolute rest, or being in motion.

In the thought experiment used to explain Lorentz contractions, the assumption, that the path length of the photon between mirrors is 2d, implicitly assumes that the frame of reference is at absolute rest. If it wasn't then the actual path length would be longer than the relative path length (relative to the carriage) and the clock would tick at a slower rate. Incidentally, the reason the relative path length remains the same is because the photon is imbued with the same horizontal velocity that the carriage and the mirrors are.

roosh

Morbert wrote: »

There are two problems with the above:

1) The exact same reasoning can be used if we assume the train is at rest and the ground is moving. The above does not deterimines the train is moving, but arbitrarily assumes it without evidence.

The point isn't to determine if the train is in motion, the point is that only a position of absolute rest will result in the photon traveling a path length of 2d.

The very same is true of a clock at rest relative to the ground. Only if the ground is at absolute rest will the photon travel a distance of 2d.Incidentally, if it is the ground that is moving and not the train, then the clock at rest relative to the ground will tick slower, because the photon in it will have to travel a longer distance between mirrors.

The point is that the light clock thought experiment implicitly assumes that both reference frames are at absolute rest, from their own perspective. It is the need to reconcile the actual path length of the photon with the assumed path length that gives rise to the idea of contractions.

Morbert wrote: »

2) The speed of light is the same for all observers. If both measure the speed of light to be c, then the only way a photon can travel a greater distance is if it is given more time to do so.

It appears as though this second postulate stems from Einstein's appreciation for Maxwell's equations, which appear to imply this; however, the speed of light is, by definition, relative to a clock at rest on the earth, because it is given as approx. 300, 000 km/s: "the second" in that measurement is defined in terms of a caesium atomic clock at rest relative to the earth.

How is the second postulate actually tested though?

roosh

firefly08 wrote: »

Roosh, it's funny that you posted this now, since a few days ago I posted a question about more or less exactly the same issue regarding the period of the light clock! One of the intriguing things for me was that no-one could prove that the observer who goes with the moving clock does not actually experience the clock slowing down. That seemed to me to be an assumption. However, I'm beginning to come around...

The heart of the issue seems to be the question: when the reflected photon arrives at the second mirror, where will it appear to have come from? Relativity says that the light will appear to have originated exactly where the first mirror is now. Whereas logic seems to tell us that the light should appear to have come from where the first mirror was at the time that the reflection took place.

Analogies involving tennis balls and such are not really helpful - if I am moving horizontally, and I launch a tennis ball vertically, then the ball will "keep up" with me so to speak, such that I will not perceive the ball to be moving horizontally, but a stationary observer (relative to whom I am moving horizontally) will see the ball moving in both directions. But this can be explained by classical mechanics: the ball has horizontal momentum, which it received from me. (In practice, if I'm outdoors, friction with the air will actually slow the ball down, and it will not come down to quite the same place, but that can be safely ignored)

But why should the light "keep up" with my reference frame? That is the difficult part for me. Let's imagine the light emanating in a sphere from the point where it reflects off the first mirror. If the centre of that sphere does not move, but the mirrors do, then the light has longer to travel by virtue of the movement of the second mirror (relative to the centre of this sphere). That accounts for the slower clock period. But here is the problem; there is an implicit reference frame in this interpretation, relative to which the centre of the sphere of light does not move. This cannot be the reference frame of the observer on the ground, since we know the earth is moving through space. Where, then, is that reference frame? Relativity says there is none, therefore the light cannot appear to come from a point relative to which the observer is moving. Another way of putting it is: measurement of the speed of light in any direction will always indicate that the observer is stationary.

Unfortunately, that last axiom is not something I can verify for myself. I have to take someone else's word for it that this has been observed by experimentation. This indicates that time dilation is something which cannot be reasoned out by though experiment.

Hey firefly, I have covered a lot of the same ground as yourself in the thread Does time exist?, with no small thanks due to Morbert, who has been equally patient with myself.

Like yourself, there are certain things that I amn't in a position to test for myself, so I have to take a position where I accept certain things, and try to reason from there.

With regard to the "last axiom" you refer to, or more pointedly, the second postulate of relativity, from what I can gather this assumption was adopted by Einstein because Maxwell's equations seemed to suggest that such was the case; that the speed of light was approx. 300, 000 km/s regardless of the motion of the observer. The issue, as mentioned in the post above, is that "the second" is defined in terms of a clock at rest relative to the earth, and by consequence, so too is the speed of light.


Tests of the second postulate
From what I can gather, there are a few tests of this second postulate, some of which I am not in a position to discuss - because I don't know enough about them - but as far as I am aware two of the tests of this are the Michelson-Morely and Kennedy-Thorndike experiments (MMX & KTX). These are two fundamental tests of relativity.

The issue with these, however, is that, in order for the results to fit with the predictions of relativity, the conclusions have to be assumed i.e. circular reasoning has to be applied. The reason being that length contraction, or time dilation, aren't actually observerd in the experiments; it is assumed that, in the reference frame of the photon, that length contracts and/or time slows down (from our perspective of the clock at rest in the photons reference frame). These of course are fundamentally un-testable, and have to be assumed. Without assuming the conclusion, I don't think the results would support the other conclusion of the constancy of the speed of light - which, of course is the assumption which, I think, necessitates the invokation of length contraction and time dilation in the first place.

It seems like we start off with the assumption of the constancy of the speed of light; then we conclude that contractions occur by assuming that they do; which leads to the conclusion of the constancy of the speed of light. It doesn't seem so much like circular reasoning, as figure of 8 reasoning.

That is no doubt an over-simplification, but assuming the conclusion of contractions is quite clear to see.


Muon decay experiments
The same is true for the muon decay experiments. Length contraction and time dilation aren't actually observed, again, it is assumed that, from the un-testable perspective of the muon, that length contracts and that "the clock traveling with it" slows down, from our persepective. Again, the conclusions of time dilation and length contraction have to be assumed.

If they weren't, then the actual observations would fit with relativity, and the conclusion might be that muons traveling close to the speed of light (relative to the earth) have a longer half-life than muons which are slowed down to a speed that leaves them at rest relative to the earth.

firefly08

Incidentally, the reason the relative path length remains the same is because the photon is imbued with the same horizontal velocity that the carriage and the mirrors are.

This would mean that an observer on the platform would see a speed of light higher than c.

roosh

firefly08 wrote: »

This would mean that an observer on the platform would see a speed of light higher than c.

I don't think it will. I may have misstated it, or perhaps saying that the photon is imbued with the horizontal velocity of the train is confusing the issue.

To the observer on the platform the light will still travel at a speed of c, but it will travel at an angle, as opposed to perpendicular from where it leaves the bottom mirror - that is what I meant by being imbued with the velocity of the train.

It will still travel at speed c relative to the observer on the platform, just as it does in the thought experiment; it will travel a path as depicted by the hypotenuse of the right angled triangle (as per the derivation of the Lorentz factor); and hence the clock will tick slower.

citrus burst

roosh wrote: »

The point isn't to demonstrate that anything is at absolute rest, so providing an example of something that is, isn't required. Incidentally, any scenario where the actual path length of a photon in a light clock is twice the distance between the mirrors, that would be absolute rest.

What exactly do you mean by this? I was under the impression that there is no such thing as absolute rest, or at least that no frame of reference can be treated as special. How does a scenario where the actual path length of a photon is twice the distance between mirrors suggest absolute rest?

If you set up two identical light clocks. Both would measure the actual path length of light to be 2d. If you set one in motion, each light clock will still measure its own optical path length to be 2d, however it will measure its twin's optical path length to be less then 2d.

By absolute rest do you mean local rest? Rest relative to another frame of reference and/or system? Sorry if this was implied in what you were saying.

roosh

citrus burst wrote: »

What exactly do you mean by this? I was under the impression that there is no such thing as absolute rest, or at least that no frame of reference can be treated as special. How does a scenario where the actual path length of a photon is twice the distance between mirrors suggest absolute rest?

If you set up two identical light clocks. Both would measure the actual path length of light to be 2d. If you set one in motion, each light clock will still measure its own optical path length to be 2d, however it will measure its twin's optical path length to be less then 2d.

By absolute rest do you mean local rest? Rest relative to another frame of reference and/or system? Sorry if this was implied in what you were saying.

It is probably worth pointing out that the contention is not that there is actually an absolute rest frame, rather that the derivation of the Lorentz factor -as per the thought experiments - carries with it the implicit, or nested, assumption that each reference frame is at absolute rest from their own perspectives. The term "absolute rest" might be a bit off-putting, because relativity theory clearly doesn't expressly state anything about absolute rest. It is however a nested assumption.

Non-accelerating frames
I think relativity theory talks about non-accelerating inertial frames, so if we work with the idea of a train that is not accelerating, then we can see that there are two scenarios where this is the case:
- when train is moving at a constant velocity
- when the train is at absolute rest.

This is in-keeping with the Galilean principle of invariance, which states that there is no experiment that an observer can carry out, which will allow them to determine if they are at rest, or in motion. The distinction here has to be between absolute rest and motion, because there are plenty of experiments that an observer could carry out to determine if they are at rest in their frame of reference. The question is whether or not that frame of reference is in motion or not; the "not in motion" is a position of absolute rest.

If we consider the difference between these two scenarios, we should hopefully be able to see that the derivation of the Lorentz factor implicitly assumes the latter, and contractions are a direct necessity of that assumption.


Absolute rest vs motion
For the purpose of explanation, It is easier to start with the latter scenario of absolute rest. When the train is at absolute rest, as before, the path length of the photon will be 2d; this will be the same as the distance relative to the carriage.

If we now consider that the train is traveling at a constant velocity, this implies that the train and therefore the light clock has, let's say, horizontal momentum. Again, if we imagine the photon leaving the mirror at the midpoint of the bottom mirror: if it travels a distance of 2d perpendicular to where it leaves the bottom mirror, then it will not reach the midpoint of the top mirror, because the top mirror will have moved in that time. In order for it to travel between the midpoints of the mirrors, it has to travel at an angle from where it leaves the bottom mirror, to where the top mirror will have moved to.

The photon will travel a distance of 2d relative to the carriage, but only because it is imbued with the horizontal momentum of the carriage and the mirrors (that may have to do with the laws governing the reflection of light from a moving mirror - I'm not sure). In order to travel a distance of 2d relative to the carriage, it must travel a longer actual distance.

Conclusion
So, the observer on the train will measure the path length of the photon as 2d relative to the carriage, but according to the principle of Galilean invariance he cannot determine if the carraige is in motion or at rest. Only if he assumes that the carriage is at absolute rest will he reason that the path length of the photon is 2d; if he assumes that it is in motion then it will be longer.

There is the issue of assumption either way, but as mentioned, only the assumption of absolute rest will mean that the path length of the photon is 2d.

The light clock thought experiment which is used to demonstrate Lorentz contractions implicitly assumes that both inertial reference frames are at rest, from their own perspective - due to the path length being given as 2d; of course, if both observers were at absolute rest then there would be no relative motion. The idea of contractions arise from the necessity to reconcile the assumed path lenght with the actual path length.

firefly08

To the observer on the platform the light will still travel at a speed of c, but it will travel at an angle, as opposed to perpendicular from where it leaves the bottom mirror - that is what I meant by being imbued with the velocity of the train.

It will still travel at speed c relative to the observer on the platform, just as it does in the thought experiment; it will travel a path as depicted by the hypotenuse of the right angled triangle (as per the derivation of the Lorentz factor); and hence the clock will tick slower.

Thanks for the pointers regarding my earlier questions btw, didn't see that until after I replied.

Anyway, I'm confused regarding what you think the 2 observers will see. You are saying that the observer on the platform will see the light having horizontal velocity, but he will not see a total speed greater than c; this means the vertical component of the velocity must appear less than c, to him, right? But that would mean that any reference frame that can't observe the horizontal component (such as the observer on the train) must see a lower value of c.

Does this mean you doubt the constancy of c for all observers? If it's true that c is always the same relative to everything, then the only logical option remaining seems to be time dilation.

It is probably worth pointing out that the contention is not that there is actually an absolute rest frame, rather that the derivation of the Lorentz factor -as per the thought experiments - carries with it the implicit, or nested, assumption that each reference frame is at absolute rest from their own perspectives

I thought the 'reference frame' of an observer is by definition that which is not moving relative to that observer.

I think relativity theory talks about non-accelerating inertial frames, so if we work with the idea of a train that is not accelerating, then we can see that there are two scenarios where this is the case:
- when train is moving at a constant velocity
- when the train is at absolute rest.

I think only the first one is allowed in relativity; if something is not moving relative to a particular reference frame, then it's not moving. The concept of 'absolute rest' doesn't seem to fit relativity at all; both the reference frame and the object under observation could be moving relative to something else.

Morbert

roosh wrote: »

The point isn't to determine if the train is in motion, the point is that only a position of absolute rest will result in the photon traveling a path length of 2d.

The very same is true of a clock at rest relative to the ground. Only if the ground is at absolute rest will the photon travel a distance of 2d.Incidentally, if it is the ground that is moving and not the train, then the clock at rest relative to the ground will tick slower, because the photon in it will have to travel a longer distance between mirrors.

That isn't the case. If the ground is moving and not the train, then observers on the ground will still measure the trains clock as ticking more slowly. As I said before, there is no physically distinguished reference frame.

The point is that the light clock thought experiment implicitly assumes that both reference frames are at absolute rest, from their own perspective. It is the need to reconcile the actual path length of the photon with the assumed path length that gives rise to the idea of contractions.

No it doesn't. It makes no reference to absolute rest at all. It describes events between two observers who are moving relative to one-another. We can use any arbitrary reference frame as a labelling system, and the physics will always be the same. Heck, if we are willing to slog through the maths, we can use reference frames that label the train as accelerating.

To illustrate this, let us suppose there is an absolute reference frame. The thought experiment is modified by labelling the train as moving at speed u, and the earth as moving at speed v, and the speed of the train, relative to the ground, as defined in an absolute reference frame as u - v. Then build the reference frames of the ground and train observers:

Under the non-linear velocity additions described by relativity, the velocity of the train, relative to the ground observer, using his reference frame, is

U = (u-v)/(1 - uv/c^2)

and the velocity of the ground observer, relative to the the train, is

V = (v-u)/(1-uv/c^2) = -U

So we have the original thought experiment, only with a velocity arbitrarily defined as U as opposed to u. You still have the exact same measurements and results as the thought experiment that makes no mention of an absolute reference frame. This is the case no matter how we define absolute rest (i.e. no matter how we define u and v). Absolute rest is therefore an entirely superfluous postulate that the thought experiment makes no assumptions about.

It appears as though this second postulate stems from Einstein's appreciation for Maxwell's equations, which appear to imply this; however, the speed of light is, by definition, relative to a clock at rest on the earth, because it is given as approx. 300, 000 km/s: "the second" in that measurement is defined in terms of a caesium atomic clock at rest relative to the earth.

How is the second postulate actually tested though?

No. It is defined locally, relative to the observer's clock, wherever he is. That is the nature of Maxwell's equations. Also, plenty of experiments don't rely on clock definitions, and instead attempt to detect violations of Lorentz invariance (the feature responsible for the constant speed of light.)

http://math.ucr.edu/home/baez/physics/Relativity/SR/experiments.html

E.g. The experiment below relies on observations that would arise due to different spatial orientations.

http://arxiv.org/pdf/gr-qc/0504109v1

Morbert

firefly08 wrote: »

Thanks for the pointers regarding my earlier questions btw, didn't see that until after I replied.

Anyway, I'm confused regarding what you think the 2 observers will see. You are saying that the observer on the platform will see the light having horizontal velocity, but he will not see a total speed greater than c; this means the vertical component of the velocity must appear less than c, to him, right? But that would mean that any reference frame that can't observe the horizontal component (such as the observer on the train) must see a lower value of c.

Does this mean you doubt the constancy of c for all observers? If it's true that c is always the same relative to everything, then the only logical option remaining seems to be time dilation.

The observer on the platform will see the light having a horizontal velocity with a speed c. Hence, he will see the vertical velocity component to be less than c. The observer on the train will see light having a purely vertical velocity, and a speed c. This is counter-intuitive under Galilean transformations (You would expect the observer on the train to see a speed less than c.) But it makes sense if Lorentz transformations are used, as these transformations permit time dilation.

I thought the 'reference frame' of an observer is by definition that which is not moving relative to that observer.

Exactly.

I think only the first one is allowed in relativity; if something is not moving relative to a particular reference frame, then it's not moving. The concept of 'absolute rest' doesn't seem to fit relativity at all; both the reference frame and the object under observation could be moving relative to something else.

This is true. Relativity tells us how different arbitrary reference frames are related to each other, but does not postulate a single, physically distinguished, "absolute reference frame".

roosh

firefly08 wrote: »

Thanks for the pointers regarding my earlier questions btw, didn't see that until after I replied.

No worries; to be honest, I'm not sure which questions you are referring to; I'm just replying as I go along.

firefly08 wrote: »

Anyway, I'm confused regarding what you think the 2 observers will see. You are saying that the observer on the platform will see the light having horizontal velocity, but he will not see a total speed greater than c; this means the vertical component of the velocity must appear less than c, to him, right? But that would mean that any reference frame that can't observe the horizontal component (such as the observer on the train) must see a lower value of c.

Does this mean you doubt the constancy of c for all observers? If it's true that c is always the same relative to everything, then the only logical option remaining seems to be time dilation.

Both observers will measure the speed of light to be c.

Again, if we consider two scenarios:
- the observer can see the ground moving relative to him
- the observer is in a windowless carriage and cannot see the ground moving relative to him.


Taking the second scenario, the observer will still measure a speed of c; the reason being that, for the observer on the train, the light will have a slower vertical velocity, as you say, but this will be offset by his slower ticking clock; that is "the second" he measures on the train will not be the same "second" measured by the observer on the ground. He will have no way of knowing that his clock is ticking slower.

This isn't "time" dilation, but rather a clock that is ticking slower because of the path length the photon has to travel.


Alternatively, the observer can see the ground moving relative to him; again, he can either assume that he is at absolute rest, or that his is actually in motion. Only by assuming that he is at absolute rest will he measure a path length of 2d. If he is in motion, then he will calculate the actual path length of the photon relative to the ground, realise that it is longer than 2d and that his clock will tick slower as a result.

firefly08 wrote: »

I thought the 'reference frame' of an observer is by definition that which is not moving relative to that observer.

As far as I know it is, but an observer can be at rest in a reference frame while the reference frame is in motion, and he will therefore be in motion.

If we think intuitively about being on a train; you can be sitting on the train and at rest relative to it, but if the train is in motion, then so too are you - only if the train is at absolute rest are you not in motion.

firefly08 wrote: »

I think only the first one is allowed in relativity; if something is not moving relative to a particular reference frame, then it's not moving. The concept of 'absolute rest' doesn't seem to fit relativity at all; both the reference frame and the object under observation could be moving relative to something else.

Again, if an observer is at rest relative to a reference frame, but the reference frame is moving relative to another reference frame, then the observer is necessarily in motion relative to that reference frame also. Just as above, you can be at rest relative to a train, but if the train is in motion then so too are you.

Again, just to bring it back to the Galilean principle of invariance, which states that there is no experiment an observer can conduct to determine if they are in motion or at rest, this must be distinguishing between absolute rest and motion, because there are numerous experiments that an observer can conduct to determine if they are at rest relative to their own reference frame.

firefly08

Taking the second scenario, the observer will still measure a speed of c; the reason being that, for the observer on the train, the light will have a slower vertical velocity, as you say, but this will be offset by his slower ticking clock; that is "the second" he measures on the train will not be the same "second" measured by the observer on the ground. He will have no way of knowing that his clock is ticking slower.

Ah I think I see what you're getting at; you're saying that the speed of light that he measures is based on the period of the light clock, so therefore it could slow down by a lot and he'd never know? Well in that case he would never know that light is slower in his frame of reference but that would be a terrible accident. If he had some independent means to measure the speed of light - let's say, a clock that doesn't rely on bouncing light between two mirrors - then he would be able to measure the difference in c, if there was one.

As far as I know it is, but an observer can be at rest in a reference frame while the reference frame is in motion, and he will therefore be in motion.

Well, in fact there is no alternative to that - his reference frame is always in motion, just not relative to him.

Imagine there were only two things in the universe, let's say two rocks floating around, and the distance between them is changing. Now any reference frame you pick, the rest of the universe is moving relative to it. There is no way out of that as long as there is more than 1 thing in the universe. Therefore, all frames of reference are always in motion!

roosh

Morbert wrote: »

That isn't the case. If the ground is moving and not the train, then observers on the ground will still measure the trains clock as ticking more slowly. As I said before, there is no physically distinguished reference frame.

