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Relativty of Simultaneity and clock synchronisation

  • 16-11-2012 05:53PM
    #1
    roosh
    Registered Users, Registered Users 2 Posts: 2,554 ✭✭✭


    I was just wondering about the following:

    Similar set-up to the thought experiment in the thread on the question on the LTs and RoS, except we have Albert synchronising two spatially separated clocks, located at the poles A and B. Again, we have Henry moving relative to Albert on the train.

    Albert sends a light pulse, simultaneously, in the direction of A and B; according to the Einstein synchronisation convention the light travels at the same speed in both directions, and so both A and B should be synchronised when the light pulse reaches them.

    Now, imagine that both clocks are set-up with a half-silvered mirror which, in the process of synchronising the clock, reflects the light pulse towards the train that Henry is on, such that the light pulse is traveling perpendicular to the direction of motion.


    Imagine that Henry's train is either infinitely long, or sufficiently long - sufficiently long is probably better - and lining the floor of Henry's train are a sufficient number of clocks, all of which can be synchronised in the manner that Albert's clocks at A and B are i.e. with a light pulse setting them going.

    The light pulse which has been reflected from Albert's synchronised clocks travels towards the train and hits two of the clocks on Henrys train - we can set it up such that the trigger mechanism is exposed such that the light pulse can hit it.


    The question is, will the two clocks which the light pulses hit be synchronised with each other; not with Albert's clocks, but with each other?


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Comments

  • #2
    dlouth15
    Registered Users, Registered Users 2 Posts: 1,169 ✭✭✭dlouth15


    Apply the Lorentz transformation. That will tell you what happens according to special relativity. This was done in the other thread by Morbert to show that there was no paradox in the situation you described in that thread.

    Rather than someone else doing the analysis I would suggest you do it yourself. Then others can critique it if they feel you are getting it wrong.

    Here's how I suggest you go about it.

    1. Draw a diagram. This will help get things clear in your own head as well as others.
    2. Define the frames of reference.
    3. Define the key events that occur in one frame. For example, light is emitted by Albert at (t1, x1, y1, z1) and is detected at (t2, x2, y2, z2) (obviously the coordinates used will depend on the events themselves). Stick to one frame here.
    4. Apply the Lorentz transformation to the events in this frame to see what is happening in another frame.

    This will tell you what special relativity predicts.

    I would humbly suggest to others that guidance should be given rather than jumping straight in with the answer.


  • #3
    roosh
    Registered Users, Registered Users 2 Posts: 2,554 ✭✭✭roosh


    dlouth15 wrote: »
    Apply the Lorentz transformation. That will tell you what happens according to special relativity. This was done in the other thread by Morbert to show that there was no paradox in the situation you described in that thread.

    Rather than someone else doing the analysis I would suggest you do it yourself. Then others can critique it if they feel you are getting it wrong.

    Here's how I suggest you go about it.

    1. Draw a diagram. This will help get things clear in your own head as well as others.
    2. Define the frames of reference.
    3. Define the key events that occur in one frame. For example, light is emitted by Albert at (t1, x1, y1, z1) and is detected at (t2, x2, y2, z2) (obviously the coordinates used will depend on the events themselves). Stick to one frame here.
    4. Apply the Lorentz transformation to the events in this frame to see what is happening in another frame.

    This will tell you what special relativity predicts.

    I would humbly suggest to others that guidance should be given rather than jumping straight in with the answer.

    What's wrong with the following reason.

    The time it takes for light to travel from poles A and B to the trian, is the same for both reference frames, because the reflected light travels perpendicular to the direction of motion and there is no point of convergence meaning that the issue isn't "resolved" in the same manner.

    Given that it takes the same amount of time in both reference frames, if light is physically reflected from one pole first, it will, necessarily, physically strike the train first, and set the clock it strikes ticking. This means that the clocks won't be synchronised, because one clock starts ticking first.

    If the light isn't reflected from one pole first, that is, it is reflected from both poles "tied for first", then it will strike the train "tied for first" and both clocks will be started together, and so should be synchronised.


  • #4
    dlouth15
    Registered Users, Registered Users 2 Posts: 1,169 ✭✭✭dlouth15


    Test it out by applying the Lorentz transformation.


  • #5
    roosh
    Registered Users, Registered Users 2 Posts: 2,554 ✭✭✭roosh


    dlouth15 wrote: »
    Test it out by applying the Lorentz transformation.
    The LTs will say that, according to Henry, on the train, the light pulses will strike non-simultaneously and so the clocks won't be synchronised, won't they?

    Our reasoning, based on what we know about the physical world leads to an apparent paradox though; so is there something wrong with the reasoning?


  • #6
    dlouth15
    Registered Users, Registered Users 2 Posts: 1,169 ✭✭✭dlouth15


    roosh wrote: »
    The LTs will say that, according to Henry, on the train, the light pulses will strike non-simultaneously and so the clocks won't be synchronised, won't they?

    Our reasoning, based on what we know about the physical world leads to an apparent paradox though; so is there something wrong with the reasoning?
    Are you saying that we may need to adjust our common-sense notions of the how the physical world works?


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  • #7
    roosh
    Registered Users, Registered Users 2 Posts: 2,554 ✭✭✭roosh


    dlouth15 wrote: »
    Are you saying that we may need to adjust our common-sense notions of the how the physical world works?
    No, I'm asking the following:
    Is the light physical?
    Is the light physically reflected by the half-silvered mirrors on the clocks?
    Does the reflected light physically hit the train/clocks?

    If the time it takes for light to travel from poles A and B to the train, perpendicular to the direction of motion, is the same for both reference frames; if light from one pole is physically reflected first will it physically strike the train first?

    Also, if the flight time is the same from both poles to the train, and the light from both poles isn't physically reflected such that one is first and the other second, rather both are "tied for first", will both physically hit the train/clocks "tied for first"?


  • #8
    dlouth15
    Registered Users, Registered Users 2 Posts: 1,169 ✭✭✭dlouth15


    Let's go back to your earlier post. I have a question for you.
    The LTs will say that, according to Henry, on the train, the light pulses will strike non-simultaneously and so the clocks won't be synchronised, won't they?

    Our reasoning, based on what we know about the physical world leads to an apparent paradox though; so is there something wrong with the reasoning?
    Let's say you are correct that the LTs indicate that the pulses will arrive non-simultaniously.

