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Thread: Plane of Simultaneity

  1. #1 Plane of Simultaneity 
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    Hello; I have seen this concept referred to in several places, but can find no real definition of what is meant by it.

    e.g. http://upload.wikimedia.org/wikipedia/commons/thumb/c/ce/Twin_Paradox_Minkowski_Diagram.svg/333px-Twin_Paradox_Minkowski_Diagram.svg.png

    But where does this idea come from?

    The nearest I can determine is that it is predicated by a line drawn out of scale in a Minkowski diagram.

    Traditional vs scale drawing.jpg

    in the traditional drawing the rotated axis has the same coordinates spacing as the stationary axis.
    But when corrected so that the rotated axis' coordinates are along the rotated axis, so that the the ct' coordinate is what the owner of the diagram is measuring; then, as expected,drawn to scale the 'plane of simultaneity' is parallel to the abscissa - the x axis. (After all that is what a line parallel to the x axis means! A particular value of ct.)

    So can someone explain this for me? For as far as I can see the very idea of a plane of simultaneity is mathematically nonsense; as it is redefining the meaning of a cartesian diagram! I mean, how can a point above a line have the same value as a point on the line? It defies the very construction of the diagram in the first place!

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    The plane of simultaneity is simply a means of establishing a simultaneity convention between two observers in relative motion. The line has no meaning in of itself, it is just a means of comparing the "now" of the stationary observer with the "now" of the moving observer.

    If there was a third observer, moving slower than the one in the diagram, those lines would cross his worldline at the point where his "now" also matches the "now" of the stationary observer.


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    Quote Originally Posted by SpeedFreek View Post
    The plane of simultaneity is simply a means of establishing a simultaneity convention between two observers in relative motion. The line has no meaning in of itself, it is just a means of comparing the "now" of the stationary observer with the "now" of the moving observer.

    If there was a third observer, moving slower than the one in the diagram, those lines would cross his worldline at the point where his "now" also matches the "now" of the stationary observer.
    But how can "now" for anyone be different from the "now" on the time axis? i.e. the line through the point on the time axis, parallel to the x-axis?

    The diagram is from the view-point of the stationary observer (system K) system K' (and system K'' etc) must be drawn as observed from system K, so as far as the diagram is concerned there is only one "now".

    Or else one is mixing the views from different systems (k,K',K''...) on the one diagram - and that surely makes no sense?
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    May I ask, is it the plane of simultaneity that you are having trouble with, or the concept of the relativity of simultaneity itself?

    Do you understand the reasoning behind Einstein's famous "train and embankment" thought experiment?
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    Quote Originally Posted by SpeedFreek View Post
    May I ask, is it
    Quote Originally Posted by SpeedFreek View Post
    the plane of simultaneity that you are having trouble with, or the concept of the relativity of simultaneity itself?

    Do you understand the reasoning behind Einstein's famous "train and embankment" thought experiment?
    Well yes, I think I do understand exactly how that works, but, to me, that understanding leads to an inevitable paradox.

    It is describing three events: Lightning striking point A, lightning striking point B and the meeting of light reflected from A and B at the midpoint of the line AB.

    Events are defined by location and time; they do not and cannot have movement. Movement is a change of location between two moments(points) of time.

    Any observer at the origin of their Frame of reference is, by definition at rest in that Frame of Reference.

    Hence, in the Embankment observer's FoR, he is at rest at M, midway between A and B and the reflected lights meet at his location.

    But the reciprocal situation obtains for the observer on the train.

    She is at rest at M', the midpoint between A and B in her FoR. In her Frame of Reference. She is at rest, stationary, unmoving at M', the midpoint of the line AB. (apologies for being repetitive, but this is an important, nay, crucial point).


    Then, as she is at rest in her FoR, she cannot be moving toward one and away from the other lightning strike!


    To her, in her own FoR she is at the midpoint when the reflected lights meet.


    To her, in her Frame of Reference, the two events, the lightning strikes meet Einstein's test of Simultaneity.


    How can they not do?


    To the Embankment observer, however, it will be equally obvious and Provable that, in his Frame of Reference, Einstein's test for simultaneity is not met, for the observer in the train; just as the reciprocal is true, in that the observer on the train will be equally assured that, in her FoR, the Embankment observer's observations do not satisfy Einstein's test.


    So, it seems to me, that the True definition of the Relativity of Simultaneity is that Einstein's test for Simultaneity will be satisfied in any and every Frame of Reference by a suitably located observer, but, such an observer will be equally convinced that the test can only be satisfied in their Frame of Reference.


    Which conclusion is satisfying as it removes the Paradox of the Planes of Simultaneity where each point on a Minkowski Diagram represents two different times in the same FoR!


    Sowhere am I going wrong???!
    Last edited by space at the centre; December 9th, 2012 at 06:41 AM. Reason: text spacing
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    The reason for the relativity of simultaneity is that light has a finite speed, but that speed is always measured to be the same by any observer, regardless of any motion of the observer.

    Let's take a simpler experiment:
    A is sitting in the centre of a train carriage and there is a bulb above his head. This bulb lights up, and the light propagates at c in both directions, up and down the carriage. The light will reach each end of the carriage at the same time, in the frame of A, regardless of whether the train is moving or not.



    Now we move to the frame of B, standing on the embankment. Just as the train passes B, and the centre of the train is directly in front of B, the bulb turns on in the centre of the carriage. The light propagates up and down the carriage at c, in relation to the rest frame of B, on the embankment. But the train is also moving in relation to B, moving across his view. So this is what happens in the frame of B:

    The light reaches the back of the carriage before it reaches the front. It does not reach the ends of the carriage at the same time, from the frame of B.

    So, did the light reach the ends of the carriage at the same time, or did it reach the back of the carriage before it reached the front?

    The answer is.... both options.

    Whether two events that are separated by space are simultaneous, or not, is frame dependent. There is no such thing as absolute simultaneity.
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    Thank you, neat little diagrams:

    But are you not falling into the usual misplacing of events, and where they are observed from?

    In Spacetime the bulb lights up at location LB; and when t=2, the light has travelled a distance L/2 in each direction.

    In the Frame of A, A being at rest with Spacetime, from her perspective, the carriage, also at rest in her Frame, occupies the space from -L/2 to +L/2 and so the light will have reached both ends of the carriage.

    However, in the Frame of B, it is he who is at rest at location LB, when the bulb lights up; and it is he who sees the light move the distance L/2 in each direction in time t=2.

    The light having made the identical journey, from event B, the distance L/2 in both directions, in both Frame A and Frame B.

    But in Frame B, where B is at rest, it is A in the carriage that is moving and by time t=2, A in the carriage, will have moved away from LB.

    So the light will have moved exactly the same distance in either Frame, but in Frame B the carriage has taken the ends of the carriage away from the locations where the light will be at t=2.


    So your question isn't: "So, did the light reach the ends of the carriage at the same time, or did it reach the back of the carriage before it reached the front?"

    It is: "So, where will the ends of the carriage be when the light has travelled the distance L/2 in both directions? Will it still be at rest relative to LB where the light went on, or will LB be back on the embankment opposite B?"

    It is surely all about what maps to where in the different Frames of Reference; all is relative and reciprocal.
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    Quote Originally Posted by space at the centre View Post
    Thank you, neat little diagrams:

    But are you not falling into the usual misplacing of events, and where they are observed from?
    No, there is no misplacing of events, and where they are observed from, or the relative motion of the observer, makes no difference here.

