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Does time exist?

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  • Registered Users Posts: 2,552 ✭✭✭roosh


    Morbert wrote: »
    I will describe the "types" of experiment that directly tests the postulate. Specific references can easily be found by googling something like "experimental evidence for speed of light isotropy".

    The first type is essentially the measurement of the speed of light by an apparatus when it is in motion and when it is stationary. If the speed of light is anisotropic, we would expect to observe changes in light patterns analogous to changes in sound patterns or water wave patterns.

    The second type is the interaction of light with moving particles. If the speed of light is anisotropic (or more inclusively, if there was no lorentz invariance), we would expect a classical Doppler effect. What we instead observe is a relativistic Doppler effect. This Doppler effect is precisely the effect predicted by the principle of Lorentz invariance.

    There are other more esoteric experiments, but this quick introduction should give you an idea of what to expect.

    Thanks, I will google that so and try and get an understanding of it.

    With regard to the question about the cars, I don't think I formulated what I was wondering very well; with the cars, the faster car will appear to pass the slower car at, say, 20km/h; but if the observer in the slower car was to measure the speed of the other car using a moving radar speed gun he would clock the "correct" speed of the car to be the same as the observer in the other car.

    The measurement of light appears to be different, is it? Where the frequency of a "beam" of light is checked to see if it differs - is that correct? I imagine this is because it's not possible to use radio signals to check the speed of light.

    But with regard to the relative motion of two observers, is it not possible then to determine their motion relative to the common background, such that both observers can be said to be in motion?

    Morbert wrote: »
    The bowling ball will still arrive at the feet of the other observer because the bowling ball has momentum imparted by the motion of the observer. There is a simple way you can verify this princple. The next time you and a friend are sitting in the back of a car, throw a tennis ball back and forth. Does the ball fly out the back window, even if the car is travelling fast? No. It arrives at your hands.

    But anyway, let's say it didn't. Both observers would indeed see the ball speed up. Just as you would see a tennis ball speed up if you threw it out the window of a moving car. But if the ball were made of light, this would mean the light sped up. Hence, the laser experiment we were discussing breaks the principle of light anisotropy.
    Apologies, I probably wasn't clear on that; the bowling ball was meant to represent the light.

    Where one observer releases the [bowling ball of] light and it travels a straight line to the feet of the other observer, where both are stationary. In the second scenario, where both are moving, observer 1 releases the [bowling ball of] light, which again travels a straight line, but bcos Observer 2 has moved from where he was, the [bowling ball of] light will not end up at his feet. In order for it to end up at his feet, the [bowling ball of] light would have to inheret the momentum of the observer who released it and travel a diagonal path - but that isn't light behaves is it?


    Another scenario which might clarify the point I am trying to understand: if the observer on the train fires a laser gun at the observer on the platform, as they pass each other, from my understanding of what has been said, from the perspective of the observer on the train, the laser will miss the observer on the platform and so he will remain alive; whereas, from the perspective of the observer on the platform the laser will hit him and kill him, meaning that he is alive according to the observer on the train, but, from his own perspective he will be dead - if you'll forgive the formulation of that.

    The scenario can be formulated such that the laser only has to make the barest contact to kill him, and that it is released at the point where any movement, whatsoever, away from him will mean it misses.


    Morbert wrote: »
    He would then realise that he forgot about the equivalence principle. The mysterious gravitational force he detected, that is responsible for the earth "mysteriously" falling behind him, is not a force at all, it is merely the geometry of events. If he labels himself as stationary, the earth will be labelled as moving. He does not need to attach any ontological significance to this labelling, because he realises labelling is arbitrary. His labels are just as consistent with physics as his friends. Then, if he is as smart as Einstein, he can devise a set of equations to generalise this principle and produce a classical theory of gravitation

    Morbert wrote: »
    They are not a matter of cause and effect. I cannot stress this enough. The motion of a train does not cause it to contract. Nor does it cause the earth to contract. A right-angled triangle does not cause Pythagoras's theorem. These are not events to be caused or affected.
    I hope I'm not misrepresenting you by slightly changing around the order of the quotes, and separating this segment out - let me know if I am.

    Firstly on the issue of cause and effect; again, I might be misunderstanding the whole thing, but to my mind, if you and I start off with rulers of identical sizes, and clocks ticking at the same rate, and one of us starts moving, or we start moving relative to each other such that our rulers lose their direct proportionality, and the clocks fall out of sync, then that is a matter of cause and effect; something has caused the rulers to lose proportionality and something has caused the clocks to fall out of sync. If there was no effect then one clock would not tick slower than the other and the relation of the length of the rulers would remain L:L not become L:ɣL.

    Morbert wrote: »
    It is simply the geometry of events is such that the relation between events, when comparing reference frames, can be characterised by length contraction and time dilation, and h^2 = x^2 + y^2 in the case of the triangle.

    A handy rule of thumb is, if two events are causally related, they can hypothetically be connected via a light signal.
    Morbert wrote: »
    It's no stranger than the notion that you can be "mangaroosh" and "roosh" at the same time. "In motion" is an arbitrary label. All that matters is we use the labels consistently.
    I think these are related to the same issue, so that's why I've grouped them together - again, let me know if there is an issue.

    I think the "roosh"/"mangaroosh" is somewhat of an over-simplification of the issue. Where "roosh" and "mangaroosh" may refer to the same observer, what we are talking about is the actions of the observer, where the actions being labelled are mutually exclusive; it's the difference between "mangaroosh" is in motion and "roosh" is at rest; both can't be simultaneously true.

    Again, it is similar to the sphere of light being centred on a rod and the rod moving away from the centre of the sphere of light.

    If it were a simple matter of labelling, then length contraction should occur simply by labelling one observer as being in motion and the other as being at rest; but that isn't the case. In order for length contraction to occur there must first be relative motion between the two, unless length contraction is only an illusion and doesn't actually occur. So the effects of length contraction and time dilation have to be attributed to a cause, in this case it is motion - of one observer or the other.

    If two observers are at rest, relative to each other, and one of them starts swinging his arms (all other things being equal) is the observer in motion or at rest, or are parts of his body capable of motion?

    Morbert wrote: »
    There are frames of reference where the button push is co-incident with one event or the other. I.e. Some observers will say the button was pushed when I wrote this. Other observers will say the button was pushed when you read this.

    It is a useful question to ask for this discussion, as it illustrates an important point. The universe would see all events related by the light-cone structure mentioned earlier. It would, in effect, see all frames of reference, and see any particular frame of reference as an arbitrary viewpoint of some mortal observer. The universe would then formulate general relativity to coherently understand this structure.
    I've taken these together, agian, bcos I think they address the same point.

    What would the present look like from the perspective of this omniscient observer?

    Morbert wrote: »
    Your concern is related to the twin paradox, which says that both twins would see the other's clock tick slowly, but only one ages faster than the other. The solution is a useful introduction to relativity.
    It is related, but I think it is somewhat different; because, am I right in saying, the twin paradox involves one twin moving through the gravity well to a location with a different measure of gravity?

    I am thinking more along the lines of the thought experiment, involving the train, being carried out at some imagined point in the future, where the train travels around the surface of the earth at 0.8c and the track is designed to ensure that both observerse maintain the same altitude.

    When the train returns to the station, or when the earth resumes it's normal rotation speed, shouldn't the observer on the train expect the clock of the observer on the platfrom to have ticked more slowly; while the observer on the platform would expect the same of the clock of the observer on the train?


  • Registered Users Posts: 3,457 ✭✭✭Morbert


    roosh wrote: »
    Thanks, I will google that so and try and get an understanding of it.

    With regard to the question about the cars, I don't think I formulated what I was wondering very well; with the cars, the faster car will appear to pass the slower car at, say, 20km/h; but if the observer in the slower car was to measure the speed of the other car using a moving radar speed gun he would clock the "correct" speed of the car to be the same as the observer in the other car.

    The measurement of light appears to be different, is it? Where the frequency of a "beam" of light is checked to see if it differs - is that correct? I imagine this is because it's not possible to use radio signals to check the speed of light.

    But with regard to the relative motion of two observers, is it not possible then to determine their motion relative to the common background, such that both observers can be said to be in motion?

    A radar gun measures the speed of an object relative to the speed of the raygun. So if the ray gun is used in the 20kph car, it would clock the speed of the other car as 40 kph.
    Apologies, I probably wasn't clear on that; the bowling ball was meant to represent the light.

    Where one observer releases the [bowling ball of] light and it travels a straight line to the feet of the other observer, where both are stationary. In the second scenario, where both are moving, observer 1 releases the [bowling ball of] light, which again travels a straight line, but bcos Observer 2 has moved from where he was, the [bowling ball of] light will not end up at his feet. In order for it to end up at his feet, the [bowling ball of] light would have to inheret the momentum of the observer who released it and travel a diagonal path - but that isn't light behaves is it?

    It is how light would behave. The photon, like the bowling ball, would inherit the velocity of the thrower. Photons are massless, but they still have momentum defined as p = E/c. The momentum of light is the principle behind solar sails.

    http://en.wikipedia.org/wiki/Solar_sail
    Another scenario which might clarify the point I am trying to understand: if the observer on the train fires a laser gun at the observer on the platform, as they pass each other, from my understanding of what has been said, from the perspective of the observer on the train, the laser will miss the observer on the platform and so he will remain alive; whereas, from the perspective of the observer on the platform the laser will hit him and kill him, meaning that he is alive according to the observer on the train, but, from his own perspective he will be dead - if you'll forgive the formulation of that.

    The scenario can be formulated such that the laser only has to make the barest contact to kill him, and that it is released at the point where any movement, whatsoever, away from him will mean it misses.

    Both observers would agree that the bolt missed. Just as both observers would agree that a bullet would miss. The speed of light is the same for all observers, but the velocity vector (i.e. speed+direction) isn't.
    I hope I'm not misrepresenting you by slightly changing around the order of the quotes, and separating this segment out - let me know if I am.

    Firstly on the issue of cause and effect; again, I might be misunderstanding the whole thing, but to my mind, if you and I start off with rulers of identical sizes, and clocks ticking at the same rate, and one of us starts moving, or we start moving relative to each other such that our rulers lose their direct proportionality, and the clocks fall out of sync, then that is a matter of cause and effect; something has caused the rulers to lose proportionality and something has caused the clocks to fall out of sync. If there was no effect then one clock would not tick slower than the other and the relation of the length of the rulers would remain L:L not become L:ɣL.

    The splitting of my paragraph has created an issue: It is simply the geometry of events is such that the relation between events, when comparing reference frames, can be characterised by length contraction and time dilation, and h^2 = x^2 + y^2 in the case of the triangle.

    The rulers only seem to have changed when we compare rulers. I will say yours has gotten smaller than mine, and you will say mine has gotten smaller than yours. The same with clocks. I will say yours is ticking more slowly, and you will say mine is ticking more slowly. Notice that each person says the other's clock is slower, and ruler is shorter. This is because we are both applying the same co-ordinate transformations. So we can't establish any causal link between the speed of a ruler and its length, as it cannot be said that the ruler has actually shortened. If you had genuinely, physically contracted, along with your ruler, you would have measured my ruler to be longer than yours, and my clock to tick faster than yours.
    I think the "roosh"/"mangaroosh" is somewhat of an over-simplification of the issue. Where "roosh" and "mangaroosh" may refer to the same observer, what we are talking about is the actions of the observer, where the actions being labelled are mutually exclusive; it's the difference between "mangaroosh" is in motion and "roosh" is at rest; both can't be simultaneously true.

    Again, it is similar to the sphere of light being centred on a rod and the rod moving away from the centre of the sphere of light.

    Why not? There is no violation of causality. There is still a coherent, global structure to everything. It does not result in any contradictions. The only way it would result in a contradiction is if it was labelled both "in motion" and "at rest" by the same labelling convention.
    If it were a simple matter of labelling, then length contraction should occur simply by labelling one observer as being in motion and the other as being at rest; but that isn't the case. In order for length contraction to occur there must first be relative motion between the two, unless length contraction is only an illusion and doesn't actually occur. So the effects of length contraction and time dilation have to be attributed to a cause, in this case it is motion - of one observer or the other.

    If two observers are at rest, relative to each other, and one of them starts swinging his arms (all other things being equal) is the observer in motion or at rest, or are parts of his body capable of motion?

    This just means the labelling has to be consistent. If an observer says something is "at rest" then all things at rest relative to that thing are also "at rest".
    What would the present look like from the perspective of this omniscient observer?

    The present, in the sense of a single 3D hyper-surface of events, would not exist. Instead, an omniscient observer would see a light-cone structure of causality, where each event has a light-cone of past an future events.
    It is related, but I think it is somewhat different; because, am I right in saying, the twin paradox involves one twin moving through the gravity well to a location with a different measure of gravity?

    I am thinking more along the lines of the thought experiment, involving the train, being carried out at some imagined point in the future, where the train travels around the surface of the earth at 0.8c and the track is designed to ensure that both observerse maintain the same altitude.

    When the train returns to the station, or when the earth resumes it's normal rotation speed, shouldn't the observer on the train expect the clock of the observer on the platfrom to have ticked more slowly; while the observer on the platform would expect the same of the clock of the observer on the train?

    The twin paradox does not involve a gravity well. The observer on the train would expect the clock of the platform observer to tick more slowly, and he would be just as correct, as relativity says no observers viewpoint is more "real". Hence the paradox. The solution is interesting, but well documented, and there is little reason for me to explain it here. The wikipedia article is a good place to start.


  • Registered Users Posts: 2,552 ✭✭✭roosh


    Morbert wrote: »
    A radar gun measures the speed of an object relative to the speed of the raygun. So if the ray gun is used in the 20kph car, it would clock the speed of the other car as 40 kph.
    There are "moving" radar speed guns though
    the gun receives reflected signals from both the target vehicle and stationary background objects, such as the road, road signs, guard rails, streetlight poles, etc. Instead of comparing the frequency of the signal reflected from the target with the transmitted signal, it compares the target signal with the background signal. The difference in frequency of these two signals gives the true speed of the target vehicle.
    wiki

    Morbert wrote: »
    It is how light would behave. The photon, like the bowling ball, would inherit the velocity of the thrower. Photons are massless, but they still have momentum defined as p = E/c. The momentum of light is the principle behind solar sails.

    http://en.wikipedia.org/wiki/Solar_sail


    Both observers would agree that the bolt missed. Just as both observers would agree that a bullet would miss. The speed of light is the same for all observers, but the velocity vector (i.e. speed+direction) isn't.
    It wasn't necessarily whether or not photons have momentum, but rather how a moving source affects that momentum, or direction of momentum; I took the principle that the velocity of light is unaffected by the speed of a moving source to mean that the photons momentum and direction of momentum are unaffected, which appears to be incorrect.

    Has that phenomenon been tested; as that is what the author's experiment is supposed to test? The result he claims is that the direction of the photon's momentum is unaffected by a moving source i.e. that it would follow the path of the [bowling ball of] light in the scenario where it doesn't end up at the feet of the moving observer.

    Also, how does it reconcile with the "expanding sphere of light" phenomenon?

    Morbert wrote: »
    The splitting of my paragraph has created an issue: It is simply the geometry of events is such that the relation between events, when comparing reference frames, can be characterised by length contraction and time dilation, and h^2 = x^2 + y^2 in the case of the triangle.
    It is the modelling of the light path, to which that equation is applied, which the author challenges with his alleged experiment. I know that the slower ticking clock has been tested, but has the direction of the photon of light, from a moving source, been experimentally verified?
    Morbert wrote: »
    The rulers only seem to have changed when we compare rulers. I will say yours has gotten smaller than mine, and you will say mine has gotten smaller than yours. The same with clocks. I will say yours is ticking more slowly, and you will say mine is ticking more slowly. Notice that each person says the other's clock is slower, and ruler is shorter. This is because we are both applying the same co-ordinate transformations. So we can't establish any causal link between the speed of a ruler and its length, as it cannot be said that the ruler has actually shortened. If you had genuinely, physically contracted, along with your ruler, you would have measured my ruler to be longer than yours, and my clock to tick faster than yours.
    The above seems to suggest that time dilation and length contraction don't actually occur, that they just appear to happen; but the time dilation experiments actually measured a slower ticking clock, or rather, the counter had registered fewer "ticks"; so it wasn't a case of seeming to tick slower, it actually did tick slower.

    Again, this is likely down to my misunderstanding of Relativity, but the thought experiment seems to suggest that length contraction (and time dilation) is a "two-way" thing i.e. both observers will measure the [contents of the] others reference frame as contracting.

    If this were actually to occur, in the sense that the clocks in the time dilation experiments actually registered fewer "ticks", then, assuming the thought experiment came to fruition in the future, the scenario would require, when both observers are at rest relative to each other, that from the perspective of Observer A, Observer B's clock should have registered fewer "ticks" and vice versa - which is not possible.


    Morbert wrote: »
    Why not? There is no violation of causality. There is still a coherent, global structure to everything. It does not result in any contradictions. The only way it would result in a contradiction is if it was labelled both "in motion" and "at rest" by the same labelling convention.
    If we combine the two examples, the light sphere and "mangaroosh", it would be like saying that "mangaroosh" is both beside the tree and the tree is moving away from "mangaroosh", at the same time - it's not possible.

    Morbert wrote: »
    The present, in the sense of a single 3D hyper-surface of events, would not exist. Instead, an omniscient observer would see a light-cone structure of causality, where each event has a light-cone of past an future events.
    But the the light cone structure only represents 2 spatial dimensions, doesn't it? How would a "3D hyper-surface of events" observe itself as having only 2 spatial dimensions?


    Morbert wrote: »
    The twin paradox does not involve a gravity well. The observer on the train would expect the clock of the platform observer to tick more slowly, and he would be just as correct, as relativity says no observers viewpoint is more "real". Hence the paradox. The solution is interesting, but well documented, and there is little reason for me to explain it here. The wikipedia article is a good place to start.
    I may be using the wrong expression in "gravity well", but the twin paradox involves one twin going into "outer space"; in the documentary "the Fabric of the Cosmos: the Illusion of time" by Brian Greene (as posted in the other thread) the scenario is actually postulated as one twin flying near a black hole; so that scenario does involve vastly different "levels" of gravity - I thought that was the correct application of the term "gravity well".

    The scenario in the thought experiment is somewhat different, as it doesn't involve either twin leaving the surface of the earth, and hence the differences in gravity experienced by both observers would either be negated, or at the very least, greatly reduced.

    Morbert wrote: »
    This just means the labelling has to be consistent. If an observer says something is "at rest" then all things at rest relative to that thing are also "at rest".
    I think we can boil this part of the discussion down to the difference, if any, between "motion" and "rest". You seem to be stating that the difference is simply one of labeling; I think there is perhaps a more fundamental difference.

    If we take a scenario similar to what we have been discussing, where two observers are at rest relative to each other; if those observers start moving relative to each other, then there are two possible scenarios:
    - either one of them is moving
    or
    - both of them are moving

    Therefore, if both observers label themselves as "being at rest" then, at least, one of them is wrong.



    Just to re-post the question from above: if two observers are at rest relative to each other, and one starts swinging his arms, is he in motion or at rest; or are his arms in motion; or, are his body parts capable of motion?


  • Registered Users Posts: 3,457 ✭✭✭Morbert


    roosh wrote: »
    There are "moving" radar speed guns though
    wiki

    "the gun receives reflected signals from both the target vehicle and stationary background objects, such as the road, road signs, guard rails, streetlight poles, etc. Instead of comparing the frequency of the signal reflected from the target with the transmitted signal, it compares the target signal with the background signal. The difference in frequency of these two signals gives the true speed of the target vehicle."

    This radar gun tells us the speed relative to the background objects, but does not say whether or not the background objects are moving. They are assumed to be stationary. Hence, you get a different reading if your "stationary" background object is a signpost, from if it is Jupiter.
    It wasn't necessarily whether or not photons have momentum, but rather how a moving source affects that momentum, or direction of momentum; I took the principle that the velocity of light is unaffected by the speed of a moving source to mean that the photons momentum and direction of momentum are unaffected, which appears to be incorrect.

    Has that phenomenon been tested; as that is what the author's experiment is supposed to test? The result he claims is that the direction of the photon's momentum is unaffected by a moving source i.e. that it would follow the path of the [bowling ball of] light in the scenario where it doesn't end up at the feet of the moving observer.

    Also, how does it reconcile with the "expanding sphere of light" phenomenon?