    As you point out, this conflicts with our common-sense notions of how the physical world works.

    They can't both be true, right? Would you agree that we must either adjust our common sense notions of how the physical world works or else reject special relativity?


  • #9
    roosh
    Registered Users, Registered Users 2 Posts: 2,554 ✭✭✭roosh


    dlouth15 wrote: »
    Let's go back to your earlier post. I have a question for you.
    Let's say you are correct that the LTs indicate that the pulses will arrive non-simultaniously.

    As you point out, this conflicts with our common-sense notions of how the physical world works.

    They can't both be true, right? Would you agree that we must either adjust our common sense notions of how the physical world works or else reject special relativity?
    Does, relativityt say the light physical?

    Does relativity say the light is physically reflected by the half-silvered mirrors on the clocks?

    Does relativity say that the reflected light physically hits the train/clocks?

    Does relativity say that the time it takes for the reflected light pulses to reach the train is the same for both observers?

    Does relativity say that when the reflected light pulses physically strike the train clocks it will start them ticking, as it did for Albert's clocks?

    Does relativity say that the light is reflected from one pole first and then the other; as well as that light is reflected, not from one pole first and then the other, but together, "tied for first place"?


  • #10
    Morbert
    Registered Users, Registered Users 2 Posts: 3,457 ✭✭✭Morbert


    roosh wrote: »
    The LTs will say that, according to Henry, on the train, the light pulses will strike non-simultaneously and so the clocks won't be synchronised, won't they?

    Yes.
    Our reasoning, based on what we know about the physical world leads to an apparent paradox though; so is there something wrong with the reasoning?

    Why do you say this? There is no paradox in Henry and Albert disagreeing if the clocks are synchronised or not, as simultaneity is relative and unphysical.


  • #11
    Morbert
    Registered Users, Registered Users 2 Posts: 3,457 ✭✭✭Morbert


    roosh wrote: »
    Does, relativityt say the light physical?

    Yes.
    Does relativity say the light is physically reflected by the half-silvered mirrors on the clocks?

    Yes
    Does relativity say that the reflected light physically hits the train/clocks?

    Yes
    Does relativity say that the time it takes for the reflected light pulses to reach the train is the same for both observers?

    No
    Does relativity say that when the reflected light pulses physically strike the train clocks it will start them ticking, as it did for Albert's clocks?

    Yes
    Does relativity say that the light is reflected from one pole first and then the other; as well as that light is reflected, not from one pole first and then the other, but together, "tied for first place"?

    No


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  • #12
    roosh
    Registered Users, Registered Users 2 Posts: 2,554 ✭✭✭roosh


    Morbert wrote: »
    Why do you say this? There is no paradox in Henry and Albert disagreeing if the clocks are synchronised or not, as simultaneity is relative and unphysical.
    No, the paradox arises in having the same two physical clocks being both synchronised and unsynchronised with each other; but your answers to some of the questions below might negate that, so we have to take a look at them.

    Morbert wrote: »
    No [he time is not the same in both reference frames]
    The speed of light is constant in both reference frames and the reflected light travels perpendicular to the direction of motion; which means that lengths, in that direction, are not contracted for either observer, doesn't it, which would imply that the distance is the same.

    Given the same distance and the same speed, the length of time it takes for the reflected light to reach the train should be the same for both observers, shouldn't it?


    Morbert wrote: »
    No
    According to S', doesn't the light pulse, that Albert uses to synchronise his clocks, hit one clock first and then the other, because, according to S', the clock on one pole is rushing towards the expanding sphere of light, while the other is moving away from it; and this is why the observer on the train disagrees with Albert over the synchronisation of bis clocks?


  • #13
    Morbert
    Registered Users, Registered Users 2 Posts: 3,457 ✭✭✭Morbert


    roosh wrote: »
    The speed of light is constant in both reference frames and the reflected light travels perpendicular to the direction of motion; which means that lengths, in that direction, are not contracted for either observer, doesn't it, which would imply that the distance is the same.

    Given the same distance and the same speed, the length of time it takes for the reflected light to reach the train should be the same for both observers, shouldn't it?

    It is only perpendicular according to S. If Albert measures the time it takes to travel from the pole to the train as t seconds, Henry will measure γt seconds.
    According to S', doesn't the light pulse, that Albert uses to synchronise his clocks, hit one clock first and then the other, because, according to S', the clock on one pole is rushing towards the expanding sphere of light, while the other is moving away from it; and this is why the observer on the train disagrees with Albert over the synchronisation of bis clocks?

    Yes, but my understanding of your question was you were asking if relativity says the strikes will be both physically simultaneous and not simultaneous. Relativity says simultaneity is non physical.


  • #14
    dlouth15
    Registered Users, Registered Users 2 Posts: 1,169 ✭✭✭dlouth15


    roosh wrote: »
    No, the paradox arises in having the same two physical clocks being both synchronised and unsynchronised with each other; but your answers to some of the questions below might negate that, so we have to take a look at them.

    Imagine we set up two stationary cameras on the track. The cameras are positioned such that at a given moment they are opposite the clocks on the moving train as the clocks pass by. A photo is simultaneously (in frame S) taken by both cameras. When we look at the pictures, the same time is shown on both cameras.

    However on the moving train a similar setup with cameras moving with will record different times.

    How can this be?

    The answer is that it is only paradoxical within our common-sense framework of the physical. It is only fully modelled using the Lorent'z transformation and is not paradoxical in the framework of special relativity.


  • #15
    dlouth15
    Registered Users, Registered Users 2 Posts: 1,169 ✭✭✭dlouth15


    This might help visualising the situation without relying on Lorentz transformations.

    There is a stationary source of light sufficiently distant that the light an be considered a plane wave in the region of the train. From a stationary point of view the light flashes and when the light hits the train it hits every part of the train simultaneously. Clocks along the track will measure the arrival of the flash simultaneously.

    However from the point of view of the moving train, the light is not coming from a direction perpendicular to the train. It appears to come from a point somewhat ahead of the where it would be if the train was stationary. This is a bit like if you are walking through rain, the rain you need to angle the umbrella forward a bit to stay dry.

    Therefore the plane wave hits the train at an angle and the front of the train is hit before the back. Clocks travelling with the train will measure the the arrival of the flash as non-simultaneous.