    The observer B on the embankment knows when he saw each light reach each end of the carriage. He knows the distance between those events and himself. He subtracts the light-travel time to those events, in order to establish the actual time those events occurred, rather than just when he saw those events.

    He will calculate those events to have occurred at different times, after calculating out the light-travel time to those events.

    But observer A on the train will calculate those events to have occurred at the same time, after calculating out the light-travel time to those events.

    Because light-travel time is not frame dependent, this means that if there is relative motion between frames then simultaneity cannot be absolute.

    When we work out what maps to where in different frames of reference, we find that there is no absolute simultaneity, but rather simultaneity is relative.

    What this means is that "now" is a purely local concept.
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    I believe the inverse of the linelenghts is proportional to the inner time. Or something like that. Either way, the diagram isn't so complex in origin.
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    Quote Originally Posted by SpeedFreek View Post
    The reason for the relativity of simultaneity is that light has a finite speed, but that speed is always measured to be the same by any observer, regardless of any motion of the observer.

    Let's take a simpler experiment:
    A is sitting in the centre of a train carriage and there is a bulb above his head. This bulb lights up, and the light propagates at c in both directions, up and down the carriage. The light will reach each end of the carriage at the same time, in the frame of A, regardless of whether the train is moving or not.



    Now we move to the frame of B, standing on the embankment. Just as the train passes B, and the centre of the train is directly in front of B, the bulb turns on in the centre of the carriage. The light propagates up and down the carriage at c, in relation to the rest frame of B, on the embankment. But the train is also moving in relation to B, moving across his view. So this is what happens in the frame of B:

    The light reaches the back of the carriage before it reaches the front. It does not reach the ends of the carriage at the same time, from the frame of B.

    So, did the light reach the ends of the carriage at the same time, or did it reach the back of the carriage before it reached the front?

    The answer is.... both options.

    Whether two events that are separated by space are simultaneous, or not, is frame dependent. There is no such thing as absolute simultaneity.
    Hey! Your description is good!
    But the ending gives me trouble.
    How did you get to your conclusion:
    "There is no such thing as absolute simultaneity."
    I try to understand, but I only get to the point:
    "we cant measure absolute simultaneity"
    H
    ow do you manage to take the next step?
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    Quote Originally Posted by SpeedFreek View Post
    The reason for the relativity of simultaneity is that light has a finite speed, but that speed is always measured to be the same by any observer, regardless of any motion of the observer.
    Quote Originally Posted by SpeedFreek View Post

    Let'stake a simpler experiment:
    Ais sitting in the centre of a train carriage and there is a bulbabove his head. This bulb lights up, and the light propagates at cinboth directions, up and down the carriage. The light will reach eachend of the carriage at the same time, in the frame of A, regardlessof whether the train is moving or not.
    Right, straightforward, nothing wrong with that.


    Now we move to the frame of B, standing on the embankment. Just as the train passes B, and the centre of the train is directly in front of B, the bulb turns on in the centre of the carriage. The light propagates up and down the carriage at c, in relation to the rest frame of B, on the embankment. But the train is also moving in relation to B, moving across his view. So this is what happens in the frame of B:

    The light reaches the back of the carriage before it reaches the front.It does not reach the ends of the carriage at the same time, from the frame of B.
    But here we do have a problem, for your example is impossible! For the simple reason that the light from the bulb is now travelling at c+v toward the back of the carriage and c-v towards the front; and as we all know light must travel at c relative to any observer and that includes relative to A from B's perspective; and relative to B from A's perspective!


    And, we also know that this conundrum is resolved by the Lorentz Transformation Equations. So that when the moving Frame of Reference is 'rotated' the measurements made in that Frame are transformed to make them relative to the observer.


    So, did the light reach the ends of the carriage at the same time, or did it reach the back of the carriage before it reached the front?



    As you say, from A's perspective, yes, it reaches both ends at the same time; but from B's perspective, the times to the ends of the carriage will both be t=2γ, both measurements transformed by the Lorentz equations; so how can they be other than equal?


    So while the light meeting the ends of the carriage must be simultaneous, it is Einstein's test for simultaneity that can't be met in B's Frame.
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    Quote Originally Posted by sigurdV View Post
    Hey! Your description is good!
    But the ending gives me trouble.
    How did you get to your conclusion:
    "There is no such thing as absolute simultaneity."
    I try to understand, but I only get to the point:
    "we cant measure absolute simultaneity"
    H
    ow do you manage to take the next step?
    If events are simultaneous in one frame of reference, but are not simultaneous in another frame of reference (where both frames subtract the light travel time from the event to the observer, so both frames know when the events actually occured in relation to themselves), then simultaneity cannot be absolute, it can only be relative. Both observers versions of the timing of the the events is reality.
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    Quote Originally Posted by space at the centre View Post
    But here we do have a problem, for your example is impossible! For the simple reason that the light from the bulb is now travelling at c+v toward the back of the carriage and c-v towards the front;
    No, it is not. The light simply travels at c, to both observers. It is the train that is moving differently in relation to one observer when compared to the other, not the light! Neither observer measures light to be travelling at anything other than c.

    Care should be taken here, as it is easy to inadventantly "mix" frames in your mind, and try to seek one answer that applies to both frames, when there is no such answer.

    Quote Originally Posted by space at the centre View Post
    And, we also know that this conundrum is resolved by the Lorentz Transformation Equations. So that when the moving Frame of Reference is 'rotated' the measurements made in that Frame are transformed to make them relative to the observer.
    This allows either observer to make the transformation to the other frame, in order for the results to be consistent in the other frame, but it does not change the relativity of simultaneity. The observer on the embankment can calculate that, in the frame of the train the events were simultaneous, but that doesn't change the fact that the events were not simultaneous from the frame of the embankment.

    Quote Originally Posted by space at the centre View Post
    As you say, from A's perspective, yes, it reaches both ends at the same time; but from B's perspective, the times to the ends of the carriage will both be t=2γ, both measurements transformed by the Lorentz equations; so how can they be other than equal?
    You never apply the Lorentz transformation to your own frame, from your own frame. You can only apply it to the other frame, or to your own frame from the other frame.

    From B's frame, the times to the ends of the carriage are NOT t=2y, as the carriage as well as the light is moving in relation to B.

    I would recommend you read through the Special Relativity Primer that is stickied at the top of the physics forum.
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    Quote Originally Posted by space at the centre View Post

    But here we do have a problem, for your example is impossible! For the simple reason that the light from the bulb is now travelling at c+v toward the back of the carriage and c-v towards the front; and as we all know light must travel at c relative to any observer and that includes relative to A from B's perspective; and relative to B from A's perspective!
    The bolded section is wrong. Relativity requires that light travels at c relative to any observer as measured by that observer, it does not require light to travel at c relative to an object that itself is moving relative to the observer. In Relativity, we don't even refer to the second example as relative speed but as "closing speed". Thus while an observer cannot measure light as moving at anything other than c with respect to himself, or anything at rest with respect to himself, this does not apply to the closing speed between light and something moving with respect to the observer.

    So for instance, if we have an observer at rest with respect to two clocks and we have a flash of light that originates at a point halfway between them, and these clocks are designed to start running when the light reaches them, we get something like this.



    The light expands at a constant speed outward from the emission point striking the two clocks simultaneously and staring them.