    It has been tested in any variation of the Michelson-Morley experiment. When a photon is reflected by the mirror, it inherits the velocity of the mirror. If this did not happen, and all that defined the trajectory of the photon was the direction it was emitted from some absolute reference frame, as you suggested, the photon would "fall behind" the mirror.

    The above seems to suggest that time dilation and length contraction don't actually occur, that they just appear to happen; but the time dilation experiments actually measured a slower ticking clock, or rather, the counter had registered fewer "ticks"; so it wasn't a case of seeming to tick slower, it actually did tick slower.

    Again, this is likely down to my misunderstanding of Relativity, but the thought experiment seems to suggest that length contraction (and time dilation) is a "two-way" thing i.e. both observers will measure the [contents of the] others reference frame as contracting.

    If this were actually to occur, in the sense that the clocks in the time dilation experiments actually registered fewer "ticks", then, assuming the thought experiment came to fruition in the future, the scenario would require, when both observers are at rest relative to each other, that from the perspective of Observer A, Observer B's clock should have registered fewer "ticks" and vice versa - which is not possible.

    That is the twin paradox. The solution is well documented.
    http://en.wikipedia.org/wiki/Twin_paradox

    "each twin sees the other twin as traveling, and so, according to a naive application of time dilation, each should paradoxically find the other to have aged more slowly."
    If we combine the two examples, the light sphere and "mangaroosh", it would be like saying that "mangaroosh" is both beside the tree and the tree is moving away from "mangaroosh", at the same time - it's not possible.

    If the tree is the extrapolated centre of a propagating sphere of light, it is perfectly possible under Lorentz transformations. This is because the centre of a sphere of light is merely a co-ordinate.

    The mistake you are making is assuming Galilean transformations, which characterise everyday experiences of relative motion, are a logical necessity. They aren't.
    But the the light cone structure only represents 2 spatial dimensions, doesn't it? How would a "3D hyper-surface of events" observe itself as having only 2 spatial dimensions?

    It represents three spatial dimensions, but is often drawn with only 2 for visualisation purposes.
    I may be using the wrong expression in "gravity well", but the twin paradox involves one twin going into "outer space"; in the documentary "the Fabric of the Cosmos: the Illusion of time" by Brian Greene (as posted in the other thread) the scenario is actually postulated as one twin flying near a black hole; so that scenario does involve vastly different "levels" of gravity - I thought that was the correct application of the term "gravity well".

    The scenario in the thought experiment is somewhat different, as it doesn't involve either twin leaving the surface of the earth, and hence the differences in gravity experienced by both observers would either be negated, or at the very least, greatly reduced.

    You used the term correctly, and the twin paradox does not involve a gravity well (The Illusion of time scene you mention is not regarding the twin paradox). In our discussion, for example, the twin paradox can be recreated by having the train leave the station and return.
    I think we can boil this part of the discussion down to the difference, if any, between "motion" and "rest". You seem to be stating that the difference is simply one of labeling; I think there is perhaps a more fundamental difference.

    If we take a scenario similar to what we have been discussing, where two observers are at rest relative to each other; if those observers start moving relative to each other, then there are two possible scenarios:
    - either one of them is moving
    or
    - both of them are moving

    Therefore, if both observers label themselves as "being at rest" then, at least, one of them is wrong.

    Why? One would only be wrong if they labelled both observers as "at rest".
    Just to re-post the question from above: if two observers are at rest relative to each other, and one starts swinging his arms, is he in motion or at rest; or are his arms in motion; or, are his body parts capable of motion?

    Both observers would agree that the arms are in motion. If there was a third observer on an arm, he would say the arm is stationary and both observers are moving.


  • Registered Users Posts: 2,552 ✭✭✭roosh


    Morbert wrote: »
    "the gun receives reflected signals from both the target vehicle and stationary background objects, such as the road, road signs, guard rails, streetlight poles, etc. Instead of comparing the frequency of the signal reflected from the target with the transmitted signal, it compares the target signal with the background signal. The difference in frequency of these two signals gives the true speed of the target vehicle."

    This radar gun tells us the speed relative to the background objects, but does not say whether or not the background objects are moving. They are assumed to be stationary. Hence, you get a different reading if your "stationary" background object is a signpost, from if it is Jupiter.
    Would we have to use Jupiter; for our solar system could we not use the sun?
    Morbert wrote: »
    It has been tested in any variation of the Michelson-Morley experiment. When a photon is reflected by the mirror, it inherits the velocity of the mirror. If this did not happen, and all that defined the trajectory of the photon was the direction it was emitted from some absolute reference frame, as you suggested, the photon would "fall behind" the mirror.
    It might not necessarily "fall behind" the mirror, but it would not necessarily hit the mirror where expected, meaning that it would be somewhat off; this effect would then be amplified as the light is bounced from one mirror to another, meaning that it would also miss the detector. As the effect is dependent on the direction of motion it could affect just one of the beams, which could potentially give rise to the null result.

    As is abundantly clear, I am no expert on such matters, but I haven't really seen anything that has tested this possible systematic error of the MMX.


    Morbert wrote: »
    That is the twin paradox. The solution is well documented.
    http://en.wikipedia.org/wiki/Twin_paradox



    "each twin sees the other twin as traveling, and so, according to a naive application of time dilation, each should paradoxically find the other to have aged more slowly."

    "a twin makes a journey into space in a high-speed rocket and returns home to find he has aged less than his identical twin who stayed on Earth"

    "Einstein, Born and Møller invoked gravitational time dilation to explain the aging based upon the effects of acceleration"
    [url=http://en.wikipedia.org/wiki/Twin_paradox

    ]Twin Paradox[/url]

    "Gravitational time dilation is the effect of time passing at different rates in regions of different gravitational potential; the lower the gravitational potential, the more slowly time passes"
    Gravitational

    Time Dilation


    The twin paradox, as it is usually formulated, involves one twin going into outer space and the other remaining on earth - I presume this means that both occupy regions with different gravitational potential.

    However, if we formulate the thought experiment using the two twins as our observers, then it doesn't involve either twin going into outer space; theoretically the experiment could be conducted using the high speed train traveling around the surface of the earth, with the track designed such that both remain equidistant to the earths core - presumably this would mean that both occupy regions with the same, or very similar, gravitational potential.

    In this scenario, where there is no change in gravitational potential, both "should paradoxically find the other to have aged more slowly".

    Morbert wrote: »
    If the tree is the extrapolated centre of a propagating sphere of light, it is perfectly possible under Lorentz transformations. This is because the centre of a sphere of light is merely a co-ordinate.

    The mistake you are making is assuming Galilean transformations, which characterise everyday experiences of relative motion, are a logical necessity. They aren't.
    It is still the difference of "mangaroosh" being at rest relative to the tree and the tree moving relative to "mangaroosh" - which is a paradoxical situation.

    Morbert wrote: »
    It represents three spatial dimensions, but is often drawn with only 2 for visualisation purposes.
    The "light cone" structure only represents two spatial dimensions, because it would no longer form a cone if it represented three.


    Morbert wrote: »
    You used the term correctly, and the twin paradox does not involve a gravity well (The Illusion of time scene you mention is not regarding the twin paradox). In our discussion, for example, the twin paradox can be recreated by having the train leave the station and return.
    The illusion of time scene, I'm pretty sure, is the "twin paradox", or at least a variation on it, demonstrating the same phenomena that the "twin paradox" is supposed to demonstrate; they simply added a region of space that would have [am I right in saying] a much, much higher gravity potential.

    My misapplication of the term may lie in it's application to the "twin paradox" as opposed to an incorrect use of it, per se; that is, the "twin paradox" may not involve a gravity well, but it does involve one twin moving between regions with different gravitation potential - I took this to mean, moving through a gravity well.

    Morbert wrote: »
    Why? One would only be wrong if they labelled both observers as "at rest".
    If we take two observers who are at rest relative to each other, then they will both label each other as "being at rest" and there will be no observable increse in distance between them. For an increase in distance to occur between them there must be relative motion; this establishes a fundamental difference between being in motion and being at rest, such that it is not possible to be both at the same time; it also establishes that being in motion and being at rest is not simply a matter of labelling - the one or the other must occur before it can be labelled.

    For there to be relative motion between the two observers either one, or both, of them must be in motion; both can't label themselves as being at rest [and both be correct] because at least one of them isn't.

    But let's say they do, as per the thought experiment; but they decide to communicate with each other; one contacts the other and says "why did you start moving?"; the other will reply "I didn't start moving, you did!"; the other will reply, "I didn't start moving, you did!"; now, this could go on ad infinitum, or they could come to the conclusion that one of them, or perhaps both of them, but at least one of them, is mistaken.
    Morbert wrote: »
    Both observers would agree that the arms are in motion. If there was a third observer on an arm, he would say the arm is stationary and both observers are moving.
    Presumably this applies to all parts of the body, including the head?


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  • Registered Users Posts: 3,457 ✭✭✭Morbert


    roosh wrote: »
    Would we have to use Jupiter; for our solar system could we not use the sun?

    We could use anything. But who says the solar system is stationary?
    It might not necessarily "fall behind" the mirror, but it would not necessarily hit the mirror where expected, meaning that it would be somewhat off; this effect would then be amplified as the light is bounced from one mirror to another, meaning that it would also miss the detector. As the effect is dependent on the direction of motion it could affect just one of the beams, which could potentially give rise to the null result.

    As is abundantly clear, I am no expert on such matters, but I haven't really seen anything that has tested this possible systematic error of the MMX.

    This effect would not produce a null result. This is especially true when we consider the modern, more sophisticated versions of the MM experiment.
    "a twin makes a journey into space in a high-speed rocket and returns home to find he has aged less than his identical twin who stayed on Earth"

    "Einstein, Born and Møller invoked gravitational time dilation to explain the aging based upon the effects of acceleration"
    Twin Paradox

    "Gravitational time dilation is the effect of time passing at different rates in regions of different gravitational potential; the lower the gravitational potential, the more slowly time passes"
    Gravitational Time Dilation

    The twin paradox, as it is usually formulated, involves one twin going into outer space and the other remaining on earth - I presume this means that both occupy regions with different gravitational potential.

    However, if we formulate the thought experiment using the two twins as our observers, then it doesn't involve either twin going into outer space; theoretically the experiment could be conducted using the high speed train traveling around the surface of the earth, with the track designed such that both remain equidistant to the earths core - presumably this would mean that both occupy regions with the same, or very similar, gravitational potential.

    In this scenario, where there is no change in gravitational potential, both "should paradoxically find the other to have aged more slowly".

    --

    The illusion of time scene, I'm pretty sure, is the "twin paradox", or at least a variation on it, demonstrating the same phenomena that the "twin paradox" is supposed to demonstrate; they simply added a region of space that would have [am I right in saying] a much, much higher gravity potential.

    My misapplication of the term may lie in it's application to the "twin paradox" as opposed to an incorrect use of it, per se; that is, the "twin paradox" may not involve a gravity well, but it does involve one twin moving between regions with different gravitation potential - I took this to mean, moving through a gravity well.

    I repeat: The twin paradox has nothing to do with occupying regions of different gravitational potential. Please just read the wikipedia article in full and take note to how they are invoking gravitational time dilation. They invoke it when one twin is accelerating or decelerating. It is explicitly dealt with in this part of the article

    http://en.wikipedia.org/wiki/Twin_paradox#Viewpoint_of_the_traveling_twin

    Also note this paragraph:

    "Other calculations have been done for the traveling twin (or for any observer who sometimes accelerates), which do not involve the equivalence principle, and which do not involve any gravitational fields. Such calculations are based only on the special theory, not the general theory, of relativity. One approach calculates surfaces of simultaneity by considering light pulses, in accordance with Hermann Bondi's idea of the k-calculus.[11] A second approach calculates a straightforward but technically complicated integral to determine how the traveling twin measures the elapsed time on the stay-at-home clock. An outline of this second approach is given in a separate section below."
    It is still the difference of "mangaroosh" being at rest relative to the tree and the tree moving relative to "mangaroosh" - which is a paradoxical situation.

    You are just reiterating your previous assertion. It is not paradoxical when you consider the hyperbolic, pseudo-Riemann geometry of Minkowski space-time. You are assuming Galilean space-time, with it's intuitive, linear, velocity addition is a logical necessity. It is not.

    So I would ask you to please demonstrate that the lorentz transformation of an expanding sphere of light generates a paradox when we consider two arbitrary observers.
    The "light cone" structure only represents two spatial dimensions, because it would no longer form a cone if it represented three.

    It is a hypercone.
    http://en.wikipedia.org/wiki/Hypercone
    If we take two observers who are at rest relative to each other, then they will both label each other as "being at rest" and there will be no observable increse in distance between them. For an increase in distance to occur between them there must be relative motion; this establishes a fundamental difference between being in motion and being at rest, such that it is not possible to be both at the same time; it also establishes that being in motion and being at rest is not simply a matter of labelling - the one or the other must occur before it can be labelled.

    For there to be relative motion between the two observers either one, or both, of them must be in motion; both can't label themselves as being at rest [and both be correct] because at least one of them isn't.

    But let's say they do, as per the thought experiment; but they decide to communicate with each other; one contacts the other and says "why did you start moving?"; the other will reply "I didn't start moving, you did!"; the other will reply, "I didn't start moving, you did!"; now, this could go on ad infinitum, or they could come to the conclusion that one of them, or perhaps both of them, but at least one of them, is mistaken.

    As I have said before, so long as the labelling convention is consistent, it is no better or worse. Any labelling convention that labels something as being "in motion" and "at rest" at the same time is, indeed, nonsensical. But, provided we are consistent, we are free to label either observer as, in motion.

    I will put it this way: There is no experiment, no matter how precise, that would physically distinguish one labelling convention from the other. And there is no entity, supernatural, omniscient, or otherwise, that would see one label convention as physically distinguished.
    Presumably this applies to all parts of the body, including the head?

    Yes.


  • Registered Users Posts: 3,457 ✭✭✭Morbert


    roosh wrote: »
    Would we have to use Jupiter; for our solar system could we not use the sun?

    We could use anything. But who says the solar system is stationary?
    It might not necessarily "fall behind" the mirror, but it would not necessarily hit the mirror where expected, meaning that it would be somewhat off; this effect would then be amplified as the light is bounced from one mirror to another, meaning that it would also miss the detector. As the effect is dependent on the direction of motion it could affect just one of the beams, which could potentially give rise to the null result.

    As is abundantly clear, I am no expert on such matters, but I haven't really seen anything that has tested this possible systematic error of the MMX.

    This effect would not produce a null result unless you specifically adjusted the positions of the mirrors. This is especially true when we consider the modern, more sophisticated versions of the MM experiment. The electromagnetic waves, when interacting with the moving mirror, would not produce the path the author alludes to. Interestingly, the author in absolute-relativity claims the MM experiment does not consider the "falling behind/ahead" path of the photon, while the other person you raised, Paul Marmet, is making the exact opposite objection. Their objections, ironically, cancel each other out. A Metaphorical destructive interference pattern.
    "a twin makes a journey into space in a high-speed rocket and returns home to find he has aged less than his identical twin who stayed on Earth"

    "Einstein, Born and Møller invoked gravitational time dilation to explain the aging based upon the effects of acceleration"
    Twin Paradox

    "Gravitational time dilation is the effect of time passing at different rates in regions of different gravitational potential; the lower the gravitational potential, the more slowly time passes"
    Gravitational Time Dilation

    The twin paradox, as it is usually formulated, involves one twin going into outer space and the other remaining on earth - I presume this means that both occupy regions with different gravitational potential.

    However, if we formulate the thought experiment using the two twins as our observers, then it doesn't involve either twin going into outer space; theoretically the experiment could be conducted using the high speed train traveling around the surface of the earth, with the track designed such that both remain equidistant to the earths core - presumably this would mean that both occupy regions with the same, or very similar, gravitational potential.

    In this scenario, where there is no change in gravitational potential, both "should paradoxically find the other to have aged more slowly".

    --

    The illusion of time scene, I'm pretty sure, is the "twin paradox", or at least a variation on it, demonstrating the same phenomena that the "twin paradox" is supposed to demonstrate; they simply added a region of space that would have [am I right in saying] a much, much higher gravity potential.

    My misapplication of the term may lie in it's application to the "twin paradox" as opposed to an incorrect use of it, per se; that is, the "twin paradox" may not involve a gravity well, but it does involve one twin moving between regions with different gravitation potential - I took this to mean, moving through a gravity well.

    I repeat: The twin paradox has nothing to do with occupying regions of different gravitational potential. Please just read the wikipedia article in full and take note to how they are invoking gravitational time dilation. They invoke it when one twin is accelerating or decelerating. It is explicitly dealt with in this part of the article

    http://en.wikipedia.org/wiki/Twin_paradox#Viewpoint_of_the_traveling_twin

    Also note this paragraph:

    "Other calculations have been done for the traveling twin (or for any observer who sometimes accelerates), which do not involve the equivalence principle, and which do not involve any gravitational fields. Such calculations are based only on the special theory, not the general theory, of relativity. One approach calculates surfaces of simultaneity by considering light pulses, in accordance with Hermann Bondi's idea of the k-calculus.[11] A second approach calculates a straightforward but technically complicated integral to determine how the traveling twin measures the elapsed time on the stay-at-home clock. An outline of this second approach is given in a separate section below."
    It is still the difference of "mangaroosh" being at rest relative to the tree and the tree moving relative to "mangaroosh" - which is a paradoxical situation.

    You are just reiterating your previous assertion. It is not paradoxical when you consider the hyperbolic, pseudo-Riemann geometry of Minkowski space-time. You are assuming Galilean space-time, with its intuitive, linear, velocity addition is a logical necessity. It is not.

    So I would ask you to please demonstrate that the lorentz transformation of an expanding sphere of light generates a paradox when we consider two arbitrary observers.
    The "light cone" structure only represents two spatial dimensions, because it would no longer form a cone if it represented three.

    It is a hypercone.
    http://en.wikipedia.org/wiki/Hypercone
    If we take two observers who are at rest relative to each other, then they will both label each other as "being at rest" and there will be no observable increse in distance between them. For an increase in distance to occur between them there must be relative motion; this establishes a fundamental difference between being in motion and being at rest, such that it is not possible to be both at the same time; it also establishes that being in motion and being at rest is not simply a matter of labelling - the one or the other must occur before it can be labelled.

    For there to be relative motion between the two observers either one, or both, of them must be in motion; both can't label themselves as being at rest [and both be correct] because at least one of them isn't.

    But let's say they do, as per the thought experiment; but they decide to communicate with each other; one contacts the other and says "why did you start moving?"; the other will reply "I didn't start moving, you did!"; the other will reply, "I didn't start moving, you did!"; now, this could go on ad infinitum, or they could come to the conclusion that one of them, or perhaps both of them, but at least one of them, is mistaken.

    As I have said before, so long as the labelling convention is consistent, it is no better or worse. Any labelling convention that labels something as being "in motion" and "at rest" at the same time is, indeed, nonsensical. But, provided we are consistent, we are free to label either observer as, in motion.

    I will put it this way: There is no experiment, no matter how precise, that would physically distinguish one labelling convention from the other. And there is no entity, supernatural, omniscient, or otherwise, that would see one label convention as physically distinguished.
    Presumably this applies to all parts of the body, including the head?

    Yes.


  • Registered Users Posts: 2,552 ✭✭✭roosh


    Morbert wrote: »
    We could use anything. But who says the solar system is stationary?
    Very true. How does an observer determine then that they are "at rest"?

    Morbert wrote: »
    This effect would not produce a null result unless you specifically adjusted the positions of the mirrors. This is especially true when we consider the modern, more sophisticated versions of the MM experiment. The electromagnetic waves, when interacting with the moving mirror, would not produce the path the author alludes to. Interestingly, the author in absolute-relativity claims the MM experiment does not consider the "falling behind/ahead" path of the photon, while the other person you raised, Paul Marmet, is making the exact opposite objection. Their objections, ironically, cancel each other out. A Metaphorical destructive interference pattern.
    As with with Etienne Brauns, I am just questioning whether these potential systematic errors have been accounted for, not necessarily that they be used in conjunction with each other.

    If the mirrors in the MMX were set up with a specific light-path in mind, then a variation on the path of the light would result in the beam being reflected to somewhere other than the intended location. If this meant that the beam did not enter the detector, then it would surely account for the null result. How do modern, more sophisticated versions demonstrate that this [potential] systematic error doesn't occur?