This is only if we assume that the clock at rest on the moving ground ticks at the same rate as that in the train i.e. that the path length is the same.

I'm trying to visualise how it would appear; we must remember though that the clock on the moving ground is actually ticking slower because of the increased path length. If the observer on the moving ground doesn't assume that they are at absolute rest, then they can calculate that the other clock is ticking slower.

It's basically just the same issue in reverse

Morbert wrote: »

No it doesn't. It makes no reference to absolute rest at all. It describes events between two observers who are moving relative to one-another. We can use any arbitrary reference frame as a labelling system, and the physics will always be the same. Heck, if we are willing to slog through the maths, we can use reference frames that label the train as accelerating.

It makes no explicit reference to absolute rest, there is an implicit assumption, however.

Morbert wrote: »

To illustrate this, let us suppose there is an absolute reference frame. The thought experiment is modified by labelling the train as moving at speed u, and the earth as moving at speed v, and the speed of the train, relative to the ground, as defined in an absolute reference frame as u - v. Then build the reference frames of the ground and train observers:

Under the non-linear velocity additions described by relativity, the velocity of the train, relative to the ground observer, using his reference frame, is

U = (u-v)/(1 - uv/c^2)

and the velocity of the ground observer, relative to the the train, is

V = (v-u)/(1-uv/c^2) = -U

So we have the original thought experiment, only with a velocity arbitrarily defined as U as opposed to u. You still have the exact same measurements and results as the thought experiment that makes no mention of an absolute reference frame. This is the case no matter how we define absolute rest (i.e. no matter how we define u and v). Absolute rest is therefore an entirely superfluous postulate that the thought experiment makes no assumptions about.

The emboldened parts, above, appear to be contradictory.

Again, though, if we start with the supposition of an absolute rest frame as above, and put a clock at rest in that absolute reference frame; then the photon in a clock on a train, moving at speed u relative to that frame, will have a longer path length as determinable by the Pythagorean theorem; similarly, a clock at rest on the ground, moving at speed v relative to the absolute rest frame, will have a longer path length as determinable by the Pythagorean theorem.

Whichever velocity is higher, u or v, will determine which clock ticks slower.

Morbert wrote: »

No. It is defined locally, relative to the observer's clock, wherever he is. That is the nature of Maxwell's equations.

That may be the nature of Maxwell's equations, but the measurements of the speed of light in the experiments, c, were presumably all relative to a clock at rest relative to the earth.

However, as per the post above:

Both observers will measure the speed of light to be c.

Again, if we consider two scenarios:
- the observer can see the ground moving relative to him
- the observer is in a windowless carriage and cannot see the ground moving relative to him.


Taking the second scenario, the observer will still measure a speed of c; the reason being that, for the observer on the train, the light will have a slower vertical velocity, as you say, but this will be offset by his slower ticking clock; that is "the second" he measures on the train will not be the same "second" measured by the observer on the ground. He will have no way of knowing that his clock is ticking slower.

This isn't "time" dilation, but rather a clock that is ticking slower because of the path length the photon has to travel.


Alternatively, the observer can see the ground moving relative to him; again, he can either assume that he is at absolute rest, or that his is actually in motion. Only by assuming that he is at absolute rest will he measure a path length of 2d. If he is in motion, then he will calculate the actual path length of the photon relative to the ground, realise that it is longer than 2d and that his clock will tick slower as a result.

Morbert wrote: »

Also, plenty of experiments don't rely on clock definitions, and instead attempt to detect violations of Lorentz invariance (the feature responsible for the constant speed of light.)

http://math.ucr.edu/home/baez/physics/Relativity/SR/experiments.html

E.g. The experiment below relies on observations that would arise due to different spatial orientations.

http://arxiv.org/pdf/gr-qc/0504109v1

I read the arxiv paper provided, and unfortunately it was a bit too technical for me, but there was something in the opening and closing paragraphs (before the acknowledgements) which may or may not serve as a useful point of discussion.

Antonini, Okhapkin, Gökl&#252 wrote: »

The first precision measurement, demonstrating LLI for light propagation, was performed by Michelson and Morley in 1887 and its result was an essential experimental foundation for the advent of Relativity.

Antonini, Okhapkin, Gökl&#252 wrote: »

In conclusion, we have described a Michelson-Morley type experiment

It could be just the untrained eye, but, as with the Kennedy-Thorndike Experiment, the Michelson-Morely Experiment appears to employ "figure of 8 reasoning", as opposed to straight forwards circular reasoning.

It appears as though a starting assumption - expressed or otherwise - is that the speed of light is c with respect to all reference frames. It also seems that, in order for the experimental results to match that of relativity, length contraction is required. Now, length contraction isn't actually observed, so it appears as though it is assumed that, from the perspective of the photon, the length of the arms of the interferometers contract - this of course is fundamentally untestable.

So, the conclusion is that length contraction occurs (from the perspective of the photon); but it hasn't actually been observer, but rather assumed; that is, the conclusion is assumed.

The conclusion then, is that the speed of light is c in all directions, which of course, was the starting assumption.


If the conclusion of contractions aren't assumed, do the experimental results of the MMX still support the second postulate?



Despite all this, it has been outlined above that all observers will still measure the speed of light to be c.

roosh

Morbert wrote: »

The observer on the platform will see the light having a horizontal velocity with a speed c. Hence, he will see the vertical velocity component to be less than c. The observer on the train will see light having a purely vertical velocity, and a speed c. This is counter-intuitive under Galilean transformations (You would expect the observer on the train to see a speed less than c.) But it makes sense if Lorentz transformations are used, as these transformations permit time dilation.

but the light can have a slower vertical velocity which would be offset by his slower ticking clock, and would still result in him measuring the speed of light to be c; it's just that "the second" as measured by his clock would be slower than that of the observer at rest on the platform.

Morbert wrote: »

This is true. Relativity tells us how different arbitrary reference frames are related to each other, but does not postulate a single, physically distinguished, "absolute reference frame".

It isn't an expressed assumption, rather an unintentional consequence of the assumed measurement of the path length of the photon.

roosh

firefly08 wrote: »

Ah I think I see what you're getting at; you're saying that the speed of light that he measures is based on the period of the light clock, so therefore it could slow down by a lot and he'd never know? Well in that case he would never know that light is slower in his frame of reference but that would be a terrible accident.
...
Well, in fact there is no alternative to that - his reference frame is always in motion, just not relative to him.

I've re-arranged your post just to address the issue of reference frames together; hopefully this doesn't misrepresent you.

That [the emboldened] is pretty much it.

The speed of light will always be c in "his reference frame", but because speed is a relative measurement, how "his reference frame" is defined is important.

Reference frames
I think the idea of frames of reference are somewhat misleading, particularly when the question is about the nature of the physical world, as this is. The reason being, that "frames of reference" are essentially just a mathematical construct and have no bearing in the physical world; they are undoubtedly helpful for calculation purposes and making certain predictions, but insofar as they are imaginary, they do not describe the physical world.

For example: we might say that the observer's reference frame is the train, and he is at rest relative to that; but the earth is just as much his reference frame and he is in motion relative to that; or the galaxy.

He could start off at rest relative to the earth, then board a train; indeed, he can be in a train at rest relative to the earth and "his reference frame" would be the earth as well as the train, and he would be in motion relative to the sun; then the train starts moving and the earth is no longer "his reference frame"; there is no logical justification for saying that "his reference frame" was the earth but now it's not; it's simply an ad hoc designation.

You mention that "his reference frame is always in motion, just not relative to him", but that strictly speaking is not necessarily true. The Galilean principle of invariance says that he cannot determine whether or not his reference frame is actually in motion; it could be the case that "his reference frame" is at absolute rest and that everything in the universe is in motion around him. So, because he cannot tell he has to make one of two assumptions:
- either he is at absolute rest
- or "his reference frame" is in motion.

Apologies for harping on about this, but only the assumption of absolute rest will lead him to conclude that the path length of the photon in his clock is 2d.

However, if he assumes that, as you mention, his reference frame is always in motion, then he will reason that the path length of the photon is greater than 2d.

Measuring speed of light
The aforementioned assumptions will materially affect how he measures the speed of light, because speed is a relative measurement.

In both cases he will measure the speed of light to be c.

• If he assumes that the carriage is at absolute rest, and it actually is, then there is nor problem.
• If he assumes that it is at absolute rest, and it isn't, then his ignorance of the change in path length is offset by his ignorance of the change in the rate of the clock.
• If he assumes that he is in motion, then he will know that he cannot measure the path length of the photon relative to the carriage, because he is ignoring the horizontal velocity of the device; therefore he would measure it against the ground he is moving relative to and discern that the photon travels a longer path length, and that his clock, therefore, ticks slower.

It is only the middle scenario where happenstance plays a role, because he is wrong in his assumptions; however, the speed of light is still actually c in "his reference frame" because "his reference frame" is in motion and he has to take into account the horizontal momentum.

Essentially, if he assumes that "his reference frame" is at rest when it isn't then it is the third scenario which is true; so the speed of light is still c - he's just working off an erroneous assumption. It just so happens that his ignorance of the horizontal momentum, is offset by his ignorance of the slower cycle rate of his clock - essentially because they are the exact same phenomenon.


There is of course the fourth scenario where he assumes he is in motion, but is actually at absolute rest, but again, I think his ignorance will cancel itself out.

firefly08 wrote: »

If he had some independent means to measure the speed of light - let's say, a clock that doesn't rely on bouncing light between two mirrors - then he would be able to measure the difference in c, if there was one.

Quite possibly.

It's difficult to say without knowing the mechanism of the clock.

firefly08 wrote: »

Well, in fact there is no alternative to that - his reference frame is always in motion, just not relative to him.

Imagine there were only two things in the universe, let's say two rocks floating around, and the distance between them is changing. Now any reference frame you pick, the rest of the universe is moving relative to it. There is no way out of that as long as there is more than 1 thing in the universe. Therefore, all frames of reference are always in motion!

Not necessarily; again, according to the Galilean principle of invariance an observer cannot determine if they are at rest or in motion. So if there is an observer on each of the rocks, from their perspective, it is just as likely that one of the rocks remains at absolute rest while the other rock moves. What definitively cannot be the case, though, is that both rocks remain at absolute rest, because then there would be no relative motion. So if both observers assume that they have remained at absolute rest, then one of them is, necessarily, mistaken.

For that reason I would be inclined to support the contention that relative motion, by necessity, demonstrates absolute motion - without being able to determine which object is absolutely in motion. Of course, another possibility is that everything is absolutely in motion and moving relative to each other; as you say, all frames of reference are always moving.


It is probably worth noting that absolute motion cannot, by definition, be measured, because measurement is, by practicality, relative i.e. it is the expression of something in relation to something else. Absolute motion is a simple yes or no answer to the question "is the thing actually moving?"

firefly08

So if both observers assume that they have remained at absolute rest, then one of them is, necessarily, mistaken.

Have you considered the possibility that both of them are mistaken?

firefly08

It is probably worth noting that absolute motion cannot, by definition, be measured, because measurement is, by practicality, relative i.e. it is the expression of something in relation to something else. Absolute motion is a simple yes or no answer to the question "is the thing actually moving?"

Then why suppose that it exists? If it can't be measured, then can't we ignore it, and not go astray?

roosh

firefly08 wrote: »

Have you considered the possibility that both of them are mistaken?

Sorry, it mightn't have been abundantly clear, but that was what was meant by the below:

roosh wrote: »

Of course, another possibility is that everything is absolutely in motion and moving relative to each other; as you say, all frames of reference are always moving.

Morbert

roosh wrote: »

This is only if we assume that the clock at rest on the moving ground ticks at the same rate as that in the train i.e. that the path length is the same.

I'm trying to visualise how it would appear; we must remember though that the clock on the moving ground is actually ticking slower because of the increased path length. If the observer on the moving ground doesn't assume that they are at absolute rest, then they can calculate that the other clock is ticking slower.

It's basically just the same issue in reverse

And reversing the issue does not produce any experimental difference. Hence, both scenarios are physically indistinguishable: One is not more real than the other. So no assumption about absolute paths needs to be made.

It makes no explicit reference to absolute rest, there is an implicit assumption, however.

It is a non-sequitur: "There must be an absolute rest", does not follow from "There is no reference frame that labels both observers as stationary".

The emboldened parts, above, appear to be contradictory.

I am demonstrating the superfluous nature of supposing there is a reference frame. The thought experiment does not change if you include an arbitrarily defined absolute reference frame. It is perfectly valid to only consider relative velocities.

Again, though, if we start with the supposition of an absolute rest frame as above, and put a clock at rest in that absolute reference frame; then the photon in a clock on a train, moving at speed u relative to that frame, will have a longer path length as determinable by the Pythagorean theorem; similarly, a clock at rest on the ground, moving at speed v relative to the absolute rest frame, will have a longer path length as determinable by the Pythagorean theorem.

Whichever velocity is higher, u or v, will determine which clock ticks slower.

And if we start with no supposition of an absolute rest frame, we get the exact same experimental result. I.e. You have not shown that absolute rest is a logical necessity.

That may be the nature of Maxwell's equations, but the measurements of the speed of light in the experiments, c, were presumably all relative to a clock at rest relative to the earth.

Plenty of experiments have been done with GPS systems. The postulates of relativity still hold in those cases. No dependency on earth's frame of reference has been established.

However, as per the post above:

Both observers will measure the speed of light to be c.

Again, if we consider two scenarios:
- the observer can see the ground moving relative to him
- the observer is in a windowless carriage and cannot see the ground moving relative to him.

Taking the second scenario, the observer will still measure a speed of c; the reason being that, for the observer on the train, the light will have a slower vertical velocity, as you say, but this will be offset by his slower ticking clock; that is "the second" he measures on the train will not be the same "second" measured by the observer on the ground. He will have no way of knowing that his clock is ticking slower.

This isn't "time" dilation, but rather a clock that is ticking slower because of the path length the photon has to travel.

Let us say he uses independent clocks, like an infinitely precise pendulum clock, or wristwatch, or hour glass to measure the speed of light in the mirror apparatus.

Or let's say he records the ticking of his clock on videotape, and gives it to the observer on the ground. The observer on the ground will watch the videotape and see the clock ticking normally, in sync with his own.

In short, there is no assumption that the observer on the train uses the mirror apparatus to calibrate his clock (That would be circular reasoning)

Alternatively, the observer can see the ground moving relative to him; again, he can either assume that he is at absolute rest, or that his is actually in motion. Only by assuming that he is at absolute rest will he measure a path length of 2d. If he is in motion, then he will calculate the actual path length of the photon relative to the ground, realise that it is longer than 2d and that his clock will tick slower as a result.

He does not have to assume any such thing. He only needs to assume the ground is in motion, relative to him. That statement says nothing about absolute motion.

Let me try illustrating the non-sequitur by posing the question in a more rigorous form.

The laws of physics in all reference frames are covariant (I.e. They are the same in all reference frames). So there is no physically distinguished reference frame. From this can you derive the claim that there must be an absolute space?

I read the arxiv paper provided, and unfortunately it was a bit too technical for me, but there was something in the opening and closing paragraphs (before the acknowledgements) which may or may not serve as a useful point of discussion.

It could be just the untrained eye, but, as with the Kennedy-Thorndike Experiment, the Michelson-Morely Experiment appears to employ "figure of 8 reasoning", as opposed to straight forwards circular reasoning.

It appears as though a starting assumption - expressed or otherwise - is that the speed of light is c with respect to all reference frames. It also seems that, in order for the experimental results to match that of relativity, length contraction is required. Now, length contraction isn't actually observed, so it appears as though it is assumed that, from the perspective of the photon, the length of the arms of the interferometers contract - this of course is fundamentally untestable.

So, the conclusion is that length contraction occurs (from the perspective of the photon); but it hasn't actually been observer, but rather assumed; that is, the conclusion is assumed.

The conclusion then, is that the speed of light is c in all directions, which of course, was the starting assumption.

If the conclusion of contractions aren't assumed, do the experimental results of the MMX still support the second postulate?

Despite all this, it has been outlined above that all observers will still measure the speed of light to be c.

The bits in red are the problem. No such assumptions are made. Those are the assumptions that are tested. To related it back to the train thought experiment. If what you said about the train clock were true (The light actually was slower), then this experiment would have detected such an effect. A slower light beam interfering with other light beams would produce a unique pattern. This pattern did not manifest.

So think of this experiment as a test of your hypothesis that the speed of light is actually slower, but the apparatus on the train was too limited to detect this. This new apparatus would detect such anisotropy by comparing the light in question with other, differently orientated light beams

himnextdoor

I just don't see why a photon should lose velocity in the vertical direction just because it has acquired a horizontal component.

Suppose we were to replace the light-clock with a cannon system. A cannon is arranged to fire balls parallel to the ground; the system is self-loading through entirely mechanical means; the fire/reload cycle has been measured to be a ten-second cycle. All the balls have the same mass and they are fired with the same amount of energy.

There are no clocks governing the cycle and while the system is powered up it will operate at its most efficient.

The train is stationary and the cannon is switched on. It fires its first missile then the train begins to accelerate. Let's assume the train is travelling along a straight line.

When the ball leaves the cannon, it begins to fall due to gravity and will land at some distance, 'd', from the train depending on the energy of propulsion. We are only concerned with the initial impact between ball and ground; we will disregard bounce.

As the train accelerates, firing balls every ten seconds, the distance between the balls increases; at the speed of light, the balls will land ten light-seconds apart. (Let's ignore the fact that these balls will have exceeded escape velocity.)

However, all the balls will land the same distance away from the track. Not only that, the time between firing the ball and it impacting with the ground will also remain constant.

Why should it be any different for photons?

Morbert

himnextdoor wrote: »

I just don't see why a photon should lose velocity in the vertical direction just because it has acquired a horizontal component.

It doesn't physically lose velocity in the vertical direction. The viewpoint of the passenger, who sees the photon travel vertically at c, is not any less correct than the viewpoint of the person on the ground. It is just that the geometry between events is Minkowski geometry, so the relation between different observers is characterised by Lorentz transformations. Hence, different observers will disagree about the vertical velocity of the photon.

Suppose we were to replace the light-clock with a cannon system. A cannon is arranged to fire balls parallel to the ground; the system is self-loading through entirely mechanical means; the fire/reload cycle has been measured to be a ten-second cycle. All the balls have the same mass and they are fired with the same amount of energy.

There are no clocks governing the cycle and while the system is powered up it will operate at its most efficient.

The train is stationary and the cannon is switched on. It fires its first missile then the train begins to accelerate. Let's assume the train is travelling along a straight line.

When the ball leaves the cannon, it begins to fall due to gravity and will land at some distance, 'd', from the train depending on the energy of propulsion. We are only concerned with the initial impact between ball and ground; we will disregard bounce.

As the train accelerates, firing balls every ten seconds, the distance between the balls increases; at the speed of light, the balls will land ten light-seconds apart. (Let's ignore the fact that these balls will have exceeded escape velocity.)

However, all the balls will land the same distance away from the track. Not only that, the time between firing the ball and it impacting with the ground will also remain constant.

Why should it be any different for photons?

It won't be any different. If we assume the balls are massless, or if we assume the balls are fired out at a speed only negligibly smaller than the speed of light, then they would behave similarly insofar as all observers would see them travelling at speed c, or close to c, no matter how fast the train was travelling.

The passenger on the train sees the balls fired out perpendicular to the train, at effectively c (assuming there is no wind of course), and land on some line on the ground parallel to the direction of the train. But since the ground is moving, the balls on the line are also moving, and hence the distance between them is length-contracted. Hence, both observers will not agree on the distance between the balls on the ground, or at the rate the balls were fired, but will both agree that the speed of the balls is c.

roosh

Apologies for the delayed response, I was trying to get a better understanding of the potential issues in postulating an idealised, infinitely precise, pendulum clock.

Morbert wrote: »

And reversing the issue does not produce any experimental difference. Hence, both scenarios are physically indistinguishable: One is not more real than the other. So no assumption about absolute paths needs to be made.

It does produce an experimental difference; in the first instance it is the clock on the train that ticks slower; in the second instance it is the clock on the earth that ticks slower.

Just to try and address the point again:

Morbert wrote: »

That isn't the case. If the ground is moving and not the train, then observers on the ground will still measure the trains clock as ticking more slowly.