    However, according to an observer with a relative motion with respect to the two clocks, something else happens. The light still expands at a constant speed outward from the emission point. The clocks, on the other hand do not maintain a constant distance from the emission point, one clock moves closer and the other further away and we get this. The closing speeds between the light and the clocks are not required to be equal to c.



    The light strikes one clock and starts it running before it hits the other and starts it running. After that, the clocks continue to run out of sync.

    Remember, these are the same clocks in the exact same scenario, just according to different frames of reference.
    "Men are apt to mistake the strength of their feelings for the strength of their argument.
    The heated mind resents the chill touch & relentless scrutiny of logic"-W.E. Gladstone


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    I feel that demonstrates a lack of understanding of what is happening and therefore of relativity.

    However one views that scenario it is physically impossible to view the same clock reading different physical displays in different Frames. Each clock's dial will read only one time at any one instant. If the two physical clock's show the same display in one frame, are synchronised, they must be,synchronised in all frames.

    They will not and cannot, read different times in different frames.

    But it is the time that is different in each frame - the length of each second that is different. It is the fact that one minute in one frame shows as 60 seconds on the clock, yet in another frame, that same minute on that same physical clock, might represent only 57 seconds or 72 seconds in the time scale of that other frame.


    SpeedFreek, I am afraid that your taking the light bulb in the train as an easier example than Einstein's train doesn't work either; for in the case of the light bulb there is no test for simultaneity, and if there were,by placing mirrors at the ends of the carriage for instance, simultaneity would be proven for the carriage's frame. However there would be no way of testing for it in the embankment observer's frame.


    In Einstein's train the lighting strikes occur in both the embankment's frame and the train's frame, so the simultaneity test can be made in either.


    In the light bulb thought experiment the bulb is in the train and in the train's frame and the light from it reaches the ends of the train simultaneously – according to Einstein's test.
    In the embankment's frame there is no light emanating from the bulb. The embankment observer is a moving observer observing another frame.
    In that other frame the light reaches the ends of the carriage simultaneously – the problem we have is: how can that happen while without compromising Einstein's 2nd Postulate?
    The answer, of course, is by rotation. The hyperbolic rotation of the train's frame from the embankment observer's perspective transforms those measurements to make them relative to the Embankment observer's frame and in doing so the light travels to each end of the train,arriving simultaneously according to the Embankment observer's measurements.


    How ever one looks at it, the light in the carriage reaches the ends of the carriage simultaneously – it can do no other as it is one light and they are equal distances from it.


    It is only when we add the motion of the external observer when we have an apparent problem, which was solved by Lorentz. The science is there and explains it all beautifully if one takes the time to work one's way through it.


    No my problem is understanding what is meant by 'planes of simultaneity'and drawing them. In the OP I shewed two diagrams which I believe purport to show how the planes of simultaneity are to be understood but they only shew when the moving body's axis is drawn out of scale.
    Last edited by space at the centre; December 29th, 2012 at 07:44 AM. Reason: spacing on copied text
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    Sorry space at the centre, but your conclusions are incorrect.

    Albert Einstein
    (1879–1955). Relativity: The Special and General Theory. 1920.

    UP to now our considerations have been referred to a particular body of reference, which we have styled a “railway embankment.” We suppose a very long train travelling along the rails with the constant velocity v and in the direction indicated in Fig. 1. People travelling in this train will with advantage use the train as a rigid reference-body (co-ordinate system); they regard all events in reference to the train. Then every event which takes place along the line also takes place at a particular point of the train. Also the definition of simultaneity can be given relative to the train in exactly the same way as with respect to the embankment. As a natural consequence, however, the following question arises:

    Are two events (e.g. the two strokes of lightning A and B) which are simultaneous with reference to the railway embankment also simultaneous relatively to the train? We shall show directly that the answer must be in the negative.



    When we say that the lightning strokes A and B are simultaneous with respect to the embankment, we mean: the rays of light emitted at the places A and B, where the lightning occurs, meet each other at the mid-point M of the length A —> B of the embankment. But the events A and B also correspond to positions A and B on the train. Let M' be the mid-point of the distance A —> B on the travelling train. Just when the flashes 1 of lightning occur, this point M' naturally coincides with the point M, but it moves towards the right in the diagram with the velocity v of the train.

    If an observer sitting in the position M’ in the train did not possess this velocity, then he would remain permanently at M, and the light rays emitted by the flashes of lightning A and B would reach him simultaneously, i.e. they would meet just where he is situated. Now in reality (considered with reference to the railway embankment) he is hastening towards the beam of light coming from B, whilst he is riding on ahead of the beam of light coming from A. Hence the observer will see the beam of light emitted from B earlier than he will see that emitted from A. Observers who take the railway train as their reference-body must therefore come to the conclusion that the lightning flash B took place earlier than the lightning flash A. We thus arrive at the important result:

    Events which are simultaneous with reference to the embankment are not simultaneous with respect to the train, and vice versa (relativity of simultaneity). Every reference-body (co-ordinate system) has its own particular time; unless we are told the reference-body to which the statement of time refers, there is no meaning in a statement of the time of an event.


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    Thank you, for referencing this excellent translation by Robert W Lawson, a most diligent, careful and, above all, precise work. Which when examined carefully, supports my conclusions.

    When I first read this I thought that he had made a good job, explaining it so clearly, that it made good sense and was easy to understand.


    It was,then, with some dismay that I found that my understanding was not in accord with the accepted one.

    Let me explain.

    It seemed very clear to me that Einstein was dealing with this from the point of view of an observer on the Railway Embankment throughout this piece. Yet the cognoscenti of the Relativity Forums, insisted that that is not so. That he is talking of what the observers on the train really see, rather than what the Embankment observer concludes that they see.

    Yet, when I try and read it that way, I still can't see how anyone could possibly conclude that.

    Firstly he writes: "Are two events (e.g. the two strokes of lightning A and B) which are simultaneous with reference to the railway embankment also simultaneous relatively to the train?"

    Here we are dealing, quite explicitly, with lightning strikes that are simultaneous with reference to (as perceived from/as judged by) the observer on the railway embankment and whether, from the same perspective (from the embankment), they will be simultaneous relatively to the train. (as the observer on the train would perceive it/in relation to the train/with respect to the train) Note that he says "relatively to the train" and not "relatively from the train".

    Secondly: "If an observer sitting in the position M' in the train did not possess this velocity, then he would remain permanently at M, and the light rays emitted by the flashes of lightning A and B would reach him simultaneously, i.e. they would meet just where he is situated."

    Now, the only Frame of Reference, that we are considering, in which the observer at M' possesses any velocity, is the Frame of Reference of the embankment.

    Thirdly: "Now in reality (considered with reference to the railway embankment) he is hastening toward the beam of light coming from B,whilst he is riding on ahead of the beam of light coming from A."

    This immediately follows the last quote and quite explicitly confirms from which Frame of Reference that view is taken, for he can only be moving toward point B as viewed from the embankment.

    Remember: "But the events A and B also correspond to positions A and B on the train." So the observer on the train will be confident that he is stationary, at the point M', mid-way between points A and B on the train while it is the embankment that is moving past him.

    Fourthly: "Hence the observer will see the beam of light emitted from B earlier than he will see that emitted from A. Observers who take the railway train as their reference-body must therefore come to the conclusion that the lightning flash B took place earlier than the lightning flash A."

    Again this is emphasizing that it is from the perspective where M' is travelling toward lightning flash B. This is the case only when considered from the embankment. For in the Frame of Reference of the observer on the train at M', she is stationary between the points A & B on the train. But more than that, the phrase: "Observers who take the railway train as their reference-body" can only mean from the perspective of those on the embankment, for otherwise he would say 'Observers for whom the train is the reference body.'