    Morbert wrote: »
    I repeat: The twin paradox has nothing to do with occupying regions of different gravitational potential. Please just read the wikipedia article in full and take note to how they are invoking gravitational time dilation. They invoke it when one twin is accelerating or decelerating. It is explicitly dealt with in this part of the article

    http://en.wikipedia.org/wiki/Twin_paradox#Viewpoint_of_the_traveling_twin
    My apologies, while I knew that I didn't fully understand all the principles of GR, there were certain basics that I thought I had understood; which I am entirely less sure about now. I may also have been applying the everyday meaning of terms to terms which are used differently.This unfortunately (or fortunately depending on how you look at it) leads to more questions.

    My understanding of gravity was that we experience "more gravty" while standing here on earth than we would if we were to go into space on a shuttle. That doesn't appear to be the case though; is this where the equivalence principle comes in?

    I also find it somewhat confusing that they refer to "the traveling twin" as undergoing acceleration and deceleration, and switching between reference frames; which I would generally understand as being in motion, or "traveling".

    They say that "the travelling twin" would analyse "the stay-at-home twin" as "freely falling in a gravitational field"; why would the "stay-at-home" twin not analyse it similarly; and why, from the perspective of "the travelling twin" would the "stay-at-home" twin not be observed to undergo the same acceleration and deceleration?


    Morbert wrote: »
    Also note this paragraph:

    "Other calculations have been done for the traveling twin (or for any observer who sometimes accelerates), which do not involve the equivalence principle, and which do not involve any gravitational fields. Such calculations are based only on the special theory, not the general theory, of relativity. One approach calculates surfaces of simultaneity by considering light pulses, in accordance with Hermann Bondi's idea of the k-calculus.[11] A second approach calculates a straightforward but technically complicated integral to determine how the traveling twin measures the elapsed time on the stay-at-home clock. An outline of this second approach is given in a separate section below."
    I had a look at that section but couldn't really understand the maths of it. Am I right in thinking that the reason that the paradox doesn't arise is due to the asymmetry (asymmetry of what I can't recall); that one of the observers undergoes acceleration and deceleration?
    Morbert wrote: »
    You are just reiterating your previous assertion. It is not paradoxical when you consider the hyperbolic, pseudo-Riemann geometry of Minkowski space-time. You are assuming Galilean space-time, with its intuitive, linear, velocity addition is a logical necessity. It is not.

    So I would ask you to please demonstrate that the lorentz transformation of an expanding sphere of light generates a paradox when we consider two arbitrary observers.
    I would say that the paradox arises in the fact that both observers are labelled as being simultaneously "in motion" and "at rest". I don't think your formulation of the issue is representative of the problem; an observer being labelled as both "mangaroosh" and "roosh" at the same time is not the same as being labelled as "in motion" and "at rest", because the latter are mutually exclusive, referring to two different states.


    Morbert wrote: »
    Which, assuming it's veracity, would represent the present to the omniscient being, were he to press the "universal pause button".

    Morbert wrote: »
    As I have said before, so long as the labelling convention is consistent, it is no better or worse. Any labelling convention that labels something as being "in motion" and "at rest" at the same time is, indeed, nonsensical. But, provided we are consistent, we are free to label either observer as, in motion.

    I will put it this way: There is no experiment, no matter how precise, that would physically distinguish one labelling convention from the other. And there is no entity, supernatural, omniscient, or otherwise, that would see one label convention as physically distinguished.
    We are, arguably, free to label either observer as "in motion"; however, both observers cannot label themselves as "at rest" if there is relative motion between them. Again, if they were to communicate with each other they may disagree with each other over who is "in motion", but they would have to conclude that they both cannot be "at rest", so one of them must be wrong.

    On the question of consistency: if both observers are at rest relative to each other and certain objects in their reference frame, then their definition of "at rest" is, "at rest" relative to those objects. If observer A then experiences relative motion between himself and all of those objects, but observer B only experiences relative motion between himself and Observer A, then Observer A would not be consistent in his application of labelling, if he labels himself as "at rest"; or at least, he would be less consistent than Observer B.

    Morbert wrote: »
    Yes.
    If an observer is capable of moving every part of his body, and he exercises that ability, why wouldn't he conclude that he was "in motion" and not "at rest"?


    Other questions
    Just a few other questions that I have trouble reconciling:

    • How did we move on from the Ptolmeic model of the solar system, if an observer would always label themselves at rest?
    • How did anyone determine that the earth is rotating?
    • How does the "laser gun" scenario mentioned earlier, reconcile with the "expanding sphere" phenomenon?
    • If two observers are at rest relative to each other, but then undergo relative motion, there must be a cause of that motion; if one observer is "running", the other observer will presumably attribute the relative motion to the "running", but what will the "runner" attribute the relative motion to?


  • Registered Users Posts: 3,457 ✭✭✭Morbert


    roosh wrote: »
    Very true. How does an observer determine then that they are "at rest"?

    They can't! They best they can do is adopt an arbitrary co-ordinate scheme.
    As with with Etienne Brauns, I am just questioning whether these potential systematic errors have been accounted for, not necessarily that they be used in conjunction with each other.

    If the mirrors in the MMX were set up with a specific light-path in mind, then a variation on the path of the light would result in the beam being reflected to somewhere other than the intended location. If this meant that the beam did not enter the detector, then it would surely account for the null result. How do modern, more sophisticated versions demonstrate that this [potential] systematic error doesn't occur?

    I am noticing the discussion has branched into to separate issues. The above deals with the experimental support. The rest deals with the logical consistency of the postulates of relativity. I would like to leave the above until after issues with the theory itself has been dealt with. Partly because this is the philosophy forum, but mainly because it makes the discussion more coherent.
    My apologies, while I knew that I didn't fully understand all the principles of GR, there were certain basics that I thought I had understood; which I am entirely less sure about now. I may also have been applying the everyday meaning of terms to terms which are used differently.This unfortunately (or fortunately depending on how you look at it) leads to more questions.

    My understanding of gravity was that we experience "more gravty" while standing here on earth than we would if we were to go into space on a shuttle. That doesn't appear to be the case though; is this where the equivalence principle comes in?

    I also find it somewhat confusing that they refer to "the traveling twin" as undergoing acceleration and deceleration, and switching between reference frames; which I would generally understand as being in motion, or "traveling".

    They say that "the travelling twin" would analyse "the stay-at-home twin" as "freely falling in a gravitational field"; why would the "stay-at-home" twin not analyse it similarly; and why, from the perspective of "the travelling twin" would the "stay-at-home" twin not be observed to undergo the same acceleration and deceleration?

    To avoid confusion, we can put the "stay-at-home" twin on a zero-gravity space station.

    Now is a good time to bring up the distinction between special relativity and general relativity. Special relativity does not say the laws of physics are the same for all observers. Special relativity says the laws of physics are the same for all "inertial" observers. One twin accelerates, and hence, is not in an inertial reference frame. We can say one twin started accelerating and the other twin didn't!

    General relativity, on the other hand, says the laws of physics are the same for all observers. It does this via the equivalence principle: A local gravitational force is equivalent to acceleration.

    http://en.wikipedia.org/wiki/Equivalence_principle

    Under genral relativity, the travelling twin labels himself as at rest and the other twin as in motion because he interprets the force he feels as a gravitational field. He says the other twin does not detect this gravitational field because he is freely falling in the field, and hence feels no force of gravity. Just as people freely falling in an aeroplane do not feel gravity.



    http://en.wikipedia.org/wiki/Vomit_comet


    Since the "stay-at-home-twin" is in this uniform gravitational field, his clock undergoes gravitational time dilation.

    You would rightly think it is absurd to invoke an entire force to reconcile viewpoints, but gravity isn't a force in that sense, it is just an expression of the geometry and chronometry of events.
    I had a look at that section but couldn't really understand the maths of it. Am I right in thinking that the reason that the paradox doesn't arise is due to the asymmetry (asymmetry of what I can't recall); that one of the observers undergoes acceleration and deceleration?

    Yes, under special relativity (but not general relativity), that is how the issue is resolved.

    *I should note that gravitational time dilation is sometime considered a part of "special relativity + equivalence principle" and people sometimes reserve the term "general relativity" for a full dynamical treatment of spacetime.
    I would say that the paradox arises in the fact that both observers are labelled as being simultaneously "in motion" and "at rest". I don't think your formulation of the issue is representative of the problem; an observer being labelled as both "mangaroosh" and "roosh" at the same time is not the same as being labelled as "in motion" and "at rest", because the latter are mutually exclusive, referring to two different states.

    Well if my analogy is unhelpful we can drop it. As it stands, no co-ordinate system labels them as simultaneously "at rest" and "in motion".
    Which, assuming it's veracity, would represent the present to the omniscient being, were he to press the "universal pause button".

    No, it would represent the boundary between events that have a causal relation with the event, and events that have no causal relation. For example, if the sun were to explode right now, we would be outside the light cone for 8 minutes, and hence could not be affected in any way until 8 minutes has passed.

    I have been thinking about the button push, and a conceptual problem might be the unphysical nature of the button. In classical physics, the present of an event is the 3D "slice" that intersects it so the event of the button push would freeze that slice of simultaneous events. But with the geometry of special relativity, there is no slice unless we start imposing arbitrary co-ordinate labels. Hence, we get relativity of simultaneity.

    In short, an omnipotent deity would see the causal structure of spacetime, and would be free to label events using any co-ordinate system he wished.
    We are, arguably, free to label either observer as "in motion"; however, both observers cannot label themselves as "at rest" if there is relative motion between them. Again, if they were to communicate with each other they may disagree with each other over who is "in motion", but they would have to conclude that they both cannot be "at rest", so one of them must be wrong.

    They can if they label the other as in motion, and if they acknowledge that they are just adopting a co-ordinate system that is not physically distinguished.
    On the question of consistency: if both observers are at rest relative to each other and certain objects in their reference frame, then their definition of "at rest" is, "at rest" relative to those objects. If observer A then experiences relative motion between himself and all of those objects, but observer B only experiences relative motion between himself and Observer A, then Observer A would not be consistent in his application of labelling, if he labels himself as "at rest"; or at least, he would be less consistent than Observer B.

    Aha! They both cannot say they are at rest "relative to those objects". Sure. But they can say they are at rest "relative to their arbitrary frame of reference"
    If an observer is capable of moving every part of his body, and he exercises that ability, why wouldn't he conclude that he was "in motion" and not "at rest"?

    He would conclude his body is in motion, but "he" (I.e. The origin point of his frame of reference) would be at rest.
    [*]How did we move on from the Ptolmeic model of the solar system, if an observer would always label themselves at rest?

    This is a good question. Physically speaking, a model where we are at rest is physically consistent. Relativity says there is no privileged position in space. This has generated Geocentrists.

    "The geocentrists that are closest to the scientific mainstream accept essentially all the observations of the mainstream. They point to the theory of general relativity, which says that all physical phenomena can be described and explained self-consistently in any frame of reference. Since the current state of physics does not single out the geocentric frame of reference as special in any way, this group claims the geocentric frame is special for alternative religious reasons."
    [*]How did anyone determine that the earth is rotating?

    In the language of relativity: "By considering the frame of reference which labels the earth as rotating, and comparing the resultant predicted motion with what they observed."
    [*]How does the "laser gun" scenario mentioned earlier, reconcile with the "expanding sphere" phenomenon?

    Perfectly naturally. I don't see where an issue would arise.
    [*]If two observers are at rest relative to each other, but then undergo relative motion, there must be a cause of that motion; if one observer is "running", the other observer will presumably attribute the relative motion to the "running", but what will the "runner" attribute the relative motion to?

    He will say his running has caused him to remain stationary, and his friend's decision not to run has caused his friend to fall behind.


  • Registered Users Posts: 2,552 ✭✭✭roosh


    Morbert wrote: »
    They can't! They best they can do is adopt an arbitrary co-ordinate scheme.
    Are the observers free to agree on the labeling i.e. can an observer label himself as being in motion?

    Morbert wrote: »
    I am noticing the discussion has branched into to separate issues. The above deals with the experimental support. The rest deals with the logical consistency of the postulates of relativity. I would like to leave the above until after issues with the theory itself has been dealt with. Partly because this is the philosophy forum, but mainly because it makes the discussion more coherent.
    no bother, it might be worth moving the former to the physics forum.

    Morbert wrote: »
    To avoid confusion, we can put the "stay-at-home" twin on a zero-gravity space station.

    Now is a good time to bring up the distinction between special relativity and general relativity. Special relativity does not say the laws of physics are the same for all observers. Special relativity says the laws of physics are the same for all "inertial" observers. One twin accelerates, and hence, is not in an inertial reference frame. We can say one twin started accelerating and the other twin didn't!

    General relativity, on the other hand, says the laws of physics are the same for all observers. It does this via the equivalence principle: A local gravitational force is equivalent to acceleration.

    http://en.wikipedia.org/wiki/Equivalence_principle

    Under genral relativity, the travelling twin labels himself as at rest and the other twin as in motion because he interprets the force he feels as a gravitational field. He says the other twin does not detect this gravitational field because he is freely falling in the field, and hence feels no force of gravity. Just as people freely falling in an aeroplane do not feel gravity.
    The part that is causing confusion for me is, I think, to do with the use of the term "acceleration" because I associate that with motion.

    If both observers start off on the zero-gravity station, will they consider themselves as freely falling in a gravitational filed? Why is it that the twin, who detects the gravitational field, doesn't conclude that he has accelerated and is therefore in motion?
    Morbert wrote: »
    Since the "stay-at-home-twin" is in this uniform gravitational field, his clock undergoes gravitational time dilation.
    Does that mean that his clock will tick slower? Again, my interpretation of the term "acceleration" would lead me to say that this is so bcos the force of acceleration/gravity would cause the other's clock to tick faster.
    Morbert wrote: »
    You would rightly think it is absurd to invoke an entire force to reconcile viewpoints, but gravity isn't a force in that sense, it is just an expression of the geometry and chronometry of events.
    This is another source of confusion for me, as I was always under the impression that gravity was a force; a "fundamental force" at that.

    I don't fully understand what is meant by "an expression of the geometry and chronometry of events" either; does that mean it is just a matter of labeling also?

    Morbert wrote: »
    Yes, under special relativity (but not general relativity), that is how the issue is resolved.

    *I should note that gravitational time dilation is sometime considered a part of "special relativity + equivalence principle" and people sometimes reserve the term "general relativity" for a full dynamical treatment of spacetime.
    Which of SR or GR applies to the following:
    - Where the stay at home twin is on earth, and the other goes into space?
    - Where both stay on earth?
    - Where both start at the zero-gravity station?

    I'm thinking SR for the latter 2 (but not presuming), and I'm not sure at all for the first one.

    Morbert wrote: »
    Well if my analogy is unhelpful we can drop it. As it stands, no co-ordinate system labels them as simultaneously "at rest" and "in motion".
    It's not so much that it is unhelpful, but I was taking it as a representation of how you viewed the problem, which I think is erroneous.

    The problem, as I see it is, again, that both observers cannot label themselves as being at rest, because at least one of them isn't. This issue isn't resolved by the use of two separate and arbitrary co-ordinate systems where both observers label themselves as being at rest.

    Again, if they contact each other and ask why the other moved, they would conclude that one of them must be mistaken - how would they determine which one was? Again, this isn't resolved by each determining that the other is mistaken, bcos they can subsequently contact each other and have the same dispute.

    I don't think that comes down to Gallilean or Lorentz transformations.
    Morbert wrote: »
    No, it would represent the boundary between events that have a causal relation with the event, and events that have no causal relation. For example, if the sun were to explode right now, we would be outside the light cone for 8 minutes, and hence could not be affected in any way until 8 minutes has passed.
    That's true, but from the perspective of the universe you would have the exploded sun, with the light traveling towards the earth.
    Morbert wrote: »
    I have been thinking about the button push, and a conceptual problem might be the unphysical nature of the button. In classical physics, the present of an event is the 3D "slice" that intersects it so the event of the button push would freeze that slice of simultaneous events. But with the geometry of special relativity, there is no slice unless we start imposing arbitrary co-ordinate labels. Hence, we get relativity of simultaneity.

    In short, an omnipotent deity would see the causal structure of spacetime, and would be free to label events using any co-ordinate system he wished.
    From the perspective of the universe, would there past, present and future?

    Morbert wrote: »
    They can if they label the other as in motion, and if they acknowledge that they are just adopting a co-ordinate system that is not physically distinguished.
    But going back the to the issue stated above. If they are at rest relative to each other and then there is relative motion between them, both cannot label themselves as being at rest. If they communicate with each other, they will come to the conclusion that one of them must be wrong.

    Morbert wrote: »
    Aha! They both cannot say they are at rest "relative to those objects". Sure. But they can say they are at rest "relative to their arbitrary frame of reference"
    Is a frame of reference not defined by the objects in it?

    Morbert wrote: »
    He would conclude his body is in motion, but "he" (I.e. The origin point of his frame of reference) would be at rest.
    Would this not mean that his model does not accurately reflect his empirical experience?

    Morbert wrote: »
    This is a good question. Physically speaking, a model where we are at rest is physically consistent. Relativity says there is no privileged position in space. This has generated Geocentrists.

    "The geocentrists that are closest to the scientific mainstream accept essentially all the observations of the mainstream. They point to the theory of general relativity, which says that all physical phenomena can be described and explained self-consistently in any frame of reference. Since the current state of physics does not single out the geocentric frame of reference as special in any way, this group claims the geocentric frame is special for alternative religious reasons."


    In the language of relativity: "By considering the frame of reference which labels the earth as rotating, and comparing the resultant predicted motion with what they observed."
    If someone labels the earth as rotating, and as orbiting the sun, does this mean that they cannot consistently label themselves as being "at rest" when on the earth?

    Morbert wrote: »
    Perfectly naturally. I don't see where an issue would arise.
    I was just thinking in terms of how each observer would observe themselves as being at the centre of an expanding sphere of light; just for visualisation purposes, if we imagine that one of "sliver" of that sphere was the laser pulse, it would mean that in one frame of reference it would hit the observer on the platform, but in the other it would miss him. But that isn't the case, so I'm wondering how it is resolved; or how I've misrepresented the phenomenon.

    Morbert wrote: »
    He will say his running has caused him to remain stationary, and his friend's decision not to run has caused his friend to fall behind.
    But how? Would he not have to conclude that both he and his friend were actually in motion before, and that he had erroneously labelled himself as "at rest"? Wouldn't he have to come up with an explanation for why his running caused him to remain at rest, and why his friends decision not to run caused him to fall behind?


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  • Registered Users Posts: 3,457 ✭✭✭Morbert


    roosh wrote: »
    Are the observers free to agree on the labeling i.e. can an observer label himself as being in motion?

    Sure. When doing calculations, scientists often change reference frames, as calculations can be easier to perform with certain co-ordinates, as illustrated by the xkcd villain talking about a rotating reference frame.

    centrifugal_force.png

    The lesson is that the physics is always the same.
    The part that is causing confusion for me is, I think, to do with the use of the term "acceleration" because I associate that with motion.

    If both observers start off on the zero-gravity station, will they consider themselves as freely falling in a gravitational filed? Why is it that the twin, who detects the gravitational field, doesn't conclude that he has accelerated and is therefore in motion?

    They will consider themselves to be stationary. To make it easier to conceptualise, place the space station a million light-years from any planet or star. The "travelling" twin doesn't conclude that he has accelerated because there is no physical distinction between him accelerating and him stationary in a gravitational field.

    When you feel a force, like pushing against a table, this is because the electron field and photon field are coupling, creating disturbances in the fields that cause electrons in your hands to move away from electrons in the table (there are other quantum correlations that are also responsible but let's just focus on force). These fields pervade space and time. But gravity is different. The gravitational field does not pervade space and time, but is instead the geometry of space and time itself.
    Does that mean that his clock will tick slower? Again, my interpretation of the term "acceleration" would lead me to say that this is so bcos the force of acceleration/gravity would cause the other's clock to tick faster.

    No, it means the spacestation twin's clock will tick faster than the "travelling" twin's clock. According to the travelling twin, the spacestation twin is higher up in the gravitational field, so his clock will tick faster. Remember that gravitational time dilation is not related to the force of gravity the clock experiences. (This misunderstanding was presumably the motivation behind your suggestion that gravitational time dilation could be due to a mechanical cause).