I think you might be working off the same assumptions as the thought experiment with this point; the assumption being that both clocks tick at the same rate in their own reference frames. That is the assumption being questioned.

It can be somewhat hard to picture, particularly when the relativity diagrams/videos - which show both clocks ticking at the same rate from their own perspective (path length of 2d) - are ingrained in our subconscious. But if we can drop the notion that they tick at the same rate in their own reference frames, and imagine the clock on the ground actually ticking slower than the one on the train, because of the increased path length [when "the ground is moving and not the train"]; then I don't think you will arrive at the same conclusion - that the observer on the ground will still calculate that the clock on the train is ticking slower.

In terms of the [Lorentz contractions] video you posted in the other thread, it might be helpful to try and imagine the scenario for Henry (the observer on the train) first. In this instance we can imagine that Albert's (the observer on the platform) frame of reference is the absolute rest frame and that the path length, of the photon in his clock, is actually 2d; this will also be the path length relative to his reference frame - again, only an assumption of absolute rest will result in both measurements being the same.

So Henry and his clock are in motion on the train, and Henry's clock is actually ticking slower than Albert's because of the increased path length of the photon, as they pass each other will Henry still measure Albert's clock to be ticking slower? I think if he knows the distance between himself and Albert he will probably be able to calculate that his clock is actually ticking slower.


Only if we assume that both clocks tick at the same rate [in their own reference frames] i.e. that the actual path length is the same in both cases- 2d implying absolute rest - will we arrive at the conclusion that, to each observer, it is the clock in the other reference frame that appears to tick slower.

Morbert wrote: »

It is a non-sequitur: "There must be an absolute rest", does not follow from "There is no reference frame that labels both observers as stationary".

The contention isn't that "there must be an absolute rest", it is that, in the thought experiment, there is an implicit assumption that, from the perspective of each observer, their reference frame is at absolute rest.

It doesn't follow from the assertion: "There is no reference frame that labels both observers as stationary"; it is a consequence of the assumed measurement of the path length of the photon as 2d; because only a position of absolute rest will result in the photon actually traveling a distance of 2d

Morbert wrote: »

I am demonstrating the superfluous nature of supposing there is a reference frame. The thought experiment does not change if you include an arbitrarily defined absolute reference frame. It is perfectly valid to only consider relative velocities.

And if we start with no supposition of an absolute rest frame, we get the exact same experimental result. I.e. You have not shown that absolute rest is a logical necessity.

I don't think you demonstrated it though, because you started with the supposition of an absolute rest frame to determine the velocities of the train and the ground, and then calculated the relative velocity of the train to the ground, on the basis of the velocities relative to the absolute rest frame.

As per the example in a previous post, we can follow your line of reasoning and place clocks in each reference frame:

Placing the clocks
You started by assuming an absolute rest frame, against which to determine the velocities of the train and the ground; so if we put a clock at rest there, then the path length of the photon will be 2d.

If we imagine a train, and a clock, moving relative to that rest frame, with a velocity u, then the actual path length of the photon will be longer than 2d and so the clock will tick slower;the difference in path length can be determined using the Pythagorean theorem. The path length relative to the carriage will be 2d but only if the observer assumes a position of absolute rest will he assume that the actual path length [which determines the cycle period of his clock] is 2d.

If we then imagine the earth moving relative to this absolute rest frame, at velocity v, then the actual path length of the photon will be longer than 2d and so the clock will tick slower;the difference in path length can be determined using the Pythagorean theorem. Again, only by assuming that they are at absolute rest, will the observer at rest on earth determine that the actual path length [which determines the cycle period of their clock] is 2d.

Removing the rest frame
So, here we have three clocks; one in the absolute rest frame; one on the train; and one are rest on earth. Both clocks moving relative to the absolute rest frame are ticking slower than the clock in that rest frame, by a rate determinable using the Pythagorean theorem, and by a factor of their velocity relative to the rest frame.

If, for the sake of explanation, we assume that the train is traveling at a higher velocity than the earth, then it is the trains clock which will be ticking the slowest of the three clocks; and therefore, slower than the earths clock.

Now, we can remove the clock in the absolute rest frame, such that we are only left with the trains clock and the earths clock. The trains clock will still run slower than the earths clock.

Now, we might have an issue in calculating the change in clock rates if there is any subsequent change in relative velocity [without the rest frame for comparison]; but, if we define "the second" as being one full cycle of the earths clock, as is the case in real world experiments (using a different kind of clock) then any subsequent change in relative velocity will always be ascribed to the train, and, therefore, it will be the trains clock which will be deemed to have changed.

Morbert wrote: »

Plenty of experiments have been done with GPS systems. The postulates of relativity still hold in those cases. No dependency on earth's frame of reference has been established.

Are there specific experiments you are referring to?

Morbert wrote: »

Let us say he uses independent clocks, like an infinitely precise pendulum clock, or wristwatch, or hour glass to measure the speed of light in the mirror apparatus.

Or let's say he records the ticking of his clock on videotape, and gives it to the observer on the ground. The observer on the ground will watch the videotape and see the clock ticking normally, in sync with his own.

In short, there is no assumption that the observer on the train uses the mirror apparatus to calibrate his clock (That would be circular reasoning)

I was trying to get a better understanding of the potential issues of using such and idealised clock and I think there are a few:
- such a clock would not work in the relocation to deep space
- a pendulum clock in a train moving at constant speed is traveling in a curved path around the earth so it is not experiencing as much g, and so will tick at a different rate to one at rest on earth.

In a footnote to the English translation of his 1905 paper, ON THE ELECTRODYNAMICS OF MOVING BODIES Einstein excluded the possibility of using pendulum clocks

Not a pendulum-clock, which is physically a system to which the Earth belongs. This case had to be excluded.

Morbert wrote: »

He does not have to assume any such thing. He only needs to assume the ground is in motion, relative to him. That statement says nothing about absolute motion.

Let me try illustrating the non-sequitur by posing the question in a more rigorous form.

The laws of physics in all reference frames are covariant (I.e. They are the same in all reference frames). So there is no physically distinguished reference frame. From this can you derive the claim that there must be an absolute space?

Again, the intention isn't to demonstrate that there must be an absolute space, it is to demonstrate that measuring a path lenght of 2d implies absolute rest.

This can be done by considering what the path length of a photon would be at absolute rest, and then reason what it would be if the train moved from this position of absolute rest.

Morbert wrote: »

The bits in red are the problem. No such assumptions are made. Those are the assumptions that are tested. To related it back to the train thought experiment. If what you said about the train clock were true (The light actually was slower), then this experiment would have detected such an effect. A slower light beam interfering with other light beams would produce a unique pattern. This pattern did not manifest.

So think of this experiment as a test of your hypothesis that the speed of light is actually slower, but the apparatus on the train was too limited to detect this. This new apparatus would detect such anisotropy by comparing the light in question with other, differently orientated light beams

Apologies, I was indeed incorrect about the starting assumption of the MMX (I think anyway), but that the conclusion of length contraction is assumed seems pretty clear. Equally so in the muon decay experiments, because they are not actually observed.

Also, insofar as the second postulate refers to the one way speed of light, it is, by all accounts, an untestable assumption.

Morbert

roosh wrote: »

Apologies for the delayed response, I was trying to get a better understanding of the potential issues in postulating an idealised, infinitely precise, pendulum clock.

It does produce an experimental difference; in the first instance it is the clock on the train that ticks slower; in the second instance it is the clock on the earth that ticks slower.

There is no such experimental difference. Any experiment carried out by the person on the train will register the ground clock as ticking slowly, and any experiment carried out by the person on the ground will register the train clock ticking slowly.

Just to try and address the point again:

I think you might be working off the same assumptions as the thought experiment with this point; the assumption being that both clocks tick at the same rate in their own reference frames. That is the assumption being questioned.

It can be somewhat hard to picture, particularly when the relativity diagrams/videos - which show both clocks ticking at the same rate from their own perspective (path length of 2d) - are ingrained in our subconscious. But if we can drop the notion that they tick at the same rate in their own reference frames, and imagine the clock on the ground actually ticking slower than the one on the train, because of the increased path length [when "the ground is moving and not the train"]; then I don't think you will arrive at the same conclusion - that the observer on the ground will still calculate that the clock on the train is ticking slower.

In terms of the [Lorentz contractions] video you posted in the other thread, it might be helpful to try and imagine the scenario for Henry (the observer on the train) first. In this instance we can imagine that Albert's (the observer on the platform) frame of reference is the absolute rest frame and that the path length, of the photon in his clock, is actually 2d; this will also be the path length relative to his reference frame - again, only an assumption of absolute rest will result in both measurements being the same.

So Henry and his clock are in motion on the train, and Henry's clock is actually ticking slower than Albert's because of the increased path length of the photon, as they pass each other will Henry still measure Albert's clock to be ticking slower? I think if he knows the distance between himself and Albert he will probably be able to calculate that his clock is actually ticking slower.

Only if we assume that both clocks tick at the same rate [in their own reference frames] i.e. that the actual path length is the same in both cases- 2d implying absolute rest - will we arrive at the conclusion that, to each observer, it is the clock in the other reference frame that appears to tick slower.

The contention isn't that "there must be an absolute rest", it is that, in the thought experiment, there is an implicit assumption that, from the perspective of each observer, their reference frame is at absolute rest.

It doesn't follow from the assertion: "There is no reference frame that labels both observers as stationary"; it is a consequence of the assumed measurement of the path length of the photon as 2d; because only a position of absolute rest will result in the photon actually traveling a distance of 2d

Again, the intention isn't to demonstrate that there must be an absolute space, it is to demonstrate that measuring a path lenght of 2d implies absolute rest.

This can be done by considering what the path length of a photon would be at absolute rest, and then reason what it would be if the train moved from this position of absolute rest.

I think you are getting hung up on the shorthand language used to frame the thought experiment. Henry and Albert do not make any metaphysical assumptions about their measurement of 2d being an absolute distance. They acknowledge their experimental reports are using arbitrary reference frames. I.e. Both the observer on the train and on the ground, assuming they are aware of relativity, know that the measurement of a distance 2d for their respective clocks, and a larger distance for the other's clocks, is no more or less valid a measurement than the other's.

I don't think you demonstrated it though, because you started with the supposition of an absolute rest frame to determine the velocities of the train and the ground, and then calculated the relative velocity of the train to the ground, on the basis of the velocities relative to the absolute rest frame.

I did this to show the superfluous nature of including absolute velocities in the reference frame. Instead of considering absolute velocities, it is possible to carry out the thought experiment by only only considering relative velocities U and V. I.e. Instead of presupposing an absolute reference frame and deriving relative velocities, we simply consider the relative velocities without any reference to an absolute reference frame.

As per the example in a previous post, we can follow your line of reasoning and place clocks in each reference frame:

Placing the clocks
You started by assuming an absolute rest frame, against which to determine the velocities of the train and the ground; so if we put a clock at rest there, then the path length of the photon will be 2d.

If we imagine a train, and a clock, moving relative to that rest frame, with a velocity u, then the actual path length of the photon will be longer than 2d and so the clock will tick slower;the difference in path length can be determined using the Pythagorean theorem. The path length relative to the carriage will be 2d but only if the observer assumes a position of absolute rest will he assume that the actual path length [which determines the cycle period of his clock] is 2d.

If we then imagine the earth moving relative to this absolute rest frame, at velocity v, then the actual path length of the photon will be longer than 2d and so the clock will tick slower;the difference in path length can be determined using the Pythagorean theorem. Again, only by assuming that they are at absolute rest, will the observer at rest on earth determine that the actual path length [which determines the cycle period of their clock] is 2d.

Why would he assume the absolute path length is 2d? Why would he consider an absolute path length at all? Special relativity does not postulate that the speed of light is c in some absolute reference frame. It postulates that all observers will measure the speed of light to be c. Time dilation and length contraction are similarly just measurements, and not statements about an absolute "passage of time" and "extension in space".

Removing the rest frame
So, here we have three clocks; one in the absolute rest frame; one on the train; and one are rest on earth. Both clocks moving relative to the absolute rest frame are ticking slower than the clock in that rest frame, by a rate determinable using the Pythagorean theorem, and by a factor of their velocity relative to the rest frame.

If, for the sake of explanation, we assume that the train is traveling at a higher velocity than the earth, then it is the trains clock which will be ticking the slowest of the three clocks; and therefore, slower than the earths clock.

Now, we can remove the clock in the absolute rest frame, such that we are only left with the trains clock and the earths clock. The trains clock will still run slower than the earths clock.

Why presuppose an absolute reference frame at all? Why not just start with relative velocities, and make no statement about absolute reference frames at all?

Are there specific experiments you are referring to?

They happen any time GPS satellites relay information to each other, or to people on the ground. The equations are entirely general, and do not presuppose and earth-centred physical properties.

I was trying to get a better understanding of the potential issues of using such and idealised clock and I think there are a few:
- such a clock would not work in the relocation to deep space
- a pendulum clock in a train moving at constant speed is traveling in a curved path around the earth so it is not experiencing as much g, and so will tick at a different rate to one at rest on earth.

In a footnote to the English translation of his 1905 paper, ON THE ELECTRODYNAMICS OF MOVING BODIES Einstein excluded the possibility of using pendulum clocks

In the thought experiment, we only consider a train moving at constant velocity, across an infinite plane. This is because the thought experiment is an exploration of the logical consequences of relativity's postulates. But with that said "pendulum" is a redundant detail. "Infinitely precise, independent clock" will do.

Apologies, I was indeed incorrect about the starting assumption of the MMX (I think anyway), but that the conclusion of length contraction is assumed seems pretty clear. Equally so in the muon decay experiments, because they are not actually observed.

Also, insofar as the second postulate refers to the one way speed of light, it is, by all accounts, an untestable assumption.

It is not assumed. In fact, length-contraction was initially assumed in order to explain the isotropy of the speed of light, and was later dropped. The dimensions of the apparatus, as described by the person in the train, are perfectly valid, and no less physical than the measurements taken by the person on the ground.

This is a good time to talk about Lorentzian relativity. You have suggested that the photon is actually travelling a distance greater than 2d, but that the apparatus used by the person in the train is moving more slowly, and hence registering a speed c. This supposes that every possible physical mechanism is slowed by the same amount, everything to his infinitely precise wristwatch, to the neurons in his brain, to the photon apparatus itself. Then, when we consider interfering lightbeams, you suggest that things actually physically contract by some amount, and no matter what material used, or what orientations used, the length contraction effect will always sync up with the "slower moving" effect at precisely the right amount to render the speed of light to be c. Why would a physical process like length-contraction be correlated with a completely separate physical process of "slowed movement"? This is what Lorentzian relativity supposes. In fact, even with these supposed physical processes, it has no physical understanding of the relativity of simultaneity.

Special relativity, on the other hand, has a very simple framework: The geometry relating all events is a pseudo-Riemannian, Minkowski geometry.

roosh

Morbert wrote: »

There is no such experimental difference. Any experiment carried out by the person on the train will register the ground clock as ticking slowly, and any experiment carried out by the person on the ground will register the train clock ticking slowly.

It's probably worth highlighting again, that we are discussing a scenario where the relative motion is ascribed to one reference frame or the other, in both reference frames; that is, either the train is moving in both reference frames, or the platform is.

Whichever frame is not moving, the photon of that clock will not trace the hypotenuse and so will tick faster.

Morbert wrote: »

I think you are getting hung up on the shorthand language used to frame the thought experiment. Henry and Albert do not make any metaphysical assumptions about their measurement of 2d being an absolute distance. They acknowledge their experimental reports are using arbitrary reference frames. I.e. Both the observer on the train and on the ground, assuming they are aware of relativity, know that the measurement of a distance 2d for their respective clocks, and a larger distance for the other's clocks, is no more or less valid a measurement than the other's.

Einsteinian relativity might not expressly state anything about an absolute rest frame, but there are certain issues which suggest that it is a tacit assumption.

Firstly, the treatment of reference frames, in Einsteinian relativity, is indistinguishable from such a treatment where reference frames are considered to be at absolute rest, from their own perspectives.

Secondly, the ascription of all motion to the other reference frame, suggests that reference frames are considered to be at absolute rest from their own perspectives; if they weren't, then the vertical velocity component of the photon in their light clock would be less than c and they would thus measure a speed of light lower than c.

Another issue pertains to the consideration of relative velocities only; as outlined below.

Morbert wrote: »

I did this to show the superfluous nature of including absolute velocities in the reference frame. Instead of considering absolute velocities, it is possible to carry out the thought experiment by only only considering relative velocities U and V. I.e. Instead of presupposing an absolute reference frame and deriving relative velocities, we simply consider the relative velocities without any reference to an absolute reference frame.

Why would he assume the absolute path length is 2d? Why would he consider an absolute path length at all? Special relativity does not postulate that the speed of light is c in some absolute reference frame. It postulates that all observers will measure the speed of light to be c. Time dilation and length contraction are similarly just measurements, and not statements about an absolute "passage of time" and "extension in space".

Why presuppose an absolute reference frame at all? Why not just start with relative velocities, and make no statement about absolute reference frames at all?

The issue is that, in the construction, you started off by assuming an absolute reference frame to define the values of U and V; and, theoretically, there should be an infinite number of possibilities that can give rise to the measured relative velocity between two reference frames; where U and V would be perfectly adequate examples; however, this is only possible when there is a common rest frame which can be used to define the velocities.

The infinite number of possibilities [for making up the relative velocity] should vary from one of the reference frames accounting for 100% of the relative velocity, to both reference frames accounting for 50%, to the other accounting for 100% of the relative velocity, however, if we only consider relative velocities then we have to treat one of the reference frames as being at absolute rest; or, as Einsteinian relativity appears to do, treat each reference frame as being at rest from its own perspecitve.

If we take the example where the relative velocity is 100km/h; if we want to consider the case where the velocities are U and V for the two reference frames, where U = 30km/h and V=100km/h, then we need a common rest frame against which to define those respective velocities, because relative to each other the velocity will always be 100km/h.

For this reason, one reference frame has to be treated as being at absolute rest, and has to ascribe all of the velocity component to the other reference frame; it appears as though, under Einsteinian relativity, each reference frame is treated thusly.

Morbert wrote: »

They happen any time GPS satellites relay information to each other, or to people on the ground. The equations are entirely general, and do not presuppose and earth-centred physical properties.

Aren't GPS systems synchronised to an earth centred inertial frame? Does the designation of this preferred frame not marginally favour Lorentzian relativity; despite the fact that Einsteinian relativity could be used.

Morbert wrote: »

In the thought experiment, we only consider a train moving at constant velocity, across an infinite plane. This is because the thought experiment is an exploration of the logical consequences of relativity's postulates. But with that said "pendulum" is a redundant detail. "Infinitely precise, independent clock" will do.

Is there a contemporary real world experiment that correlates to this thought experiment?

Also, would this scenario be one such scenario where Larmor dilation would apply?

Morbert wrote: »

It is not assumed. In fact, length-contraction was initially assumed in order to explain the isotropy of the speed of light, and was later dropped. The dimensions of the apparatus, as described by the person in the train, are perfectly valid, and no less physical than the measurements taken by the person on the ground.

Length contraction isn't observed in any experiment though is it; at least it doesn't appear to be in the interferometer experiments or in the muon decay experiments.

Morbert wrote: »

This is a good time to talk about Lorentzian relativity. You have suggested that the photon is actually travelling a distance greater than 2d, but that the apparatus used by the person in the train is moving more slowly, and hence registering a speed c. This supposes that every possible physical mechanism is slowed by the same amount, everything to his infinitely precise wristwatch, to the neurons in his brain, to the photon apparatus itself. Then, when we consider interfering lightbeams, you suggest that things actually physically contract by some amount, and no matter what material used, or what orientations used, the length contraction effect will always sync up with the "slower moving" effect at precisely the right amount to render the speed of light to be c. Why would a physical process like length-contraction be correlated with a completely separate physical process of "slowed movement"? This is what Lorentzian relativity supposes. In fact, even with these supposed physical processes, it has no physical understanding of therelativity of simultaneity.

Special relativity, on the other hand, has a very simple framework: The geometry relating all events is a pseudo-Riemannian, Minkowski geometry.

I'm not familiar with that analysis of Lorentzian relativity tbh, but it looks like a bit of a skewed comparison of the two theories.