    Fifthly: "Events which are simultaneous with reference to the embankment are not simultaneous with respect to the train, and vice versa (relativity of simultaneity)."

    How many times does the great man have to repeat: "with reference to the embankment" before his point of view is accepted?

    Note again; "with reference to the embankment" and "with respect to the train" not "with reference to the train"

    And finally: "vice versa (relativity of simultaneity)."

    What else can vice versa mean but that the whole of what has been written above would apply in reverse if considered from the train observer's point of view in position M'? - The Relativity of Simultaneity then surely means: That simultaneity is relative to where it is observed from; is relative to the Frame of Reference.

    If the observer, sitting in the position M', were to consider his own Frame of Reference; then it is he that would be stationary; and it would be point M on the embankment that would be moving toward strike A.Leading to the inevitable conclusion that M' would see the strikes simultaneously while M would see strike A before strike B.

    The constant events that will be the same from whichever Frame they are observed are the two pulses of light meeting at the midpoint of the line AB. The question we must ask is: what are the coordinates of that location in the individual Frames of Reference?

    Now with in each Frame of Reference we have to consider what is at that mid-point of AB at the time the pulses of light meet. And that this could be either M or M' depending on which is stationary in the Frame of Reference of the particular observer. M for the embankment and M' for the train.

    Summary

    That is the Relativity of Simultaneity; each observer will see it within his own Frame of Reference but deny that it happens in any Frame of Reference that he observes to be moving.

    Which is exactly what Einstein was saying when he wrote:

    "Events which are simultaneous with reference to the embankment are not simultaneous with respect to the train, and vice versa (relativity of simultaneity)."
    Last edited by space at the centre; December 30th, 2012 at 10:17 AM. Reason: punctuation
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    Don't worry, I can now see where you are coming from. Sorry it took me so long.

    Quote Originally Posted by space at the centre View Post

    Yet, when I try and read it that way, I still can't see how anyone could possibly conclude that.
    The simplest solution is to use the mathematics, which are not open to interpretation, rather than the words used to describe them, which are.

    Quote Originally Posted by space at the centre View Post
    Firstly he writes: "Are two events (e.g. the two strokes of lightning A and B) which are simultaneous with reference to the railway embankment also simultaneous relatively to the train?"

    Here we are dealing, quite explicitly, with lightning strikes that are simultaneous with reference to (as perceived from/as judged by) the observer on the railway embankment and whether, from the same perspective (from the embankment), they will be simultaneous relatively to the train. (as the observer on the train would perceive it/in relation to the train/with respect to the train) Note that he says "relatively to the train" and not "relatively from the train".
    Yes, he means relatively to the train, from the frame of the embankment.

    Quote Originally Posted by space at the centre View Post
    Secondly: "If an observer sitting in the position M' in the train did not possess this velocity, then he would remain permanently at M, and the light rays emitted by the flashes of lightning A and B would reach him simultaneously, i.e. they would meet just where he is situated."

    Now, the only Frame of Reference, that we are considering, in which the observer at M' possesses any velocity, is the Frame of Reference of the embankment.
    But from the frame of M', it is the embankment which in motion.

    Quote Originally Posted by space at the centre View Post
    Thirdly: "Now in reality (considered with reference to the railway embankment) he is hastening toward the beam of light coming from B,whilst he is riding on ahead of the beam of light coming from A."

    This immediately follows the last quote and quite explicitly confirms from which Frame of Reference that view is taken, for he can only be moving toward point B as viewed from the embankment.
    This is where things can get confusing. From the frame of the embankment, M' is hastening towards point B, but from the frame of the train M' measures the speed of light from both A and B, and the distance to both A and B, to be the same. (Note: that distance will NOT be the same distance as he measures it for the other frame, due to the Lorentz transformation - this is important)

    Quote Originally Posted by space at the centre View Post
    Remember: "But the events A and B also correspond to positions A and B on the train." So the observer on the train will be confident that he is stationary, at the point M', mid-way between points A and B on the train while it is the embankment that is moving past him.
    Correct.

    Quote Originally Posted by space at the centre View Post
    Fourthly: "Hence the observer will see the beam of light emitted from B earlier than he will see that emitted from A. Observers who take the railway train as their reference-body must therefore come to the conclusion that the lightning flash B took place earlier than the lightning flash A."

    Again this is emphasizing that it is from the perspective where M' is travelling toward lightning flash B. This is the case only when considered from the embankment. For in the Frame of Reference of the observer on the train at M', she is stationary between the points A & B on the train. But more than that, the phrase: "Observers who take the railway train as their reference-body" can only mean from the perspective of those on the embankment, for otherwise he would say 'Observers for whom the train is the reference body.'
    Yes, it is quite confusing, isn't it? It makes it very easy to inadvertently mix frames without performing the appropriate transformation between them...

    Quote Originally Posted by space at the centre View Post
    Fifthly: "Events which are simultaneous with reference to the embankment are not simultaneous with respect to the train, and vice versa (relativity of simultaneity)."

    How many times does the great man have to repeat: "with reference to the embankment" before his point of view is accepted?
    Notice the emphasis on "and vice versa".

    From frame of the embankment, the lightning strikes are simultaneous, but when the embankment looks at the frame of the train, the events are not simultaneous. This is because the train is in motion relative to the embankment.

    And vice versa.

    From the frame of the train, the lightning strikes are simultaneous, but when the train looks at the frame of the embankment, the events are not simultaneous. This is because the embankment is in motion relative to the train.

    Light always propagates from a point at rest in relation to the observer, whatever the motion of the observer.



    EDIT: This single section is wrong, in that from the frame of the train the strikes are NOT simultaneous, but when the train looks at the frame of the embankment the events ARE simultaneous. Sorry for any confusion caused here. I realised something wasn't clicking with you after this post and re-explained it properly in post #20, but I hadn't noticed that it was my mistake that caused the confusion. I must learn not to post when I am tired.

    Quote Originally Posted by space at the centre View Post
    Note again; "with reference to the embankment" and "with respect to the train" not "with reference to the train"

    And finally: "vice versa (relativity of simultaneity)."

    What else can vice versa mean but that the whole of what has been written above would apply in reverse if considered from the train observer's point of view in position M'? - The Relativity of Simultaneity then surely means: That simultaneity is relative to where it is observed from; is relative to the Frame of Reference.
    Yes, simultaneity is relative. Both observers get different answers for the other frame. This means simultaneity cannot be absolute, as the laws of physics have to apply from your own frame of reference.

    Quote Originally Posted by space at the centre View Post
    If the observer, sitting in the position M', were to consider his own Frame of Reference; then it is he that would be stationary; and it would be point M on the embankment that would be moving toward strike A.Leading to the inevitable conclusion that M' would see the strikes simultaneously while M would see strike A before strike B.
    Correct.

    Quote Originally Posted by space at the centre View Post
    The constant events that will be the same from whichever Frame they are observed are the two pulses of light meeting at the midpoint of the line AB. The question we must ask is: what are the coordinates of that location in the individual Frames of Reference?
    And here is the crux of the matter...

    Quote Originally Posted by space at the centre View Post
    Now with in each Frame of Reference we have to consider what is at that mid-point of AB at the time the pulses of light meet. And that this could be either M or M' depending on which is stationary in the Frame of Reference of the particular observer. M for the embankment and M' for the train.