    This is another source of confusion for me, as I was always under the impression that gravity was a force; a "fundamental force" at that.

    Hence the problem with the standard model. Physicists have been unable to relate gravity to the other fundamental forces because gravity is not the same as the other forces. They are effectively trying to quantise spacetime.
    I don't fully understand what is meant by "an expression of the geometry and chronometry of events" either; does that mean it is just a matter of labeling also?

    Events have a geometric structure that is physical (i.e. Independent of what labelling you use). If a dog barks and causes you to jump, the dog's bark will cause you to jump no matter how you label events. The curvature of this structure is coupled to the distribution of energy in the universe, so gravity is physical. But the observed motion we associate with this physical structure is dependent on labelling.
    Which of SR or GR applies to the following:
    - Where the stay at home twin is on earth, and the other goes into space?
    - Where both stay on earth?
    - Where both start at the zero-gravity station?

    I'm thinking SR for the latter 2 (but not presuming), and I'm not sure at all for the first one.

    You can apply either to any of those situations. Special relativity is just a special case of general relativity, the more complete theory of gravitation.
    The problem, as I see it is, again, that both observers cannot label themselves as being at rest, because at least one of them isn't. This issue isn't resolved by the use of two separate and arbitrary co-ordinate systems where both observers label themselves as being at rest.

    Both observers cannot label themselves as at rest with respect to the other. Under one co-ordinate system, one twin started moving while the other is always at rest. Under the other co-ordinate system, the situation is reversed. Both get completely consistent physics, and labelling systems can be "transformed" from one to the other by the Lorentz transformations.
    Again, if they contact each other and ask why the other moved, they would conclude that one of them must be mistaken - how would they determine which one was? Again, this isn't resolved by each determining that the other is mistaken, bcos they can subsequently contact each other and have the same dispute.

    I don't think that comes down to Gallilean or Lorentz transformations.

    --

    But going back the to the issue stated above. If they are at rest relative to each other and then there is relative motion between them, both cannot label themselves as being at rest. If they communicate with each other, they will come to the conclusion that one of them must be wrong.

    Why would they conclude that one must be mistaken. In fact, relativity says they cannot make such a claim. They must acknowledge their labels as no more or less arbitrary than the other, and in no way a distinguished representation of reality. I can't say yours is mistaken if I can't say mine is absolute.
    That's true, but from the perspective of the universe you would have the exploded sun, with the light traveling towards the earth.

    All frames of reference would have this. That is what is "real". The respective velocities, on the other hand, would be due to labelling (It goes without saying at this stage that all labelling systems will label the light as travelling at speed c).
    From the perspective of the universe, would there past, present and future?

    Each event would have a unique past and future carved out by a hypercone. The present would not be extensive, but the universe (and, to be fair, people) would understand that events outside the hypercone of a given event can be arbitrarily labelled as simultaneous with that event, since there is no causal connection between events.
    Is a frame of reference not defined by the objects in it?

    No. It's a completely abstract, mathematical construct. I can define a reference frame in empty space if I want to.
    Would this not mean that his model does not accurately reflect his empirical experience?

    In what way? There may be crossed wires here.
    If someone labels the earth as rotating, and as orbiting the sun, does this mean that they cannot consistently label themselves as being "at rest" when on the earth?

    Yes. If they want to label themselves as at rest, then the sun must be labelled as moving around the earth. They are free to switch between whichever is more convenient because they know labels are just labels.
    I was just thinking in terms of how each observer would observe themselves as being at the centre of an expanding sphere of light; just for visualisation purposes, if we imagine that one of "sliver" of that sphere was the laser pulse, it would mean that in one frame of reference it would hit the observer on the platform, but in the other it would miss him. But that isn't the case, so I'm wondering how it is resolved; or how I've misrepresented the phenomenon.

    They will disagree about the angle of the sliver. But as you can guess, if you have a sliver at all angles, then no matter how the angles are designated, you will still get a sphere. Rotating a sphere does not change the shape of the sphere.

    You have actually stumbled close to Terrell rotation.
    But how? Would he not have to conclude that both he and his friend were actually in motion before, and that he had erroneously labelled himself as "at rest"? Wouldn't he have to come up with an explanation for why his running caused him to remain at rest, and why his friends decision not to run caused him to fall behind?

    If you choose not to run when the ground is moving beneath you, you fall behind. And to guess your next question: He did not cause the ground to move by running. He knows the ground is moving because he has arbitrarily labelled it as moving. Just has his friend has arbitrarily labelled the ground as always stationary.


  • Registered Users Posts: 2,552 ✭✭✭roosh


    Morbert wrote: »
    Sure. When doing calculations, scientists often change reference frames, as calculations can be easier to perform with certain co-ordinates, as illustrated by the xkcd villain talking about a rotating reference frame.


    The lesson is that the physics is always the same.
    That xkcd comic strip might actually be helpful in demonstrating where I am having difficulty. I understand that we are free label things as we please, and that we can perform calculations on that basis. I understand that we can label things as being in motion and ourselves as at rest; but, in the case of the cartoon, when Bond is at rest relative the scientist i.e. not spinning in the scientists device he won't "die" but something will happen which will cause him to "die" - or at least have a different experience to that which he had when at rest e.g. he will experience increased "G-force".

    Again, I know he can calculate it from the perspective of him being at rest, but I don't understand what he will deem to be the cause of that change in experience; for example if he says he is experiencing a gravitational force, what will he say occurred to cause that change; will it be that everything started spinning in relation to him?

    Morbert wrote: »
    They will consider themselves to be stationary. To make it easier to conceptualise, place the space station a million light-years from any planet or star. The "travelling" twin doesn't conclude that he has accelerated because there is no physical distinction between him accelerating and him stationary in a gravitational field.

    When you feel a force, like pushing against a table, this is because the electron field and photon field are coupling, creating disturbances in the fields that cause electrons in your hands to move away from electrons in the table (there are other quantum correlations that are also responsible but let's just focus on force). These fields pervade space and time. But gravity is different. The gravitational field does not pervade space and time, but is instead the geometry of space and time itself.
    Again, I have similar trouble here. If both twins start off in the zero-gravity station, they will consider themselves as being in free-fall won't they? Will they not reason that something will have to happen for either of them to experience a gravitational force i.e. if they remain at rest they will continue to experience zero-gravity, but they will experience an effect similar, or equivalent, to a gravitational force if they start moving?

    If the "traveling twin" experiences this gravitational force, while he maintains that his twin remains in free-fall, why doesn't he conclude that he is the one who is in motion?

    Again, I know that he can calculate it from the perspective of him being at rest, but his experience of being at rest in the station with his twin is different to his being at rest when moving relative to his twin.
    Morbert wrote: »
    No, it means the spacestation twin's clock will tick faster than the "travelling" twin's clock. According to the travelling twin, the spacestation twin is higher up in the gravitational field, so his clock will tick faster. Remember that gravitational time dilation is not related to the force of gravity the clock experiences. (This misunderstanding was presumably the motivation behind your suggestion that gravitational time dilation could be due to a mechanical cause).
    Has that scenario been tested; where both clocks start off at zero-gravity and one undergoes acceleration?

    Morbert wrote: »
    Events have a geometric structure that is physical (i.e. Independent of what labelling you use). If a dog barks and causes you to jump, the dog's bark will cause you to jump no matter how you label events. The curvature of this structure is coupled to the distribution of energy in the universe, so gravity is physical. But the observed motion we associate with this physical structure is dependent on labelling.
    When you say that gravity is an expression of that geometry, what do you mean?

    Morbert wrote: »
    You can apply either to any of those situations. Special relativity is just a special case of general relativity, the more complete theory of gravitation.
    OK, sorry, so the paradox is resolved under SR because of asymmetry, but asymmetry doesn't apply in GR - have I that much right? Why is there no asymmetry in GR, does one twin not undergo acceleration and therefore change reference frames under GR, leading to asymmetry as well?

    Morbert wrote: »
    Both observers cannot label themselves as at rest with respect to the other. Under one co-ordinate system, one twin started moving while the other is always at rest. Under the other co-ordinate system, the situation is reversed. Both get completely consistent physics, and labelling systems can be "transformed" from one to the other by the Lorentz transformations.

    Why would they conclude that one must be mistaken. In fact, relativity says they cannot make such a claim. They must acknowledge their labels as no more or less arbitrary than the other, and in no way a distinguished representation of reality. I can't say yours is mistaken if I can't say mine is absolute.
    OK, I understand the part about the labeling conventions, but the issue I'm having might be more to do with what the labels "in motion" and "at rest" refer to. As said before, if both observers are at rest relative to each other and then there is relative motion, both of them cannot be "at rest", because at least one of them has to be moving. How do they determine which one moved? They can't both maintain that they remained exactly where they were and that the other moved, because if that was the case, then the distance between them wouldn't have increased.

    Morbert wrote: »
    All frames of reference would have this. That is what is "real". The respective velocities, on the other hand, would be due to labelling (It goes without saying at this stage that all labelling systems will label the light as travelling at speed c).
    That is what I was trying to get at with the idea of a universal present i.e. "what is 'real' in all reference frames"; no doubt you have a different interpretation of this.

    Morbert wrote: »
    Each event would have a unique past and future carved out by a hypercone. The present would not be extensive, but the universe (and, to be fair, people) would understand that events outside the hypercone of a given event can be arbitrarily labelled as simultaneous with that event, since there is no causal connection between events.
    Do all these hypercones combine to form the block universe?


    Morbert wrote: »
    No. It's a completely abstract, mathematical construct. I can define a reference frame in empty space if I want to.

    In what way [is it not an accurate model of the physical world]? There may be crossed wires here.
    In the physical world we can't remain at rest relative to an imaginary reference frame, can we, does it not have to be in relation to other objects?

    Morbert wrote: »
    Yes. If they want to label themselves as at rest, then the sun must be labelled as moving around the earth. They are free to switch between whichever is more convenient because they know labels are just labels.
    This again is something I have trouble with. I understand the idea of being able to switch labels arbitrarily and being able to calculate taking either position, but as has been established, the act of being in motion is different from being at rest. If we arbitrarily switch labels we are saying that one thing is moving at one time and stationary at another.

    Morbert wrote: »
    They will disagree about the angle of the sliver. But as you can guess, if you have a sliver at all angles, then no matter how the angles are designated, you will still get a sphere. Rotating a sphere does not change the shape of the sphere.

    You have actually stumbled close to Terrell rotation.
    Sorry, I probably confused matters introducing the sphere, instead of clarifying them. I didn't mean that the sliver would be at all angles, because that isn't necessarily how the laser would work is it. As you mentioned, the laser would miss the "stationary" observer in both reference frames, but if the laser were fired at the same instance as another light source (which forms a sphere), and from the same position, then the laser would form the radius for one sphere but not the other.

    Morbert wrote: »
    If you choose not to run when the ground is moving beneath you, you fall behind. And to guess your next question: He did not cause the ground to move by running. He knows the ground is moving because he has arbitrarily labelled it as moving. Just has his friend has arbitrarily labelled the ground as always stationary.
    :)

    This is true, but if you start of by labeling the ground as being at rest, and you are standing, at rest, on the ground, then something must occur for there to be relative motion between you and the ground - or something must cause there to be relative motion, otherwise you would remain at rest relative to the ground.

    If you then start running, but maintain that you are remaining at rest then there must be a reason why running can cause you to stay at rest; if the reason you give is that the ground has started moving, then there must be a reason why the ground has gone from being at rest, to being in motion, which leads you to label it as being in motion.


  • Registered Users Posts: 3,457 ✭✭✭Morbert


    roosh wrote: »
    That xkcd comic strip might actually be helpful in demonstrating where I am having difficulty. I understand that we are free label things as we please, and that we can perform calculations on that basis. I understand that we can label things as being in motion and ourselves as at rest; but, in the case of the cartoon, when Bond is at rest relative the scientist i.e. not spinning in the scientists device he won't "die" but something will happen which will cause him to "die" - or at least have a different experience to that which he had when at rest e.g. he will experience increased "G-force".

    Again, I know he can calculate it from the perspective of him being at rest, but I don't understand what he will deem to be the cause of that change in experience; for example if he says he is experiencing a gravitational force, what will he say occurred to cause that change; will it be that everything started spinning in relation to him?

    --

    Again, I have similar trouble here. If both twins start off in the zero-gravity station, they will consider themselves as being in free-fall won't they? Will they not reason that something will have to happen for either of them to experience a gravitational force i.e. if they remain at rest they will continue to experience zero-gravity, but they will experience an effect similar, or equivalent, to a gravitational force if they start moving?

    If the "traveling twin" experiences this gravitational force, while he maintains that his twin remains in free-fall, why doesn't he conclude that he is the one who is in motion?

    Again, I know that he can calculate it from the perspective of him being at rest, but his experience of being at rest in the station with his twin is different to his being at rest when moving relative to his twin.

    To quote Einstein himself:

    "Is it not possible for me to regard the earth as free from rotation, if I conceive of the centrifugal force, which acts on all bodies at rest relatively to the earth, as being a "real" gravitational field of gravitation, or part of such a field? If this idea can be carried out, then we shall have proved in very truth the identity of gravitation and inertia. For the same property which is regarded as inertia from the point of view of a system not taking part of the rotation can be interpreted as gravitation when considered with respect to a system that shares this rotation. According to Newton, this interpretation is impossible, because in Newton's theory there is no "real" field of the "Coriolis-field" type. But perhaps Newton's law of field could be replaced by another that fits in with the field which holds with respect to a "rotating" system of co-ordiantes? My conviction of the identity of inertial and gravitational mass aroused within me the feeling of absolute confidence in the correctness of this interpretation."

    So the short answer is the gravitational field.
    Has that scenario been tested; where both clocks start off at zero-gravity and one undergoes acceleration?

    Not in the raw "twin paradox" form that we have been talking about. But the relativistic equations which resolve the twin paradox have been tested and incorporated into GPS clocks.
    When you say that gravity is an expression of that geometry, what do you mean?

    In physics, events are related to one another by considering a manifold and a metric. This structure can exhibit properties like weyl and ricci curvature, which are experienced as gravitational forces. Since the gravitational field is characterised by this manifold and metric, any inertial force felt by an accelerating object is equivalent to a gravitational field in the reference frame of the object.

    http://en.wikipedia.org/wiki/Gravitational_field
    "In general relativity the gravitational field is determined as the solution of Einstein's field equations. These equations are dependent on the distribution of matter and energy in a region of space, unlike Newtonian gravity, which is dependent only on the distribution of matter. The fields themselves in general relativity represent the curvature of spacetime. General relativity states that being in a region of curved space is equivalent to accelerating up the gradient of the field. By Newton's second law, this will cause an object to experience a fictitious force if it is held still with respect to the field. This is why a person will feel himself pulled down by the force of gravity while standing still on the Earth's surface. In general the gravitational fields predicted by general relativity differ in their effects only slightly from those predicted by classical mechanics, but there are a number of easily verifiable differences, one of the most well known being the bending of light in such fields."

    OK, sorry, so the paradox is resolved under SR because of asymmetry, but asymmetry doesn't apply in GR - have I that much right? Why is there no asymmetry in GR, does one twin not undergo acceleration and therefore change reference frames under GR, leading to asymmetry as well?

    In SR, one twin is singled out as undergoing acceleration. In GR, either twin can be arbitrarily labelled as undergoing acceleration.
    OK, I understand the part about the labeling conventions, but the issue I'm having might be more to do with what the labels "in motion" and "at rest" refer to. As said before, if both observers are at rest relative to each other and then there is relative motion, both of them cannot be "at rest", because at least one of them has to be moving. How do they determine which one moved? They can't both maintain that they remained exactly where they were and that the other moved, because if that was the case, then the distance between them wouldn't have increased.

    All that is "real" is their velocity with respect to one another. Both agree on this. How they label this change in respective velocity is arbitrary.
    That is what I was trying to get at with the idea of a universal present i.e. "what is 'real' in all reference frames"; no doubt you have a different interpretation of this.

    That is what physicists look for:Rules and principles which hold in all frames of reference. These are physical. These represent "real" behaviour.

    http://en.wikipedia.org/wiki/General_covariance

    "The essential idea is that coordinates do not exist a priori in nature, but are only artifices used in describing nature, and hence should play no role in the formulation of fundamental physical laws."
    Do all these hypercones combine to form the block universe?

    Yes. They are the structure of the block universe.
    In the physical world we can't remain at rest relative to an imaginary reference frame, can we, does it not have to be in relation to other objects?

    Sure we can. It wouldn't always be useful, but there's nothing stopping us.
    This again is something I have trouble with. I understand the idea of being able to switch labels arbitrarily and being able to calculate taking either position, but as has been established, the act of being in motion is different from being at rest. If we arbitrarily switch labels we are saying that one thing is moving at one time and stationary at another.

    Yes.
    Sorry, I probably confused matters introducing the sphere, instead of clarifying them. I didn't mean that the sliver would be at all angles, because that isn't necessarily how the laser would work is it. As you mentioned, the laser would miss the "stationary" observer in both reference frames, but if the laser were fired at the same instance as another light source (which forms a sphere), and from the same position, then the laser would form the radius for one sphere but not the other.

    It would form the radius from both perspectives. How? Length contraction and time dilation! Throw the numbers into the lorentz equations and you'll see.
    :)

    This is true, but if you start of by labeling the ground as being at rest, and you are standing, at rest, on the ground, then something must occur for there to be relative motion between you and the ground - or something must cause there to be relative motion, otherwise you would remain at rest relative to the ground.

    If you then start running, but maintain that you are remaining at rest then there must be a reason why running can cause you to stay at rest; if the reason you give is that the ground has started moving, then there must be a reason why the ground has gone from being at rest, to being in motion, which leads you to label it as being in motion.

    Sure. The relative motion is caused by your foot kicking off the ground. If you label yourself as at rest, then the ground has started moving because of a gravitational field. As Einstein said, you cannot do this under a Newtonian theory of gravity, but you can if you treat gravitational field as spacetime.


  • Registered Users Posts: 2,552 ✭✭✭roosh


    Morbert wrote: »
    To quote Einstein himself:

    "Is it not possible for me to regard the earth as free from rotation, if I conceive of the centrifugal force, which acts on all bodies at rest relatively to the earth, as being a "real" gravitational field of gravitation, or part of such a field? If this idea can be carried out, then we shall have proved in very truth the identity of gravitation and inertia. For the same property which is regarded as inertia from the point of view of a system not taking part of the rotation can be interpreted as gravitation when considered with respect to a system that shares this rotation. According to Newton, this interpretation is impossible, because in Newton's theory there is no "real" field of the "Coriolis-field" type. But perhaps Newton's law of field could be replaced by another that fits in with the field which holds with respect to a "rotating" system of co-ordiantes? My conviction of the identity of inertial and gravitational mass aroused within me the feeling of absolute confidence in the correctness of this interpretation."

    So the short answer is the gravitational field.
    OK, I'm not sure if I'm articulating very well, what it is that I'm asking. Sticking with the example of the zero-gravity station:

    Both twins start off in the zero-gravity station - both are free falling in a gravitational filed (is that correct?).

    Both label themselves as being at rest. If they remain at rest then they will continue to be in free-fall in the gravitational field.

    One twins experience of the gravitational field changes. What does he attribute this change to i.e. what is the reason for the change in his experience of the gravitational field; or what happens to give rise to this different experience of the gravitational field?

    Morbert wrote: »
    Not in the raw "twin paradox" form that we have been talking about. But the relativistic equations which resolve the twin paradox have been tested and incorporated into GPS clocks.
    Is the example of GPS clocks not different; does it not involve a clock in space and a clock on earth, as opposed to two clocks both either in space or on earth?

    Morbert wrote: »
    In physics, events are related to one another by considering a manifold and a metric. This structure can exhibit properties like weyl and ricci curvature, which are experienced as gravitational forces. Since the gravitational field is characterised by this manifold and metric, any inertial force felt by an accelerating object is equivalent to a gravitational field in the reference frame of the object.

    http://en.wikipedia.org/wiki/Gravitational_field
    "In general relativity the gravitational field is determined as the solution of Einstein's field equations. These equations are dependent on the distribution of matter and energy in a region of space, unlike Newtonian gravity, which is dependent only on the distribution of matter. The fields themselves in general relativity represent the curvature of spacetime. General relativity states that being in a region of curved space is equivalent to accelerating up the gradient of the field. By Newton's second law, this will cause an object to experience a fictitious force if it is held still with respect to the field. This is why a person will feel himself pulled down by the force of gravity while standing still on the Earth's surface. In general the gravitational fields predicted by general relativity differ in their effects only slightly from those predicted by classical mechanics, but there are a number of easily verifiable differences, one of the most well known being the bending of light in such fields."
    Is an accelerating object necessarily in motion?