. . . [in the context of contractions] the crucial difference between the two theories, of course, is that the Lorentz contraction, in the former theory, is viewed as a result of the (electromagnetic) forces responsible for the microstructure of matter in the context of Lorentz’s theory of the electron, whereas this same contraction, in Einstein’s theory, is viewed as a direct reflection —independent of all hypotheses concerning microstructure and its dynamics—of a new kinematical structure for space and time involving essential relativized notions of duration, length, and simultaneity. In terms of Poincar´e’s hierarchical conception of the sciences, then, Poincar locates the Lorentz contraction (and the Lorentz group more generally) at the level of experimental physics, while keeping Newtonian structure at the next higher level (what Poincar´e calls mechanics) completely intact. Einstein, by contrast, locates the Lorentz contraction (and the Lorentz group more generally) at precisely this next higher level, while postponing to the future all further discussion of the physical forces and material structures actually responsible for the physical phenomenon of rigidity.
The Lorentz contraction, in Einstein’s hands, now receives a direct
kinematical interpretation.

Minkowski space-time: a glorious non-entity

Other sources suggest the difference lies in the postulation of an absolute rest frame in Lorentzian relativity

the last vestiges of a substantial ether had been eliminated from Lorentz's "ether" theory, and it became both empirically and deductively equivalent to special relativity. The only difference was the metaphysical postulate of a unique absolute rest frame, which was empirically undetectable and played no role in the physical predictions of the theory

wiki-LET current status

I suspect that even that absolute rest frame could be removed - without treating reference frames as being at absolute rest - by simply having a preferred reference frame, or rest frame, for units of measurement.

EDIT: just on the point of relativity of siumultaneity; Lorentzian relativity doesn't have a physical understanding of it, because it's not actually part of it; absolute simultaneity is prevalent un LR.

Morbert

roosh wrote: »

It's probably worth highlighting again, that we are discussing a scenario where the relative motion is ascribed to one reference frame or the other, in both reference frames; that is, either the train is moving in both reference frames, or the platform is.

Whichever frame is not moving, the photon of that clock will not trace the hypotenuse and so will tick faster.

It doesn't matter how you ascribe anything. There will be no experimental difference.

Einsteinian relativity might not expressly state anything about an absolute rest frame, but there are certain issues which suggest that it is a tacit assumption.

Firstly, the treatment of reference frames, in Einsteinian relativity, is indistinguishable from such a treatment where reference frames are considered to be at absolute rest, from their own perspectives.

Secondly, the ascription of all motion to the other reference frame, suggests that reference frames are considered to be at absolute rest from their own perspectives; if they weren't, then the vertical velocity component of the photon in their light clock would be less than c and they would thus measure a speed of light lower than c.

The expressions in bold are oxymorons. If you are considering something, relative to a reference frame ('from their own perspective'), they are not making any statements, implicit, suggestive, or otherwise, about absolute reference frames. "The train is at rest, from my perspective" simply means "The coordinate system which labels me as at rest, also labels the train as at rest. This is an entirely arbitrary coordinate, not derived from any implicit or explicit assumption about the concept of absolute rest."

The issue is that, in the construction, you started off by assuming an absolute reference frame to define the values of U and V; and, theoretically, there should be an infinite number of possibilities that can give rise to the measured relative velocity between two reference frames; where U and V would be perfectly adequate examples; however, this is only possible when there is a common rest frame which can be used to define the velocities.

The infinite number of possibilities [for making up the relative velocity] should vary from one of the reference frames accounting for 100% of the relative velocity, to both reference frames accounting for 50%, to the other accounting for 100% of the relative velocity, however, if we only consider relative velocities then we have to treat one of the reference frames as being at absolute rest; or, as Einsteinian relativity appears to do, treat each reference frame as being at rest from its own perspecitve.

If we take the example where the relative velocity is 100km/h; if we want to consider the case where the velocities are U and V for the two reference frames, where U = 30km/h and V=100km/h, then we need a common rest frame against which to define those respective velocities, because relative to each other the velocity will always be 100km/h.

For this reason, one reference frame has to be treated as being at absolute rest, and has to ascribe all of the velocity component to the other reference frame; it appears as though, under Einsteinian relativity, each reference frame is treated thusly.

Such a scenario is impossible. V is always -U. I think this explains the confusion. U is the velocity of the train using the coordinate system of the ground observer. V is the velocity of the earth using the coordinate system of the train observer. These terms are not in any way related to some other, third coordinate system, absolute or otherwise.

Aren't GPS systems synchronised to an earth centred inertial frame? Does the designation of this preferred frame not marginally favour Lorentzian relativity; despite the fact that Einsteinian relativity could be used.

Is there a contemporary real world experiment that correlates to this thought experiment?

Also, would this scenario be one such scenario where Larmor dilation would apply?

Length contraction isn't observed in any experiment though is it; at least it doesn't appear to be in the interferometer experiments or in the muon decay experiments.

The conversations seems to be fragmenting again. While I don't have an issue going into real-world experiments, we first need to settle any thought experiment issues you might have. Once the consistency and implications of relativity is understood, we can move on to experimental support.

I'm not familiar with that analysis of Lorentzian relativity tbh, but it looks like a bit of a skewed comparison of the two theories.

Minkowski space-time: a glorious non-entity

Other sources suggest the difference lies in the postulation of an absolute rest frame in Lorentzian relativity
wiki-LET current status

I suspect that even that absolute rest frame could be removed - without treating reference frames as being at absolute rest - by simply having a preferred reference frame, or rest frame, for units of measurement.

EDIT: just on the point of relativity of siumultaneity; Lorentzian relativity doesn't have a physical understanding of it, because it's not actually part of it; absolute simultaneity is prevalent un LR.

To try and keep the topic focused (We could spend a long time talking about obscure facets): Can I ask you why you would be more comfortable with assuming an undetectable absolute reference frame exists, than with the assumption that time, as part of the relation between events, exists?

roosh

Morbert wrote: »

It doesn't matter how you ascribe anything. There will be no experimental difference.

Would that be the case under the Loerntzian interpretation also?

Morbert wrote: »

The expressions in bold are oxymorons. If you are considering something, relative to a reference frame ('from their own perspective'), they are not making any statements, implicit, suggestive, or otherwise, about absolute reference frames. "The train is at rest, from my perspective" simply means "The coordinate system which labels me as at rest, also labels the train as at rest. This is an entirely arbitrary coordinate, not derived from any implicit or explicit assumption about the concept of absolute rest."

I don't think they are oxymoronic, are they? They are not contradictory in and of themselves; they only become contradictory if we consider that two reference frames treat themselves as being at absolute rest - which will hopefully be clarified further below.

It is probably worth stating that the tacit assumptions aren't present in the formulation used above, but they are necessary consequences of the treatment discussed below.

Morbert wrote: »

Such a scenario is impossible. V is always -U. I think this explains the confusion. U is the velocity of the train using the coordinate system of the ground observer. V is the velocity of the earth using the coordinate system of the train observer. These terms are not in any way related to some other, third coordinate system, absolute or otherwise.

I think I may have confused the issue by not sticking more rigidly to the terms you defined from the outset, u and v, and U and V.


The issue is that, in the construction, you started off by assuming an absolute reference frame to define the values of u and v; such that either u or v could have had a higher value, relative to the assumed absolute rest frame; they also could have had equal values, or either could have had a value of zero, relative to the absolute rest frame i.e. it would have been at absolute rest.

Theoretically, that should be correct; there should be an infinite number of values for u and v that will give rise to the relative velocites of V and U (which are essentially the same value [with opposite signs perhaps]). However, in order to facilitate this possibility, a common rest frame is required to define u and v.


For example, if the relative velocity (V or U), between two reference frames, is 100km/h; there should be an infinite range of values for u and v which give rise to this relative velocity: u = 30km/h and v = 70km/h; u = 50km/h and v = 50km/h; u = 1km/h and v = 99km/h; etc. etc.. However, this is only possible if we consider a common rest frame, against which to define the values for u and v; because if we only consider the relative velocity between reference frames, the value will always be 100km/h.

It is for this reason that one reference frame has to be treated as being at absolute rest, and has to ascribe all of the velocity component to the other reference frame; it appears as though, under Einsteinian relativity, from the perspective of each reference frame i.e. from their own perspective, they are treated as being at absolute rest.

EDIT: If they weren't treated as being at absolute rest, then, in the thought experiment, the vertical velocity component of the photon in their light clock would be less than c and they would thus measure a speed of light to be lower than c.

Morbert wrote: »

The conversations seems to be fragmenting again. While I don't have an issue going into real-world experiments, we first need to settle any thought experiment issues you might have. Once the consistency and implications of relativity is understood, we can move on to experimental support.

Fair enough, but we probably won't be able to differentiate between Lorentzian relativity and Einsteinian will we, because both are equally supported by the evidence? I've read arguments that Lorentzian relativity is the more straight forward approach, when it comes to the GPS system, because of the preferred reference frame, but that Einsteinian relativity can equally be applied.

Morbert wrote: »

To try and keep the topic focused (We could spend a long time talking about obscure facets): Can I ask you why you would be more comfortable with assuming an undetectable absolute reference frame exists, than with the assumption that time, as part of the relation between events, exists?

There are probably a number of reasons; some of them include the fact that what a clock counter actually measures, or rather counts, is the number of events in the clock, not necessarily the relation between them; that only a spatial relationship between the events in a clock can be deduced, and not a temporal one; the fact that there is no experiment that can ever be conducted that will not be in the present moment, meaning that the temporal dimension (past and future) have to be assumed to exist.

Another reason is that I don't think it is necessary for Lorentzian relativity to assume that an undetectable, absolute reference frame actually exists, we can just treat the possibility that it could exist; as per the principle of invariance; we just wouldn't be able to detect such a frame, even if it did exist.

I also think the need for an absolute reference frame, in LR, is negated simply by defining a rest frame for units of measurement; which is something which, arguably, occurs necessarily in the real world.

Morbert

roosh wrote: »

Would that be the case under the Loerntzian interpretation also?

Yes, provided you included the usual neo-lorentzian plethora of assumptions about the co-incidental behaviour of the laws of physics.

I don't think they are oxymoronic, are they? They are not contradictory in and of themselves; they only become contradictory if we consider that two reference frames treat themselves as being at absolute rest - which will hopefully be clarified further below.

It is probably worth stating that the tacit assumptions aren't present in the formulation used above, but they are necessary consequences of the treatment discussed below.

I think I may have confused the issue by not sticking more rigidly to the terms you defined from the outset, u and v, and U and V.

The issue is that, in the construction, you started off by assuming an absolute reference frame to define the values of u and v; such that either u or v could have had a higher value, relative to the assumed absolute rest frame; they also could have had equal values, or either could have had a value of zero, relative to the absolute rest frame i.e. it would have been at absolute rest.

Theoretically, that should be correct; there should be an infinite number of values for u and v that will give rise to the relative velocites of V and U (which are essentially the same value [with opposite signs perhaps]). However, in order to facilitate this possibility, a common rest frame is required to define u and v.

And I don't need to define u and v at all. I am certainly free to. There is nothing special about the reference frames where u = U or v = V, but I don't have to. U and V are arbitrary labels adopted by the observers, with no compulsion to adopt them, or any other reference frame.

For example, if the relative velocity (V or U), between two reference frames, is 100km/h; there should be an infinite range of values for u and v which give rise to this relative velocity: u = 30km/h and v = 70km/h; u = 50km/h and v = 50km/h; u = 1km/h and v = 99km/h; etc. etc.. However, this is only possible if we consider a common rest frame, against which to define the values for u and v; because if we only consider the relative velocity between reference frames, the value will always be 100km/h.

And why consider u and v at all? Why introduce a third rest frame at all? And furthermore, even if we did arbitrarily choose a third rest frame, why call it absolute?

It is for this reason that one reference frame has to be treated as being at absolute rest, and has to ascribe all of the velocity component to the other reference frame; it appears as though, under Einsteinian relativity, from the perspective of each reference frame i.e. from their own perspective, they are treated as being at absolute rest.

Again, this is a contradiction in terms. If they acknowledge "from their own perspective", they acknowledge that they are not being treated "absolutely" in any way. What you should have said is "from their own perspective, they are labelled as at rest". This in no way implies "from their own perspective, they are labelled as at absolute rest".

EDIT: If they weren't treated as being at absolute rest, then, in the thought experiment, the vertical velocity component of the photon in their light clock would be less than c and they would thus measure a speed of light to be lower than c.

That does not follow in any way from the coordinate labels or transformations.

If I may be blunt, I think you might have an agenda. Your belief that relativity must be somehow inherently wrong or inconsistent gets in the way of understanding the simple and uncontroversial formalism of relativity:

Coordinate labels are arbitray.
Coordinate labels all label the speed of light as c.
Coordinate labels can be related by lorentz transformations.

These in no way imply an "absolute" non-arbitrary coordinate label. Even advocates of neo-Lorentzian relativity fully accept this.

Fair enough, but we probably won't be able to differentiate between Lorentzian relativity and Einsteinian will we, because both are equally supported by the evidence? I've read arguments that Lorentzian relativity is the more straight forward approach, when it comes to the GPS system, because of the preferred reference frame, but that Einsteinian relativity can equally be applied.

The different formalisms of Einstein's relativity are more easily applicable in different situations. Sometimes it is useful and illuminating to talk about reference frames and coordinate time (GPS systems). Sometimes it is more useful to talk about symmetry groups and spacetime structure (Particle accelerator), but both are very much a part of Einsteinian relativity. Lorentzian relativity, as it stands, is a less elegant interpretation of data, with a greater number of assumptions. It is most common among theologians like William Lain Craig, who want there to be a privileged reference frame for God.

There are probably a number of reasons; some of them include the fact that what a clock counter actually measures, or rather counts, is the number of events in the clock, not necessarily the relation between them; that only a spatial relationship between the events in a clock can be deduced, and not a temporal one; the fact that there is no experiment that can ever be conducted that will not be in the present moment, meaning that the temporal dimension (past and future) have to be assumed to exist.

That is like saying a ruler counts the number of atoms between two events, not necessarily the spatial relation between the events. You cannot say time is any less real than space. And again, I stress that relativity itself says time, on its own, is illusory, and space on its own is illusory, and only consider relation between events as a whole, are they in some way preserved.

Another reason is that I don't think it is necessary for Lorentzian relativity to assume that an undetectable, absolute reference frame actually exists, we can just treat the possibility that it could exist; as per the principle of invariance; we just wouldn't be able to detect such a frame, even if it did exist.

You can do that either way. That is just a rephrasing of the statement "Lorentzian and Einsteinian relativity both predict the same things".

I also think the need for an absolute reference frame, in LR, is negated simply by defining a rest frame for units of measurement; which is something which, arguably, occurs necessarily in the real world.

And that rest frame can be arbitrarily chosen. You are presumably not, however, arguing that the present can be arbitrarily chosen. You are claiming there is an actual, non-arbitrary rest frame that labels the true present as the present.

roosh

It might be worth addressing this point first.

Morbert wrote: »

If I may be blunt, I think you might have an agenda. Your belief that relativity must be somehow inherently wrong or inconsistent gets in the way of understanding the simple and uncontroversial formalism of relativity:

I think your being blunt can be entirely beneficial to the discussion; whether we like to admit it or not, both of us are biased, for different reasons perhaps; we are both entering this with pre-existing beliefs; our attachment to which can affect our understanding of the points being made. I'm sure you are familiar with the "God is in the neurons" youtube video, which outlines how our attachment to our pre-existing beliefs can materially affect how we receive information.

I'm not entirely sure what you mean, or mean to imply, by "agenda". I don't take it negatively, although I suspect that it may, in some way, be linked to the mention, below, of a certain theologian. This may, perhaps, be one of your own preconceptions - indeed, it could simply be my pre-conceived idea of what your preconceptions are .

Either way, my "agenda" is little more than the [saccharine] desire to develop a better understanding of the nature of reality. Inevitably I have empirically based, pre-existing beliefs with which I am approaching this. That I have pre-existing beliefs does not imply that they are incorrect; that I, inevitably, apply confirmation bias does not mean that the proposition being confirmed is incorrect; no more than it means that the, inevitable, presence of the same cognitive biases in yourself, invalidates your pre-existing beliefs. It is precisely through such reasoned discussions that we both have the opportunity to cut through those cognitive biases, and hopefully shed those erroneous beliefs that affect our perception of reality.


We could of course discuss the nature of belief and knowledge, and the nature of attachment to belief, which would make for a more holistic discussion, but for the time being, and in this thread, I think we can concentrate on the existing theme of the thread.

Morbert wrote: »

Yes, provided you included the usual neo-lorentzian plethora of assumptions about the co-incidental behaviour of the laws of physics.

It might be better to discuss this in the thread on neo-Lorentzian relativity.

Morbert wrote: »

And I don't need to define u and v at all. I am certainly free to. There is nothing special about the reference frames where u = U or v = V, but I don't have to. U and V are arbitrary labels adopted by the observers, with no compulsion to adopt them, or any other reference frame.

And why consider u and v at all? Why introduce a third rest frame at all? And furthermore, even if we did arbitrarily choose a third rest frame, why call it absolute?

The reason for considering u and v is because, in your example, you started off by assuming an absolute rest frame to define the velocities, u and v, of two systems moving relative to that absolute rest frame; you then derived a formula for relative velocity between those two systems, based on the initial velocities, relative to that absolute rest frame.

The labels, 'u' & 'v' and 'U' & 'V', themselves, are essentially immaterial, but we need some placeholders for the relative velocity, so they are as good as any other arbitrary labels. What is under discussion is what those labels represent, and the logical consequences of what they represent.


Relative velocity
As mentioned before, theoretically, there should be an infinite number of values that can contribute to the relative velocity between two systems. The example above was of two systems with a relative velocity of 100km/h, where one system could be traveling at a velocity of 30km/h, and the other at 70km/h, or the infinite range of values that could contribute to a relative velocity of 100km/h. This, however, requires an arbitrary, not necessarily absolute, common rest frame, in order to define that infinite range of values. Einsteinian relativity doesn't allow for such a common rest frame, because only the relative velocities between systems is considered; with contractions being reciprocal between relatively moving systems.

By only considering the relative velocities, one of the systems has to be treated as being at absolute rest; because, in the absence of a common rest frame, or "background", 100% of the velocity has to be ascribed to the other reference frame, meaning that one of the reference frames is ascribed a zero velocity; a system with zero velocity is, I presume, a system at absolute rest.

Morbert wrote: »

Again, this is a contradiction in terms. If they acknowledge "from their own perspective", they acknowledge that they are not being treated "absolutely" in any way. What you should have said is "from their own perspective, they are labelled as at rest". This in no way implies "from their own perspective, they are labelled as at absolute rest".

Apologies, my terminology may have been a little loose, but the point is essentially a semantical.

I should probably have said that their co-ordinate system ascribes a zero velocity to their reference frame and therefore treats that reference frame as being at absolute rest. There is the alternative where their co-ordinate system ascribes a zero velocity to the other reference frame, but that just means that the other reference frame is treated as being at absolute rest.

Morbert wrote: »

That does not follow in any way from the coordinate labels or transformations.

Coordinate labels are arbitray.
Coordinate labels all label the speed of light as c.
Coordinate labels can be related by lorentz transformations.

These in no way imply an "absolute" non-arbitrary coordinate label. Even advocates of neo-Lorentzian relativity fully accept this.

The point being made is that the co-ordinate labeling system, tacitly, treats specific reference frames as being at absolute rest.

Whether it is mere coincidence or not, the thought experiment involving Albert and Henry lends itself to comparison with a similar thought experiment, where either Albert or Henry is at absolute rest. This is because the two scenarios are indistinguishable from one another. That is, if we consider the Einsteinian thought experiment from Albert's perspective, there would be no difference if we were to consider a similar thought experiment where Albert is at absolute rest. So, we are free to start with this possibility and see what conclusions we can derive.

This is another reason for considering an absolute rest frame.

Henry & Albert
Just for the purpose of explanation, we can formulate the thought experiment where both Albert and Henry are in separate train carriages; replacing Albert's platform for a train carriage doesn't have any material effects; I just think it's more intuitive to talk about a train moving than it is the platform, but either is fine.

If we simply start with the idea of the relative velocity, between Henry and Albert, both, as mentioned above, ascribe a zero velocity (and therefore absolute rest) to their own reference frames; but we can hopefully be demonstrate the point more clearly by considering the mechanics (is that the right use of the term?) of the situation.

The issue is difficult to see initially, if we only consider the Einsteinian thought experiment at it is, with no apparent tacit assumptions or consequences pertaining to absolute rest. However, if we juxtapose the Einsteinian thought experiment with the same thought experiment, except with the notion of absolute rest included, we can, hopefully, see those tacit consequences and/or assumptions emerge.