    Indeed. That coordinate is not the same in both frames (you may need to apply the Lorentz transformation here, to see why). Which is why simultaneity cannot be absolute, but can only be relative. Hence the relativity of simultaneity.

    Quote Originally Posted by space at the centre View Post
    Summary

    That is the Relativity of Simultaneity; each observer will see it within his own Frame of Reference but deny that it happens in any Frame of Reference that he observes to be moving.

    Which is exactly what Einstein was saying when he wrote:

    "Events which are simultaneous with reference to the embankment are not simultaneous with respect to the train, and vice versa (relativity of simultaneity)."
    Bingo! So we agree that simultaneity cannot be absolute, but can only be relative.

    This leads us to the conclusion that "now" is a relative concept, rather than an absolute concept. That there is no absolute notion of time.

    Nobody should think that measurements in their own frame reflect any reality in the other frame, but those measurements DO reflect the reality for the other frame, relative to your own.
    Last edited by SpeedFreek; January 12th, 2013 at 10:58 AM.
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    Quote Originally Posted by SpeedFreek View Post
    Quote Originally Posted by sigurdV View Post
    Hey! Your description is good!
    But the ending gives me trouble.
    How did you get to your conclusion:
    "There is no such thing as absolute simultaneity."
    I try to understand, but I only get to the point:
    "we cant measure absolute simultaneity"
    H
    ow do you manage to take the next step?
    If events are simultaneous in one frame of reference, but are not simultaneous in another frame of reference (where both frames subtract the light travel time from the event to the observer, so both frames know when the events actually occured in relation to themselves), then simultaneity cannot be absolute, it can only be relative. Both observers versions of the timing of the the events is reality.
    Perhaps the problem is I cant follow the maths?
    Is it true that no time passes in the frame of a photon?
    Are then big bang and the moment it hits my eye simultaneous in its frame?
    If so: Is the photon newborn or is it fifteen billion years old?

    If events are simultaneous in one frame of reference,
    but are not simultaneous in another frame of reference
    then perhaps something is wrong instead of relative.

    Frames are not independent surely?

    Time passes with different speed in the frames:
    When the universe (the absolute and fastest clock)
    ages one amount of time
    the various frames ages with lesser amounts
    depending on their speed relative to the universe...
    zero amounts in the case of local frames of photons.
    So where do I make the mistake and why is it a mistake?
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    I can see that I am not doing a good job of explaining this.

    Quote Originally Posted by sigurdV View Post
    Is it true that no time passes in the frame of a photon?
    Are then big bang and the moment it hits my eye simultaneous in its frame?
    If so: Is the photon newborn or is it fifteen billion years old?
    Well, strictly speaking a photon does not have a valid frame of reference, but that does not matter here as the concept itself is sound. Let's just imagine a dust particle that is travelling a tiny fraction slower than c, instead.

    In the "rest frame" of the universe, it is 14 billion years old. But in the frame of the relativistic dust particle, it is only 14 years old! Both results are correct, for the frames involved. All experiments performed in the frames involved will confirm the answers for that frame.

    Now, if an observer on the dust particle knows the relative speed involved between himself and another frame, he can calculate what the results will be in the other frame, and thus can calculate that in the "rest frame" of the universe, the age of the universe is 14 billion years. But that makes no difference to the age of the universe calculated directly from the frame of the dust particle, using the laws of physics which apply as equally in one frame as another.

    In the frame of the dust particle, all physical processes act as normal. An observer in the frame of the dust particle will measure the speed of light to be ~300,000 km/s faster than the dust particle. In that frame, a caesium atom still "vibrates" 9,192,631,770 times a second (the basis of an atomic clock). They will get the same results for any experiment performed in their own frame as anyone else gets when they perform an experiment in their own frame.

    If, say, the universe was going to explode after 100 billion years in the rest frame of the universe, then to the dust particle the universe would explode after only 100 years. That is reality, to the dust particle. Telling the observer in the frame of the dust particle that the universe is actually ageing a billion times faster than they see it to age makes no difference to the age of the observer in the frame of the dust particle. They can only live to a maximum age of 100 years before the end of the universe!

    So, there is no preferred frame of reference for the laws of physics themselves.

    Quote Originally Posted by sigurdV View Post
    If events are simultaneous in one frame of reference,
    but are not simultaneous in another frame of reference
    then perhaps something is wrong instead of relative.

    Frames are not independent surely?
    Yes, frames are independent. Elapsed time is a purely local concept, local to the frame involved.

    Quote Originally Posted by sigurdV View Post
    Time passes with different speed in the frames:
    When the universe (the absolute and fastest clock)
    ages one amount of time
    the various frames ages with lesser amounts
    depending on their speed relative to the universe...
    zero amounts in the case of local frames of photons.
    So where do I make the mistake and why is it a mistake?
    How can the clock of the universe be absolute, when an observer in the frame of our relativistic dust particle measures the universe to age a billion times slower?

    The clock of the universe is only absolute to those in a frame of reference at rest in relation to the universe. It is not absolute to all observers. Relative motion shows us that time itself is not absolute across all frames of reference.

    But the laws of physics (measurement of all physical process in your own frame) ARE the same to all frames of reference. That is the only basis upon which we can do science.

    So, back to the relativity of simultaneity (which, whilst related to time-dilation is not the same thing)

    Using my example from earlier, with a bulb in the centre of the train carriage:

    To an observer in the rest frame of the train, the light reaches each end of the carriage at the same time. The light propagates at the same speed in all directions, and the spherical wave-front reaches the back of the carriage at the same time as it reaches the front of the carriage. The spherical wave-front is at rest in relation to the train.

    But to an observer standing on the embankment as the train passes them:

    The light propagates at the same speed in all directions, but the train is also moving from left to right, so the train is moving through that propagating spherical wave-front. Thus, the light reaches the back of the carriage before it reaches the front of the carriage. The spherical wave-front is at rest in relation to the embankment, but the train is not!

    If we put a light activated light bulb at each end of the carriage, which only lights up when the light from the central bulb reaches it, those bulbs will light up at different times, relative to the frame of the embankment, but they will light up at the same time relative to the train.

    The observer on the embankment can, if they know the relative speed of the train, calculate that the light reaches the ends of the carriage at the same time in the frame of the carriage, but this makes no difference to the fact that the light does not reach the ends of the carriage at the same time from the frame of the embankment. The observer on the embankment can calculate the light-travel time from those end bulbs to himself, to calculate not just when he saw them light up, but when they actually lit up relative to himself. He will find they lit up at different times, due to the trains motion through the propagating spherical wave-front of light.

    Both measurements are reality for the frames involved.
    Last edited by SpeedFreek; December 31st, 2012 at 09:08 AM.
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    Thank you! This will take me some time to ponder.
    How come the rate of change of time is seldom if ever spoken of?
    If we say that time slows in a frame when it accelerates
    isnt it really the rate of change of time that changes?
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    Quote Originally Posted by sigurdV View Post
    How come the rate of change of time is seldom if ever spoken of?
    Because the rate of change of time never changes in any reference frame you care to measure it in. Time always passes at 1 second per second for you, whatever you do.

    Quote Originally Posted by sigurdV View Post
    If we say that time slows in a frame when it accelerates
    isnt it really the rate of change of time that changes?
    Time does not slow within a frame when it accelerates. Someone in that frame will always measure time to pass at 1 second per second. The caesium atoms in that frame always "vibrate" at the same rate, as measured from within that frame, even if the frame is accelerating.

