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the [possible] fallacy of Lorentz contractions
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13-01-2012 11:10am#1Mods 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.0
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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.0
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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.0 -
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.0 -
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.0 -
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?0 -
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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.0 -
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.0 -
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.0 -
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.
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.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.
How is the second postulate actually tested though?0 -
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.0 -
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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.0 -
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.This would mean that an observer on the platform would see a speed of light higher than c.
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.0 -
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.0 -
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.0 -
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.0 -
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/0504109v10 -
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".0 -
No worries; to be honest, I'm not sure which questions you are referring to; I'm just replying as I go along.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.
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.
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.I thought the 'reference frame' of an observer is by definition that which is not moving relative to that observer.
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.
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.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, 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.0 -
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!0 -
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.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.
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
It makes no explicit reference to absolute rest, there is an implicit assumption, however.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.
The emboldened parts, above, appear to be contradictory.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.
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.
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.No. It is defined locally, relative to the observer's clock, wherever he is. That is the nature of Maxwell's equations.
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.
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.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/0504109v1Antonini, Okhapkin, Göklü 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, Göklü 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.0 -
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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.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.
It isn't an expressed assumption, rather an unintentional consequence of the assumed measurement of the path length of the photon.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".0 -
I've re-arranged your post just to address the issue of reference frames together; hopefully this doesn't misrepresent you.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.
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Well, in fact there is no alternative to that - his reference frame is always in motion, just not relative to him.
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.
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.
Quite possibly.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.
It's difficult to say without knowing the mechanism of the clock.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?"0 -
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?0 -
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?0 -
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: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.0 -
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 beams0 -
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?0 -
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.0 -
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.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.
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.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.
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 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".
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
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 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.
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.
Are there specific experiments you are referring to?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.
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: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)
- 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 clocksNot a pendulum-clock, which is physically a system to which the Earth belongs. This case had to be excluded.
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.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?
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.
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.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
Also, insofar as the second postulate refers to the one way speed of light, it is, by all accounts, an untestable assumption.0 -
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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.0
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