Absolute Frames
If we start with Albert being at absolute rest, then the photon in his clock would trace a path perpendicular to the centre point of both mirrors, and a path length of 2d.

If Henry were moving relative to Albert's absolute reference frame, then Albert would observe the photon in Hnery's clock to travel a path represented by the hypotenuse of a right angled triangle; hence he would observer his clock to be ticking slower (and lengths in Henry's reference frame as contracted). On the other hand, if Henry was at absolute rest and it was Albert moving relative to this frame, then Henry would see the same effects in Albert's reference frame.

As mentioned, this is indistinguishable from the Einsteinian thought experiment, except with an absolute reference frame expressly stated. What can hopefully demonstrated is that the Einsteinian thought experiment necessarily includes this absolute reference frame.

Absolute Albert
For the purpose of explanation, we can consider the scenario where Albert's co-ordinate labeling system labels him as "at rest".

If Albert's train were traveling at an inertial velocity, relative to the absolute rest frame - as would be necessitated by the scenario where "at rest" doesn't imply "absolute rest" - then the photon in his clock would be imparted with a horizontal velocity component, equal to the horizontal velocity of the train and the clock - much like he would observe in Henry's reference frame. This horizontal velocity component, along with the existing vertical velocity component, would cause the photon to trace a diagonal line between the centre points of the mirrors - because a line perpendicular from the centre point of one mirror would not meet the centre point of the other mirror, if both mirrors are moving; the path of the photon could be represented by the hypotenuse of a right angled triangle. The photon would still travel a distance of 2d relative to the carriage, because the horizontal velocity component of both would be equal. However, as you highlighted in the example above, this would cause the photon to have a vertical velocity component of less than c.

Because Albert measures the vertical velocity component of the photon to be c, it implies that that the clock, the carriage, and Albert himself, are at absolute rest.

Morbert wrote: »

The different formalisms of Einstein's relativity are more easily applicable in different situations. Sometimes it is useful and illuminating to talk about reference frames and coordinate time (GPS systems). Sometimes it is more useful to talk about symmetry groups and spacetime structure (Particle accelerator), but both are very much a part of Einsteinian relativity. Lorentzian relativity, as it stands, is a less elegant interpretation of data, with a greater number of assumptions. It is most common among theologians like William Lain Craig, who want there to be a privileged reference frame for God.

Lorentzian relativity applies just as well in the case of particle accelerators, I presume, or else there might be a way to distinguish between the two. As for elegance, I'm not sure reality relies on elegance to decide what is real and what is not. Indeed, Einsteinian relativity might have a number of tacit assumptions itself, that migh make it appear less "elegant".

With regard to Craig: it was only through discussing Einsteinian relativity that I became aware of Lorentzian relativity; and only through searching for information about the latter that I found out that Craig had latched onto Lorentzian relativity for the reason you state above. It is perhaps, paradoxically, both fortunate and unfortunate at the same time. However, I don't think his motivation for doing so should be allowed to cast aspersions on the theory of the late Dutchman; nor should they prejudice people's interpretation of his analysis - even if they do prejudice his own analysis (which is not to suggest that they actually do).

Although, I'm not au fait with Craigs arguments in favour of Lorentzian relativity, I have come across a few tidbits of information pertaining to the same. From what I can gather, he advocates an A-theory of time, as opposed to a B-theory. I'm not familiar enough, however, to know if timelessness fits in with his argument.

Morbert wrote: »

That is like saying a ruler counts the number of atoms between two events, not necessarily the spatial relation between the events. You cannot say time is any less real than space. And again, I stress that relativity itself says time, on its own, is illusory, and space on its own is illusory, and only consider relation between events as a whole, are they in some way preserved.

Not necessarily; the counter on an atomic clock actually counts the number of "events" inside the clock without any measurement of the relation between theose events, while there is no counter on a ruler which counts the number of atoms.

Morbert wrote: »

You can do that either way. That is just a rephrasing of the statement "Lorentzian and Einsteinian relativity both predict the same things".

I don't think it is; it more a question of removing what are perceived to be superfluous assumptions form the theory; without, unintentionally hiding them.

Morbert wrote: »

And that rest frame can be arbitrarily chosen. You are presumably not, however, arguing that the present can be arbitrarily chosen. You are claiming there is an actual, non-arbitrary rest frame that labels the true present as the present.

The suggestion is not that there is a rest frame which labels the present as the "true present"; the suggestion is that absolute simultaneity prevails in the universe; that a timeless A-theory, if you will, prevails.

Morbert

roosh wrote: »

The reason for considering u and v is because, in your example, you started off by assuming an absolute rest frame to define the velocities, u and v, of two systems moving relative to that absolute rest frame; you then derived a formula for relative velocity between those two systems, based on the initial velocities, relative to that absolute rest frame.

The labels, 'u' & 'v' and 'U' & 'V', themselves, are essentially immaterial, but we need some placeholders for the relative velocity, so they are as good as any other arbitrary labels. What is under discussion is what those labels represent, and the logical consequences of what they represent.

Relative velocity
As mentioned before, theoretically, there should be an infinite number of values that can contribute to the relative velocity between two systems. The example above was of two systems with a relative velocity of 100km/h, where one system could be traveling at a velocity of 30km/h, and the other at 70km/h, or the infinite range of values that could contribute to a relative velocity of 100km/h. This, however, requires an arbitrary, not necessarily absolute, common rest frame, in order to define that infinite range of values. Einsteinian relativity doesn't allow for such a common rest frame, because only the relative velocities between systems is considered; with contractions being reciprocal between relatively moving systems.

By only considering the relative velocities, one of the systems has to be treated as being at absolute rest; because, in the absence of a common rest frame, or "background", 100% of the velocity has to be ascribed to the other reference frame, meaning that one of the reference frames is ascribed a zero velocity; a system with zero velocity is, I presume, a system at absolute rest.

Apologies, my terminology may have been a little loose, but the point is essentially a semantical.

I should probably have said that their co-ordinate system ascribes a zero velocity to their reference frame and therefore treats that reference frame as being at absolute rest. There is the alternative where their co-ordinate system ascribes a zero velocity to the other reference frame, but that just means that the other reference frame is treated as being at absolute rest.

The point being made is that the co-ordinate labeling system, tacitly, treats specific reference frames as being at absolute rest.

Whether it is mere coincidence or not, the thought experiment involving Albert and Henry lends itself to comparison with a similar thought experiment, where either Albert or Henry is at absolute rest. This is because the two scenarios are indistinguishable from one another. That is, if we consider the Einsteinian thought experiment from Albert's perspective, there would be no difference if we were to consider a similar thought experiment where Albert is at absolute rest. So, we are free to start with this possibility and see what conclusions we can derive.

This is another reason for considering an absolute rest frame.

Henry & Albert
Just for the purpose of explanation, we can formulate the thought experiment where both Albert and Henry are in separate train carriages; replacing Albert's platform for a train carriage doesn't have any material effects; I just think it's more intuitive to talk about a train moving than it is the platform, but either is fine.

If we simply start with the idea of the relative velocity, between Henry and Albert, both, as mentioned above, ascribe a zero velocity (and therefore absolute rest) to their own reference frames; but we can hopefully be demonstrate the point more clearly by considering the mechanics (is that the right use of the term?) of the situation.

The issue is difficult to see initially, if we only consider the Einsteinian thought experiment at it is, with no apparent tacit assumptions or consequences pertaining to absolute rest. However, if we juxtapose the Einsteinian thought experiment with the same thought experiment, except with the notion of absolute rest included, we can, hopefully, see those tacit consequences and/or assumptions emerge.

Absolute Frames
If we start with Albert being at absolute rest, then the photon in his clock would trace a path perpendicular to the centre point of both mirrors, and a path length of 2d.

If Henry were moving relative to Albert's absolute reference frame, then Albert would observe the photon in Hnery's clock to travel a path represented by the hypotenuse of a right angled triangle; hence he would observer his clock to be ticking slower (and lengths in Henry's reference frame as contracted). On the other hand, if Henry was at absolute rest and it was Albert moving relative to this frame, then Henry would see the same effects in Albert's reference frame.

As mentioned, this is indistinguishable from the Einsteinian thought experiment, except with an absolute reference frame expressly stated. What can hopefully demonstrated is that the Einsteinian thought experiment necessarily includes this absolute reference frame.

Absolute Albert
For the purpose of explanation, we can consider the scenario where Albert's co-ordinate labeling system labels him as "at rest".

If Albert's train were traveling at an inertial velocity, relative to the absolute rest frame - as would be necessitated by the scenario where "at rest" doesn't imply "absolute rest" - then the photon in his clock would be imparted with a horizontal velocity component, equal to the horizontal velocity of the train and the clock - much like he would observe in Henry's reference frame. This horizontal velocity component, along with the existing vertical velocity component, would cause the photon to trace a diagonal line between the centre points of the mirrors - because a line perpendicular from the centre point of one mirror would not meet the centre point of the other mirror, if both mirrors are moving; the path of the photon could be represented by the hypotenuse of a right angled triangle. The photon would still travel a distance of 2d relative to the carriage, because the horizontal velocity component of both would be equal. However, as you highlighted in the example above, this would cause the photon to have a vertical velocity component of less than c.

Because Albert measures the vertical velocity component of the photon to be c, it implies that that the clock, the carriage, and Albert himself, are at absolute rest.

What you have shown (and what my earlier consideration showed), is that "absolute" is entirely superfluous. You can start out defining an absolute rest, or you can start out explicitly stating there is no absolute rest, and you will still get the same result. To phrase it more formally, if an absolute rest was implicitly assumed, then the additional assumption ("There is no such thing as absolute rest") should lead to a contradiction, yet clearly it doesn't, as the entire thought experiment can be carried out using "at rest according to coordinate system A/B" without any supposition of "absolute" rest.

Lorentzian relativity applies just as well in the case of particle accelerators, I presume, or else there might be a way to distinguish between the two. As for elegance, I'm not sure reality relies on elegance to decide what is real and what is not. Indeed, Einsteinian relativity might have a number of tacit assumptions itself, that migh make it appear less "elegant".

It applies if you introduce more mysterious ad-hoc dynamical processes that all happen to provide an illusion of spacetime.

With regard to Craig: it was only through discussing Einsteinian relativity that I became aware of Lorentzian relativity; and only through searching for information about the latter that I found out that Craig had latched onto Lorentzian relativity for the reason you state above. It is perhaps, paradoxically, both fortunate and unfortunate at the same time. However, I don't think his motivation for doing so should be allowed to cast aspersions on the theory of the late Dutchman; nor should they prejudice people's interpretation of his analysis - even if they do prejudice his own analysis (which is not to suggest that they actually do).

True, but it should be pointed out that objections to Einstein's relativity do not stem from perceived insufficiencies in the theory, and Craig is an example of this.

Not necessarily; the counter on an atomic clock actually counts the number of "events" inside the clock without any measurement of the relation between theose events, while there is no counter on a ruler which counts the number of atoms.

And the the relation between points on a ruler is defined by counting the number of units or "simultaneous events" between the points on the ruler. Hence the 1,2,3,4... marks on the ruler.

The suggestion is not that there is a rest frame which labels the present as the "true present"; the suggestion is that absolute simultaneity prevails in the universe; that a timeless A-theory, if you will, prevails.

If my frame of reference says the lightning bolts strike at the same time, and yours say they strike at different times, is there a way to determine which is the absolute present?

roosh

Morbert wrote: »

What you have shown (and what my earlier consideration showed), is that "absolute" is entirely superfluous. You can start out defining an absolute rest, or you can start out explicitly stating there is no absolute rest, and you will still get the same result. To phrase it more formally, if an absolute rest was implicitly assumed, then the additional assumption ("There is no such thing as absolute rest") should lead to a contradiction, yet clearly it doesn't, as the entire thought experiment can be carried out using "at rest according to coordinate system A/B" without any supposition of "absolute" rest.

I don't think that arriving at the same results, when including the absolute reference frame, demonstrates that it is superfluous; I would be more inclined to say that it demonstrates that the absolute reference frame is a tacit assumption. Also, simply stating that there is no absolute rest, does not mean that absolute rest is not a tacit assumption; in itself, it is indeed a contradiction, but, in order to see more clearly, where the contradictions arise, we need to examine the thought experiment critically.

We can look at it in two ways: ignoring the absolute rest frame and considering only the relative velocity; or including the absolute rest frame and considering the mechanics.

Relative velocity
If we consider only the relative velocity, then we can see that the co-ordinate labeling system of Einsteinian relativity necessitates that one reference frame be ascribed a zero velocity. Again, I presume that a reference frame with a velocity of zero is a reference frame at absolute rest.

Mechanics
Demonstrating the tacit assumption, of absolute rest, is best done by considering the mechanics of both scenarios: where Albert is at absolute rest; and where Albert is not at absolute rest. The position of absolute rest is exactly the same as the thought experiment. But if we consider the scenario where he is not at absolute rest, then the conclusions do not concur with Einsteinian relativity.

Again, if Albert is at absolute rest, then the photon in his clock will have no horizontal velocity component, only a vertical one; which will equal c. If Albert is not at absolute rest - the scenario where "at rest" under his labeling system doesn't mean "absolute rest" - then the photon in his clock will have a horizontal velocity component equal to that of the train (or platform) and clock. As you highlighted above, if this is the case, then the vertical velocity component will be less than c.

If Albert measures the speed of light in his clock to be c, then it implies that he is at absolute rest - or that the vertical velocity component is greater than c, such that it yields a measurement of c, relative to the moving carriage.

Alternatively, the contention of Lorentzian relativity could apply; that the instruments in Albert's reference frame are contracted by an amount unknown to him, due to the motion of the reference frame (where "at rest" doesn't mean "absolute rest"); relative to what, though, is the question which is begged. It can't be relative to Henry's reference frame, because he labels his reference frame as "at rest" relative to that (itself a contradiction perhaps), and he has to ascribe all the velocity to Henry's reference frame; meaning he has to label himself as having a zero velocity.

Morbert wrote: »

It applies if you introduce more mysterious ad-hoc dynamical processes that all happen to provide an illusion of spacetime.

. . . the crucial difference between the two theories, of course, is that
the Lorentz contraction, in the former theory, is viewed as a result
of the (electromagnetic) forces responsible for the microstructure of matter in the context of Lorentz’s theory of the electron, whereas
this same contraction, in Einstein’s theory, is viewed as a direct
reflection—independent of all hypotheses concerning microstructure
and its dynamics—of a new kinematical structure for space and time
involving essential relativized notions of duration, length, and simultaneity.

On the one hand we have a theory which seeks to explain things in the context of the micro-structure of matter (which we know to exist); on the other we have a theory which explains things by introducing a "new kinematical structure for space and time involving essential relativized notions of duration, length, and simultaneity"; which can, incidentally, only be detected by measuring the effects of the micro-structure of matter, or the macro-structure of matter, which we know to be comprised of the micro-structure of matter. In the latter "complex material bodies are constrained (somehow!) to 'directly reflect' its [spacetime's] structure, in a way that is 'independent of all hypotheses concerning microstructure and its dynamics' [again, things we know to exist]."

One can postpone (as Einstein did) the detailed investigation into the forces and structures actually responsible for the phenomena that are paradigmatic of space-time’s Minkowskian geometry, without thereby relinquishing the idea that these forces and structures are, indeed, 'actually responsible' for the phenomena in question

Brown & Pooley (2004)

The emphasis and brackets are mine, and the quotes are taken out of context and don't represent the authors opinions; but the points made are applicable here.

Morbert wrote: »

True, but it should be pointed out that objections to Einstein's relativity do not stem from perceived insufficiencies in the theory, and Craig is an example of this.

I haven't read any of his writings on the subject, so I can't offer too much insight; but I would imagine that his entire analysis is not based solely on the contention that a preferred reference frame fits with his theory of God. That is more based on comments in a paper by Brown & Pooley (Minkowski spacetime: a glorious non-entity).

Morbert wrote: »

And the the relation between points on a ruler is defined by counting the number of units or "simultaneous events" between the points on the ruler. Hence the 1,2,3,4... marks on the ruler.

This just demonstrates that matter has a spatial dimension; the same cannot be said for a temporal dimension.

Morbert wrote: »

If my frame of reference says the lightning bolts strike at the same time, and yours say they strike at different times, is there a way to determine which is the absolute present?

Experimentally, is there a way to determine relativity of simultaneity?

Morbert

roosh wrote: »

I don't think that arriving at the same results, when including the absolute reference frame, demonstrates that it is superfluous; I would be more inclined to say that it demonstrates that the absolute reference frame is a tacit assumption. Also, simply stating that there is no absolute rest, does not mean that absolute rest is not a tacit assumption; in itself, it is indeed a contradiction, but, in order to see more clearly, where the contradictions arise, we need to examine the thought experiment critically.

We can look at it in two ways: ignoring the absolute rest frame and considering only the relative velocity; or including the absolute rest frame and considering the mechanics.

Relative velocity
If we consider only the relative velocity, then we can see that the co-ordinate labeling system of Einsteinian relativity necessitates that one reference frame be ascribed a zero velocity. Again, I presume that a reference frame with a velocity of zero is a reference frame at absolute rest.

You do not need to claim the reference frame has a velocity of 0. When mathematicians say a reference frame S' has a velocity V in reference frame S, what they mean is an object that is labelled as stationary in S' will have a velocity V in S. You can explicitly state the nearly tautological fact that a reference frame will have a velocity of 0, according to itself, or an object that is labelled as stationary in S' will have a velocity of 0 in S', but that is no more a statement about absolute rest than "I am at rest with respect to myself".

Mechanics
Demonstrating the tacit assumption, of absolute rest, is best done by considering the mechanics of both scenarios: where Albert is at absolute rest; and where Albert is not at absolute rest. The position of absolute rest is exactly the same as the thought experiment. But if we consider the scenario where he is not at absolute rest, then the conclusions do not concur with Einsteinian relativity.

Again, if Albert is at absolute rest, then the photon in his clock will have no horizontal velocity component, only a vertical one; which will equal c. If Albert is not at absolute rest - the scenario where "at rest" under his labeling system doesn't mean "absolute rest" - then the photon in his clock will have a horizontal velocity component equal to that of the train (or platform) and clock. As you highlighted above, if this is the case, then the vertical velocity component will be less than c.

If Albert measures the speed of light in his clock to be c, then it implies that he is at absolute rest - or that the vertical velocity component is greater than c, such that it yields a measurement of c, relative to the moving carriage.

The bit in red is incorrect. Einstein's relativity says all observers will measure the speed of light to be c. Therefore Albert would measure the speed of light in his clock to be c regardless of whether or not he is at absolute rest, so the implication that he is at absolute rest cannot be made.

Alternatively, the contention of Lorentzian relativity could apply; that the instruments in Albert's reference frame are contracted by an amount unknown to him, due to the motion of the reference frame (where "at rest" doesn't mean "absolute rest"); relative to what, though, is the question which is begged. It can't be relative to Henry's reference frame, because he labels his reference frame as "at rest" relative to that (itself a contradiction perhaps), and he has to ascribe all the velocity to Henry's reference frame; meaning he has to label himself as having a zero velocity.

On the one hand we have a theory which seeks to explain things in the context of the micro-structure of matter (which we know to exist); on the other we have a theory which explains things by introducing a "new kinematical structure for space and time involving essential relativized notions of duration, length, and simultaneity"; which can, incidentally, only be detected by measuring the effects of the micro-structure of matter, or the macro-structure of matter, which we know to be comprised of the micro-structure of matter. In the latter "complex material bodies are constrained (somehow!) to 'directly reflect' its [spacetime's] structure, in a way that is 'independent of all hypotheses concerning microstructure and its dynamics' [again, things we know to exist]."

Brown & Pooley (2004)

The emphasis and brackets are mine, and the quotes are taken out of context and don't represent the authors opinions; but the points made are applicable here.

I haven't read any of his writings on the subject, so I can't offer too much insight; but I would imagine that his entire analysis is not based solely on the contention that a preferred reference frame fits with his theory of God. That is more based on comments in a paper by Brown & Pooley (Minkowski spacetime: a glorious non-entity).

Brown and Pooley argue that Einstein's relativity has the same issues as Lorentzian relativity. It doesn't, for the following reasons.