    Time only changes in that frame when measured from a different frame.
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    Quote Originally Posted by SpeedFreek View Post
    Quote Originally Posted by sigurdV View Post
    How come the rate of change of time is seldom if ever spoken of?
    Because the rate of change of time never changes in any reference frame you care to measure it in. Time always passes at 1 second per second for you, whatever you do.

    Quote Originally Posted by sigurdV View Post
    If we say that time slows in a frame when it accelerates
    isnt it really the rate of change of time that changes?
    Time does not slow within a frame when it accelerates. Someone in that frame will always measure time to pass at 1 second per second. The caesium atoms in that frame always "vibrate" at the same rate, as measured from within that frame, even if the frame is accelerating.

    Time only changes in that frame when measured from a different frame.
    Of course I meant that the rate of change of time within a frame
    is measured from another frame..
    I thought that would be obvious to any serious conversation partner
    :

    I am comparing two (distinct) frames from another: one travelling fast the other one slow . Time in the fast frame passes slow and time in the slow passes fast (seen from the observer frame)...
    The observed frames are NOT independent of each other because they are correlated by the observers frame.

    And should not all frames in the universe likewise be correlated with each other? (Two frames in different universes might of course be truly independent. But being in the same universe makes them related surely?) So in any set of frames (again:within the same universe, observed from a frame) theres a natural order of frames: ordering them from lowest speed of time to fastest... and "the universal frame" should then be just another natural limit (like the speed of light is)... a frame with fastest possible speed. Or can the speed of time in a frame be infinite?

    Dont bother answering if you cant come up with a serious answer.
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    Quote Originally Posted by sigurdV View Post
    Quote Originally Posted by SpeedFreek View Post
    Quote Originally Posted by sigurdV View Post
    How come the rate of change of time is seldom if ever spoken of?
    Because the rate of change of time never changes in any reference frame you care to measure it in. Time always passes at 1 second per second for you, whatever you do.

    Quote Originally Posted by sigurdV View Post
    If we say that time slows in a frame when it accelerates
    isnt it really the rate of change of time that changes?
    Time does not slow within a frame when it accelerates. Someone in that frame will always measure time to pass at 1 second per second. The caesium atoms in that frame always "vibrate" at the same rate, as measured from within that frame, even if the frame is accelerating.

    Time only changes in that frame when measured from a different frame.
    Of course I meant that the rate of change of time within a frame
    is measured from another frame..
    I thought that would be obvious to any serious conversation partner
    :
    I thought it would be obvious that, contrary to your first assertion that it is seldom spoken of, what you are referring to is time-dilation, which is one of the most talked about topics in physics forums. Seldom spoken of, my ass.

    Don't accuse me of not being serious just because you cannot make your intentions clear. I answered the question you asked. It is not my fault you didn't ask the right question.

    Quote Originally Posted by sigurdV View Post
    Dont bother answering if you cant come up with a serious answer.
    My answers in this thread have all been serious. Perhaps you need to work on how you ask questions, rather than alienating someone who is trying to help here.
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    For readers with a serious interest:

    Quote Originally Posted by sigurdV View Post
    I am comparing two (distinct) frames from another: one travelling fast the other one slow . Time in the fast frame passes slow and time in the slow passes fast (seen from the observer frame)...
    The observed frames are NOT independent of each other because they are correlated by the observers frame.
    Between the frames involved there is no such thing as a fast frame and a slow frame. Whilst in inertial motion you can consider yourself to be at rest and that it is only the other frame that is moving in relation to you. All experiments between the frames, posed either way, will confirm this.

    Quote Originally Posted by sigurdV View Post
    And should not all frames in the universe likewise be correlated with each other? (Two frames in different universes might of course be truly independent. But being in the same universe makes them related surely?) So in any set of frames (again:within the same universe, observed from a frame) theres a natural order of frames: ordering them from lowest speed of time to fastest... and "the universal frame" should then be just another natural limit (like the speed of light is)... a frame with fastest possible speed.
    Imagine a frame at rest in relation to the cosmic microwave background radiation - at rest in relation to the expansion of the universe. Let's call that frame A.

    Now imagine another frame in motion in relation to the rest frame of the universe. Let's call that frame B.

    In the rest frame of B, it is a clock in the frame of A that is slower!

    If the two frames pass close to each other and synchronize their clocks via light signals, and then A subsequently accelerates to meet B, the results when they meet will confirm that the clock in A was always ticking slower since they performed the synchronization.
    Quote Originally Posted by sigurdV View Post
    Or can the speed of time in a frame be infinite?
    The speed of time in a frame is always 1 second per second. The speed of time in a frame, as measured from another frame, can only be slower, when due to relative motion. It tends towards zero as the other frame tends towards the speed of light.

    We have to be really careful with our terminology, lest we are misunderstood.
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    Quote Originally Posted by SpeedFreek View Post
    Don't worry, I can now see where you are coming from. Sorry it took me so long.
    This leads us to the conclusion that "now" is a relative concept, rather than an absolute concept. That there is no absolute notion of time.

    Very good up to here! but I cannot see how you come to that last statement.

    There were two lightning strikes at A and at B.
    They occurred when A and B on the train were aligned with A and B on the embankment; this was stated in Einstein's description.
    Each observer measured that, using Einstein's own test for simultaneity, that A and B were simultaneous.
    They occupied the same now in each Frame.
    It was Einstein's test of simultaneity that neither observer could apply in the other Frame, which was why neither could confirm simultaneity in the other Frame.

    But we do have two unique events in Spacetime that were proven to be simultaneous in each of two Frames.

    Therefore that simultaneity was absolute.
    [/QUOTE]
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    Quote Originally Posted by space at the centre View Post
    Very good up to here! but I cannot see how you come to that last statement.
    What you might be missing is that the laws of physics have to apply from the frame you are in. You cannot simply "jump" between frames of reference and say simultaneity is absolute, you have to find a frame of reference where simultaneity is actually absolute in order to say it, but there is no such frame.

    There is no possible frame of reference from which the lightning strikes were both simultaneous on the train and simultaneous on the embankment. Or to go further, even if you find a highly convoluted frame of reference in which they are both simultaneous, there will be a third frame where they are not. You cannot find a frame of reference where the events are simultaneous in all other frames of reference, so there is no absolute simultaneity.

    There is no "gods-eye view" of the experiment. All you are doing is mixing frames of reference.
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    The passage of time in any Inertial Frame of Reference is the same - derived from the 1st postulate.
    Time only varies, is dilated, when measured from another Frame.
    Therefore it is the measuring from another Frame, i.e. the conditions under which the measurements are taken, that cause the dilation.
    It is the measurement that is dilated not the time; for the time passes at exactly the same rate as in any other inertial Frame.

    A Frame of Reference is a particular view of Spacetime.

    Let us take the bulb in the carriage scenario and say that there are photoelectric sensors at each end of the carriage; and that if both are triggered simultaneously, a circuit is completed that fires a flare from the train.
    In the stationary train, i.e. from the train observer's perspective, light will travel to the ends of the train, equal distances in equal times and the flare will be triggered.

    What does the observer on the embankment see. He sees the flare. He has to because it is something that happens in another frame. So his difficulty is not solved by saying that if the bulb had been in his Frame the light would have travelled at c and caught up with the train, no what he has to explain is how he can measure the light travelling to either end of the train at c relative to him and reaching those ends simultaneously.