    So we have two sets of clocks that disagree with one another.

    The key to the effect is that light travels at the same speed regardless of the motion of the observer. The other property is that the wave front is always perpendicular to the direction of motion of the light.


  • #16
    roosh
    Registered Users, Registered Users 2 Posts: 2,554 ✭✭✭roosh


    Morbert wrote: »
    It is only perpendicular according to S. If Albert measures the time it takes to travel from the pole to the train as t seconds, Henry will measure γt seconds.
    I'll question that below, but it essentially doesn't matter to the point in question, what does matter is that Henry agrees that the time it takes the reflected phtons to hit the train is the same from both poles; because he will still say that they hit the train in the order in which they are reflected, and thus say that the clocks are not synchronised.

    Different times?
    The distance from the pole to the train should be the same in both reference frames though, shouldn't it not? If we were to draw a line to map the path of the photon from the pole to the train, only the width of the line would be contracted, wouldn't it; so should the distance not be the same, for both? In a previous discussion, where we were talking about one observer firing a laser to kill the other, you mentioned something about the path of the photon forming the radius of the sphere for both observer, it's just that it is rotated at different angles for both, but the radius is still the same is it?

    If the speed of light is constant for both, then the time should not be the same?

    Barrel of the gun
    I think we can use this though, to maybe highlight the issue I've referred to about the treatment of reference frames in Einsteinian relativity. You say that it is only perpendicular according to S, but I think we can demonstrate that it is also perpendicular for S', and that the apparent angle of the line is just an optical effect.

    If we introduce fibre optic cables, or even a laser with a long, see-through barrel, which stretches from the pole to any given distance from the train, the closer the better for us to visualise, so let's say it comes to within millimetres of the train; we coul almost postulate a null distance could we?

    If we imagine the train flying past, from the perspective of Albert, then the barrels of the lasers, mounted on both poles, always form a perpendicular line to the train. The same is true if we consider things from the perspective of someone on the train; as the scenery outside flies past and the lasers fly past the train, they will form a line perpendicular to the train at every point along the train that they pass. This is the path that the reflected photons take; we could just use the lasers if we wish, but the path travelled along the barrel is the path that the light takes, and this forms a perpendicular line to the train at every point along the train. If we imagine see-through barrels it might help.

    Reference frames
    I'll try and outline the issue with the use of reference frames, as I see it, if I can. First, it might be helpful to try and imagine the co-ordinate grid bering projected from just the train, for the time being; imagine being the observer on the train and seeing a grid reference being projected onto the outside world by means of lasers, or whatever means is easiest to imagine.

    Let's take away the barrells of the lasers for the time being, and just use the pole as the physical reference point; as the pole is flying past the window imagine that point on the grid reference system, as represented by the co-ordinates, turns red as the laser fires, and the point on the grid, where the phooton hits the train, turns red as well. Now, if draw a line connecting those two points, the line does form a perpendicular. The issue, however, is that the original red point, on the reference grid, no longer corresponds to where the photon was physically fired from. The photon was physically fired from the laser which has moved along the reference grid and has new co-ordinates. The original red point, on the reference grid, no longer corresponds to a physical location; it forms a point through which the physcal scenery outside rushes through.

    If we re-introduce the barrels of the laser though, we can see the true path of the photon relative to the train, and we can see that it forms a line perpendicular to the train, as well as the referenc grid in S.



    Morbert wrote: »
    Yes, but my understanding of your question was you were asking if relativity says the strikes will be both physically simultaneous and not simultaneous. Relativity says simultaneity is non physical.
    As you've attested to, the light reflected by the half-silvered mirrors in the clocks is physical, so the light which hits the mirrors/clocks on the poles is physical. Also, S' says that the light hits one clock first and then the other. Therefore, the light physically strikes one clock first and then the other; or, using the parlance from the other thread, light physically strikes the clocks in the order of one first, then the other.

    We know that it must strike the clocks physically, because otherwise Henry would disagree that Albert's clocks were running; we know that it must physically strike them in the order of one first, then the other, otherwise Henry would agree that Albert's clocks are synchronised.

    Dual synchronicity
    As the light reflected form both poles physically strikes the clocks on the train, it sets them running; as we've seen, according to S' the light reflected from the poles physically strikes the clocks on the train in the order of one first then the other; this is because, as you've attested to, the light hits the half-silvered mirrors on one pole first and the othe second, and it does so physically; given that the time it takes, for the reflected light to reach the clocks on the train, is the same from each pole, the light physically strikes the clocks in the order of one first then the other. Therefore, the clocks on the train are not synchronised with each other.


    On the other hand, S says that the light physically strikes the clocks, not in the order of one first, then the other, but together, "tied for first"; therefore the clocks on the train are synchronised with each other.


    So, while "the order" of events may not be physical, photons do physically strike clocks and mirrors in a given order; the order in which physically strike seems to be, according to relativity, "frame dependent"; and the synchronisation of clocks is a physical process, and the same two clocks cannot be physically set "in motion" both in the order of one first, then the other, and not in that order.

    Essentially, both statements cannot be true, and both follow from "what relativity says".



    What would relativity say
    I know there's usually a thing made about observers disagreeing on the synchronicity of the clocks - although that doesn't apply when we consider the physical synchronisation of the same clocks - but agreeing on the readings on the clocks, so I'm just wondering how we could go about checking this.

    What would relativity say about two clocks with equal battery life; would a relatively moving observer disagree over the order in which the batteries die?


  • #17
    roosh
    Registered Users, Registered Users 2 Posts: 2,554 ✭✭✭roosh


    dlouth15 wrote: »
    Imagine we set up two stationary cameras on the track. The cameras are positioned such that at a given moment they are opposite the clocks on the moving train as the clocks pass by. A photo is simultaneously (in frame S) taken by both cameras. When we look at the pictures, the same time is shown on both cameras.

    However on the moving train a similar setup with cameras moving with will record different times.

    How can this be?

    The answer is that it is only paradoxical within our common-sense framework of the physical. It is only fully modelled using the Lorent'z transformation and is not paradoxical in the framework of special relativity.
    Yes, but here I think the issue is "resolved" by the disagreement between the observers over the synchronicity of their counterparts clocks, isn't it; that is they will disagree that the photos were taken simultaneously, that one photo was taken after the other, in one of the reference frames.