(a) The 'constraint' of Minkowski geometry occurs precisely because of the absence of mysterious dynamical forces. Brown and Pooley argue that a Minkowski geometry doesn't necessarily mean the laws of physics are Lorentz invariant. This is true insofar as you can postulate mysterious accidental dynamics to break Lorentz invariance, just as neo-Lorentzian relativity postulates mysterious dynamics to break Galilean invariance. But in the absence of such mysterious dynamics, Minkowski kinematics implies Lorentz invariant laws. And since the absence of mysterious dynamics is the virtue of Einstein's relativity, there is no problem.

(b) Neo-Lorentzian relativity does not explain this "accidental" microstructure of matter. Brown and Pooley adimit as much ("all explanation must stop somewhere").

(c) There is an interesting rebuttal found here

http://philsci-archive.pitt.edu/3895/

as well as other criticisms

http://philsci-archive.pitt.edu/3655/1/Constructive_Relativity.pdf

http://philsci-archive.pitt.edu/3108/1/Physical_Relativityfin.pdf

I don't draw anything particular from them (yet) as directly relevant to our conversation, but you might find them interesting.

When it comes to the "philosophy" of relativity, I take the (seemingly dismissive) position that Minkowski spacetime is the simplest mathematical model connecting the postulates of relativity to experimental observations.

This just demonstrates that matter has a spatial dimension; the same cannot be said for a temporal dimension.

And a clock just demonstrates that a set of events (not a single event) has a temporal dimension, just as the set of simultaneous events across a ruler (not a single event) has a spatial dimension. We can generalise this by saying there is a spatio-temporal relation between events.

Experimentally, is there a way to determine relativity of simultaneity?

In other words: "I accept that the postulated true present is unknown, and cannot even be known to exist at all, but you cannot tender an experiment to show it definitely does not exist". This is true(ish) insofar as any test of simultaneity could be explained by invoking contrived neo-lorentzian dynamics, but relativity of simultaneity is simply the relaxation of the assumption that there is a true, simultaneous present. Why assume what you cannot demonstrate?

roosh

Morbert wrote: »

You do not need to claim the reference frame has a velocity of 0. When mathematicians say a reference frame S' has a velocity V in reference frame S, what they mean is an object that is labelled as stationary in S' will have a velocity V in S. You can explicitly state the nearly tautological fact that a reference frame will have a velocity of 0, according to itself, or an object that is labelled as stationary in S' will have a velocity of 0 in S', but that is no more a statement about absolute rest than "I am at rest with respect to myself".

The issue isn't quite as simplistic as saying "I am at rest with respect to myself".


EDIT: of course, the "I am at rest with respect to myself" applies just as much to an observer at absolute rest.

If we were considering a lone observer in an empty universe, or considering the observer without reference to anything else in the universe, then a co-ordinate system which implies "I am at rest with respect to myself" would be fine; but we are considering the co-ordinate labeling system which labels the reference frame as "at rest" and a relatively moving reference frame as "in motion".

When we do this, there is no need to claim that a reference frame has a velocity of zero, it is a logical consequence of the co-ordinate labeling system. If you only consider the relative velocity between systems, then it is impossible not to label one as having a zero velocity, and, therefore, as being at absolute rest; regardless of what mathematicians wish to imply, that is a consequence of such a labeling system. This is what is meant by saying that the co-ordinate labeling system of Einsteinian relativity treats reference frames as being at absolute rest, from it's own perspective, or "according to itself".

The "from it's own perspective" or "according to itself" is a semantical point, with which we shouldn't get bogged down. The essential point is that the co-ordinate labeling system applied to reference frames in Einsteinian relativity, treat that reference frame as being at absolute rest, precisely because it ascribes a zero velocity to it.

Infinite reference frames
If we consider the infinite, possible, reference frames in the universe, and - sticking with the basic thought experiment for now - if we start with the perspective of one observer; then 100% of the velocity, of any relatively moving system, is ascribed to the other system, under that observers co-ordinate labeling system. That means that the co-ordinate labeling system ascribes a zero velocity to the "at rest" reference frame.

If it doesn't imply "at absolute rest" then the reference frame must be in motion relative to something other than the other detectable, relatively moving reference frames; an undetectable reference frame perhaps. But even if we postulate an infinite number of undetectable reference frames which would help satisfy the condition that "at rest" doesn't mean "absolute rest", if we extend the logic of the co-ordinate labeling system, then the co-ordinate labeling system would still apply 100% of the relative velocity to those undetectable reference frames, and consequently imply a state of absolute rest.

The co-ordinate labeling system could, of course, ascribe 100% of the relative velocity to an observers own reference frame, but this just shifts the problem of absolute rest to another reference frame.

Morbert wrote: »

The bit in red is incorrect. Einstein's relativity says all observers will measure the speed of light to be c. Therefore Albert would measure the speed of light in his clock to be c regardless of whether or not he is at absolute rest, so the implication that he is at absolute rest cannot be made.

To say that Einsteinian relativity says all observers will measure the speed of light to be c, therefore Albert will measure the speed of light to be c, is circular reasoning. The point, which is presumably clear enough at this stage, is that the implication of absolute rest can indeed be made, even if Einsteinian relativity doesn't expressly state it.

I presume you don't have an issue with the notion that the photon in the clock will inherit the horizontal velocity component of the train (or platform) and the clock, if the train is in motion; or if the train is not at absolute rest (which are just two ways of saying the same thing). If not, then there shouldn't really be any issue in following the logic.

"at rest"
If "at rest" doesn't mean "at absolute rest", then it means that "at rest" also means "in motion", which itself is a contradiction in terms; but that is a semantical argument, which doesn't need to be pursued. We only need to reason from some simple principles we already appear to have established - namely, the imparting of a horizontal velocity component to the photon.

If "at rest" doesn't mean "at absolute rest", then, by necessity, the photon in the light clock will be imparted with a horizontal velocity component. You stated above that this would result in the vertical velocity component being less than c, and so the observer on the train would measure the speed of light to be less than c; this would be at odds with Einsteinian relativity.

Alternatively, we can draw the conclusion that the vertical velocity component of the photon is greater than c, such that the observer on the train measures the speed of light to be c, relative to the train carriage; this too is at odds with Einsteinian relativity.

We could conclude that the photon doesn't get imparted with a horizontal velocity component, and only has a vertical velocity component; this however would result in the photon "falling out of the clock"; this is also at odds with Einsteinian relativity, and is contrary to something we have established in discussion.

Another alternative is that Albert is at absolute rest; this fits perfectly with the Einsteinian thought experiment, and indeed with practicalities of Einsteinian relativity, even if it is at odds with certain beliefs about Einsteinian relativity.

Another alternative, if "at rest" doesn't mean "at absolute rest", is that the equipment in Albert's reference frame is contracted by an amount unknown to himself, due to his motion relative to an undetectable reference frame; which result in his measuring a speed of c for the light. This, however, is closer to Lorentzian relativity than it is Einsteinian.

Morbert wrote: »

Brown and Pooley argue that Einstein's relativity has the same issues as Lorentzian relativity. It doesn't, for the following reasons.

<snip>

My apologies, I know I added to this line of the discussion, but I'll respond in the neo-Lorentzian thread.

The choice seems to be between mysterious dynamics affecting something we know to exist - the microstructure of matter - and a mysterious universe wide entity, which can only be detected through the observations of the micro-structure of matter, or the macro-structure of matter (which is comprised of the micro-structure).

Morbert wrote: »

And a clock just demonstrates that a set of events (not a single event) has a temporal dimension, just as the set of simultaneous events across a ruler (not a single event) has a spatial dimension. We can generalise this by saying there is a spatio-temporal relation between events.

We've been discussing this already in the thread on clocks, and I don't think it was established that a clock demonstrates a temporal dimension at all; only a spatial relationship between the events in a clock can be demonstrated. This applies equally to any other process.

Morbert wrote: »

In other words: "I accept that the postulated true present is unknown, and cannot even be known to exist at all, but you cannot tender an experiment to show it definitely does not exist". This is true(ish) insofar as any test of simultaneity could be explained by invoking contrived neo-lorentzian dynamics, but relativity of simultaneity is simply the relaxation of the assumption that there is a true, simultaneous present. Why assume what you cannot demonstrate?

In other words, "just as 'the true present' cannot be established experimentally, neither can relativity of simultaneity. Also, there is only evidence for the present moment; there is no experiment which has ever been conducted, or can ever be conducted, that was not, or will not be, in the present; therefore, there is no evidence that either 'past' or 'future' exist - they have to be assumed to exist. There is also no evidence for the existence of time, because it cannot be demonstrated that a clock measures time, without the assumption that it does.

Why indeed assume something that cannot be demonstrated?

Also, Einsteinian relativity appears to treat reference frames as being at absolute rest"

Morbert wrote: »

If my frame of reference says the lightning bolts strike at the same time, and yours say they strike at different times, is there a way to determine which is the absolute present?

If the above scenario occurs, is there a way to determine relativity of simultaneity?

Morbert

roosh wrote: »

The issue isn't quite as simplistic as saying "I am at rest with respect to myself".

EDIT: of course, the "I am at rest with respect to myself" applies just as much to an observer at absolute rest.

If we were considering a lone observer in an empty universe, or considering the observer without reference to anything else in the universe, then a co-ordinate system which implies "I am at rest with respect to myself" would be fine; but we are considering the co-ordinate labeling system which labels the reference frame as "at rest" and a relatively moving reference frame as "in motion".

When we do this, there is no need to claim that a reference frame has a velocity of zero, it is a logical consequence of the co-ordinate labeling system. If you only consider the relative velocity between systems, then it is impossible not to label one as having a zero velocity, and, therefore, as being at absolute rest; regardless of what mathematicians wish to imply, that is a consequence of such a labeling system. This is what is meant by saying that the co-ordinate labeling system of Einsteinian relativity treats reference frames as being at absolute rest, from it's own perspective, or "according to itself".

The "from it's own perspective" or "according to itself" is a semantical point, with which we shouldn't get bogged down. The essential point is that the co-ordinate labeling system applied to reference frames in Einsteinian relativity, treat that reference frame as being at absolute rest, precisely because it ascribes a zero velocity to it.


Infinite reference frames
If we consider the infinite, possible, reference frames in the universe, and - sticking with the basic thought experiment for now - if we start with the perspective of one observer; then 100% of the velocity, of any relatively moving system, is ascribed to the other system, under that observers co-ordinate labeling system. That means that the co-ordinate labeling system ascribes a zero velocity to the "at rest" reference frame.

If it doesn't imply "at absolute rest" then the reference frame must be in motion relative to something other than the other detectable, relatively moving reference frames; an undetectable reference frame perhaps. But even if we postulate an infinite number of undetectable reference frames which would help satisfy the condition that "at rest" doesn't mean "absolute rest", if we extend the logic of the co-ordinate labeling system, then the co-ordinate labeling system would still apply 100% of the relative velocity to those undetectable reference frames, and consequently imply a state of absolute rest.

The co-ordinate labeling system could, of course, ascribe 100% of the relative velocity to an observers own reference frame, but this just shifts the problem of absolute rest to another reference frame.

To say that Einsteinian relativity says all observers will measure the speed of light to be c, therefore Albert will measure the speed of light to be c, is circular reasoning. The point, which is presumably clear enough at this stage, is that the implication of absolute rest can indeed be made, even if Einsteinian relativity doesn't expressly state it.

I presume you don't have an issue with the notion that the photon in the clock will inherit the horizontal velocity component of the train (or platform) and the clock, if the train is in motion; or if the train is not at absolute rest (which are just two ways of saying the same thing). If not, then there shouldn't really be any issue in following the logic.

"at rest"
If "at rest" doesn't mean "at absolute rest", then it means that "at rest" also means "in motion", which itself is a contradiction in terms; but that is a semantical argument, which doesn't need to be pursued. We only need to reason from some simple principles we already appear to have established - namely, the imparting of a horizontal velocity component to the photon.

If "at rest" doesn't mean "at absolute rest", then, by necessity, the photon in the light clock will be imparted with a horizontal velocity component. You stated above that this would result in the vertical velocity component being less than c, and so the observer on the train would measure the speed of light to be less than c; this would be at odds with Einsteinian relativity.

Alternatively, we can draw the conclusion that the vertical velocity component of the photon is greater than c, such that the observer on the train measures the speed of light to be c, relative to the train carriage; this too is at odds with Einsteinian relativity.

We could conclude that the photon doesn't get imparted with a horizontal velocity component, and only has a vertical velocity component; this however would result in the photon "falling out of the clock"; this is also at odds with Einsteinian relativity, and is contrary to something we have established in discussion.

Another alternative is that Albert is at absolute rest; this fits perfectly with the Einsteinian thought experiment, and indeed with practicalities of Einsteinian relativity, even if it is at odds with certain beliefs about Einsteinian relativity.

Another alternative, if "at rest" doesn't mean "at absolute rest", is that the equipment in Albert's reference frame is contracted by an amount unknown to himself, due to his motion relative to an undetectable reference frame; which result in his measuring a speed of c for the light. This, however, is closer to Lorentzian relativity than it is Einsteinian.

You are not treating your co-ordinate systems consistently. Points highlighted in orange are examples of where you are mushing together reference frames, and hence producing inconsistencies. Reference frames are the arbitrary coordinate systems. They do not sit in some higher absolute coordinate system. Points highlighted in blue are mistakes in logic. The claim "At rest does not imply absolute rest", for example, does not imply anything about the necessity of absolute rest. Points highlighted in red are factual errors. Hence, your conclusions do not hold.

This mishandling of reference frames is probably due to a lack of practise with them. You need to start from the beginning, and strip everything down to its essentials.

We start with a set of three events:

A photon leaves an emitter/detector.
A photon bounces off a mirror.
A photon returns to the emitter/detector.

Now let us apply an arbitrary coordinate system, in order to label these events.

A photon leaves an emitter/detector. (r_1,t_1)
A photon bounces off a mirror. (r_2,t_2)
A photon returns to the emitter/detector. (r_3,t_3)

We can transform this arbitrary coordinate system into any other arbitrary coordinate system via the Lorentz transformations. This is how you treat coordinates, and this is how you make coordinate dependent statements. Note that, since we employ arbitrary coordinate systems, we can only relate coordinate systems to each other, and cannot infer that any coordinate system is "absolute". Again (for emphasis), we discuss arbitrary coordinate systems, and the relation between those coordinate systems, but we do not talk about an absolute coordinate system.

Any absolutes come in as coordinate independent relations between events (spacetime structure) and the laws governing events (general covariance).

My apologies, I know I added to this line of the discussion, but I'll respond in the neo-Lorentzian thread.

The choice seems to be between mysterious dynamics affecting something we know to exist - the microstructure of matter - and a mysterious universe wide entity, which can only be detected through the observations of the micro-structure of matter, or the macro-structure of matter (which is comprised of the micro-structure).

It is not mysterious at all, and instead has a very well defined mathematical structure, described with pseudo-riemannian differential geometry, that has been directly incorporated into not only "clocks and planes/trains" experiments, but also particle experiments, where the spacetime metric explicitly appears in equations.

We've been discussing this already in the thread on clocks, and I don't think it was established that a clock demonstrates a temporal dimension at all; only a spatial relationship between the events in a clock can be demonstrated. This applies equally to any other process.

My point is you are treating the measures inconsistently. You say the measure of time is merely a construct built from the set of events between ticks in a clock, but you say the measure of space is not just a construct built from the set of events across a ruler.

In other words, "just as 'the true present' cannot be established experimentally, neither can relativity of simultaneity. Also, there is only evidence for the present moment; there is no experiment which has ever been conducted, or can ever be conducted, that was not, or will not be, in the present; therefore, there is no evidence that either 'past' or 'future' exist - they have to be assumed to exist. There is also no evidence for the existence of time, because it cannot be demonstrated that a clock measures time, without the assumption that it does.

What is the evidence for the present moment (and according to whom)?

If the above scenario occurs, is there a way to determine relativity of simultaneity?

I am going to interpret this as an admission that you believe that the "true" present exists, but accept that it cannot be experimentally verified. It then comes back to the discussion on neo-Lorentzian relativity, where, instead of relaxing the assumption of Newtonian presentism, you postulate a variety of mysterious ad-hoc dynamics to explain away the details.

roosh

Morbert wrote: »

You are not treating your co-ordinate systems consistently. Points highlighted in orange are examples of where you are mushing together reference frames, and hence producing inconsistencies. Reference frames are the arbitrary coordinate systems. They do not sit in some higher absolute coordinate system. Points highlighted in blue are mistakes in logic. The claim "At rest does not imply absolute rest", for example, does not imply anything about the necessity of absolute rest. Points highlighted in red are factual errors. Hence, your conclusions do not hold.

This mishandling of reference frames is probably due to a lack of practise with them. You need to start from the beginning, and strip everything down to its essentials.

We start with a set of three events:

A photon leaves an emitter/detector.
A photon bounces off a mirror.
A photon returns to the emitter/detector.

Now let us apply an arbitrary coordinate system, in order to label these events.

A photon leaves an emitter/detector. (r_1,t_1)
A photon bounces off a mirror. (r_2,t_2)
A photon returns to the emitter/detector. (r_3,t_3)

We can transform this arbitrary coordinate system into any other arbitrary coordinate system via the Lorentz transformations. This is how you treat coordinates, and this is how you make coordinate dependent statements. Note that, since we employ arbitrary coordinate systems, we can only relate coordinate systems to each other, and cannot infer that any coordinate system is "absolute". Again (for emphasis), we discuss arbitrary coordinate systems, and the relation between those coordinate systems, but we do not talk about an absolute coordinate system.

Any absolutes come in as coordinate independent relations between events (spacetime structure) and the laws governing events (general covariance).

Mushing reference frames

There is no "mushing together" of reference frames, whatsoever. We only
need to consider one single reference frame, Albert's for example; Albert's co-ordinate system ascribes a zero velocity to his reference frame, and ascribes 100% of the [relative] velocity to any other reference frame that is moving relative to his, Henry's for example. Again, a system with a zero velocity is a system at absolute rest. This doesn't involve mixing reference frames any more than the Einsteinian thought experiment does.

Mistakes in logic

If you believe there are mistakes in the logic, it might be worth pointing out where the logic breaks down.


Circular reasoning
If the starting assumption is that all observers will measure the speed of light to be c, regardless of whether they are in motion or at absolute rest, and the conclusion which follows directly afterwards is, therefore an observer will measure the speed of light to be c, regardless of whether they are in motion or at absolute rest; then it is circular reasoning.


Zero velocity
A system at absolute rest has a velocity of zero; and any system moving relative to that system is "responsible" for 100% of the relative velocity; therefore, any system with a velocity of zero is at absolute rest.

Example: an observer on a train has a velocity of zero relative to the train; there is a relative velocity of X between the train (and observer) and another relatively moving system. If the other system is "responsible" for all of X (positive or minus signs are immaterial), then the train and the observer are at absolute rest.


If a co-ordinate system ascribes a zero velocity to a reference frame, then that co-ordinate system treats the zero velocity reference frame as being at absolute rest - because any system with a velocity of zero is at absolute rest.


"at rest" & "at absolute rest"
If a system is not at absolute rest, then, by necessity, it must be "in motion". If "at rest" doesn't mean "at absolute rest", then [by necessity] it means that "at rest" also means "in motion".

If "at rest" means "in motion" then it must mean in motion relative to something. If a co-ordinate labeling system ascribes a zero velocity to a reference frame - and therefore implies that it is not in motion - and ascribes 100% of the relative velocity of all detectable, relatively moving reference frames, to those other reference frames, then, if "at rest" does not mean "at absolute rest" (and therefore means "in motion"), the motion must be relative to some other undetectable relatively moving reference frame. Again, however, the co-ordinate labeling system would still ascribe 100% of the relative velocity to all other detectable, and undetectable reference frames; thereby treating the particular reference frame as being at absolute rest.

Horizontal velocity component
The photon in a clock that is in motion will be imparted with a horizontal velocity component equal to the horizontal velocity component of the clock.

If "at rest" doesn't mean "at absolute rest", then, by necessity, it also means "in motion"; if a clock is "at rest", but not "at absolute rest", then, by necessity, it is "in motion"; if a clock is "in motion" then the photon in the clock will be imparted with a horizontal velocity component equal to that of the clock. Therefore, If "at rest" doesn't mean "at absolute rest", then, by necessity, the photon in the light clock will be imparted with a horizontal velocity component.

Factual errors

As above, if a system is not at absolute rest, then, by necessity, it must be "in motion"; therefore, saying a train is in motion and saying a train is not at absolute rest are just two ways of saying the same thing.