    This is where the Lorentz Transformations come in. This is what they mean, what they are there for.
    For it is the rotation, the hyperbolic rotation measured by the moving observer of the stationary Frame, that transforms the measurements so that they are measured as c from the embankment.

    This understanding comes directly from Mikowski's Spacetime.
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    Quote Originally Posted by SpeedFreek View Post
    Quote Originally Posted by space at the centre View Post
    Very good up to here! but I cannot see how you come to that last statement.
    What you might be missing is that the laws of physics have to apply from the frame you are in. You cannot simply "jump" between frames of reference and say simultaneity is absolute, you have to find a frame of reference where simultaneity is actually absolute in order to say it, but there is no such frame.

    There is no possible frame of reference from which the lightning strikes were both simultaneous on the train and simultaneous on the embankment. Or to go further, even if you find a highly convoluted frame of reference in which they are both simultaneous, there will be a third frame where they are not. You cannot find a frame of reference where the events are simultaneous in all other frames of reference, so there is no absolute simultaneity.

    There is no "gods-eye view" of the experiment. All you are doing is mixing frames of reference.
    True, there is no Frame of Reference that has any more than one view of Spacetime.
    Yet that does not mean that Spacetime does not exist as a homogeneous and isotropic entity, the same everywhere in every direction.

    We have seen that A and B are simultaneous, meet Einstein's test for simultaneity, in two separate Frames and we can go on to prove that they will meet that test in any Frame, in each and every Frame. Not in any one Frame but in all Frames. How much more absolute can you wish?



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    Quote Originally Posted by space at the centre View Post
    The passage of time in any Inertial Frame of Reference is the same - derived from the 1st postulate.
    Time only varies, is dilated, when measured from another Frame.
    Therefore it is the measuring from another Frame, i.e. the conditions under which the measurements are taken, that cause the dilation.
    It is the measurement that is dilated not the time; for the time passes at exactly the same rate as in any other inertial Frame.
    Tell that to those famous identical twins, who end up having different ages at the end of the thought-experiment. Or more empirically, tell it to the muons created from cosmic rays when they hit our atmosphere and reach the ground even though their "rest frame" decay times are too short to allow them to reach the ground. Time-dilation is real, even if we only ever measure it to occur in a different frame.
    Time dilation - Wikipedia, the free encyclopedia
    muon mean lifetime

    Quote Originally Posted by space at the centre View Post
    A Frame of Reference is a particular view of Spacetime.
    Yes and the laws of physics apply equally in all (inertial) frames.

    Quote Originally Posted by space at the centre View Post
    Let us take the bulb in the carriage scenario and say that there are photoelectric sensors at each end of the carriage; and that if both are triggered simultaneously, a circuit is completed that fires a flare from the train.
    In the stationary train, i.e. from the train observer's perspective, light will travel to the ends of the train, equal distances in equal times and the flare will be triggered.

    What does the observer on the embankment see. He sees the flare. He has to because it is something that happens in another frame. So his difficulty is not solved by saying that if the bulb had been in his Frame the light would have travelled at c and caught up with the train, no what he has to explain is how he can measure the light travelling to either end of the train at c relative to him and reaching those ends simultaneously.
    How he explains it is through the understanding that time and distance work differently in the frame of the train, when compared to how time and distance work in his own frame... but the laws of physics still have to be totally valid from within his own frame, and it doesn't change the fact that he calculates the light to reach the ends of the carriage at different times from his own frame. He just understands that time is relative, rather than absolute. Time is a local concept that cannot be extended to other frames without changing the relationship of time between those frames.

    Quote Originally Posted by space at the centre View Post
    This is where the Lorentz Transformations come in. This is what they mean, what they are there for.
    For it is the rotation, the hyperbolic rotation measured by the moving observer of the stationary Frame, that transforms the measurements so that they are measured as c from the embankment.
    Yes, and the result is that it transforms time and distance in the other frame, in order to retain the constancy of the speed of light to both frames. From the frame of the train, the embankment is time-dilated and contracted in length, and from the frame of the embankment the train is time-dilated and contracted in length.

    But the whilst Lorentz contraction is a device that allows us to make sense of reality and causality in the other frame, it does not change reality or causality in relation to our own frame.

    So what if there is a second flare, on the embankment, set to go off if the light reaches the ends of the carriage simultaneously in relation to the observer on the embankment, just using light signals and light-travel time according to the laws of physics on the embankment? The flare would not go off. Unless, that is, it is set up to transform its results to the frame of the train, in which case they are not the results for the embankment any more. The light did not reach the ends of the carriage simultaneously, from the frame of reference of the embankment, and this is true whichever frame the initial source of that light is in, due to the motion of the train through that propagating light, from the frame of the embankment.

    The problem with Einstein's example is that it seems to be set up as a totally symmetrical scenario, which introduces ambiguity. The "light in the carriage" example removes this ambiguity.

    From the frame of the embankment, the light does not hit the ends of the carriage simultaneously. That is reality, in relation to the embankment, even if the light source was also in the frame of the embankment, because the carriage is moving in relation to the observer.

    Two events separated by space cannot be considered to be simultaneous in any way that is absolute. There will always be frames of reference in motion in relation to those events for which they were not simultaneous. That is the meaning of the relativity of simultaneity, and it is all about causality relative to your own frame of reference.
    Last edited by SpeedFreek; December 31st, 2012 at 06:04 PM. Reason: reworded a sentence for clarity.
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    Quote Originally Posted by space at the centre View Post

    We have seen that A and B are simultaneous, meet Einstein's test for simultaneity, in two separate Frames and we can go on to prove that they will meet that test in any Frame, in each and every Frame. Not in any one Frame but in all Frames.

    Not at all. Try it without flitting instantaneously between frames. Just stick to finding one frame from which the events are simultaneous in all other frames. After all, the laws of physics, and causality, have to apply in that frame.

    To the laws of physics, no Gods-eye view is allowed. You will never find a frame of reference from which events are simultaneous in all other frames.

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    Quote Originally Posted by SpeedFreek View Post
    Quote Originally Posted by sigurdV View Post
    Quote Originally Posted by SpeedFreek View Post
    Quote Originally Posted by sigurdV View Post
    How come the rate of change of time is seldom if ever spoken of?
    Because the rate of change of time never changes in any reference frame you care to measure it in. Time always passes at 1 second per second for you, whatever you do.

    Quote Originally Posted by sigurdV View Post
    If we say that time slows in a frame when it accelerates
    isnt it really the rate of change of time that changes?
    Time does not slow within a frame when it accelerates. Someone in that frame will always measure time to pass at 1 second per second. The caesium atoms in that frame always "vibrate" at the same rate, as measured from within that frame, even if the frame is accelerating.

    Time only changes in that frame when measured from a different frame.
    Of course I meant that the rate of change of time within a frame
    is measured from another frame..
    I thought that would be obvious to any serious conversation partner
    :
    I thought it would be obvious that, contrary to your first assertion that it is seldom spoken of, what you are referring to is time-dilation, which is one of the most talked about topics in physics forums. Seldom spoken of, my ass.

    Don't accuse me of not being serious just because you cannot make your intentions clear. I answered the question you asked. It is not my fault you didn't ask the right question.