    The issue we have here is the physicaly synchronisation process of the same two clocks; if we follow the logic of one reference frame, then the physical clocks on the train are not synchronised with each other; if we follow the logic of the other, then the physical clocks on the train are synchronised with each other.

    It's not possible for the same physical clocks to have been physically started in the order of one first, then the other, as well as not having been physically started in that order.


    What does relativity say about two clocks with the same battery life, will there be a disagreement over which battery dies first?


  • #18
    roosh
    Registered Users, Registered Users 2 Posts: 2,554 ✭✭✭roosh


    dlouth15 wrote: »
    This might help visualising the situation without relying on Lorentz transformations.

    There is a stationary source of light sufficiently distant that the light an be considered a plane wave in the region of the train. From a stationary point of view the light flashes and when the light hits the train it hits every part of the train simultaneously. Clocks along the track will measure the arrival of the flash simultaneously.

    However from the point of view of the moving train, the light is not coming from a direction perpendicular to the train. It appears to come from a point somewhat ahead of the where it would be if the train was stationary. This is a bit like if you are walking through rain, the rain you need to angle the umbrella forward a bit to stay dry.

    Therefore the plane wave hits the train at an angle and the front of the train is hit before the back. Clocks travelling with the train will measure the the arrival of the flash as non-simultaneous.

    So we have two sets of clocks that disagree with one another.

    The key to the effect is that light travels at the same speed regardless of the motion of the observer. The other property is that the wave front is always perpendicular to the direction of motion of the light.
    The issue we are talking about though is that you don't have two sets of clocks which disagree with each other, you have one set of clocks which both disagree and agree with each other.

    The issue lies in the physical synchronisation process of the clocks; you say that, from a stationary POV, the light hits very part of the train simultaneosuly, indeed, it does so physically. When it hits the train, as well as physically hitting the censors on the clocks, not in order but all at the same time, the clocks are physically synchronised with each other. From the POV of the train, however, the clocks on the train are not physically synchronised with each other.

    The clocks cannot be both physically synchronised and physically unsynchronised.


  • #19
    Morbert
    Registered Users, Registered Users 2 Posts: 3,457 ✭✭✭Morbert


    roosh wrote: »
    Different times?
    The distance from the pole to the train should be the same in both reference frames though, shouldn't it not? If we were to draw a line to map the path of the photon from the pole to the train, only the width of the line would be contracted, wouldn't it; so should the distance not be the same, for both? In a previous discussion, where we were talking about one observer firing a laser to kill the other, you mentioned something about the path of the photon forming the radius of the sphere for both observer, it's just that it is rotated at different angles for both, but the radius is still the same is it?

    No, it's not the same. This is where you really need to start doing the Lorentz transformations. A simple calculation shows that they're not the same.
    Barrel of the gun
    I think we can use this though, to maybe highlight the issue I've referred to about the treatment of reference frames in Einsteinian relativity. You say that it is only perpendicular according to S, but I think we can demonstrate that it is also perpendicular for S', and that the apparent angle of the line is just an optical effect.

    If we introduce fibre optic cables, or even a laser with a long, see-through barrel, which stretches from the pole to any given distance from the train, the closer the better for us to visualise, so let's say it comes to within millimetres of the train; we coul almost postulate a null distance could we?

    If we imagine the train flying past, from the perspective of Albert, then the barrels of the lasers, mounted on both poles, always form a perpendicular line to the train. The same is true if we consider things from the perspective of someone on the train; as the scenery outside flies past and the lasers fly past the train, they will form a line perpendicular to the train at every point along the train that they pass. This is the path that the reflected photons take; we could just use the lasers if we wish, but the path travelled along the barrel is the path that the light takes, and this forms a perpendicular line to the train at every point along the train. If we imagine see-through barrels it might help.

    Now, using the Lorentz transformations, I want you to describe what Henry measures.
    Reference frames
    I'll try and outline the issue with the use of reference frames, as I see it, if I can. First, it might be helpful to try and imagine the co-ordinate grid bering projected from just the train, for the time being; imagine being the observer on the train and seeing a grid reference being projected onto the outside world by means of lasers, or whatever means is easiest to imagine.

    Let's take away the barrells of the lasers for the time being, and just use the pole as the physical reference point; as the pole is flying past the window imagine that point on the grid reference system, as represented by the co-ordinates, turns red as the laser fires, and the point on the grid, where the phooton hits the train, turns red as well. Now, if draw a line connecting those two points, the line does form a perpendicular. <snip>

    That is not what the Lorentz transformations say will happen.
    As you've attested to, the light reflected by the half-silvered mirrors in the clocks is physical, so the light which hits the mirrors/clocks on the poles is physical. Also, S' says that the light hits one clock first and then the other. Therefore, the light physically strikes one clock first and then the other <snip>

    That is a non sequitur. That the events are physical in no way implies the simultaneity of events are physical. Relativity treats simultaneity as unphysical.
    Dual synchronicity
    As the light reflected form both poles physically strikes the clocks on the train, it sets them running; as we've seen, according to S' the light reflected from the poles physically strikes the clocks on the train in the order of one first then the other; this is because, as you've attested to, the light hits the half-silvered mirrors on one pole first and the othe second, and it does so physically; given that the time it takes, for the reflected light to reach the clocks on the train, is the same from each pole, the light physically strikes the clocks in the order of one first then the other. Therefore, the clocks on the train are not synchronised with each other.


    On the other hand, S says that the light physically strikes the clocks, not in the order of one first, then the other, but together, "tied for first"; therefore the clocks on the train are synchronised with each other.


    So, while "the order" of events may not be physical, photons do physically strike clocks and mirrors in a given order; the order in which physically strike seems to be, according to relativity, "frame dependent"; and the synchronisation of clocks is a physical process, and the same two clocks cannot be physically set "in motion" both in the order of one first, then the other, and not in that order.

    You are being ambiguous here. All that needs to be true for relativity to be consistent is the ordering between physical strikes is not physical. In S, the physical strikes occur simultaneously. In S', they are not. And while the strikes are physical, the ordering of the strikes are not, so it is consistent with relativity.
    Essentially, both statements cannot be true, and both follow from "what relativity says".

    Each statement is true in the appropriate context.
    What would relativity say
    I know there's usually a thing made about observers disagreeing on the synchronicity of the clocks - although that doesn't apply when we consider the physical synchronisation of the same clocks - but agreeing on the readings on the clocks, so I'm just wondering how we could go about checking this.