    Morbert wrote: »
    In SR, one twin is singled out as undergoing acceleration. In GR, either twin can be arbitrarily labelled as undergoing acceleration.
    Sorry about this now, this could be my association of the term acceleration with motion, if one twin is singled out as accelerating, how does he label himself as being at rest; and why can't either twin be labelled as accelerating under SR?

    Also, why doesn't the paradox arise under GR?

    Morbert wrote: »
    That is what physicists look for:Rules and principles which hold in all frames of reference. These are physical. These represent "real" behaviour.

    http://en.wikipedia.org/wiki/General_covariance

    "The essential idea is that coordinates do not exist a priori in nature, but are only artifices used in describing nature, and hence should play no role in the formulation of fundamental physical laws."
    OK, we were talking about slightly different things; I was referring more to occurences - I use the term instead of events, to avoid confusing the issue - like the sun exploding which must be true in all reference frames.

    Morbert wrote: »
    Yes. They are the structure of the block universe.
    Actually, you may be able to explain this also, because it is something I can't immediately imagine. In the portrayal of the block universe, with the reference frames, or the "slices" of "nows", the past is said to exist and also the future; or the reference frames do - is that roughly correct? Did you characterise it as there being a reference frame where I am celebrating my 8th birthday existing in the past?

    I'm not sure what terminology to use, but to put it crudely, if we say that this reference frame we are in is tending towards the future, are all the other reference frames not tending towards the future also?

    I'm just wondering how "my 8th birthday" didn't "keep up" with my reference frame i.e. it should be sharing the "now" with me.





    I've grouped the following couple of quotes, because I think the point is related:
    Morbert wrote: »
    All that is "real" is their velocity with respect to one another. Both agree on this. How they label this change in respective velocity is arbitrary.
    What I have difficulty with, is what the labels refer to, that they refer to mutually exclusive actions; which, for me, takes away the arbitrariness with which they can be applied.
    roosh wrote:
    In the physical world we can't remain at rest relative to an imaginary reference frame, can we, does it not have to be in relation to other objects?
    Morbert wrote: »
    Sure we can. It wouldn't always be useful, but there's nothing stopping us.
    In the physical world we can't be at rest relative to an imaginary reference frame, because it isn't physical; we will always be at rest, or in motion, relative to physical objects.

    Morbert wrote: »
    Yes.
    Given the fundamental difference between moving and not moving, it seems like some justification is required for the labeling.

    Morbert wrote: »
    It would form the radius from both perspectives. How? Length contraction and time dilation! Throw the numbers into the lorentz equations and you'll see.
    Sorry, I was trying to explain what it was I was visualising, but didn't do it very well.

    If we imagine an LED on the barrel of the laser gun, which flashes the moment the shot is fired; in the reference frame of the observer on the trian he will remain at the centre of the sphere and the laser pulse will form the radius of the sphere directly in front of him; but, for the observer on the platform the laser pulse will not form the radius directly in front of him, but to the side of him.

    But, if we trace the imaginary line of the photon* which forms the radius of the sphere that is directly in front of each observer, in the reference frame of the observer on the train, the line the photon* takes will trace the line of the laser pulse; but in the other reference frame it won't.

    I'm just wondering why the light behaves differently?

    *I'm not sure if the photon is real or imaginary, bcos I'm not sure what the physical make up of the sphere is

    Morbert wrote: »
    Sure. The relative motion is caused by your foot kicking off the ground. If you label yourself as at rest, then the ground has started moving because of a gravitational field. As Einstein said, you cannot do this under a Newtonian theory of gravity, but you can if you treat gravitational field as spacetime.
    If I am at rest relative to the ground, and then start running, and the ground starts moving because of a gravitational field, what caused this change in the gravitational field i.e. why wasn't it in effect before I started running, and how does it come into effect at the precise moment I started running?


  • Registered Users Posts: 3,457 ✭✭✭Morbert


    roosh wrote: »
    OK, I'm not sure if I'm articulating very well, what it is that I'm asking. Sticking with the example of the zero-gravity station:

    Both twins start off in the zero-gravity station - both are free falling in a gravitational filed (is that correct?).

    Both label themselves as being at rest. If they remain at rest then they will continue to be in free-fall in the gravitational field.

    One twins experience of the gravitational field changes. What does he attribute this change to i.e. what is the reason for the change in his experience of the gravitational field; or what happens to give rise to this different experience of the gravitational field?

    ---

    If I am at rest relative to the ground, and then start running, and the ground starts moving because of a gravitational field, what caused this change in the gravitational field i.e. why wasn't it in effect before I started running, and how does it come into effect at the precise moment I started running?

    Remember that, unlike in Newton's picture, gravity is not a force in any traditional sense. So starting to run does not cause anything but a change in relative velocity. It's just that, if you perform the relevant calculations using a co-ordinate system centred on you, the earth, and all the galaxies, will be labelled as falling when you begin to run. This is not a grandiose violation of causality because gravity is not an effect to be caused. It is just an expression of geometry under different labelling systems.
    Is the example of GPS clocks not different; does it not involve a clock in space and a clock on earth, as opposed to two clocks both either in space or on earth?

    It's all the same theory. The equations which govern the conclusions of the twin paradox also govern GPS satellites. The gravitational time dilation equations that govern GPS satellites is the same that would govern the gravitational time dilation in the twin paradox.
    Is an accelerating object necessarily in motion?

    Yes. If an object is labelled "accelerating" then it must be labelled as "in motion".
    Sorry about this now, this could be my association of the term acceleration with motion, if one twin is singled out as accelerating, how does he label himself as being at rest; and why can't either twin be labelled as accelerating under SR?

    Also, why doesn't the paradox arise under GR?

    The paradox doesn't arise in either case. It's not a true paradox. It just seems so at first glance.

    One twin is singled out under SR because SR says the laws of physics are the same for all inertial reference frames. One twin is not in an inertial reference frame, and so can be singled out.

    GR (or SR + equivalence principle), on the other hand, says the laws of physics are the same for all reference frames. Gravity imposes a symmetry for all viewpoints, so no twin can claim their co-ordinate system is more valid, distinguished, or more of a representation of reality than the other's.
    Actually, you may be able to explain this also, because it is something I can't immediately imagine. In the portrayal of the block universe, with the reference frames, or the "slices" of "nows", the past is said to exist and also the future; or the reference frames do - is that roughly correct? Did you characterise it as there being a reference frame where I am celebrating my 8th birthday existing in the past?

    The reference frames are arbitrary. Just as you can slice a loaf of bread at arbitrary angles.

    In the old, classical picture, the block universe had a natural grain or structure that foliated into unique slices or "moments". This would allow you to recover presentism, the idea that the universe is a single, changing, 3D hypersurface in which the only thing that exists is the present.

    But there is no such grain in relativistic spacetime. The is no unique set of "nows". Instead there is a light-cone structure.
    I'm not sure what terminology to use, but to put it crudely, if we say that this reference frame we are in is tending towards the future, are all the other reference frames not tending towards the future also?

    Reference frames have time co-ordinates as well as space co-ordinates, so you would not say a reference frame is moving towards the future, as a "labelling convention" does not move to the future. You would instead say that the world line of a physical object is time-like or light-like. Time-like curves can be characterised by moving from the pas to the future, but they cannot be generalised to a physically distinguished picture of the entire universe moving from the past to the future.

    http://en.wikipedia.org/wiki/World_line
    I'm just wondering how "my 8th birthday" didn't "keep up" with my reference frame i.e. it should be sharing the "now" with me.

    Remember what I said about the light-cone structure though. Every event has a light-cone structure determining the past and future of that specific event. Your 8th birthday is in the past light-cone of you reading this, so all reference frames will agree that your 8th birthday happened before before.
    I've grouped the following couple of quotes, because I think the point is related:

    What I have difficulty with, is what the labels refer to, that they refer to mutually exclusive actions; which, for me, takes away the arbitrariness with which they can be applied.
    In the physical world we can't be at rest relative to an imaginary reference frame, because it isn't physical; we will always be at rest, or in motion, relative to physical objects.

    This is a non-sequitur. The unphysical nature of reference frames in no way prohibits relating velocities to reference frames. You did it earlier when you discussed motion with respect to the centre of a light sphere, an entirely unphysical co-ordinate.
    Given the fundamental difference between moving and not moving, it seems like some justification is required for the labeling.

    How do you define moving without reference to something else?
    Sorry, I was trying to explain what it was I was visualising, but didn't do it very well.

    If we imagine an LED on the barrel of the laser gun, which flashes the moment the shot is fired; in the reference frame of the observer on the trian he will remain at the centre of the sphere and the laser pulse will form the radius of the sphere directly in front of him; but, for the observer on the platform the laser pulse will not form the radius directly in front of him, but to the side of him.

    But, if we trace the imaginary line of the photon* which forms the radius of the sphere that is directly in front of each observer, in the reference frame of the observer on the train, the line the photon* takes will trace the line of the laser pulse; but in the other reference frame it won't.

    I'm just wondering why the light behaves differently?

    *I'm not sure if the photon is real or imaginary, bcos I'm not sure what the physical make up of the sphere is

    The line of the photon from the sphere will trace the same line as the laser photon for both observers. They will simply label the angle of each of the sphere (and laser) photons differently, but a sphere rotated by an angle is still a sphere. An analogy would be a tire with a single spoke. The spoke is still attached to the same bit of steel even if you rotate the wheel.


  • Registered Users Posts: 2,552 ✭✭✭roosh


    Morbert wrote: »
    Remember that, unlike in Newton's picture, gravity is not a force in any traditional sense. So starting to run does not cause anything but a change in relative velocity. It's just that, if you perform the relevant calculations using a co-ordinate system centred on you, the earth, and all the galaxies, will be labelled as falling when you begin to run. This is not a grandiose violation of causality because gravity is not an effect to be caused. It is just an expression of geometry under different labelling systems.
    If we stick with the zero-gravity station, it might be easier to explain what I'm trying to get at, and might make it easier to highlight the error in reasoning.

    If both observers are on the zero-gravity station they will experience certain effects: weighltessness; objects floating around the place bcos of the aforementioned; and whatever other effects one experiences in a zero-gravity station. These effects must have a cause; I'm wondering what that cause is.

    My understanding is, that one twin will then experience certain effects which will differ from the "stay-at-home" twin. The cause you mentioned is a gravitational field, but I'm wondering what causes the expression of geometry to change such that it results in the "traveling" twin experiencing the different effects?

    Morbert wrote: »
    It's all the same theory. The equations which govern the conclusions of the twin paradox also govern GPS satellites. The gravitational time dilation equations that govern GPS satellites is the same that would govern the gravitational time dilation in the twin paradox.
    I understand that, but the twin paradox appears to represent a different scenario than GPS sattellites; that they are the same equations doesn't necessarily mean that predicted effect will be observed.


    Morbert wrote: »
    Yes. If an object is labelled "accelerating" then it must be labelled as "in motion".
    If one twin is singled out as undergoing acceleration under SR, then how can he label himself as being at rest, if he is, by necessity "in motion"?


    Morbert wrote: »
    The paradox doesn't arise in either case. It's not a true paradox. It just seems so at first glance.

    One twin is singled out under SR because SR says the laws of physics are the same for all inertial reference frames. One twin is not in an inertial reference frame, and so can be singled out.

    GR (or SR + equivalence principle), on the other hand, says the laws of physics are the same for all reference frames. Gravity imposes a symmetry for all viewpoints, so no twin can claim their co-ordinate system is more valid, distinguished, or more of a representation of reality than the others.
    OK, so the parts I don't understand are:
    - Under SR, how can one twin label himself as "at rest" if he is, by necessity, "in motion".

    - Why doesn't the paradox arise under GR, if neither is singled out as being in motion? My reasoning is that the paradox should arise, unless there is a mitigating factor; unless there is some asymmetry between the twins - by asymmetry, I simply mean a difference, other than merely visual, between their experiences.

    Morbert wrote: »
    The reference frames are arbitrary. Just as you can slice a loaf of bread at arbitrary angles.

    In the old, classical picture, the block universe had a natural grain or structure that foliated into unique slices or "moments". This would allow you to recover presentism, the idea that the universe is a single, changing, 3D hypersurface in which the only thing that exists is the present.

    But there is no such grain in relativistic spacetime. The is no unique set of "nows". Instead there is a light-cone structure.


    Reference frames have time co-ordinates as well as space co-ordinates, so you would not say a reference frame is moving towards the future, as a "labelling convention" does not move to the future. You would instead say that the world line of a physical object is time-like or light-like. Time-like curves can be characterised by moving from the pas to the future, but they cannot be generalised to a physically distinguished picture of the entire universe moving from the past to the future.

    http://en.wikipedia.org/wiki/World_line




    Remember what I said about the light-cone structure though. Every event has a light-cone structure determining the past and future of that specific event. Your 8th birthday is in the past light-cone of you reading this, so all reference frames will agree that your 8th birthday happened before before.
    What I am trying to do, is develop an understanding of what it means for the past to exist. I would agree that there is no unique "set of 'nows'", I would say that there is just the present moment - not present moment in time. I would agree that my 8th birthday happened before this moment, but I wouldn't say that my 8th birthday still exists; I have a memory of it, but I would say that it exists in my memory only.

    By definition an imaginary reference frame needs an observer to imagine it, if "I" was an observer at my 8th birthday, then that observer "moved through time" to this present; if there is a reference frame where "my 8th birthday" represents the present, then do "I" exist in both frames of reference i.e. in my past and in my present?



    Morbert wrote: »
    This is a non-sequitur. The unphysical nature of reference frames in no way prohibits relating velocities to reference frames. You did it earlier when you discussed motion with respect to the centre of a light sphere, an entirely unphysical co-ordinate.
    And as you pointed out [in not so many words], it wasn't a correct model of reality, because the centre doesn't actually exist. What we can do however is speak about the relation of the sphere to the physical matter, with respect to which it moves; there will always be matter located at the co-ordinate we designate as the centre of the sphere.

    In the physical world, you cannot move or be at rest relative to an imaginary reference frame, because it is not physical - this doesn't stop us using it as a means of communication, but it does affect our application of definitions, given that we cannot move relative to it.

    Morbert wrote: »
    How do you define moving without reference to something else?
    This is probably the difference between absolute motion and relative motion. Absolute motion is simply the question of whether or not there is movement; if there is relative motion then, by definition there is movement, and so there is absolute motion. Determining what is moving, however, is a different matter.

    Morbert wrote: »
    The line of the photon from the sphere will trace the same line as the laser photon for both observers. They will simply label the angle of each of the sphere (and laser) photons differently, but a sphere rotated by an angle is still a sphere. An analogy would be a tire with a single spoke. The spoke is still attached to the same bit of steel even if you rotate the wheel.
    Does length contraction cause the sphere to rotate?


  • Registered Users Posts: 3,457 ✭✭✭Morbert


    roosh wrote: »
    If we stick with the zero-gravity station, it might be easier to explain what I'm trying to get at, and might make it easier to highlight the error in reasoning.

    If both observers are on the zero-gravity station they will experience certain effects: weighltessness; objects floating around the place bcos of the aforementioned; and whatever other effects one experiences in a zero-gravity station. These effects must have a cause; I'm wondering what that cause is.

    My understanding is, that one twin will then experience certain effects which will differ from the "stay-at-home" twin. The cause you mentioned is a gravitational field, but I'm wondering what causes the expression of geometry to change such that it results in the "traveling" twin experiencing the different effects?

    It's literally just an artefact of to co-ordinate labels. Both twins will agree that one twin experiences an inertial force. That much is physical. But when we look at how this is labelled, one will attribute it to acceleration, the other will attribute it to remaining stationary while experiencing a gravitational force. You seem to be bothered by the idea that a gravitational force coincidently "switches on" when he applies his rockets (or breaks), but gravity isn't a force. It's simply the case that, when you work out the physics under one co-ordinate system, the twin remains stationary while everything else "falls" through spacetime.
    I understand that, but the twin paradox appears to represent a different scenario than GPS sattellites; that they are the same equations doesn't necessarily mean that predicted effect will be observed.

    While technically true, it is on par with saying just because my pen falls when I drop it off a building doesn't mean I will.

    Also, it seems the clock experiments did look at both gravitational time dilation induced by the earth and due to the relative paths of the clocks. They were in very good agreement with relativity.

    http://en.wikipedia.org/wiki/Time_dilation#Experimental_confirmation
    If one twin is singled out as undergoing acceleration under SR, then how can he label himself as being at rest, if he is, by necessity "in motion"?

    OK, so the parts I don't understand are:
    - Under SR, how can one twin label himself as "at rest" if he is, by necessity, "in motion".

    Under SR, he can't.
    - Why doesn't the paradox arise under GR, if neither is singled out as being in motion? My reasoning is that the paradox should arise, unless there is a mitigating factor; unless there is some asymmetry between the twins - by asymmetry, I simply mean a difference, other than merely visual, between their experiences.

    Well both twins agree there is a difference, both twins agree on the relative velocity between them. But GR let's us freely label either twin (but not both) as at rest.
    What I am trying to do, is develop an understanding of what it means for the past to exist. I would agree that there is no unique "set of 'nows'", I would say that there is just the present moment - not present moment in time. I would agree that my 8th birthday happened before this moment, but I wouldn't say that my 8th birthday still exists; I have a memory of it, but I would say that it exists in my memory only.

    By definition an imaginary reference frame needs an observer to imagine it, if "I" was an observer at my 8th birthday, then that observer "moved through time" to this present; if there is a reference frame where "my 8th birthday" represents the present, then do "I" exist in both frames of reference i.e. in my past and in my present?

    If we were had a newtonian/galiean spacetime, there would be no issue with saying your 8th birthday is just a memory, and that labelling your 8th birthday as "the present" is imaginary. There would be a unique "present" that evolves under physical laws of motions, and time could be some abstract parameter.

    But we can't do this. Different, real, observers "slice" spacetime into past, present, and future differently. Everyone agrees that your 8th birthday happened before you read this. But different people will say your 8th birthday is happening now, or that you reading this is happening now, or that your 80th birthday is happening now. All we can say is that at each event there is a causal structure that defines past and future, but no unique present, as the light-cone structure, unlike the "presentism" structure, does not specify which events are simultaneous with other events beyond the fact that if two events at different locations are causally linked, they cannot be simultaneous.
    And as you pointed out [in not so many words], it wasn't a correct model of reality, because the centre doesn't actually exist. What we can do however is speak about the relation of the sphere to the physical matter, with respect to which it moves; there will always be matter located at the co-ordinate we designate as the centre of the sphere.

    In the physical world, you cannot move or be at rest relative to an imaginary reference frame, because it is not physical - this doesn't stop us using it as a means of communication, but it does affect our application of definitions, given that we cannot move relative to it.

    How does it affect application of definitions? Not only can I define movement with respect a frame of reference, I can specify the movement of one frame with respect to another. Sure, it's merely a calculational tool, but that doesn't matter. I can easily construct a reference frame such that you are moving at 99.99999999% of the speed of light with respect to the frame. If you like, I can use more specific language and say the co-ordinates imposed by a reference frame will label you as moving or stationary, and that co-ordinate systems can be related to one-another by lorentz transformations, revealing the underlying, co-ordinate free, physical structure of the universe.
    This is probably the difference between absolute motion and relative motion. Absolute motion is simply the question of whether or not there is movement; if there is relative motion then, by definition there is movement, and so there is absolute motion. Determining what is moving, however, is a different matter.

    You have argued that relative motion is absolute. This is true. If I am moving relative to you, all observers will agree. However, it does not show that absolute motion, in the sense of an absolute, physically distinguished criteria which determines whether or not something is in motion, exists.
    Does length contraction cause the sphere to rotate?

    They're just looking at it from different perspectives, so that one person will label it differently. The lorentz transformations, which are responsible for "length contraction" explain why one see the sphere as rotated, as opposed to moving with the train.