Morbert wrote: »

It is not mysterious at all, and instead has a very well defined mathematical structure, described with pseudo-riemannian differential geometry, that has been directly incorporated into not only "clocks and planes/trains" experiments, but also particle experiments, where the spacetime metric explicitly appears in equations.

A physical entity, which has no substance, permeating the entire universe, which bends, warps, tears, slows down and forms tunnels, due to the presence of matter, or the motion of a system, or some other reason, but which cannot be detected, and whose effects can only be detected through observation of the micro- and macro-structures of matter, sounds a little mysterious to me.

In an ontological sense, it also sounds a little superfluous, even if it is mathematically useful. If there is no region of space that is not filled with matter, then surely all that exists is matter. Any of the observed effects that "give the illiusion of spacetime" are equally attributable effects observed in matter; more so, because they are actually observed in matter. The question of how, might just be another one of those things we don't yet have an answer to; attributing it to a mysterious spacetime structure that exactly resembles all matter and natural forces, which permeates the entire universe, but doesn't affect the micro-structure of matter when it contracts and warps, seems like answering the question of "why something instead of nothing" with the answer that an invisible bearded man in the sky did it.

Morbert wrote: »

My point is you are treating the measures inconsistently. You say the measure of time is merely a construct built from the set of events between ticks in a clock, but you say the measure of space is not just a construct built from the set of events across a ruler.

I don't think I've made that point; but it is perhaps best saved for the other thread.

Morbert wrote: »

What is the evidence for the present moment (and according to whom)?

Have you ever existed in a time that wasn't the present; not the present moment "in time", but that wasn't the present tense?

Morbert wrote: »

I am going to interpret this as an admission that you believe that the "true" present exists, but accept that it cannot be experimentally verified. It then comes back to the discussion on neo-Lorentzian relativity, where, instead of relaxing the assumption of Newtonian presentism, you postulate a variety of mysterious ad-hoc dynamics to explain away the details.

I wouldn't quite say that; it might be worth pointing out that looking for evidence of an absolute present is a category mistake; it is like being presented with the buildings of a university and saying there is no evidence of the university. Given that the only evidence that any observer has, had, or will ever have, is of the present moment, I would say that evidence to the contrary is required.

Also, the the alternative, as opposed to, euphemistically, requiring a "relaxing" of the assumption of presentism, requires a "new kinematical structure for space and time involving essential relativized notions of duration, length, and simultaneity"; assumptions which directly contradict the experience of every observer, living or dead, as well as assumptions about the measurement of time.

It also seems to require the treatment of reference frames as being at absolute rest, under their respective co-ordinate labeling systems.

Morbert

roosh wrote: »

Mushing reference frames

There is no "mushing together" of reference frames, whatsoever. We only
need to consider one single reference frame, Albert's for example; Albert's co-ordinate system ascribes a zero velocity to his reference frame, and ascribes 100% of the [relative] velocity to any other reference frame that is moving relative to his, Henry's for example. Again, a system with a zero velocity is a system at absolute rest. This doesn't involve mixing reference frames any more than the Einsteinian thought experiment does.

You are doing it again here. If Albert ascribes a velocity of absolute zero to his reference frame, he is referencing an external frame to describe his own reference frame. You have implicitly introduced an absolute reference frame to describe Albert's reference frame, and treating it as his own. Instead, you should have said, "When we describe Albert's measurements, we use the arbitrary coordinate system that labels Albert as stationary."

Again, I explicitly stated as much in my last post, and you seem to have ignored it. Here is is again.

We start with a set of three events:

A photon leaves an emitter/detector.
A photon bounces off a mirror.
A photon returns to the emitter/detector.

Now let us apply an arbitrary coordinate system, in order to label these events.

A photon leaves an emitter/detector. (r_1,t_1)
A photon bounces off a mirror. (r_2,t_2)
A photon returns to the emitter/detector. (r_3,t_3)

We can transform this arbitrary coordinate system into any other arbitrary coordinate system via the Lorentz transformations. This is how you treat coordinates, and this is how you make coordinate dependent statements. Note that, since we employ arbitrary coordinate systems, we can only relate coordinate systems to each other, and cannot infer that any coordinate system is "absolute". Again (for emphasis), we discuss arbitrary coordinate systems, and the relation between those coordinate systems, but we do not talk about an absolute coordinate system.

Any absolutes come in as coordinate independent relations between events (spacetime structure) and the laws governing events (general covariance).

Mistakes in logic

If you believe there are mistakes in the logic, it might be worth pointing out where the logic breaks down.

"P does not imply Q", does not imply anything about Q, other than it is not implied by P. "At rest does not imply absolute rest" does not imply anything about absolute rest, other than it is not implied by "at rest".

Circular reasoning
If the starting assumption is that all observers will measure the speed of light to be c, regardless of whether they are in motion or at absolute rest, and the conclusion which follows directly afterwards is, therefore an observer will measure the speed of light to be c, regardless of whether they are in motion or at absolute rest; then it is circular reasoning.

I don't think you are following this line of the discussion. The assumption that all observers will measure the speed of light to be c is not what you are disputing. You presumably accept that assumption. If you don't then you not only reject relativity, but also neo-Lorentzian relativity, and all experimental evidence. Hence, any line of reasoning I tender is an exploration of the consequences of that assumption, not an attempt to prove the assumption. The reasoning I tendered was "All observers will measure the speed of light to be c." implies "You cannot infer any statement about absolute rest from a measurement of the speed of light."

Zero velocity
A system at absolute rest has a velocity of zero; and any system moving relative to that system is "responsible" for 100% of the relative velocity; therefore, any system with an [absolute] velocity of zero is at absolute rest.

Without my added "[absolute]", the above is a non-sequitur. "A system at absolute rest has an absolute velocity of zero" does not imply "Employing an arbitrary coordinate system that labels an object as stationary implies the object is at absolute rest". Again, a coordinate system is just a set of labels we place on events.

Example: an observer on a train has a velocity of zero relative to the train;

Correct. In more rigorous circumlocution, we say the coordinate system that labels the train as "at rest" also labels the observer on the train as "at rest".

there is a relative velocity of X between the train (and observer) and another relatively moving system.

If by this you mean: "The coordinate system which labels the train (and observer) as stationary will label another object (E.g. the ground) as moving with a velocity X" then you are correct.

If the other system is "responsible" for all of X (positive or minus signs are immaterial), then the train and the observer are at absolute rest.

This is where the problems arise. I do not know what it means to claim the other system is responsible for X. It does not follow from any of the previous statements, hence the conditional cannot be used to imply the train and observer are actually at absolute rest.

If a co-ordinate system ascribes a zero velocity to a reference frame, then that co-ordinate system treats the zero velocity reference frame as being at absolute rest - because any system with an [absolute] velocity of zero is at absolute rest.

As before, the statement in blue is a non-sequitur unless you include the [absolute].

The statement in orange is again a mishandling of coordinate systems. A coordinate system is a reference frame. A reference frame is an arbitrary labelling system. So arbitrarily adding an "extra" arbitrary labelling system to label your arbitrary labelling system as at rest does not imply the extra arbitrary labelling system is anything other than arbitrary.

"at rest" & "at absolute rest"
If a system is not at absolute rest, then, by necessity, it must be "in motion". If "at rest" doesn't mean "at absolute rest", then [by necessity] it means that "at rest" also means "in motion".

If "at rest" means "in motion" then it must mean in motion relative to something. If a co-ordinate labeling system ascribes a zero velocity to a reference frame - and therefore implies that it is not in motion - and ascribes 100% of the relative velocity of all detectable, relatively moving reference frames, to those other reference frames, then, if "at rest" does not mean "at absolute rest" (and therefore means "in motion"), the motion must be relative to some other undetectable relatively moving reference frame. Again, however, the co-ordinate labeling system would still ascribe 100% of the relative velocity to all other detectable, and undetectable reference frames; thereby treating the particular reference frame as being at absolute rest.

The bit in blue is a non-sequitur. Arbitrarily labelling something as at rest does not imply it is absolutely at rest or in motion.

Horizontal velocity component
The photon in a clock that is in motion will be imparted with a horizontal velocity component equal to the horizontal velocity component of the clock.

Correct. This is an example of an absolute or "invariant" statement. It is true, independent of whatever coordinate system you use. It is the conservation of momentum.

If "at rest" doesn't mean "at absolute rest", then, by necessity, it also means "in motion"; if a clock is "at rest", but not "at absolute rest", then, by necessity, it is "in motion"; if a clock is "in motion" then the photon in the clock will be imparted with a horizontal velocity component equal to that of the clock. Therefore, If "at rest" doesn't mean "at absolute rest", then, by necessity, the photon in the light clock will be imparted with a horizontal velocity component.

This is the same non-sequitur as before. Arbitrarily labelling a system as at rest says nothing about whether or not the system is at absolute rest. if what you said was true, then even neo-lorentzian relativity would fall apart.

A physical entity, which has no substance, permeating the entire universe, which bends, warps, tears, slows down and forms tunnels, due to the presence of matter, or the motion of a system, or some other reason, but which cannot be detected, and whose effects can only be detected through observation of the micro- and macro-structures of matter, sounds a little mysterious to me.

You are describing an aether. This is not what spacetime is. Spacetime, as previously mentioned before, is a structure, a "field" in the physical sense (specifically, the gravitational field). "It bends and warps" is mysterious and imprecise language, but in the strict language of physics, we say it exhibits non-euclidean geometry between events.

In an ontological sense, it also sounds a little superfluous, even if it is mathematically useful. If there is no region of space that is not filled with matter, then surely all that exists is matter. Any of the observed effects that "give the illiusion of spacetime" are equally attributable effects observed in matter; more so, because they are actually observed in matter. The question of how, might just be another one of those things we don't yet have an answer to; attributing it to a mysterious spacetime structure that exactly resembles all matter and natural forces, which permeates the entire universe, but doesn't affect the micro-structure of matter when it contracts and warps, seems like answering the question of "why something instead of nothing" with the answer that an invisible bearded man in the sky did it.

Again, spacetime is not mysterious at all. "Mysterious" implies a "filler" or a "gap" for something not understood. Spacetime has a very precise and well understood structure. What is genuinely mysterious is the dynamics of neo-Lorentzian relativity.

I don't think I've made that point; but it is perhaps best saved for the other thread.

You have been saying a clock does not demonstrate time, but a ruler demonstrates space.

Have you ever existed in a time that wasn't the present; not the present moment "in time", but that wasn't the present tense?

Who's present? Yours? Yes. But since we are moving at such slow speeds relative to each other, "the present" is a good approximation for both of us.

I wouldn't quite say that; it might be worth pointing out that looking for evidence of an absolute present is a category mistake; it is like being presented with the buildings of a university and saying there is no evidence of the university. Given that the only evidence that any observer has, had, or will ever have, is of the present moment, I would say that evidence to the contrary is required.

It is not a category mistake. We know that different observers must disagree about what is the present, according to their reference frames. This much is agreed upon by everyone. The neo-Lorentzian position says "we will recover the idea of an absolute present by postulating mysterious and unexplained dynamics to explain this apparent discrepancy in simultaneity".

Also, the the alternative, as opposed to, euphemistically, requiring a "relaxing" of the assumption of presentism, requires a "new kinematical structure for space and time involving essential relativized notions of duration, length, and simultaneity"; assumptions which directly contradict the experience of every observer, living or dead, as well as assumptions about the measurement of time.

How do they directly contradict experience at all? You are parting ways even with the neo-Lorentzian crowd.

It also seems to require the treatment of reference frames as being at absolute rest, under their respective co-ordinate labeling systems.

An assertion you have not shown. Let's try something. In all future posts, let's use the more rigorous phrasing, because it is clear that your misunderstanding stems from the shorthand language used in thought experiments. For example:

"A train has a velocity of zero" -> "Consider an arbitrary coordinate system labelling the train as stationary."

"The speed of the ground, relative to the train, is X" -> "A coordinate system that labels the train as stationary, labels the ground has having a speed |X|"

roosh

Morbert wrote: »

You are doing it again here. If Albert ascribes a velocity of absolute zero to his reference frame, he is referencing an external frame to describe his own reference frame. You have implicitly introduced an absolute reference frame to describe Albert's reference frame, and treating it as his own. Instead, you should have said, "When we describe Albert's measurements, we use the arbitrary coordinate system that labels Albert as stationary."

There is no implicit introduction of an external, or separate reference frame, because the absolute reference frame is one and the same with Albert's, by virtue of his arbitrary co-ordinate labeling system. We don't say, there is an absolute rest frame and then there is Albert's reference frame; what is being said is that Albert's arbitrary co-ordinate labeling system treats his reference frame as one and the same thing as an absolute reference frame; not external, not separate, but the same - arbitrarily or otherwise.


His arbitrary, co-ordinate labeling system makes no distinction between "absolute" zero and plain old zero, because no distinction can be made without implying that Albert's reference frame is in motion relative to an undetectable reference frame; because his co-ordinate labeling system labels him as having a zero velocity relative to all other, detectable, reference frames. So, if Albert's zero velocity [relative to all detectable reference frames] doesn't correspond to an absolute velocity of zero, then Albert's reference frame must have a velocity relative to some other, undetectable reference frame.

However, even if there was relative velocity between Albert's reference frame and any number of other infinite, undetectable reference frames, Albert's arbitrary co-ordinate labeling system would still label him as being at absolute rest, because it would ascribe a zero velocity him and ascribe 100% of the relative velocity to the other, relatively moving, reference frames.

Morbert wrote: »

Again, I explicitly stated as much in my last post, and you seem to have ignored it. Here is is again.

We start with a set of three events:

A photon leaves an emitter/detector.
A photon bounces off a mirror.
A photon returns to the emitter/detector.

Now let us apply an arbitrary coordinate system, in order to label these events.

A photon leaves an emitter/detector. (r_1,t_1)
A photon bounces off a mirror. (r_2,t_2)
A photon returns to the emitter/detector. (r_3,t_3)

We can transform this arbitrary coordinate system into any other arbitrary coordinate system via the Lorentz transformations. This is how you treat coordinates, and this is how you make coordinate dependent statements. Note that, since we employ arbitrary coordinate systems, we can only relate coordinate systems to each other, and cannot infer that any coordinate system is "absolute". Again (for emphasis), we discuss arbitrary coordinate systems, and the relation between those coordinate systems, but we do not talk about an absolute coordinate system.

Any absolutes come in as coordinate independent relations between events (spacetime structure) and the laws governing events (general covariance).

We are discussing the implications of the co-ordinate labeling system, and the expected behaviour of the photon under different circumstances, and seeing what logical conclusions we can draw from that; we don't need to consider transforming the arbitrary co-ordinate labels into another reference frame just yet.

Morbert wrote: »

"P does not imply Q", does not imply anything about Q, other than it is not implied by P. "At rest does not imply absolute rest" does not imply anything about absolute rest, other than it is not implied by "at rest".

"P does not imply Q"; however "P and Q are not mutually exclusive"; indeed "Q satisfies the conditions for P, while A-Z (excluding P & Q) arguably don't"; therefore "P must be Q".

Morbert wrote: »

I don't think you are following this line of the discussion. The assumption that all observers will measure the speed of light to be c is not what you are disputing. You presumably accept that assumption. If you don't then you not only reject relativity, but also neo-Lorentzian relativity, and all experimental evidence. Hence, any line of reasoning I tender is an exploration of the consequences of that assumption, not an attempt to prove the assumption. The reasoning I tendered was "All observers will measure the speed of light to be c." implies "You cannot infer any statement about absolute rest from a measurement of the speed of light."

The assumption that is, effectivily, being challenged is, that the photon in Albert's clock won't be imparted with a horizontal velocity component, which would mean that the vertical velocity component would be less than c, such that he would measure the speed of light to be less than c, unless - and this is an important point - unless his instruments are contracted by an amount unknown to himself, due to his motion relative to an undetectable, absolute reference frame. We can examine this simply by considering Albert's reference frame, according to his own arbitrary labeling system, in the two possible scenarios under discussion: at absolute rest; and not at absolute rest. As has been outlined, only a position of absolute rest satisfies the conditions for Einsteinian relativity.

Keypoints
OK, so there are two key points that we need to consider, just to see where the issue lies in this; do you agree with the following?

- a system that is not at absolute rest, is, by necessity, in motion? If not, why not?
- the photon in any clock that is in motion will be imparted with a horizontal velocity component equal to the motion of the system? If not, why not?

Morbert wrote: »

Without my added "[absolute]", the above is a non-sequitur. "A system at absolute rest has an absolute velocity of zero" does not imply "Employing an arbitrary coordinate system that labels an object as stationary implies the object is at absolute rest". Again, a coordinate system is just a set of labels we place on events.

That a co-ordinate system is just a set of arbitrary labels is not in question; what is in question is the logical implications of such a co-ordinate system. If a co-ordinate system arbitrarily treats a reference frame as being at absolute rest, then regardless of the arbitrariness, it still treats that reference frame as being at absolute rest.

If we look at the two contentions:
A system at absolute rest has a velocity of zero

"Employing an arbitrary coordinate system that labels an object as [having a velocity of zero] implies the object is at absolute rest"

Morbert wrote: »

Correct. In more rigorous circumlocution, we say the coordinate system that labels the train as "at rest" also labels the observer on the train as "at rest".

If by this you mean: "The coordinate system which labels the train (and observer) as stationary will label another object (E.g. the ground) as moving with a velocity X" then you are correct.

This is where the problems arise. I do not know what it means to claim the other system is responsible for X. It does not follow from any of the previous statements, hence the conditional cannot be used to imply the train and observer are actually at absolute rest.

I'm not sure how you can deduce that the conditional can't be used, if you don't know what it means.

What was meant is probably easier explained with an example; if we imagine the relative velocity between two cars is 100 km/h; theoretically there is an infinite range of values that could contribute to the relative velocity of 100km/h; one car could be traveling at 70km/h, the other at 30; both could be traveling at 50km/h; one could be traveling at 99km/h while the other is traveling at 1km/h; of course, another possibility is that one car is stationary, while the other car is traveling at 100km/h. In the intended context, we would say that the proportion of the relative velocity that each car is responsible for corresponds to their speeds.

It is probably further clarified using the now familiar absolute rest frame. If there is relative velocity between the absolute rest frame and another system, then the other system is "responsible" for all of the relative velocity.

If a co-ordinate system ascribes 100% of the relative velocity to every other, relatively moving, reference frame, then that arbitrary, co-ordinate labeling system treats the zero velocity reference frame as being at absolute rest - because it makes every other reference frame "responsible" for the entirety of the relative velocity;à la the absolute reference frame.

Morbert wrote: »

As before, the statement in blue is a non-sequitur unless you include the [absolute].

The statement in orange is again a mishandling of coordinate systems. A coordinate system is a reference frame. A reference frame is an arbitrary labelling system. So arbitrarily adding an "extra" arbitrary labelling system to label your arbitrary labelling system as at rest does not imply the extra arbitrary labelling system is anything other than arbitrary.

I think you might be getting caught up in semantics here; but I'm sure you get the point that is being made, because you've been discussing it thus far without recourse to semantics (at every turn).

Albert's co-ordinate labeling system ascribes a zero velocity to him, and ascribes 100% of the relative velocity to other relatively moving reference frames, à la the absolute reference frame.

Morbert wrote: »

The bit in blue is a non-sequitur. Arbitrarily labelling something as at rest does not imply it is absolutely at rest or in motion.

The questions are posed abvoe, but for the purpose of re-iteration they can be restated:

Do you agree with the following?

-If something is not at absolute rest, then, by necessity it is in motion
if not, why not?


If you agree that something which is not at absolute rest is, by necessity, in motion, then we can reason thusly:

If something not at absolute rest is necessarily in motion; then, if something doesn't imply absolute rest, it must imply motion; therefore, if "at rest" doesn't imply "absolute rest" then it necessarily implies motion - arbitrarily or otherwise.

Morbert wrote: »

Correct. This is an example of an absolute or "invariant" statement. It is true, independent of whatever coordinate system you use. It is the conservation of momentum.

Excellent, so we have a point of agreement. The outstanding issue then is whether "not at absolute rest" implies "in motion" or not.

Morbert wrote: »

This is the same non-sequitur as before. Arbitrarily labelling a system as at rest says nothing about whether or not the system is at absolute rest. if what you said was true, then even neo-lorentzian relativity would fall apart.

I don't think there's any need to restate the contention above.

Morbert wrote: »

You are describing an aether. This is not what spacetime is. Spacetime, as previously mentioned before, is a structure, a "field" in the physical sense (specifically, the gravitational field). "It bends and warps" is mysterious and imprecise language, but in the strict language of physics, we say it exhibits non-euclidean geometry between events.