    What would relativity say about two clocks with equal battery life; would a relatively moving observer disagree over the order in which the batteries die?

    Henry would say one clock runs out of battery before the other, since one clock was started before the other. Albert will say both clocks will run out of battery life at the same time. And since these events are not causally connected, there is no contradiction or paradox.


  • #20
    dlouth15
    Registered Users, Registered Users 2 Posts: 1,169 ✭✭✭dlouth15


    roosh wrote: »
    The issue we are talking about though is that you don't have two sets of clocks which disagree with each other, you have one set of clocks which both disagree and agree with each other.

    The issue lies in the physical synchronisation process of the clocks; you say that, from a stationary POV, the light hits very part of the train simultaneosuly, indeed, it does so physically. When it hits the train, as well as physically hitting the censors on the clocks, not in order but all at the same time, the clocks are physically synchronised with each other. From the POV of the train, however, the clocks on the train are not physically synchronised with each other.

    The clocks cannot be both physically synchronised and physically unsynchronised.
    Special relativity predicts that the same set can be both synchronised and unsynchronised. This is what I was trying to illustrate. You can only measure from one frame of reference however and whether or not the clocks are measured to be synchronised will depend on this frame of reference. This was the purpose of the cameras on the platform. They were there to measure the what the clocks were saying from the "stationary" frame. The clocks on the train are "physically" synchronised from this stationary frame, but "physically" unsynchronised when measured from the frame moving with the train.

    I put "physically" in quotes here because as Morbert points out, simultaneity is dependent on the frame of reference. It doesn't exist in the spacetime that relativity proposes.


  • #21
    roosh
    Registered Users, Registered Users 2 Posts: 2,554 ✭✭✭roosh


    As I mentioned, it's not actually integral to the point; the two necessary points are that Henry measures the same flight time from both poles, from his perspective, the physicality of the photons which are reflected, and the order they are reflected in. We can look at this below, but just to examine the other question first:
    Morbert wrote: »
    No, it's not the same. This is where you really need to start doing the Lorentz transformations. A simple calculation shows that they're not the same.
    ...
    Now, using the Lorentz transformations, I want you to describe what Henry measures.
    ...
    That is not what the Lorentz transformations say will happen.
    As I mentioned, I think the application of the LTs in Einsteinian relativity simply demonstrates what should be an optical effect, if we follow the formalism of relativity. You say that the path of the photon is only perpendicular for S, but if we examine the extension of a continuous physical object, from the poles, we can see that it forms a line perpendicular to the train, not an angled one; the continuous physical object can be used to represent the path of the photon.


    So, imagine that a long pole is being extended from A or B; the pole is extended perpendicularly according to the grid reference of S. As the train rushes past it is continuously extended until it is as close to the train as it can possibly be. From the perspective of the observer on the platform the pole forms a line perpendicular to the train.

    From the perspective of the observer on the train, the pole appears to come at the train from an angle, but when it is right beside the train, it can be seen that it actually forms a line perpendicular to the train.

    This is the same path that the reflected photons take; so the angled line derived using the LTs doesn't correspond to the path that the pole, or the photon took; it corresponds to the path it appears to take from the moving train, or from the stationary train while the platform rushes past.

    We can even extend the pole so that it rips through the train on both sides; when the pole goes through the far side of the train it will cut the train perpendicularly, despite the fact that the point where it first starts cutting one side forms an angled line to where it starts cutting the other. That is just due to the motion of either the train or the platform, but it still forms a perpendicular line to both.

    Morbert wrote: »
    That is a non sequitur. That the events are physical in no way implies the simultaneity of events are physical. Relativity treats simultaneity as unphysical.
    You are right to an extent "the simultaneity" isn't physical; "the simultaneity" doesn't consist of matter; "the simultaneity" is a concept. But I'm not saying "the simultaneity" is physical, I'm saying that the photon strikes are physical and that they happen in the order of one first, then the other, according to the measurements of the relatively moving observer; these measurements supposedly correspond to the physical world, so we can deduce that the photons physically strike the clocks, and they do so in the order of one first, then the other, in the physical world.

    So, we are perfectly entitled to say that the photons physically strike in the order of one first then the other. Only if the relatively moving observers measurements didn't correspond to the physical world would we not be able to say that; but they, supposedly, do, so we can.

    Morbert wrote: »
    You are being ambiguous here. All that needs to be true for relativity to be consistent is the ordering between physical strikes is not physical. In S, the physical strikes occur simultaneously. In S', they are not. And while the strikes are physical, the ordering of the strikes are not, so it is consistent with relativity.
    And "the ordering" isn't physical, it doesn't consist of matter, it's a concept; but the photons do physically strike the clocks according to both observers, but according to one observer they physically strike in the order of one first, then the other, while according to the other they physically strike, not in that order, but "tied for first".

    This is why Henry disagrees that Albert's clocks are synchronised; it's because he says that a photon physically strikes one clock first, to set it in motion before the other; if he were to say that the photons don't physically strike the clocks in that order then he would either conclude that Albert's clocks are not set running, or that Albert's clocks are synchronised, and he wouldn't disagree about the synchronicity.


    Morbert wrote: »
    Each statement is true in the appropriate context.
    "The physical clocks on the train have been physically synchronised with each other" and "the physical clocks on the train are physically unsynchronised with each other" are mutually exclusive statements in any context.


    Morbert wrote: »
    Henry would say one clock runs out of battery before the other, since one clock was started before the other. Albert will say both clocks will run out of battery life at the same time. And since these events are not causally connected, there is no contradiction or paradox.
    Of course, I was thinking of both clocks being switched on with the battery running, but didn't factor in the ticking of the clocks consuming more energy.

    Either way, we can't have two physical clocks on a train being physically started both synchronously and asynchronously by the same photons.


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  • #22
    roosh
    Registered Users, Registered Users 2 Posts: 2,554 ✭✭✭roosh


    dlouth15 wrote: »
    Special relativity predicts that the same set can be both synchronised and unsynchronised. This is what I was trying to illustrate. You can only measure from one frame of reference however and whether or not the clocks are measured to be synchronised will depend on this frame of reference. This was the purpose of the cameras on the platform. They were there to measure the what the clocks were saying from the "stationary" frame. The clocks on the train are "physically" synchronised from this stationary frame, but "physically" unsynchronised when measured from the frame moving with the train.