  • Registered Users Posts: 2,552 ✭✭✭roosh


    Morbert wrote: »
    It's literally just an artefact of to co-ordinate labels. Both twins will agree that one twin experiences an inertial force. That much is physical. But when we look at how this is labelled, one will attribute it to acceleration, the other will attribute it to remaining stationary while experiencing a gravitational force. You seem to be bothered by the idea that a gravitational force coincidently "switches on" when he applies his rockets (or breaks), but gravity isn't a force. It's simply the case that, when you work out the physics under one co-ordinate system, the twin remains stationary while everything else "falls" through spacetime.
    It appears as though what is being said, is that, according to relativity, the different effects that each twin experiences is just an artefact of co-ordinate labeling; that the effects each twin experiences is as a result of how they label the scenario. This may be an over-simplification, but it almost seems as though, according to relativity, the distance between the two observers increases because each labels the other as being "in motion".

    I would see it the other way around, that each [rightly or wrongly] labels the other as being "in motion" because the distance between them increases. I'm just wondering what causes the distance between them to increase?

    If one twin attributes it to "acceleration" how can he then, consistently, label himself as being "at rest" if, by necessity, he is in motion, and attributes the effect to necessarily being in motion?

    Morbert wrote: »
    While technically true, it is on par with saying just because my pen falls when I drop it off a building doesn't mean I will.
    I think it's somewhat different; I think it's more like saying, that, although the equations calculate that when I drop my pen off a building on earth it will behave the exact same way as if I dropped it off a building in a zero-gravity compound, that doesn't necessarily verify that it will.

    Morbert wrote: »
    Also, it seems the clock experiments did look at both gravitational time dilation induced by the earth and due to the relative paths of the clocks. They were in very good agreement with relativity.

    http://en.wikipedia.org/wiki/Time_dilation#Experimental_confirmation
    Which experiments are you referring to specifically, because, again it could be my lack of understanding, but there are a number there which involve the measurement of a clock at different locations on the earths surface with different degrees of gravitational potential - or something to that effect.

    Morbert wrote: »
    Under SR, he can't.



    Well both twins agree there is a difference, both twins agree on the relative velocity between them. But GR let's us freely label either twin (but not both) as at rest.
    It might be helpful to repost the video from earlier in the thread; it might be able to help clarify where I am going wrong.
    [/QUOTE]

    If we take the thought experiment as it is in the video; with both observers labeling themselves as being at rest and the other as being in motion, with each carrying a clock. As the thought experiment is set-up there, the paradox does arise; because each should observe the same effect in the others reference frame i.e. both will observe the others clock ticking more slowly.

    In the physical world, however, such a scenario will not arise naturally, because at least one observer would have to undergo acceleration, and asymmetry would occur. This appears to be how the "paradox" is resolved under SR.

    Under GR, however [to my understanding], where asymmetry doesn't resolve the issue, the paradox should arise - unless there is another mitigating factor. I'm just wondering what that mitigating factor is.


    Another query I have: If we go back to SR however, where the paradox is resolved due to asymmetry, arising from the fact that one twin undergoes acceleration, the question arises, how can one twin label himself as being "at rest", if by necessity he is "in motion". This also raises the question of whether length contraction actually occurs.

    The derivation of the Lorentz factor, as per the video posted, is carried out on the basis that the photon, in the clock on the train, travels a path perpendicular to the mirror. It certainly appears that way to the observer on the train. However, if he is the twin singled out as undergoing acceleration, then his clock is also undergoing acceleration. If his clock is undergoing acceleration then, according to what we have discussed, the photon must inheret the velocity of the mirror, such that it doesn't travel a path perpendicular to the mirror, but at the angle as observed by the observer on the platform. This would mean that there is no actual length contraction; the clock ticks slower because the photon has to travel a longer distance due to the motion of the clock.


    Morbert wrote: »
    If we were had a newtonian/galiean spacetime, there would be no issue with saying your 8th birthday is just a memory, and that labelling your 8th birthday as "the present" is imaginary. There would be a unique "present" that evolves under physical laws of motions, and time could be some abstract parameter.

    But we can't do this. Different, real, observers "slice" spacetime into past, present, and future differently. Everyone agrees that your 8th birthday happened before you read this. But different people will say your 8th birthday is happening now, or that you reading this is happening now, or that your 80th birthday is happening now. All we can say is that at each event there is a causal structure that defines past and future, but no unique present, as the light-cone structure, unlike the "presentism" structure, does not specify which events are simultaneous with other events beyond the fact that if two events at different locations are causally linked, they cannot be simultaneous.
    If "my 8th birthday" is happening now for someone, am I there?

    I ask, because that 8yr old observer has aged since then and is here in this present. How can I still be 8yrs old and at my birthday celebrations in "someone elses present", while simultaneously being in "my present"?

    Morbert wrote: »
    How does it affect application of definitions? Not only can I define movement with respect a frame of reference, I can specify the movement of one frame with respect to another. Sure, it's merely a calculational tool, but that doesn't matter. I can easily construct a reference frame such that you are moving at 99.99999999% of the speed of light with respect to the frame. If you like, I can use more specific language and say the co-ordinates imposed by a reference frame will label you as moving or stationary, and that co-ordinate systems can be related to one-another by lorentz transformations, revealing the underlying, co-ordinate free, physical structure of the universe.
    You may be able to define movement with respect to a frame of reference, but that definition would remain entirely theoretical, and wouldn't accurately represent the physical world. In the physical world you cannot move relative to an imaginary frame of reference, for the simple fact that it is not physical. To say that you are moving, or at rest, relative to an imaginary reference frame is to imagine that you are.

    Morbert wrote: »
    You have argued that relative motion is absolute. This is true. If I am moving relative to you, all observers will agree. However, it does not show that absolute motion, in the sense of an absolute, physically distinguished criteria which determines whether or not something is in motion, exists.
    Absolute motion cannot be relative, because that would make it relative motion; relative motion, however, proves absolute motion. Again, absolute motion is simply a question of whether or not there is motion; if there is relative motion then there is absolute motion, simply for the fact that if there was no motion, there would be no relative motion.

    Morbert wrote: »
    They're just looking at it from different perspectives, so that one person will label it differently. The lorentz transformations, which are responsible for "length contraction" explain why one see the sphere as rotated, as opposed to moving with the train.
    Again, this seems to suggest that two observers, a good million miles apart, will observe themselves as being at the centre of the same expanding sphere because of how they apply an imaginary set of co-ordinates.

    To my mind, their application of the imaginary set of co-ordinates won't determine whether or not they are at the centre of a physical sphere; their location with respect to the physical sphere will determine that, and their co-ordinates should reflect their physical location.

    How I imagine it is thus, two observers side by side in an expanding sphere, at the centre; their co-ordinate systems reflect this. One starts moving from that location, such that he is no longer at the centre; his co-ordinates should reflect this - otherwise the sphere isn't a sphere. If length contraction, due to a co-ordinate transfer puts him at the centre, then the co-ordinate transfer must be erroneous - unless he's not in a sphere.

    Granted, that is based on a fairly basic understanding of spheres.


  • Registered Users Posts: 3,457 ✭✭✭Morbert


    roosh wrote: »
    It appears as though what is being said, is that, according to relativity, the different effects that each twin experiences is just an artefact of co-ordinate labeling; that the effects each twin experiences is as a result of how they label the scenario. This may be an over-simplification, but it almost seems as though, according to relativity, the distance between the two observers increases because each labels the other as being "in motion".

    It is only gravity which can be "transformed away" by co-ordinate transformations, as gravity enforces the symmetry over spacetime transformations.

    The other three forces cannot be transformed away in this regard. This is what singles out gravity. Though with that said, the other forces also enforce their own symmetries, though they are somewhat more abstract.
    I would see it the other way around, that each [rightly or wrongly] labels the other as being "in motion" because the distance between them increases. I'm just wondering what causes the distance between them to increase?

    If one twin attributes it to "acceleration" how can he then, consistently, label himself as being "at rest" if, by necessity, he is in motion, and attributes the effect to necessarily being in motion?

    He attributes it to the other twin's acceleration, not his own.
    I think it's somewhat different; I think it's more like saying, that, although the equations calculate that when I drop my pen off a building on earth it will behave the exact same way as if I dropped it off a building in a zero-gravity compound, that doesn't necessarily verify that it will.

    And dropping a pen off a roof does not necessarily verify that you will also drop. But again, this could be moot.
    Which experiments are you referring to specifically, because, again it could be my lack of understanding, but there are a number there which involve the measurement of a clock at different locations on the earths surface with different degrees of gravitational potential - or something to that effect.

    I am referencing the ones where they synchronise two clocks, and then take one on a journey.
    It might be helpful to repost the video from earlier in the thread; it might be able to help clarify where I am going wrong.


    If we take the thought experiment as it is in the video; with both observers labeling themselves as being at rest and the other as being in motion, with each carrying a clock. As the thought experiment is set-up there, the paradox does arise; because each should observe the same effect in the others reference frame i.e. both will observe the others clock ticking more slowly.

    They do!
    In the physical world, however, such a scenario will not arise naturally, because at least one observer would have to undergo acceleration, and asymmetry would occur. This appears to be how the "paradox" is resolved under SR.

    Under GR, however [to my understanding], where asymmetry doesn't resolve the issue, the paradox should arise - unless there is another mitigating factor. I'm just wondering what that mitigating factor is.

    The equivalence principle. The asymmetry I am referring to is the asymmetry of physical laws under smooth one-to-one spacetime transformations. In SR there is only symmetry over transformations between inertial reference frames. But when we consider the equivalence principle, we can recognise the symmetry of physical laws over all reference frames, thereby removing any notion of a physically distinguished set of reference frames.
    Another query I have: If we go back to SR however, where the paradox is resolved due to asymmetry, arising from the fact that one twin undergoes acceleration, the question arises, how can one twin label himself as being "at rest", if by necessity he is "in motion". This also raises the question of whether length contraction actually occurs.

    In SR, he doesn't label himself as at rest. Or more precisely, he acknowledges that he is the one changing reference frames.
    The derivation of the Lorentz factor, as per the video posted, is carried out on the basis that the photon, in the clock on the train, travels a path perpendicular to the mirror. It certainly appears that way to the observer on the train. However, if he is the twin singled out as undergoing acceleration, then his clock is also undergoing acceleration. If his clock is undergoing acceleration then, according to what we have discussed, the photon must inheret the velocity of the mirror, such that it doesn't travel a path perpendicular to the mirror, but at the angle as observed by the observer on the platform. This would mean that there is no actual length contraction; the clock ticks slower because the photon has to travel a longer distance due to the motion of the clock.

    Yep. Length contraction does not occur perpendicular to the motion. And yes, the photon does not travel along a path perpendicular to the mirror according to the observer on the track. But unlike, say, a sound wave or a bullet, both observers must agree on the speed of the photon. Hence, they must disagree on the time passed.
    If "my 8th birthday" is happening now for someone, am I there?

    I ask, because that 8yr old observer has aged since then and is here in this present. How can I still be 8yrs old and at my birthday celebrations in "someone elses present", while simultaneously being in "my present"?

    Remember that events can be arbitrarily simultaneous only if they are not causally connected. So the observer must be sufficiently far enough away (many galaxies away), such that the observer at your 8th or 80th birthday cannot have been affected by it, and you cannot have been affected by them.
    You may be able to define movement with respect to a frame of reference, but that definition would remain entirely theoretical, and wouldn't accurately represent the physical world. In the physical world you cannot move relative to an imaginary frame of reference, for the simple fact that it is not physical. To say that you are moving, or at rest, relative to an imaginary reference frame is to imagine that you are.

    It's not theoretical. It's a physical definition. Tools like Minkowski geometry or Lorentz transformations are theoretical devices used to illustrate and describe physical movement. For example, the movement you are insisting is physical is one described by a Euclidean, Riemannian manifold. Where there is symmetry over locations, but not over velocities. The movement we observe in experiment is pseudo-Riemannian, non-euclidean with a Minkowski signature, where there is symmetry over locations, velcoties, an accelerations. So you are right in saying definining movement with respect to an imaginary reference frame is not physical, as it is in reference to arbitrary co-ordinates. But you cannot then say that there exists an absolute set of co-ordinates that physically distinguishes actual motion.
    Absolute motion cannot be relative, because that would make it relative motion; relative motion, however, proves absolute motion. Again, absolute motion is simply a question of whether or not there is motion; if there is relative motion then there is absolute motion, simply for the fact that if there was no motion, there would be no relative motion.

    We can say, absolutely, that there is motion relative to things. We cannot say that any given body or object is absolutely in motion.
    Again, this seems to suggest that two observers, a good million miles apart, will observe themselves as being at the centre of the same expanding sphere because of how they apply an imaginary set of co-ordinates.

    To my mind, their application of the imaginary set of co-ordinates won't determine whether or not they are at the centre of a physical sphere; their location with respect to the physical sphere will determine that, and their co-ordinates should reflect their physical location.

    It is no more imaginary than the intuitive galilean rules of transformation that you are using to convince yourself that it is logically inconsistent to claim both observers can say they are at the centre of the same sphere. If we lived in a relativistic regime, where relativistics affects were noticeable in everyday life, you would have no qualms with intuitively accepting the sphere phenomenon, because you would intuitively use hyperbolic geometry as the underpinning relation between all events.
    How I imagine it is thus, two observers side by side in an expanding sphere, at the centre; their co-ordinate systems reflect this. One starts moving from that location, such that he is no longer at the centre; his co-ordinates should reflect this - otherwise the sphere isn't a sphere. If length contraction, due to a co-ordinate transfer puts him at the centre, then the co-ordinate transfer must be erroneous - unless he's not in a sphere.

    Granted, that is based on a fairly basic understanding of spheres.

    If he is no longer in the centre, then he cannot say the speed of light is c. If, say, the centre has fallen behind him, then the front of the sphere is moving slightly slower than c, and the back of the sphere is moving slightly faster than c. Do you at least accept that much: If both observers are at the centre of the sphere when the light begins its journey, and if both observers measure the speed of the light to be c in all directions, then both observes must say they are at the centre of the sphere.

    Furthermore, your claim that it would no longer be a sphere is not true under Lorentz transformations. You would be right if we were discussing galilean transformations, but we're not.


  • Registered Users Posts: 2,552 ✭✭✭roosh


    Morbert wrote: »
    It is only gravity which can be "transformed away" by co-ordinate transformations, as gravity enforces the symmetry over spacetime transformations.

    The other three forces cannot be transformed away in this regard. This is what singles out gravity. Though with that said, the other forces also enforce their own symmetries, though they are somewhat more abstract.
    It does seem as though cause and effect get lost in transformation, or "transformed away" as you put it, such that the suggestion appears to be that simply re-labeling something can result in a physical change.

    To put it in more blatant terms, it would be like suggesting that two observers label a piece of fruit as "an apple", but then one observer changes the label to "an orange" and this results in the flesh of the fruit, and the skin changing. That would be an example of where an effect is attributable to a change in labeling convention. Which seems ludicrous, but appears to be what is being suggested - in less crude terms, of course.

    If the increasing distance between observers is just an artefact of co-ordinate labels, then this seems to suggest that the physical effect of the increasing distance arises due to labeling.

    Morbert wrote: »
    He attributes it to the other twin's acceleration, not his own.
    Did you mean that one twin is singled out, by the other, as undergoing acceleration, as opposed to one twin being singled out as undergoing acceleration?

    Because if each twin attributes it to the other's acceleration, then that just leads us back to the paradox.

    Morbert wrote: »
    And dropping a pen off a roof does not necessarily verify that you will also drop. But again, this could be moot.
    There is a critical difference between the two, in that one takes place under the force of gravity, while the other doesn't.

    Morbert wrote: »
    I am referencing the ones where they synchronise two clocks, and then take one on a journey.
    By "take one on a journey" do you mean that it undergoes accleration?

    Morbert wrote: »
    They do!
    and hence the paradox.


    Morbert wrote: »
    The equivalence principle. The asymmetry I am referring to is the asymmetry of physical laws under smooth one-to-one spacetime transformations. In SR there is only symmetry over transformations between inertial reference frames. But when we consider the equivalence principle, we can recognise the symmetry of physical laws over all reference frames, thereby removing any notion of a physically distinguished set of reference frames.
    The equivalence principle is partly the reason why the paradox should occur; if neither is singled out as undergoing accleration then both should observe the other's clock as ticking slower hence the paradox.

    Morbert wrote: »
    In SR, he doesn't label himself as at rest. Or more precisely, he acknowledges that he is the one changing reference frames.
    Does he acknowledge that he is "in motion", or has undergone acceleration?

    Morbert wrote: »
    Yep. Length contraction does not occur perpendicular to the motion. And yes, the photon does not travel along a path perpendicular to the mirror according to the observer on the track. But unlike, say, a sound wave or a bullet, both observers must agree on the speed of the photon. Hence, they must disagree on the time passed.
    Again, apologies, I might have confused matters more than clarifying them.

    I was referring to the clock on the train. In the derivation of the Lorentz factor, the path of the photon is depicted as traveling in a line perpendicular to each mirror, such that it forms a right angle to the mirror. When coupled with the path of the photon as observed by the observer on the platform, the application of pythagoras's theorem gives rise to the length contraction formula, or time dilation formula.

    Now, if neither observer is singled out as undergoing acceleration, then the paradox would arise, because each would observe the others clock as ticking more slowly.

    If, however, one observer is singled out as undergoing accleration, and that observer is the observer on the train, then if he was to model the path of the photon as forming a right angle to each mirror, he would be mistaken, because not only is he under acceleration, but so too his is his clock.

    If, as was previously discussed, light inherits the velocity of the device from which it was emitted, then in order for the photon to give the appearance [to the observer on the train] of traveling in a line perpendicular to the mirrors, it would have to travel the path as observed by the observer on the platform.

    This would mean that his clock ticks slower, not because of length contraction, or time dilation, but becuase the photon has a longer distance to travel between the mirrors.

    Morbert wrote: »
    Remember that events can be arbitrarily simultaneous only if they are not causally connected. So the observer must be sufficiently far enough away (many galaxies away), such that the observer at your 8th or 80th birthday cannot have been affected by it, and you cannot have been affected by them.
    If we step into the physical world for a moment, and pretend that you and I were at my 8th birthday; now both of us have grown up since then (in many ways); that is, those two 8yr olds (assumption for the basis of explanation) didn't remain 8yrs old, we both moved "through time" to the ages we are now, and no co-ordinate system can change that. How then can our 8yr old selves still exist? They can't exist in our past (and someone elses present) because we remained in our present all the time and are in our present now; we didn't get stuck as 8yrs olds.

    Morbert wrote: »
    It's not theoretical. It's a physical definition. Tools like Minkowski geometry or Lorentz transformations are theoretical devices used to illustrate and describe physical movement. For example, the movement you are insisting is physical is one described by a Euclidean, Riemannian manifold. Where there is symmetry over locations, but not over velocities. The movement we observe in experiment is pseudo-Riemannian, non-euclidean with a Minkowski signature, where there is symmetry over locations, velcoties, an accelerations. So you are right in saying definining movement with respect to an imaginary reference frame is not physical, as it is in reference to arbitrary co-ordinates. But you cannot then say that there exists an absolute set of co-ordinates that physically distinguishes actual motion.
    I wouldn't say there is an absolute set of co-ordinates, because co-ordinates are imaginary; in the physical world we can only move with respect to physical objects.


    Morbert wrote: »
    We can say, absolutely, that there is motion relative to things. We cannot say that any given body or object is absolutely in motion.
    We may not be able to identify which body is in absolute motion, but we can deduce that some bodies must be in absolute motion because if there weren't bodies in absolute motion, there would be no relative motion.

    If we take our two observers for example, and put them in "empty space" apart from themselves. If they are at rest relative to each other and then the distance between them increases, we can know that at least one of them has to be in absolute motion. We may have no way of distinguishing which one it is, but we know that at least one of them must be - if not both of them.

    We measure their motion relative to each other, beacuse that is what measurement does, it seeks to quantify one thing in terms of another.

    Morbert wrote: »
    It is no more imaginary than the intuitive galilean rules of transformation that you are using to convince yourself that it is logically inconsistent to claim both observers can say they are at the centre of the same sphere. If we lived in a relativistic regime, where relativistics affects were noticeable in everyday life, you would have no qualms with intuitively accepting the sphere phenomenon, because you would intuitively use hyperbolic geometry as the underpinning relation between all events.
    I'll have to take your word for that, for the time being.