Again, spacetime is not mysterious at all. "Mysterious" implies a "filler" or a "gap" for something not understood. Spacetime has a very precise and well understood structure. What is genuinely mysterious is the dynamics of neo-Lorentzian relativity.



You have been saying a clock does not demonstrate time, but a ruler demonstrates space.



Who's present? Yours? Yes. But since we are moving at such slow speeds relative to each other, "the present" is a good approximation for both of us.



It is not a category mistake. We know that different observers must disagree about what is the present, according to their reference frames. This much is agreed upon by everyone. The neo-Lorentzian position says "we will recover the idea of an absolute present by postulating mysterious and unexplained dynamics to explain this apparent discrepancy in simultaneity".



How do they directly contradict experience at all? You are parting ways even with the neo-Lorentzian crowd.

I'll have to take my share of the responsibility but the discussion appears to be fragmenting again; it would probably be better to establish, or refute, the "absolute rest" contention.

Morbert wrote: »

An assertion you have not shown. Let's try something. In all future posts, let's use the more rigorous phrasing, because it is clear that your misunderstanding stems from the shorthand language used in thought experiments. For example:

"A train has a velocity of zero" -> "Consider an arbitrary coordinate system labelling the train as stationary."

"The speed of the ground, relative to the train, is X" -> "A coordinate system that labels the train as stationary, labels the ground has having a speed |X|"

I'm not sure introducing euphemisms will be entirely productive, even if euphemisms is the language usually employed.

How about:
"A train has a velocity of zero" -> "Consider an arbitrary coordinate system labelling the train as having a zero velocity"

"The relative velocity between the the ground and the train, is X" -> "A coordinate system that labels the train as having a zero velocity, labels the ground has having a velocity |X| i.e. it ascribes the entirety of the relative velocity to the ground"


If we're going to be more rigorous then I don;t think semantics is the way to go; we need to consider the logical implications of the language.

Morbert

roosh wrote: »

There is no implicit introduction of an external, or separate reference frame, because the absolute reference frame is one and the same with Albert's, by virtue of his arbitrary co-ordinate labeling system. We don't say, there is an absolute rest frame and then there is Albert's reference frame; what is being said is that Albert's arbitrary co-ordinate labeling system treats his reference frame as one and the same thing as an absolute reference frame; not external, not separate, but the same - arbitrarily or otherwise.

It is not one and the same at all. Albert may not be at absolute rest, or he might be at absolute rest. If his reference frame is arbitrary, it is independent of whether or not he is at absolute rest. It is independent of whether or not an absolute rest exists at all. It says nothing about absolute rest. It is a physical labelling system, not a metaphysical claim.

I have identified a single line of reasoning in the following paragraphs:

His arbitrary, co-ordinate labeling system makes no distinction between "absolute" zero and plain old zero, because no distinction can be made without implying that Albert's reference frame is in motion relative to an undetectable reference frame; because his co-ordinate labeling system labels him as having a zero velocity relative to all other, detectable, reference frames. So, if Albert's zero velocity [relative to all detectable reference frames] doesn't correspond to an absolute velocity of zero, then Albert's reference frame must have a velocity relative to some other, undetectable reference frame.

However, even if there was relative velocity between Albert's reference frame and any number of other infinite, undetectable reference frames, Albert's arbitrary co-ordinate labeling system would still label him as being at absolute rest, because it would ascribe a zero velocity him and ascribe 100% of the relative velocity to the other, relatively moving, reference frames.

We are discussing the implications of the co-ordinate labeling system, and the expected behaviour of the photon under different circumstances, and seeing what logical conclusions we can draw from that; we don't need to consider transforming the arbitrary co-ordinate labels into another reference frame just yet.

"P does not imply Q"; however "P and Q are not mutually exclusive"; indeed "Q satisfies the conditions for P, while A-Z (excluding P & Q) arguably don't"; therefore "P must be Q".

The assumption that is, effectivily, being challenged is, that the photon in Albert's clock won't be imparted with a horizontal velocity component, which would mean that the vertical velocity component would be less than c, such that he would measure the speed of light to be less than c, unless - and this is an important point - unless his instruments are contracted by an amount unknown to himself, due to his motion relative to an undetectable, absolute reference frame. We can examine this simply by considering Albert's reference frame, according to his own arbitrary labeling system, in the two possible scenarios under discussion: at absolute rest; and not at absolute rest. As has been outlined, only a position of absolute rest satisfies the conditions for Einsteinian relativity.

Keypoints
OK, so there are two key points that we need to consider, just to see where the issue lies in this; do you agree with the following?

- a system that is not at absolute rest, is, by necessity, in motion? If not, why not?
- the photon in any clock that is in motion will be imparted with a horizontal velocity component equal to the motion of the system? If not, why not?

That a co-ordinate system is just a set of arbitrary labels is not in question; what is in question is the logical implications of such a co-ordinate system. If a co-ordinate system arbitrarily treats a reference frame as being at absolute rest, then regardless of the arbitrariness, it still treats that reference frame as being at absolute rest.

If we look at the two contentions:
A system at absolute rest has a velocity of zero

"Employing an arbitrary coordinate system that labels an object as [having a velocity of zero] implies the object is at absolute rest"

I'm not sure how you can deduce that the conditional can't be used, if you don't know what it means.

What was meant is probably easier explained with an example; if we imagine the relative velocity between two cars is 100 km/h; theoretically there is an infinite range of values that could contribute to the relative velocity of 100km/h; one car could be traveling at 70km/h, the other at 30; both could be traveling at 50km/h; one could be traveling at 99km/h while the other is traveling at 1km/h; of course, another possibility is that one car is stationary, while the other car is traveling at 100km/h. In the intended context, we would say that the proportion of the relative velocity that each car is responsible for corresponds to their speeds.

It is probably further clarified using the now familiar absolute rest frame. If there is relative velocity between the absolute rest frame and another system, then the other system is "responsible" for all of the relative velocity.

If a co-ordinate system ascribes 100% of the relative velocity to every other, relatively moving, reference frame, then that arbitrary, co-ordinate labeling system treats the zero velocity reference frame as being at absolute rest - because it makes every other reference frame "responsible" for the entirety of the relative velocity;à la the absolute reference frame.

I think you might be getting caught up in semantics here; but I'm sure you get the point that is being made, because you've been discussing it thus far without recourse to semantics (at every turn).

Albert's co-ordinate labeling system ascribes a zero velocity to him, and ascribes 100% of the relative velocity to other relatively moving reference frames, à la the absolute reference frame.

The questions are posed abvoe, but for the purpose of re-iteration they can be restated:

Do you agree with the following?

-If something is not at absolute rest, then, by necessity it is in motion
if not, why not?

If you agree that something which is not at absolute rest is, by necessity, in motion, then we can reason thusly:

If something not at absolute rest is necessarily in motion; then, if something doesn't imply absolute rest, it must imply motion; therefore, if "at rest" doesn't imply "absolute rest" then it necessarily implies motion - arbitrarily or otherwise.

I'm not sure introducing euphemisms will be entirely productive, even if euphemisms is the language usually employed.

"A train has a velocity of zero" -> "Consider an arbitrary coordinate system labelling the train as having a zero velocity"

"The relative velocity between the the ground and the train, is X" -> "A coordinate system that labels the train as having a zero velocity, labels the ground has having a velocity |X| i.e. it ascribes the entirety of the relative velocity to the ground"

If we're going to be more rigorous then I don;t think semantics is the way to go; we need to consider the logical implications of the language.

I have a few issues with the above paragraphs (E.g. the euphemism claim), but to avoid further fragmentation, I will focus on the only important one. You are claiming that, since Albert's reference frame, which labels him as "at rest" is consistent with the metaphysical statement "Albert is at absolute rest", it must mean Albert's reference frame is making a metaphysical statement about absolute rest. This is the non-sequitur that is causing all the problems. Albert's reference frame is also consistent, for example, with the metaphysical claim "Albert is not at absolute rest" or even "There is no such thing as absolute rest." They are consistent because Albert's coordinate labels are not metaphysical claims at all. They are book-keeping tools. Analogously, the laws of physics are consistent with the metaphysical claim "The absolute truth is we are all brains in a jar, hooked up to the matrix". But this does not show that we are all hooked up to the matrix.

In other words, show that the following two suppositions are inconsistent.

Suppose Albert is not at absolute rest.
Suppose Albert uses his arbitrary reference frame to label all events (the reference frame which labels himself as at rest).

I argue that there is no inconsistency at all.

roosh

Morbert wrote: »

It is not one and the same at all. Albert may not be at absolute rest, or he might be at absolute rest. If his reference frame is arbitrary, it is independent of whether or not he is at absolute rest. It is independent of whether or not an absolute rest exists at all. It says nothing about absolute rest. It is a physical labelling system, not a metaphysical claim.

I have identified a single line of reasoning in the following paragraphs:



I have a few issues with the above paragraphs (E.g. the euphemism claim), but to avoid further fragmentation, I will focus on the only important one. You are claiming that, since Albert's reference frame, which labels him as "at rest" is consistent with the metaphysical statement "Albert is at absolute rest", it must mean Albert's reference frame is making a metaphysical statement about absolute rest. This is the non-sequitur that is causing all the problems. Albert's reference frame is also consistent, for example, with the metaphysical claim "Albert is not at absolute rest" or even "There is no such thing as absolute rest." They are consistent because Albert's coordinate labels are not metaphysical claims at all. They are book-keeping tools. Analogously, the laws of physics are consistent with the metaphysical claim "The absolute truth is we are all brains in a jar, hooked up to the matrix". But this does not show that we are all hooked up to the matrix.

In other words, show that the following two suppositions are inconsistent.

Suppose Albert is not at absolute rest.
Suppose Albert uses his arbitrary reference frame to label all events (the reference frame which labels himself as at rest).

I argue that there is no inconsistency at all.

The point being made isn't simply: since Albert's reference frame, which labels him as "at rest" is consistent with the metaphysical statement "Albert is at absolute rest", it must mean Albert's reference frame is making a metaphysical statement about absolute rest.

The point being made is that, given the fact that a photon will inherit the horizontal velocity component of a clock that is in motion, then only a position of absolute rest satisfies the conditions for Einsteinian relativity.


The issue can be distilled down to one foundational question (and possibly a follow up question):
Is a system which is not at absolute rest, necessarily in motion?

If not, why not?

Morbert

roosh wrote: »

The point being made isn't simply: since Albert's reference frame, which labels him as "at rest" is consistent with the metaphysical statement "Albert is at absolute rest", it must mean Albert's reference frame is making a metaphysical statement about absolute rest.

The point being made is that, given the fact that a photon will inherit the horizontal velocity component of a clock that is in motion, then only a position of absolute rest satisfies the conditions for Einsteinian relativity.

The issue can be distilled down to one foundational question (and possibly a follow up question):
Is a system which is not at absolute rest, necessarily in motion?

If not, why not?

You are confusing Einsteinian relativity with Galilean relativity. Einsteinian relativity says all coordinate systems measure the speed of light to be c, the laws of physics are the same under all coordinate systems, and all coordinate systems are related by lorentz transformations. Inheriting horizontal velocity is not a problem.

Consider the three relevant events:

A photon leaves the emitter.
A photon bounces off a mirror.
A photon hits the detector.

Now consider two coordinate systems S and S'. The apparatus is stationary in S, and is moving at a speed of 0.5 c in S'. The distance between the detector and the mirror in S is 1 lightsecond. Now let us look at the positions of the three events (and hence the speed of the photon) in each case. First, we consider the Galilean transformation.



The time (T) dimension is on the Y axis, and position (X) is on the X axis (both in natural units). The red line is the photon path between the three events in S. The green line is the photon path in S'. Note that, in diagrams like these, velocity is represented by the inverse of slope of the line (speed/time). You can see that the slope is different for S and S'. This is because of the inherited velocity of the photon. It is travelling faster in S' than it is in S. But now consider lorentz transformations.



Note that the slopes are the same in each case. This is because, even though the photon inherits the velocity of the apparatus, lorentz transformations tell us S and S' will not label events with the same time stamps (unlike galilean transformations).

Hence, the issue of absolute rest doesn't even come up. It is entirely superflous.

Morbert

Oh yes, I should mention that the diagrams shown are for an apparatus oriented along the direction of motion. I can do the same for apparatus oriented perpendicular to the direction of motion, though the diagrams will require an extra dimension.

roosh

Morbert wrote: »

You are confusing Einsteinian relativity with Galilean relativity. Einsteinian relativity says all coordinate systems measure the speed of light to be c, the laws of physics are the same under all coordinate systems, and all coordinate systems are related by lorentz transformations. Inheriting horizontal velocity is not a problem.

Consider the three relevant events:

A photon leaves the emitter.
A photon bounces off a mirror.
A photon hits the detector.

Now consider two coordinate systems S and S'. The apparatus is stationary in S, and is moving at a speed of 0.5 c in S'. The distance between the detector and the mirror in S is 1 lightsecond. Now let us look at the positions of the three events (and hence the speed of the photon) in each case. First, we consider the Galilean transformation.

<removed to shorten reply length>

The time (T) dimension is on the Y axis, and position (X) is on the X axis (both in natural units). The red line is the photon path between the three events in S. The green line is the photon path in S'. Note that, in diagrams like these, velocity is represented by the inverse of slope of the line (speed/time). You can see that the slope is different for S and S'. This is because of the inherited velocity of the photon. It is travelling faster in S' than it is in S. But now consider lorentz transformations.

<removed to shorten reply length>

Note that the slopes are the same in each case. This is because, even though the photon inherits the velocity of the apparatus, lorentz transformations tell us S and S' will not label events with the same time stamps (unlike galilean transformations).

Hence, the issue of absolute rest doesn't even come up. It is entirely superflous.

I may have it wrong; I may not be explaining it correctly; conditioning in Einsteinian relativity might be making it difficult to see; or it could be a combination of the latter two; but hopefully I can state this lucidly enough to try and negate the latter two, or highlight where my misunderstanding lies, and we can hopefully resolve it.

It might initially seem like I am mistaking Einsteinian relativity of Galilean, but I'll try to illucidate why this isn't the case; this will, largely, be done by considering only the Einsteinian thought experiment, and highlighting where the relevant Galilean, Einsteinian, or Lorentzian conclusions would apply.


"not at absolute rest"
Firstly, we need to establish whether a reference frame that is not at "absolute rest" is, by necessity, "in motion"; I would like to say that I could take the fact that you didn't answer the question, directly, as an acceptance of that point, but I don't think I can; however, I think it's a matter of definition, so I think it is a fair point; unless you reason otherwise.

Horizontal velocity
If the above point is accepted, and if "at rest" doesn't imply "at absolute rest", then we can reason that Albert's labeling system (or reference frame), which labels him as "at rest" is actually in motion. This means that the photon in Albert's clock will be imparted with a horizontal velocity component.

Now, under Galilean relativity, this would indeed lead to the vertical velocity component being less than c, such that Albert would measure the speed of light to be lower than c.

However, if this isn't the case, and Albert measures the speed of light to be c, as Einsteinian relativity states, then Albert's measuring instruments must have contracted by an amount unknown to himself, due to the motion of his "not at absolute rest" reference frame. This, however, is a Lorentzian interpretation.

relative to what?
The question is, relative to what is Alberts' "not at absolute rest" reference frame in motion? Presumably it must be an undetectable reference frame, because Albert's, arbitrary, co-ordinate labeling system labels him as at rest relative to all other relatively moving, detectable reference frames (itself somewhat contradictory, but that isn't necessary here).

This too would be a Lorentzian interpretation.

Morbert

roosh wrote: »

I may have it wrong; I may not be explaining it correctly; conditioning in Einsteinian relativity might be making it difficult to see; or it could be a combination of the latter two; but hopefully I can state this lucidly enough to try and negate the latter two, or highlight where my misunderstanding lies, and we can hopefully resolve it.

It might initially seem like I am mistaking Einsteinian relativity of Galilean, but I'll try to illucidate why this isn't the case; this will, largely, be done by considering only the Einsteinian thought experiment, and highlighting where the relevant Galilean, Einsteinian, or Lorentzian conclusions would apply.


"not at absolute rest"
Firstly, we need to establish whether a reference frame that is not at "absolute rest" is, by necessity, "in motion"; I would like to say that I could take the fact that you didn't answer the question, directly, as an acceptance of that point, but I don't think I can; however, I think it's a matter of definition, so I think it is a fair point; unless you reason otherwise.

This brings me back to "P does not imply Q" does not mean "P implies notQ". That we cannot say a reference frame implies absolute rest, does not mean we can say a reference frame implies absolute motion. You can metaphysically suppose absolute rest, or you can metaphysically reject absolute rest. It will not have any effect on the coordinate descriptions of Einstein's relativity.

Horizontal velocity
If the above point is accepted, and if "at rest" doesn't imply "at absolute rest", then we can reason that Albert's labeling system (or reference frame), which labels him as "at rest" is actually in motion. This means that the photon in Albert's clock will be imparted with a horizontal velocity component.

Now, under Galilean relativity, this would indeed lead to the vertical velocity component being less than c, such that Albert would measure the speed of light to be lower than c.

However, if this isn't the case, and Albert measures the speed of light to be c, as Einsteinian relativity states, then Albert's measuring instruments must have contracted by an amount unknown to himself, due to the motion of his "not at absolute rest" reference frame. This, however, is a Lorentzian interpretation.

Under Galilean relativity, the vertical velocity component would be unchanged, but one frame describes the photon as also having a non-zero horizontal velocity, and hence a speed greater than c. This does not happen under lorentz transformations because, under lorentz transformations, time is transformed as well as space.

relative to what?
The question is, relative to what is Alberts' "not at absolute rest" reference frame in motion? Presumably it must be an undetectable reference frame, because Albert's, arbitrary, co-ordinate labeling system labels him as at rest relative to all other relatively moving, detectable reference frames (itself somewhat contradictory, but that isn't necessary here).

This too would be a Lorentzian interpretation.

This relates back to the above: "We do not say Albert is at absolute rest" is not the same as "We say Albert is not at absolute rest." You can suppose absolute rest, or you can suppose no absolute rest. The physics won't change.

roosh

Morbert wrote: »

This brings me back to "P does not imply Q" does not mean "P implies notQ". That we cannot say a reference frame implies absolute rest, does not mean we can say a reference frame implies absolute motion. You can metaphysically suppose absolute rest, or you can metaphysically reject absolute rest. It will not have any effect on the coordinate descriptions of Einstein's relativity.

That depends on what P and Q are though; when dealing with the law of the excluded middle, as I believe we are, not P does imply Q, just as not Q does imply P.

As far as I can see it is a matter of definition; if something is "not at absolute rest" it must, by necessity, be "in motion".

Morbert wrote: »

Under Galilean relativity, the vertical velocity component would be unchanged, but one frame describes the photon as also having a non-zero horizontal velocity, and hence a speed greater than c. This does not happen under lorentz transformations because, under lorentz transformations, time is transformed as well as space.

OK, I presume that this is taking the assumption that Albert will measure the speed of light to be c, relative to the carriage. In the case above you mentioned that the vertical velocity component would be less than c, this would be the case without the assumption I take it.

Morbert wrote: »

This relates back to the above: "We do not say Albert is at absolute rest" is not the same as "We say Albert is not at absolute rest." You can suppose absolute rest, or you can suppose no absolute rest. The physics won't change.

The implications of the co-ordinate labeling system are a little more explicit, however, because they make positive statements about Albert, as opposed to negative statements i.e. they say what Albert is, not what he isn't.

The co-ordinate labeling system labels Albert with a zero velocity and labels him as "at rest", despite the fact that there is motion relative to another reference frame. The question is, does this "at rest" mean at absolute rest, or not? Not expressly stating which it is, is fine; but we are free to deduce what it must mean i.e. what the tacit assumption (or consequence) must be.

If Albert's reference frame, which is labelled as "at rest" is not at absolute rest, then as above, according to the law of the excluded middle, it must mean that Albert's reference frame is necessarily in motion. Which begs the question, relative to what is it in motion? It must be an undetectable reference frame because his co-ordinate labeling system labels all relatively moving, detectable reference frames as "in motion"; it ascribes 100% of the velocity to them, and labels Albert as "at rest" with a zero velocity.

If his reference frame is "in motion", then, if he measures the speed of light to be c, his instruments must be contracted by an amount unknown to himself, due to this motion relative to the undetectable reference frame.

As mentioned, this is the conclusion of Lorentzian relativity.