    I put "physically" in quotes here because as Morbert points out, simultaneity is dependent on the frame of reference. It doesn't exist in the spacetime that relativity proposes.
    "Simultaneity" might be frame dependent, but the synchronisation process of the clocks is physical, not in the inverted commas sense. Here we have a case of the same clocks being physically started in the order of one first, then the other, and not being started in that order, by the same photons physically striking the clocks.

    That can't happen in the physical world.


  • #23
    Morbert
    Registered Users, Registered Users 2 Posts: 3,457 ✭✭✭Morbert


    roosh wrote: »
    As I mentioned, it's not actually integral to the point; the two necessary points are that Henry measures the same flight time from both poles, from his perspective, the physicality of the photons which are reflected, and the order they are reflected in. We can look at this below, but just to examine the other question first:


    As I mentioned, I think the application of the LTs in Einsteinian relativity simply demonstrates what should be an optical effect, if we follow the formalism of relativity. You say that the path of the photon is only perpendicular for S, but if we examine the extension of a continuous physical object, from the poles, we can see that it forms a line perpendicular to the train, not an angled one; the continuous physical object can be used to represent the path of the photon.


    So, imagine that a long pole is being extended from A or B; the pole is extended perpendicularly according to the grid reference of S. As the train rushes past it is continuously extended until it is as close to the train as it can possibly be. From the perspective of the observer on the platform the pole forms a line perpendicular to the train.

    From the perspective of the observer on the train, the pole appears to come at the train from an angle, but when it is right beside the train, it can be seen that it actually forms a line perpendicular to the train.

    This is the same path that the reflected photons take; so the angled line derived using the LTs doesn't correspond to the path that the pole, or the photon took; it corresponds to the path it appears to take from the moving train, or from the stationary train while the platform rushes past.

    We can even extend the pole so that it rips through the train on both sides; when the pole goes through the far side of the train it will cut the train perpendicularly, despite the fact that the point where it first starts cutting one side forms an angled line to where it starts cutting the other. That is just due to the motion of either the train or the platform, but it still forms a perpendicular line to both.

    Do the relevant Lorentz transformations. They are not optical illusions and hold for any arbitrary system whether or not light is involved. Heck, even do the Galilean transformations. They are sufficient, at least, in showing you the path isn't perpendicular. Your statement about the barrel being at an angle is also nonsensical. The barrel is always perpendicular to the train. I am saying the path of the photon which, according to S', is travelling down a moving barrel, is not perpendicular. We had a nearly identical discussion ages ago regarding the MM experiment.

    There seems to be an emerging pattern here. You tender an elaborate thought experiment, only considering part of the solution, and I present the Lorentz transformations between two observers to exhibit the consistency between two observers.

    If you are not confident in using LTs, that's fine. Let me know and I will help. But trying to work out the consequences in various thought experiments by haphazardly supposing this and that clearly isn't working.
    You are right to an extent "the simultaneity" isn't physical; "the simultaneity" doesn't consist of matter; "the simultaneity" is a concept. But I'm not saying "the simultaneity" is physical, I'm saying that the photon strikes are physical and that they happen in the order of one first, then the other, according to the measurements of the relatively moving observer; these measurements supposedly correspond to the physical world, so we can deduce that the photons physically strike the clocks, and they do so in the order of one first, then the other, in the physical world.

    So, we are perfectly entitled to say that the photons physically strike in the order of one first then the other. Only if the relatively moving observers measurements didn't correspond to the physical world would we not be able to say that; but they, supposedly, do, so we can.

    And "the ordering" isn't physical, it doesn't consist of matter, it's a concept; but the photons do physically strike the clocks according to both observers, but according to one observer they physically strike in the order of one first, then the other, while according to the other they physically strike, not in that order, but "tied for first".

    This is why Henry disagrees that Albert's clocks are synchronised; it's because he says that a photon physically strikes one clock first, to set it in motion before the other; if he were to say that the photons don't physically strike the clocks in that order then he would either conclude that Albert's clocks are not set running, or that Albert's clocks are synchronised, and he wouldn't disagree about the synchronicity.

    "The physical clocks on the train have been physically synchronised with each other" and "the physical clocks on the train are physically unsynchronised with each other" are mutually exclusive statements in any context.

    The only mutually exclusive statements are the statement you made above, acknowledging that simultaneity is unphysical, and the statement you made at the end, claiming the clocks must be either physically synchronised or physically desynchronised. Since simultaneity is frame-dependent and unphysical, synchronisation is also unphysical, as it relies on simultaneity to coordinate events.


  • #24
    dlouth15
    Registered Users, Registered Users 2 Posts: 1,169 ✭✭✭dlouth15


    roosh wrote: »
    "Simultaneity" might be frame dependent, but the synchronisation process of the clocks is physical, not in the inverted commas sense. Here we have a case of the same clocks being physically started in the order of one first, then the other, and not being started in that order, by the same photons physically striking the clocks.

    That can't happen in the physical world.
    Paradoxical and counter intuitive though it may seem, this is what is predicted. The same photons strike the same clocks. However in one frame they strike simultaneously and in the other frame they strike in order. The clocks are therefore synchronised (and remain synchronised) in one frame and unsynchronised (and remain unsynchronised) in the other.

    Yes the synchronisation process is physical but this physical process consists of a set of distinct spacetime events. The temporal order of those events, whether they are simultaneous or not in a given frame depends on the frame of reference itself.

    In special relativity this is not paradoxical even though it conflicts strongly with our intuition of how things should be.


  • #25
    roosh
    Registered Users, Registered Users 2 Posts: 2,554 ✭✭✭roosh


    Morbert wrote: »
    For the love of God.

    Do the relevant Lorentz transformations. They are not optical illusions and hold for any arbitrary system whether or not light is involved. Heck, even do the Galilean transformations. They are sufficient, at least, in showing you the path isn't perpendicular. Your statement about the barrel being at an angle is also nonsensical. The barrel is always perpendicular to the train. I am saying the path of the photon which, according to S', is travelling down a moving barrel, is not perpendicular. We had a nearly identical discussion ages ago regarding the MM experiment.