    Morbert wrote: »
    If he is no longer in the centre, then he cannot say the speed of light is c. If, say, the centre has fallen behind him, then the front of the sphere is moving slightly slower than c, and the back of the sphere is moving slightly faster than c. Do you at least accept that much: If both observers are at the centre of the sphere when the light begins its journey, and if both observers measure the speed of the light to be c in all directions, then both observes must say they are at the centre of the sphere.
    Not necessarily. Both observers can still measure the speed of light to be c in all directions, even if one observer is moving in the same direction as part of the sphere, and the opposite direction of another part of it.
    Morbert wrote: »
    Furthermore, your claim that it would no longer be a sphere is not true under Lorentz transformations. You would be right if we were discussing galilean transformations, but we're not.
    Is a Lorentz transformation necessary though? As above, if an observer is singled out as being in motion, then a more accurate representation of the EDIT: phenomenon might negate the necessity for a Lorentz transformation.


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  • Registered Users Posts: 3,457 ✭✭✭Morbert


    roosh wrote: »
    It does seem as though cause and effect get lost in transformation, or "transformed away" as you put it, such that the suggestion appears to be that simply re-labeling something can result in a physical change.

    To put it in more blatant terms, it would be like suggesting that two observers label a piece of fruit as "an apple", but then one observer changes the label to "an orange" and this results in the flesh of the fruit, and the skin changing. That would be an example of where an effect is attributable to a change in labeling convention. Which seems ludicrous, but appears to be what is being suggested - in less crude terms, of course.

    If the increasing distance between observers is just an artefact of co-ordinate labels, then this seems to suggest that the physical effect of the increasing distance arises due to labeling.

    Nothing physical changes. That is the whole point. There is no physically distinguished labelling system. Both co-ordinate systems label the distance as increasing. Both systems have the rocket propulsion force. It's simply that one co-ordinate system labels things as falling through spacetime while the other labels things as stationary in spacetime.
    Did you mean that one twin is singled out, by the other, as undergoing acceleration, as opposed to one twin being singled out as undergoing acceleration?

    Because if each twin attributes it to the other's acceleration, then that just leads us back to the paradox.

    Again, under SR, both twins agree that one twin accelerated or switched reference frames, thus resolving the paradox. Under GR, either twin can label the other as accelerating, since the equivalence principle resolves the paradox.
    There is a critical difference between the two, in that one takes place under the force of gravity, while the other doesn't.

    I don't think you understand the formalism of GR. There is not a separate equation for "under gravity" and "not under gravity". Just as Newtonian physics does not have separate equations for "pen falling" and "person falling".
    By "take one on a journey" do you mean that it undergoes accleration?

    Yes, with respect to the other clock.
    and hence the paradox.

    That is not a paradox. There is no problem with each labelling the other's clock as slower, provided they are in motion with respect to each other. Causality is preserved. The paradox arises when, at a later time, they are at rest to one another. But again, this is not a paradox in the strict, formal sense.
    The equivalence principle is partly the reason why the paradox should occur; if neither is singled out as undergoing accleration then both should observe the other's clock as ticking slower hence the paradox.

    Gravitational time dilation is different to the time dilation due to relative velocities. The twin in the ship labels the other twin's clock as ticking fast due to a uniform gravitational field. The twin in the spacestation labels the other twin's clock as ticking slow due to his motion.
    [According to SR] Does he acknowledge that he is "in motion", or has undergone acceleration?

    Effectively yes. It is a little more subtle, in the sense that his reference frame still labels himself as at rest but he acknowledges that his reference frame is physically different. But for the purposes of this conversation, yes.
    Again, apologies, I might have confused matters more than clarifying them.

    I was referring to the clock on the train. In the derivation of the Lorentz factor, the path of the photon is depicted as traveling in a line perpendicular to each mirror, such that it forms a right angle to the mirror. When coupled with the path of the photon as observed by the observer on the platform, the application of pythagoras's theorem gives rise to the length contraction formula, or time dilation formula.

    Now, if neither observer is singled out as undergoing acceleration, then the paradox would arise, because each would observe the others clock as ticking more slowly.

    If, however, one observer is singled out as undergoing accleration, and that observer is the observer on the train, then if he was to model the path of the photon as forming a right angle to each mirror, he would be mistaken, because not only is he under acceleration, but so too his is his clock.

    If, as was previously discussed, light inherits the velocity of the device from which it was emitted, then in order for the photon to give the appearance [to the observer on the train] of traveling in a line perpendicular to the mirrors, it would have to travel the path as observed by the observer on the platform.

    This would mean that his clock ticks slower, not because of length contraction, or time dilation, but becuase the photon has a longer distance to travel between the mirrors.

    But if the photon inherits the velocity of the device, it should move faster. But it doesn't. Both observers observe the photon to be travelling at speed c.

    For example, say we replace the photon with a rubber ball. If the passenger on the train measures the rubber ball to be emitted from the device at speed u, and if the passenger at the station measures the train to be travelling at speed v, he would measure the speed of the ball to be the square root of v^2 + u^2. Both observers label the speed differently. But since we are dealing with a photon, both observers label the speed as the same. Hence, me must concede that time is labelled differently.

    But you are right that special relativity lets us physically distinguish inertial and non-inertial reference frames. We could look at the past history of the train and the station, and see which experienced pseudo-forces due to acceleration. It would not tell us which is in absolute motion, but it would tell us which changed velocity.

    General relativity, on the other hand, lets us freely label either as accelerating.
    If we step into the physical world for a moment, and pretend that you and I were at my 8th birthday; now both of us have grown up since then (in many ways); that is, those two 8yr olds (assumption for the basis of explanation) didn't remain 8yrs old, we both moved "through time" to the ages we are now, and no co-ordinate system can change that. How then can our 8yr old selves still exist? They can't exist in our past (and someone elses present) because we remained in our present all the time and are in our present now; we didn't get stuck as 8yrs olds.

    We exist as a world line, a locus of events, and hence don't actually travel through time (remember that time is not a substance. It is the measure of a relation between events). The question of why we don't experience events in the opposite direction, or eternally experience an 8th birthday is an interesting one, and involves another branch of physics: thermodynamics and the structure of memory. I will happily delve into this, but after we have established the logical consistency of relativity, and the logical inconsistency of presentism.
    I wouldn't say there is an absolute set of co-ordinates, because co-ordinates are imaginary; in the physical world we can only move with respect to physical objects.

    By absolute, I mean physically distinguished set of co-ordinates, labelling things as they "absolutely" are. If it labels a person as "at rest", it is because they are absolutely at rest. And if it labels a simultaneous set of events as the present, it is because it truly is the present.

    This idea is incompatible with the invariant speed of light.
    We may not be able to identify which body is in absolute motion, but we can deduce that some bodies must be in absolute motion because if there weren't bodies in absolute motion, there would be no relative motion.


    If we take our two observers for example, and put them in "empty space" apart from themselves. If they are at rest relative to each other and then the distance between them increases, we can know that at least one of them has to be in absolute motion. We may have no way of distinguishing which one it is, but we know that at least one of them must be - if not both of them.

    We measure their motion relative to each other, beacuse that is what measurement does, it seeks to quantify one thing in terms of another.

    I think I see the problem: In relativity, bodies exist as a world-line (or world-sheet) of events. The world-lines of two bodies have an absolute structure, and hence can be related to one another in an absolute sense. "Motion", however, emerges from how we parametrise this relation. So bodies have an absolute structure that allows us to label one as in motion with respect to the other. But motion itself is not an absolute thing in relativity.
    Not necessarily. Both observers can still measure the speed of light to be c in all directions, even if one observer is moving in the same direction as part of the sphere, and the opposite direction of another part of it.

    No they can't. Simple algebra shows they can't. Let's take an arbitrary observer that is at the centre of a flash of light. Any observer measures the speed of light to be c. This means the front of the sphere will be travelling ahead of him at speed c, and the back of the sphere will be travelling behind him at speed c. After an arbitrary amount of time T, the front of the sphere will have travelled cT, and the back will have also travelled a distance cT in the opposite direction. No matter how the observer decides to move, he will always measure the speed of light to be c, so the distance travelled by any wave front will always be cT. Therefore, he is equally distant to any part of the wavefront, and hence in the centre. If, at time T, he was not in the centre of the sphere, it would mean he measures some parts of the sphere as travelling further than cT, and others less than cT. Hence, the speed of light, relative to him, would not have been c.
    Is a Lorentz transformation necessary though? As above, if an observer is singled out as being in motion, then a more accurate representation of the EDIT: phenomenon might negate the necessity for a Lorentz transformation.

    Lorentz transformations were derived from the requirement that the speed of light is the same for all observers. They would be necessary even if you singled out an observer as in motion, because all observers, singled out or otherwise, still measure the speed of light to be c.


  • Registered Users Posts: 2,552 ✭✭✭roosh


    Morbert wrote: »
    Nothing physical changes. That is the whole point. There is no physically distinguished labelling system. Both co-ordinate systems label the distance as increasing. Both systems have the rocket propulsion force. It's simply that one co-ordinate system labels things as falling through spacetime while the other labels things as stationary in spacetime.
    OK, this is mainly where we are at odds I think, the idea that nothing physical changes.

    Apologies for restating some of this, but I'm doing it more for my train of thought than anything; here is my thinking on it:

    If both observers are at rest relative to each other, and there is no physical change then they should remain at rest relative to each other; they cannot label the distance as increasing unless something happens to increase the distance; well, actually, they could, but that wouldn't mean that the distance actually increases between them. This is what I meant by the difference between labeling an apple as an orange; where in one scenario the labeling changes the flesh and the skin of the fruit.

    Cable Guys
    If we imagine our two observers both holding the end of a length of cable such that, when they are at rest relative to each other, side-by-side, the cable is slack.

    Here both label themselves as being at rest relative to the other, as well as the space station around them. They acknowledge that if they remain at rest relative to those objects, then the cable will remain remain slack. They acknowledge, that in order for the cable to extend to its full length, and become taught between them, one or both of them will have to undergo acceleration.

    So, it happens; the cable becomes fully extended and taught between them. Now, labeling can't cause the cable to extend between then, and become taught; something must happen to cause this physical change in the cable.

    The observable change in the cable is attributed to the relative motion between the two observers; now, labeling doesn't cause relative motion, things are labeled as being in motion relative to each other because at least one undergoes acceleration. To express it in the terms you used earlier, I would say that the change in distance between the two observers is not an artefact of co-ordinate labeling, rather, the co-ordinate labeling is an artefact of the relative motion.

    Defining the co-ordinate system
    Here is where I think there is another breakdown in communication:
    if the cable was slack when both observers were at rest relative to each other, and side by side, then they would have defined a co-ordinate system based on their relative position to the objects around them. This would have included the other twin, and their relative position to the same objects. They would have labeled this as being "at rest", such that their definition of being "at rest" was based on their relative position to the aforementioned objects. They would also have labeled the other twin as being "at rest", which equally would have been based on their [the other twin's] relative position with respect to those same objects.

    When defining this initial co-ordinate system, where they are at rest relative the other observer, they would have defined certain things about the geometry, and therefore gravity and acceleration. They would have said that both were in a uniform gravitational field and neither was undergoing acceleration.

    Then they observe relative motion between them and the objects, while observing that there is no relative motion between the other twin and the objects. This means that what they previously defined as being "at rest" they are now labeling as "in motion". Which seems somewhat inconsistent.

    Here is where I think there is another breakdown in communication:
    They would see the slack cable extend to its full length, and become taught. Something, other than labeling, must cause the cable to extend. You mentioned that
    one will attribute it to acceleration, the other will attribute it to remaining stationary while experiencing a gravitational force
    I thought that the twin who attributed it to acceleration would have to label himself as being "in motion" but you mentioned that
    He attributes it to the other twin's acceleration, not his own.
    So here, both attribute it to the acceleration of the other, while they themselves remain stationary while experiencing a gravitational force; is that correct?

    Will this actually be the case though? Will the twin who remains in the zero-gravity station experience a gravitational force? My thinking would have been that the twin in the zero-gravity station would not experience a gravitational force, so the twin that experiences a gravitational force should, due to the equivalence principle, conclude that he is undergoing accelerationl, and hence, "in motion".

    Morbert wrote: »
    Again, under SR, both twins agree that one twin accelerated or switched reference frames, thus resolving the paradox.
    Again, we have somewhat different reasoning on this one, but hopefully we can resolve it.

    As I see it, the paradox can indeed be resolved by acknowledging that one twin undergoes acceleration; but it is only resolved if both twins agree on which twin it is.

    If we look at it from the perspective of each individual twin:

    Twin A maintains that it is Twin B that undergoes acceleration, so he should observe Twin B's clock ticking slower, and displaying fewer ticks when they return to common ground.

    Twin B maintains that it is Twin A who undergoes acceleration, so he should observer Twin A's clock ticking slower, and displaying fewer ticks when they return to common ground.

    Both twins agree that one twin underwent acceleration, but they disagree on which one it is and so the paradox remains.


    Morbert wrote: »
    Under GR, either twin can label the other as accelerating, since the equivalence principle resolves the paradox.
    Again, we must have somewhat different reasoning on this, but hopefully it can be resolved.

    As I see it, if each twin labels the other as undergoing acceleration, the paradox arises, because each should observe the others clock as ticking slower, and as registering fewer ticks when they return to common ground.


    To my mind there doesn't seem to be much difference between the two; in both cases each twin maintains that it is the other that has undergone acceleration and themselves that has remained at rest, which is what gives rise to the paradox.

    Morbert wrote: »
    I don't think you understand the formalism of GR. There is not a separate equation for "under gravity" and "not under gravity". Just as Newtonian physics does not have separate equations for "pen falling" and "person falling".
    That much is probably clear

    I'm just wondering if I drop a pen off a building on earth, will it behave identically were I to drop it off a building in a zero-gravity compound; or it might be better to ask if, if I knock a pen off my desk on earth, will it behave the same way as if I knocked it off a desk in a zero-gravity station?

    Morbert wrote: »
    Yes, with respect to the other clock.
    OK, this is another thing I have trouble with, which is directly related to the twin paradox. How do we distinguish which clock gets taken "on a journey"?

    Morbert wrote: »
    That is not a paradox. There is no problem with each labelling the other's clock as slower, provided they are in motion with respect to each other. Causality is preserved. The paradox arises when, at a later time, they are at rest to one another. But again, this is not a paradox in the strict, formal sense.
    The paradox arises, I think, when both observers label the other as being i motion and themselves as being at rest.

    Morbert wrote: »
    Gravitational time dilation is different to the time dilation due to relative velocities. The twin in the ship labels the other twin's clock as ticking fast due to a uniform gravitational field. The twin in the spacestation labels the other twin's clock as ticking slow due to his motion.
    Apologies, the term "uniform gravitational field" is throwing me somewhat; I take that to mean that the gravitational field is the same for both observers; is that accurate?

    Morbert wrote: »
    Effectively yes. It is a little more subtle, in the sense that his reference frame still labels himself as at rest but he acknowledges that his reference frame is physically different. But for the purposes of this conversation, yes.
    OK, this is another area I don't fully understand; how, if he acknowledges that he has undergone acceleration can he consistently label himself as being "at rest" if by necessity he is in motion?

    Morbert wrote: »
    But if the photon inherits the velocity of the device, it should move faster. But it doesn't. Both observers observe the photon to be travelling at speed c.

    For example, say we replace the photon with a rubber ball. If the passenger on the train measures the rubber ball to be emitted from the device at speed u, and if the passenger at the station measures the train to be travelling at speed v, he would measure the speed of the ball to be the square root of v^2 + u^2. Both observers label the speed differently. But since we are dealing with a photon, both observers label the speed as the same. Hence, me must concede that time is labelled differently.
    I would agree, to a certain extent, that we must conclude that time is "labeled differently"; but we may differ on what that means. I would say that they "label time" differently because the clock of the observer on the train is ticking more slowly, than that of the observer on the platform.

    If the speed of light is constant, and the observer on the train is in motion, then the photon pinging between the mirrors of his clock will have to travel a longer distance between the mirrors, than the photon of the stationary observer, and hence it will actually tick more slowly.

    "Inherits the velocity" is probably the wrong terminology for what I am trying to get at; it might be more accurate to say that it affects the direction of the photon. If we go back to the rubber ball example, and imagine ourselves standing on a platform as a train roars past; if we throw the ball against the train it will not come straight back to us, but bounce away at an angle; the rubber ball would inherit the velocity, but if the speed of light is constant then it would only inherit the direction; and hence the photon would have to travel a longer distance between mirrors.
    Morbert wrote: »
    But you are right that special relativity lets us physically distinguish inertial and non-inertial reference frames. We could look at the past history of the train and the station, and see which experienced pseudo-forces due to acceleration. It would not tell us which is in absolute motion, but it would tell us which changed velocity.

    General relativity, on the other hand, lets us freely label either as accelerating.
    Does SR actually allow us to physically distinguish inertial and non-inertial reference frames? I know it's stated that one reference frame, or observer, has undergone acceleration, but if both observers label themselves as at rest and the other as in motion, then is that not just the equivalence principle in effect, if not in name?

    Morbert wrote: »
    We exist as a world line, a locus of events, and hence don't actually travel through time (remember that time is not a substance. It is the measure of a relation between events). The question of why we don't experience events in the opposite direction, or eternally experience an 8th birthday is an interesting one, and involves another branch of physics: thermodynamics and the structure of memory. I will happily delve into this, but after we have established the logical consistency of relativity, and the logical inconsistency of presentism.
    I have trouble with the idea of us existing as a worldline, because I struggle to see how there is evidence for this without assuming a priori that both the past and future exist.

    I don't question our ability to develop a theoretical model where we can trace the worldlines of particles, and even ourselves; I don't doubt the ability of such a model to predict things about "the future"; what I do question is how we can test the assumption that past and future actually exist; particularly when any predictions of such a model will always manifest in the present. I know we can remember (imagine) the past, and project (imagine) the future, and we can construct a predictive model on that basis, but any such model appears to be based on an a priori assumption that both exist.

    Morbert wrote: »
    By absolute, I mean physically distinguished set of co-ordinates, labelling things as they "absolutely" are. If it labels a person as "at rest", it is because they are absolutely at rest. And if it labels a simultaneous set of events as the present, it is because it truly is the present.
    OK, we mean pretty much the same thing by the term absolute (I think).

    To say that there can exist a physically distinguished set of co-ordinates, where things can be labeled as they "absolutely" are, may be somewhat contentious, because a co-ordinate system requires a person to imagine them, or to think them. However, the inability of the human race to determine the absolute motion of an object does not mean that there is no absolute motion. It is sufficient that we can reason that there is absolute motion, and so that a physically distinguished "set of co-ordinates" must exist.

    Would the effects of "the Big Bang" necessitate that everything be in motion?

    Morbert wrote: »
    This idea is incompatible with the invariant speed of light.
    That is because the speed of light, by definition, is relative, not absolue; insofar as speed is a form of comparison. That doesn't mean that a photon is not absolutely in motion.

    Morbert wrote: »
    I think I see the problem: In relativity, bodies exist as a world-line (or world-sheet) of events. The world-lines of two bodies have an absolute structure, and hence can be related to one another in an absolute sense. "Motion", however, emerges from how we parametrise this relation. So bodies have an absolute structure that allows us to label one as in motion with respect to the other. But motion itself is not an absolute thing in relativity.
    It makes sense that motion is not an absolute thing in relativity, bcos absolute motion is not, by definition, relative.

    The world-line issue is one I have difficulty with, because, to my mind, it assumes the existence of past and future.

    How I would characterise it is thus: if we imagine the universe full of objects all at absolute rest; in this case there will be no relative motion. For relative motion to occur, something has to, absolutely, move. The measurement of it's movement will be relative, because the nature of measurement is comparison i.e. it is to describe one thing in terms of another. This may preclude us from saying which one is absolutely in motion, but we can reason that at least one of the objects has to be in motion, and so must be absolutely in motion.