    There seems to be an emerging pattern here. You tender an elaborate thought experiment, only considering part of the solution, and I present the Lorentz transformations between two observers to exhibit the consistency between two observers.

    If you are not confident in using LTs, that's fine. Let me know and I will help. But trying to work out the consequences in various thought experiments by haphazardly supposing this and that clearly isn't working.
    So the point you made in the other thread, about the photons tracing the radius of the sphere - where one observer attempted to kill the other using a laser - but just that the sphere is rotated, can we take it that the radii are different lengths then?

    Extended poles
    The point about the poles being extended out from A and B is an attempt to demonstrate that the path of the photon should be perpendicular for the observer on the train also, even if it appears to be a different angle.

    Again, if we imagine the pole starting to extend out from pole A towards the train, it will always form a right angle to the train, even from the perspective of someone on the train; this is easiest to imagine if we picture the pole just outside the window of the train.

    As mentioned, the pole extends through the side of the train; we can allow for a slit that goes almost the length of the train on both sides, so that the pole can freely pass through the train out the other side.

    Now, if the pole had followed an angled path towards the train, then it should intersect the train at an angle, such that if there were two observers in the carriage, standing on either side, who can see the pole which approaching them, then they should see the pole as being angled towards one of them; but they won't because the pole will form a line perpendicular to both sides of the carriage that it has passed through.

    All this despite the fact that it appears to approach at an angle, from the perspective of some observers on the train, who only see the pole being extended, but don't see it extended through the carriage.


    The path of the photon matches the path of the pole exactly.
    Morbert wrote: »
    The only mutually exclusive statements are the statement you made above, acknowledging that simultaneity is unphysical, and the statement you made at the end, claiming the clocks must be either physically synchronised or physically desynchronised. Since simultaneity is frame-dependent and unphysical, synchronisation is also unphysical, as it relies on simultaneity to coordinate events.
    You're conflating the idea that the concept called "simultaneity", or "the order", is non-physical, that is not constituted of matter, with the idea that photons physically strike a physical clock in a given order.

    You have already stated that the photons strike the clocks in the order of one first and then the other, according to one observer, and that these strikes are physical. So it follows perfectly that the photons physically strike the clocks in the order of one first then the other.


  • #26
    Morbert
    Registered Users, Registered Users 2 Posts: 3,457 ✭✭✭Morbert


    roosh wrote: »
    So the point you made in the other thread, about the photons tracing the radius of the sphere - where one observer attempted to kill the other using a laser - but just that the sphere is rotated, can we take it that the radii are different lengths then?

    Extended poles
    The point about the poles being extended out from A and B is an attempt to demonstrate that the path of the photon should be perpendicular for the observer on the train also, even if it appears to be a different angle.

    Again, if we imagine the pole starting to extend out from pole A towards the train, it will always form a right angle to the train, even from the perspective of someone on the train; this is easiest to imagine if we picture the pole just outside the window of the train.

    As mentioned, the pole extends through the side of the train; we can allow for a slit that goes almost the length of the train on both sides, so that the pole can freely pass through the train out the other side.

    Now, if the pole had followed an angled path towards the train, then it should intersect the train at an angle, such that if there were two observers in the carriage, standing on either side, who can see the pole which approaching them, then they should see the pole as being angled towards one of them; but they won't because the pole will form a line perpendicular to both sides of the carriage that it has passed through.

    All this despite the fact that it appears to approach at an angle, from the perspective of some observers on the train, who only see the pole being extended, but don't see it extended through the carriage.

    The path of the photon matches the path of the pole exactly.

    Do the Lorentz transformations. If you can't let me know and I will help. Otherwise you are going to keep digging yourself into a hole.

    [edit]- Also, I am beginning to wonder if you are even reading my posts. You go to great lengths above to argue that the barrel is perpendicular to the train, even though I said in my previous post that nobody says the barrel isn't perpendicular to the train.
    You're conflating the idea that the concept called "simultaneity", or "the order", is non-physical, that is not constituted of matter, with the idea that photons physically strike a physical clock in a given order.

    Again, you are hiding behind ambiguous phrasing. If by "photons physically strike in a given order" you mean "the photon strikes are physical, but the order in which they strike is unphysical", then there is no problem. If you mean something contrary to that, then you are wrong.
    You have already stated that the photons strike the clocks in the order of one first and then the other, according to one observer, and that these strikes are physical. So it follows perfectly that the photons physically strike the clocks in the order of one first then the other.

    I.e. The photons physically strike, but the order in which they physically strike is unphysical. The contradiction you are attempting to establish rests on the assumption that the ordering of the physical strikes is also physical. It's not, so no contradiction.


  • #27
    roosh
    Registered Users, Registered Users 2 Posts: 2,554 ✭✭✭roosh


    Morbert wrote: »
    Do the Lorentz transformations. If you can't let me know and I will help. Otherwise you are going to keep digging yourself into a hole.
    I'm not questioning what the Lorentz transformations say, I'm questioning what they represent, in the case of Einsteinian relativity.

    In the example of the pole, the observers on the train won't see it disecting the carriage at an angle, so it can't have arrived at an angle, despite the fact that it appears to do so, as it approaches the train.

    In the case of the radii of the [rotated] spheres, are the radii different legnths?


    Morbert wrote: »
    Again, you are hiding behind ambiguous phrasing. If by "photons physically strike in a given order" you mean "the photon strikes are physical, but the order in which they strike is unphysical", then there is no problem. If you mean something contrary to that, then you are wrong.
    As I have stated, you are conflating two ideas; "the order" isn't physical; that is, the concept isn't constituted out of matter; but the photons physically strike one clock first, then the other. You have stated as much yourself, although indirectly. So you're not even hiding behind ambiguity, you're simply not being consistent in what you've explicitly stated.

    Again, the concept of "the order" is not constituted out of matter, so the concept isn't physical; that doesn't affect the point being made though, bcos the photons physically strike the clocks in the order of one first, then the other.

    Here, the clause "one first, then the other", refers to the sequence in which the physical photon strikes occur; it's a descriptive clause which describes the phyiscal photon strikes; it functions like an adjective, not a noun; it's not a thing, it's not physical; but the photons do physically strike in the given order.

    This leads to a physical paradox.


    Morbert wrote: »
    I.e. The photons physically strike, but the order in which they physically strike is unphysical. The contradiction you are attempting to establish rests on the assumption that the ordering of the physical strikes is also physical. It's not, so no physical contradiction.
    That's not what its based on, as I have pointed out above. So there is a physical contradiction.


  • #28
    Morbert
    Registered Users, Registered Users 2 Posts: 3,457 ✭✭✭Morbert


    roosh wrote: »
    I'm not questioning what the Lorentz transformations say, I'm questioning what they represent, in the case of Einsteinian relativity.

    In the example of the pole, the observers on the train won't see it disecting the carriage at an angle, so it can't have arrived at an angle, despite the fact that it appears to do so, as it approaches the train.

    In the case of the radii of the [rotated] spheres, are the radii different legnths?

    And as I said before, nobody is arguing that the barrel is not perpendicular to the train. The path of the photon travelling down the moving barrel, however, is not perpendicular to the train.

    The sphere question is easily answered with a Lorentz transformation, as is the entire question of whether or not the photon path is perpendicular.
    As I have stated, you are conflating two ideas; "the order" isn't physical; that is, the concept isn't constituted out of matter; but the photons physically strike one clock first, then the other. You have stated as much yourself, although indirectly. So you're not even hiding behind ambiguity, you're simply not being consistent in what you've explicitly stated.

    Again, the concept of "the order" is not constituted out of matter, so the concept isn't physical; that doesn't affect the point being made though, bcos the photons physically strike the clocks in the order of one first, then the other.

    Here, the clause "one first, then the other", refers to the sequence in which the physical photon strikes occur; it's a descriptive clause which describes the phyiscal photon strikes; it functions like an adjective, not a noun; it's not a thing, it's not physical; but the photons do physically strike in the given order.

    This leads to a physical paradox.

    You are entirely, completely, missing the point. "One first, then the other" is a frame-dependent, descriptive clause, referencing an unphysical attribute for a physical strike. The same way "boring" and "interesting" are unphysical, person-dependent descriptions of a film, a physical thing.


  • #29
    roosh
    Registered Users, Registered Users 2 Posts: 2,554 ✭✭✭roosh


    Morbert wrote: »
    And as I said before, nobody is arguing that the barrel is not perpendicular to the train. The path of the photon travelling down the moving barrel, however, is not perpendicular to the train.
    Forget about the already extended barrel, and imagine a pole being extended from A; you can picture the barrel of the laser being extended from the top of A out towards the train if its helpful, such that it starts from the top of A and moves towards the train, at whatever speed.

    We can imagine that the sides of the train have been designed such that the middle section of each sidewall has been removed, but connected at either end of the train; this means that the pole which is being extended from A can pass right through the train unimpeded and the train can travel on unimpeded.

    Now, as the pole approaches the train, it always forms a right angle to the train; as it moves through the first sidewall of the carriage, it forms a right angle to it, and as it proceeds through the other side wall it passes through it at a right angle also. It might be helpful to imagine the barrel of the laser extending through the sidewalls of the train carriage.

    Imagine there are two observers at the back of the carriage, one on either side of the aisle, and they see the pole, fully extended through the side walls of the carriage, coming towards them; they won't see the pole coming at them angled towards one of them, they will see the pole approaching them equally, by forming right angles to the sidewalls of the train.

    This is true, despite the fact that, as the pole was being launched from A, it appeared to travel towards the train at an angle, and if we use the reference frame S', it would depict the path of the tip of the pole as following an angled line, as well as all subsequent points on the pole; but the pole disects the train perpendicularly; this can clearly be seen by the observers on the train when the pole passes through, still moving relative to the train.

    Morbert wrote: »
    The sphere question is easily answered with a Lorentz transformation, as is the entire question of whether or not the photon path is perpendicular.
    So is that a:
    - yes, the radii of the sphere are different lengths
    - no, the radii are the same length
    - each observer measures the same length of the radius but disagrees about their counterparts measurement
    or
    - some other explanation?

    Morbert wrote: »
    You are entirely, completely, missing the point. "One first, then the other" is a frame-dependent, descriptive clause, referencing an unphysical attribute for a physical strike. The same way "boring" and "interesting" are unphysical, person-dependent descriptions of a film, a physical thing.
    Except that whether or not an observer measures the photons stiking in order doesn't depends on their previous life experiences, their culture, etc., as the concepts of "boring" and "interesting" do.

    I'm not arguing that its not frame dependent; the point is that the statement; "the photons physically strike the clocks on the train in the order of one first, then the other" is a valid statement under relativity.

    So too is, "the same photons physically strike the same clocks on the train in a different order".


    The point is that, that is not physically possible, and is physically paradoxical.


  • #30
    dlouth15
    Registered Users, Registered Users 2 Posts: 1,169 ✭✭✭dlouth15


    Nice Youtube video here:

    http://www.youtube.com/watch?v=wteiuxyqtoM

    Bolts of light hitting the train are simultaneous from frame of the platform but non-simultaneous when observed from the frame of the moving train. Although not in the video clocks on the train started by those bolts of lightning will therefore be synchronised when viewed from the frame of the platform but non-synchronised when viewed from the moving train.

    The same bolts of lightning. The same clocks. Different frames. Therefore different observations of simultaneity of physical events. Simples!


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  • #31
    roosh
    Registered Users, Registered Users 2 Posts: 2,554 ✭✭✭roosh


    dlouth15 wrote: »
    Nice Youtube video here:

    http://www.youtube.com/watch?v=wteiuxyqtoM

    Bolts of light hitting the train are simultaneous from frame of the platform but non-simultaneous when observed from the frame of the moving train. Although not in the video clocks on the train started by those bolts of lightning will therefore be synchronised when viewed from the frame of the platform but non-synchronised when viewed from the moving train.

    The same bolts of lightning. The same clocks. Different frames. Therefore different observations of simultaneity of physical events. Simples!
    You may want to watch the video again, but this time imagine two clocks which are back to back in the centre of the train, where the passenger is. According to the observer on the platform, the clock facing the front of the train gets struck first and is started first, while the rear facing clock gets started second; here both observers agree that the clocks are not synchronised.

    Note also that the video depicts the light physically meeting the passenger in the order of one first, then the other.


    EDIT: it might also be worth pointing out that the reason the clocks are supposedly both synchronised and unsynchronised is because the lightning supposedly physically strikes the clocks in the order of one first, then the other, according to one reference frame, but physically strikes them in a different order according to the other.


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