    Morbert wrote: »
    No they can't. Simple algebra shows they can't. Let's take an arbitrary observer that is at the centre of a flash of light. Any observer measures the speed of light to be c. This means the front of the sphere will be travelling ahead of him at speed c, and the back of the sphere will be travelling behind him at speed c. After an arbitrary amount of time T, the front of the sphere will have travelled cT, and the back will have also travelled a distance cT in the opposite direction. No matter how the observer decides to move, he will always measure the speed of light to be c, so the distance travelled by any wave front will always be cT. Therefore, he is equally distant to any part of the wavefront, and hence in the centre. If, at time T, he was not in the centre of the sphere, it would mean he measures some parts of the sphere as travelling further than cT, and others less than cT. Hence, the speed of light, relative to him, would not have been c.
    Wouldn't that depend on how he measures the speed of light? If he measures his own speed relative to the "stationary" background, then he can also measure the speed of light relative to the "stationary" background. He would still calculate the speed of light to be c and his own speed as 0.8c.

    If he is measuring the speed of light relative to himself, is there not the potential for error; because the speed of light is defined in terms of a stationary clock, and not a moving one. While the speed of light relative to him might actually be slower, his slower ticking clock would make it seem as though it is traveling at the same speed as when he is stationary.

    Morbert wrote: »
    Lorentz transformations were derived from the requirement that the speed of light is the same for all observers. They would be necessary even if you singled out an observer as in motion, because all observers, singled out or otherwise, still measure the speed of light to be c.
    This would be my reasoning, just going on the derivation in the video you posted; the modeling of the photon [in the photon clock], for the observer on the train, would be erroneous, if the train is considered to be "in motion".

    The video shows the path of the photon from the perspective of both observers; from the perspective of the observer on the train, the photon is depicted as traveling at right angles to the mirrors; while the observer on the platform sees it travel the path as depicted by the hypotenuse of a right angled triangle.

    However, if the train is in motion, and the mirrors along with it, then assuming that the photon inherits the direction of the emitter - which was the phenomenon that spared the observer on the platform from death, by the laser pulse from the train - then, for the observer on the train, the photon also travels the path as depicted by the hypotenuse of the right angled triangle.

    "Time" dilation, or rather clock dilation, will occur due to the increased distance the photon has to travel in its journey between mirrors, without the need for invoking length contraction. The notion of length contraction is only necessitated if the observer on the train assumes that he is "at rest"; which gives rise to the [arguably] unresolved paradox as outlined above.


  • Registered Users Posts: 3,457 ✭✭✭Morbert


    roosh wrote: »
    OK, this is mainly where we are at odds I think, the idea that nothing physical changes.

    Nothing physical changes when we swap co-ordinate labels the ignition of the rockets clearly is a physical change. And both observers agree that this is what causes the change in distance. A uniform gravitational field of any kind could not induce any change in distance. It's only affect is labelling who is at rest and who isn't.
    Apologies for restating some of this, but I'm doing it more for my train of thought than anything; here is my thinking on it:

    If both observers are at rest relative to each other, and there is no physical change then they should remain at rest relative to each other; they cannot label the distance as increasing unless something happens to increase the distance; well, actually, they could, but that wouldn't mean that the distance actually increases between them. This is what I meant by the difference between labeling an apple as an orange; where in one scenario the labeling changes the flesh and the skin of the fruit.

    Cable Guys
    If we imagine our two observers both holding the end of a length of cable such that, when they are at rest relative to each other, side-by-side, the cable is slack.

    Here both label themselves as being at rest relative to the other, as well as the space station around them. They acknowledge that if they remain at rest relative to those objects, then the cable will remain remain slack. They acknowledge, that in order for the cable to extend to its full length, and become taught between them, one or both of them will have to undergo acceleration.

    So, it happens; the cable becomes fully extended and taught between them. Now, labeling can't cause the cable to extend between then, and become taught; something must happen to cause this physical change in the cable.

    The observable change in the cable is attributed to the relative motion between the two observers; now, labeling doesn't cause relative motion, things are labeled as being in motion relative to each other because at least one undergoes acceleration. To express it in the terms you used earlier, I would say that the change in distance between the two observers is not an artefact of co-ordinate labeling, rather, the co-ordinate labeling is an artefact of the relative motion.

    Defining the co-ordinate system
    Here is where I think there is another breakdown in communication:
    if the cable was slack when both observers were at rest relative to each other, and side by side, then they would have defined a co-ordinate system based on their relative position to the objects around them. This would have included the other twin, and their relative position to the same objects. They would have labeled this as being "at rest", such that their definition of being "at rest" was based on their relative position to the aforementioned objects. They would also have labeled the other twin as being "at rest", which equally would have been based on their [the other twin's] relative position with respect to those same objects.

    When defining this initial co-ordinate system, where they are at rest relative the other observer, they would have defined certain things about the geometry, and therefore gravity and acceleration. They would have said that both were in a uniform gravitational field and neither was undergoing acceleration.

    Then they observe relative motion between them and the objects, while observing that there is no relative motion between the other twin and the objects. This means that what they previously defined as being "at rest" they are now labeling as "in motion". Which seems somewhat inconsistent.

    Here is where I think there is another breakdown in communication:
    They would see the slack cable extend to its full length, and become taught. Something, other than labeling, must cause the cable to extend. You mentioned that I thought that the twin who attributed it to acceleration would have to label himself as being "in motion" but you mentioned that So here, both attribute it to the acceleration of the other, while they themselves remain stationary while experiencing a gravitational force; is that correct?

    Will this actually be the case though? Will the twin who remains in the zero-gravity station experience a gravitational force? My thinking would have been that the twin in the zero-gravity station would not experience a gravitational force, so the twin that experiences a gravitational force should, due to the equivalence principle, conclude that he is undergoing accelerationl, and hence, "in motion".

    Let's say we switch on the uniform gravitational field before one twin leaves the station. Would there be any physical change? No. The rope between them would still be slack. They would still be the same distance from all the stars. The only difference is they would all be labelled as "falling". When you are freely falling in a gravitational field, you do not feel it. So there is no physical difference between being stationary in no gravitational field, and freely falling in a uniform gravitational field. This was Einstein's great insight.

    So what physically happens? Both twins are at rest. One ignites rockets, causing the distance between them to increase. This much they both agree on because this much is physical. But they are free to label themselves as stationary, or freely falling in a gravitational field because they are physically equivalent (hence the name "equivalence principle"). In the latter case, the rockets act against this free-fall, and that twin would be labelled as stationary.
    If we look at it from the perspective of each individual twin:

    Twin A maintains that it is Twin B that undergoes acceleration, so he should observe Twin B's clock ticking slower, and displaying fewer ticks when they return to common ground.

    Twin B maintains that it is Twin A who undergoes acceleration, so he should observer Twin A's clock ticking slower, and displaying fewer ticks when they return to common ground.

    Both twins agree that one twin underwent acceleration, but they disagree on which one it is and so the paradox remains.

    Again, we must have somewhat different reasoning on this, but hopefully it can be resolved.

    As I see it, if each twin labels the other as undergoing acceleration, the paradox arises, because each should observe the others clock as ticking slower, and as registering fewer ticks when they return to common ground.

    To my mind there doesn't seem to be much difference between the two; in both cases each twin maintains that it is the other that has undergone acceleration and themselves that has remained at rest, which is what gives rise to the paradox.

    You are not taking into account gravitational time dilation. I cannot remember which twin is which, so I will say the space station twin is twin A.

    Here are the two arbitrary labelling systems: "Both twins are stationary." and "Both twins are in a gravitational field." Both these systems are physically equivalent because freely falling in a gravitational field is the same as being stationary with no gravitational field.

    So let's take the first labelling system: Twin A is at rest. Twin B travels away and back due to his rockets. Twin B is in motion, so his clock will tick slower than A. Conclusion:Twin A's clock is faster by N seconds

    Now consider the second labelling system: Twin B uses his rockets to remain stationary in the uniform gravitational field. Twin A freely falls away and back due to the gravitational field. Twin A is in motion, so his clock ticks slower, BUT twin A is further up the uniform gravitational potential, making his clock tick faster than B. Conclusion:Twin A's clock is faster by N seconds

    There is no experiment, conceptual or otherwise that can physically distinguish these two labelling conventions. Any experiment carried out under one labelling system will have an equivalent result under the other.
    That much is probably clear

    I'm just wondering if I drop a pen off a building on earth, will it behave identically were I to drop it off a building in a zero-gravity compound; or it might be better to ask if, if I knock a pen off my desk on earth, will it behave the same way as if I knocked it off a desk in a zero-gravity station?

    It will be governed by the exact same law. Just as the law which tells us about the Twin experiment also predicts GPS time dilation, or time dilation of caesium clocks taken on journeys, or the bending of light around massive bodies, or the orbit of mercury, or the doppler shift of particles. All these have been tested, so there is no compelling reason to believe the twin scenario needs some new, different law.
    Apologies, the term "uniform gravitational field" is throwing me somewhat; I take that to mean that the gravitational field is the same for both observers; is that accurate?

    It means a gravitational field of the same strength everywhere. It will cause you to accelerate just as much as it would cause the rest of the universe to accelerate. In fact, the interpretation of the field in relativity is an expression of spacetime. The uniform field is only present under one labelling system, however. The twin in the spacestation (twin A) says there is no gravitational field, which is why he does not feel one. The twin who "leaves" says there is a gravitational field, and the spacestation is freely falling in it, which is why twin A does not detect the gravitational field. Hence, only twin B invokes gravitational time dilation to account for the difference in clock ticks.

    You might think such a treatment of gravity is impossible. And indeed it is in Newtonian mechanics. But it isn't in relativistic mechanics as the gravitational field is spacetime, and Newtonian gravity makes predictions that fail, where relativity makes predictions about gravity that succeed (E.g. The warping of light paths, and the perihelion of mercury).
    OK, this is another area I don't fully understand; how, if he acknowledges that he has undergone acceleration can he consistently label himself as being "at rest" if by necessity he is in motion?

    If he acknowledges that he has undergone acceleration, he does not label himself as at rest. Under SR, he labels himself as accelerating. Under GR, he is free to label himself as accelerating or at rest.
    I would agree, to a certain extent, that we must conclude that time is "labeled differently"; but we may differ on what that means. I would say that they "label time" differently because the clock of the observer on the train is ticking more slowly, than that of the observer on the platform.

    If the speed of light is constant, and the observer on the train is in motion, then the photon pinging between the mirrors of his clock will have to travel a longer distance between the mirrors, than the photon of the stationary observer, and hence it will actually tick more slowly.

    This happens whether or not the train is stationary and the platform moving, or the platform is stationary and the train is moving. The person on the platform will always see the train clock tick more slowly than the person on the train sees it. This does not tell us who is moving.
    Does SR actually allow us to physically distinguish inertial and non-inertial reference frames? I know it's stated that one reference frame, or observer, has undergone acceleration, but if both observers label themselves as at rest and the other as in motion, then is that not just the equivalence principle in effect, if not in name?

    They don't both label themselves as at rest under SR. They only do this if they use GR (or at least SR + equivalence principle).
    I have trouble with the idea of us existing as a worldline, because I struggle to see how there is evidence for this without assuming a priori that both the past and future exist.

    I don't question our ability to develop a theoretical model where we can trace the worldlines of particles, and even ourselves; I don't doubt the ability of such a model to predict things about "the future"; what I do question is how we can test the assumption that past and future actually exist; particularly when any predictions of such a model will always manifest in the present. I know we can remember (imagine) the past, and project (imagine) the future, and we can construct a predictive model on that basis, but any such model appears to be based on an a priori assumption that both exist.

    The world-line issue is one I have difficulty with, because, to my mind, it assumes the existence of past and future.

    The accusation that it is an assumption has already been dealt with in the Physics & Chemistry thread.
    OK, we mean pretty much the same thing by the term absolute (I think).

    To say that there can exist a physically distinguished set of co-ordinates, where things can be labeled as they "absolutely" are, may be somewhat contentious, because a co-ordinate system requires a person to imagine them, or to think them. However, the inability of the human race to determine the absolute motion of an object does not mean that there is no absolute motion. It is sufficient that we can reason that there is absolute motion, and so that a physically distinguished "set of co-ordinates" must exist.

    How I would characterise it is thus: if we imagine the universe full of objects all at absolute rest; in this case there will be no relative motion. For relative motion to occur, something has to, absolutely, move. The measurement of it's movement will be relative, because the nature of measurement is comparison i.e. it is to describe one thing in terms of another. This may preclude us from saying which one is absolutely in motion, but we can reason that at least one of the objects has to be in motion, and so must be absolutely in motion.

    That is a non-sequitur. The "absolute" structure could be the co-ordinate-free, invariant structure of spacetime, with "motion" only emerging when we arbitrarily talk of space independent of time. Remember that space is relative and time is relative, but space-time is invariant or "absolute".

    There is a 4D analogy of motion that can be used. We can talk of worldlines that trace a geodesic or non-geodesic path through spacetime. In the twin scenario, for example, both twins would agree that only the spacestation twin is following a geodesic path through spacetime, even if either twin can consider themselves as at rest.
    Would the effects of "the Big Bang" necessitate that everything be in motion?

    No. The Big bang involves the expansion of space itself.
    That is because the speed of light, by definition, is relative, not absolue; insofar as speed is a form of comparison. That doesn't mean that a photon is not absolutely in motion.

    Yes, a photon is labelled as in motion under all co-ordinate labels. In absolute terms, this means photons lie along the null-cone structure of spacetime. This does not, however, imply a "true" or "absolute" co-ordinate system.
    Wouldn't that depend on how he measures the speed of light? If he measures his own speed relative to the "stationary" background, then he can also measure the speed of light relative to the "stationary" background. He would still calculate the speed of light to be c and his own speed as 0.8c.

    He will always measure the speed of light to be c. This is an incredibly important point. The person on the train, the person at the station, the twin in the spacestation and the twin in the spaceship will all measure the speed of light to be c with respect to themselves. To put it more formally: The speed of light will be c in any co-ordinate system. It is not simply that the speed of light is c with respect to some stationary background. Hence, the observer will measure the expanding to have a centre at his location.
    If he is measuring the speed of light relative to himself, is there not the potential for error; because the speed of light is defined in terms of a stationary clock, and not a moving one. While the speed of light relative to him might actually be slower, his slower ticking clock would make it seem as though it is traveling at the same speed as when he is stationary.

    This would be my reasoning, just going on the derivation in the video you posted; the modeling of the photon [in the photon clock], for the observer on the train, would be erroneous, if the train is considered to be "in motion".

    The video shows the path of the photon from the perspective of both observers; from the perspective of the observer on the train, the photon is depicted as traveling at right angles to the mirrors; while the observer on the platform sees it travel the path as depicted by the hypotenuse of a right angled triangle.

    However, if the train is in motion, and the mirrors along with it, then assuming that the photon inherits the direction of the emitter - which was the phenomenon that spared the observer on the platform from death, by the laser pulse from the train - then, for the observer on the train, the photon also travels the path as depicted by the hypotenuse of the right angled triangle.

    "Time" dilation, or rather clock dilation, will occur due to the increased distance the photon has to travel in its journey between mirrors, without the need for invoking length contraction. The notion of length contraction is only necessitated if the observer on the train assumes that he is "at rest"; which gives rise to the [arguably] unresolved paradox as outlined above.

    Even supposing that velocity mechanically slows down a clock (it doesn't), this would not account for the speed of light being c. No matter what clock you use, a photon coming towards you and a photon moving away from you will always be c (just in opposite directions). A mechanically slow ticking clock might explain why a photon moving away from your direction would be c, but you would need a fast ticking clock to align the speed of a photon coming towards you. The only way this "error" supposition might work is if you assume, a priori, a mystical substance that bends the dimensions and motions of things, but which cannot be physically detected. Not only is this unnecessary, but it would run into problems when it comes to quantum field theory.


  • Closed Accounts Posts: 8 canbai


    Wow!Very glad to see this thread!

    Time is the recorder of the state of material movement. Time is born out of movement. Without movement, there would be no time. Time exists within the interior of every moving objects and pervades the universe space of all objects.

    Time has eight great characteristics:
    1. Time is nonmaterial;
    2. Time can be negative and positive;
    3. Time has particularity and universality;
    4. Time is a variable;
    5. Time pervades all the material space;
    6. Time is both longitudinal and latitudinal;
    7. Time has different connotations in different spaces;
    8. Time can be compressed, expanded and dissolved

    Comprehensive exposition refer to: http://lifechanyuan.org/bbs/forum.php?mod=viewthread&tid=46


  • Registered Users Posts: 2,552 ✭✭✭roosh


    @Morbert - Apologies again; I've been fairly busy over the past couple of weeks and haven't had the time to give a considered reply to the latest post.

    It could be the new year before I get the chance.


  • Registered Users Posts: 2,552 ✭✭✭roosh


    Once again, apologies for the delayed response; I was very busy in the run up to Christmas and afterwards I wanted to try and brush up on my understanding of relativity. I'd had a copy of "why does E=mc^2?", by Brian Cox and Jeff Forshaw, for a while, so decided to finally read it; someone else recommended a paper entitled "Understanding the special theory of relativity" by Anders Manson; and from among the recommendations of books, to help develop a better understanding of physics in general, I got a copy of "the fundamentals of physics" by Halliday, Resnick, and Walter. Admittedly I skipped [almost] immediately to the section on relativity - so as you can imagine, I'm now, pretty much, an expert :D


    On a serious note though, if I haven't already exhausted your patience, I'd like to take the latter as a jumping off point, for no other reason that it ties in with the opening paragraph; and also because it will be helpful for me in presenting this point. There is no special significance in the text by H,R, & W, that differentiates it from any other text - to my knowledge - but it just happens to be the one that I've read.

    This may seem like going back over old ground, but hopefully the way it is presented will justify it and make it clearer where the potential issue lies.


    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 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.

    H, R, & W - time dilation
    In "the fundamentals of physics" (Chapter 39.4 - p1257) the authors use a variation on the light clock thought experiment, 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.


  • Registered Users Posts: 3,457 ✭✭✭Morbert


    For posterity, I'll point out that this discussion is being continued in the Physics & Chemsitry forum.


  • Registered Users Posts: 2,552 ✭✭✭roosh


    Also, just for posterity, it is probably worth highlighting that the notion of an absolute present is perfectly compatible with Lorentzian relativity, which is equally supported by all relativity experiments.


  • Registered Users Posts: 26 Upthedubs32


    Time is the name given to whats happens as a part of nature. Ive never given alot of thought to why it was called time it was explained to me in a very simple manner via a standard clock as a child and i now i use it as a means of planning out my day. I think i have always had alot more things to be concerned about, and trying to figure out why time is called time was never really top of my list. After saying all of that i know some of the people who spent alot of time (see my use of the word in question) thinking about this have actually used alot of there time considering it all and i have now spent alot of time writing this but its always worth saying whats on your mind as from time to time we make some sense. I hope anyone who might spend the time reading my few lines will appreciate the amout of time i have spent using the word time in this thread about whether or not time exsits and if anoyone can come up with a better way of keeping track of things then let me know but for the Time been im going to stick to the tried and tested clock and hope that im always on time!!


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  • Registered Users Posts: 2,552 ✭✭✭roosh


    Time is the name given to whats happens as a part of nature. Ive never given alot of thought to why it was called time it was explained to me in a very simple manner via a standard clock as a child and i now i use it as a means of planning out my day. I think i have always had alot more things to be concerned about, and trying to figure out why time is called time was never really top of my list. After saying all of that i know some of the people who spent alot of time (see my use of the word in question) thinking about this have actually used alot of there time considering it all and i have now spent alot of time writing this but its always worth saying whats on your mind as from time to time we make some sense. I hope anyone who might spend the time reading my few lines will appreciate the amout of time i have spent using the word time in this thread about whether or not time exsits and if anoyone can come up with a better way of keeping track of things then let me know but for the Time been im going to stick to the tried and tested clock and hope that im always on time!!
    I too use a clock as a tool for organising my life, I recall memories of times past, I project images of times in the future, but never have I actually ever spent any time outside the present moment.

    The clock is very useful indeed; originally it was used to measure the apparent motion of the sun around the earth, and to break that motion into more manageable chunks, so that people could arrange things more easily, so that they think more easily about how much daylight they had to carry out the things they needed to do; it allowed them to communicate with others about things that needed to be done. The clock has evolved however, and now we have pendulum clocks, digital clocks, and atomic clocks.

    But if I consider any of these clocks, if I open them up and look at their internal mechanisms (or even just think about doing it), I start to wonder, where is this thing that "happens as a part of nature" actually measured? I can see all the parts of the clock that are "a part of nature"; if I think of a sundial, I can see that the sun is a part of nature and so too is the matter that makes up the sundial, but where, oh where, is this mysterious other aspect of nature called time?


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