    Quote Originally Posted by sigurdV View Post
    Dont bother answering if you cant come up with a serious answer.
    My answers in this thread have all been serious. Perhaps you need to work on how you ask questions, rather than alienating someone who is trying to help here.
    Good riposte!
    It SEEMS as if your trying to help in here but you never know you know... So the rate of change of time...the speed of time... is time dilation. Nice to know. That should mean im not mistaken in my opinion that there IS such a thing as the rate of change of time and that it can be shown that this rate can differ between frames. But I believe time dilation(indeed a more handy expression for rate of change of time) cannot be observed directly ... isnt it only inferred by determining the relative speed between frames? Or objects, I think its safer to say, since there are no observed frames in reality surely? Frames are useful figments of imagination like points. So whats the point in denying that theres a universal frame? Arent what you are saying only that you do not know how to measure the rate of change of the age of the universe?

    If so theres a difference in attitude in claiming that something isnt ...how can you foolishly believe it to exist huh? ... and admitting that you dont know how to detect it! Come to think of it, wasnt there a scientific attempt to do just that (or something equivalent) recently?
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    Quote Originally Posted by sigurdV View Post
    So the rate of change of time...the speed of time... is time dilation. Nice to know. That should mean im not mistaken in my opinion that there IS such a thing as the rate of change of time and that it can be shown that this rate can differ between frames.
    This topic is supposed to be about the relativity of simultaneity, rather than time-dilation, which although related are not the same thing.

    Now then, time-dilation or the rate of change of time only ever occurs in the other frame, never in your own. As I said, time always passes at 1 second per second in your own frame. This is known as the difference between proper time (which is the time between events measured in your own frame, with a clock you carry between those events) and coordinate time (which is the time you measure for another frame in relation to your own).
    Proper time - Wikipedia, the free encyclopedia
    Coordinate time - Wikipedia, the free encyclopedia

    Your own "proper" time will be shorter if you are in motion in relation to events, but the rate of change of time is always the same - 1 second per second. What changes is your path through space-time and the way you break down space from time. But this is getting too deep for this thread, and possibly needs a whole thread of its own, as we are veering way off the topic of the relativity of simultaneity here.

    Quote Originally Posted by sigurdV View Post
    But I believe time dilation(indeed a more handy expression for rate of change of time) cannot be observed directly ... isnt it only inferred by determining the relative speed between frames? Or objects, I think its safer to say, since there are no observed frames in reality surely? Frames are useful figments of imagination like points. So whats the point in denying that theres a universal frame? Arent what you are saying only that you do not know how to measure the rate of change of the age of the universe?
    No. We know how to measure the rate of change of the age of the universe, but that rate of change is not the same as the rate of change of time on Earth.

    We directly measure time-dilation in objects that are in motion in relation to us. One good example is GPS satellites. We had to set their clock rate to be "wrong" before we sent them into space, to account for the time-dilation that would be present in orbit. Without this adjustment, the GPS system would lose accuracy at a rate of 10 km per day. We do not just "infer" time-dilation - it has been proven.

    We also proved time-dilation in the Hafele-Keating experiment, where we put atomic clocks on jet planes and sent them around the world and then compared them to an atomic clock at the U.S. Naval observatory. This experiment has been repeated.

    We also prove time-dilation daily, in particle accelerators, where a particles decay rate when "at rest" (or in the frame of the laboratory) is shown to be time-dilated after we accelerate those particles to a relativistic speed.
    Last edited by SpeedFreek; December 31st, 2012 at 07:12 PM. Reason: reworded for clarity (again!)
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    I forgot that. Well then what is simultanity? In how many ways can it be defined?
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    Quote Originally Posted by space at the centre View Post
    The passage of time in any Inertial Frame of Reference is the same - derived from the 1st postulate.
    Time only varies, is dilated, when measured from another Frame.
    Therefore it is the measuring from another Frame, i.e. the conditions under which the measurements are taken, that cause the dilation.
    It is the measurement that is dilated not the time; for the time passes at exactly the same rate as in any other inertial Frame.

    A Frame of Reference is a particular view of Spacetime.

    Let us take the bulb in the carriage scenario and say that there are photoelectric sensors at each end of the carriage; and that if both are triggered simultaneously, a circuit is completed that fires a flare from the train.
    In the stationary train, i.e. from the train observer's perspective, light will travel to the ends of the train, equal distances in equal times and the flare will be triggered.

    What does the observer on the embankment see. He sees the flare. He has to because it is something that happens in another frame. So his difficulty is not solved by saying that if the bulb had been in his Frame the light would have travelled at c and caught up with the train, no what he has to explain is how he can measure the light travelling to either end of the train at c relative to him and reaching those ends simultaneously.
    No. Just say that the light reaching the ends of the carriage simultaneously triggers a flare is not enough. The photo-sensors are at opposite ends of the carriage, thus any circuit would have to span the length of the carriage, and the electric signal, which travels at a finite speed would have to travel along it. The easiest way to ensure that the flare goes off if the light hits both ends simultaneously (in the frame of the carriage) is to put the flare at the middle of the of the carriage. Thus if the signals arrive from the photo-sensors at the same time, the flare goes off.

    It is the signals arriving at the flare at the same time that sets the flare off in both frames.

    Now let's say that the carriage is traveling at 0.75c relative to the embankment and the signal speed as measured from the carriage is also 0.75c (A good value for insulated wire).

    In this case, you have to use relativistic velocity addition to get the signal speed with respect to the embankment. This gives 0 for the signal coming from the front of the carriage and 0.96c for the signal coming from the rear.

    If we call the distance from the flare to each photo-sensor "L" (in light secs), then it takes L/(0.75c-0) sec for the signal to reach the flare from the front of the carriage, and L/(0.96c-0.75c) sec for the signal to reach the flare from the rear of the carriage. These are different values. IOW, in order for the signal to arrive at the flare at the same time and ignite the flare in the embankment frame as it does in the carriage frame, then the signals have to leave the photo sensors at different times in the embankment frame. and since the sensors send the signals upon being struck by the light, the light must reach the ends of the carriage at different times in the embankment frame.

    You can come up with different schemes to ensure that the flare goes off if the light reaches the ends simultaneously in the carriage frame, but they all will lead to the embankment frame determining that the light reaches the ends at different times.
    "Men are apt to mistake the strength of their feelings for the strength of their argument.
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    Thank you Janus, for explaining exactly how the flare on the train goes off, from the frame of the embankment, when the light did not reach the ends of the carriage simultaneously, from the frame of the embankment.

    My explanation was far too vague and didn't actually answer the question, as I was only really saying how the observer on the embankment reconciles the lack of simultaneity between the events of the light hitting each end of the carriage in his own frame with the fact that the light did hit the ends of the carriage simultaneously in the frame in of the carriage, via the Lorentz transformation.

    But I completely neglected to explain how the actual mechanism that sets off the flare still complies to the laws of physics from the frame of the embankment, whilst retaining the lack of simultaneity between the events that caused it!

    And this really helps to illustrate how simultaneity is a separate issue from time-dilation.

    So, if the flare on the train is set to go off when the light reaches receptors at each end of the carriage, the simplest way to do this is to have the flare at the centre of the carriage, set to go off if the signals from the end receptors reach the flare at the same time. If we have all the signals involved propagating at c in relation to the embankment, then even though the signals propagate up and down the carriage and reach the ends at different times, due to the motion of the carriage, the return signals to the flare will reach it at the same time, due to the motion of the carriage. Whilst the light reaches the back of the carriage first, due to the back of the carriage moving towards the light, the return signal to the flare takes longer, due to the carriage moving away from the signal. And vice versa.
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    Quote Originally Posted by sigurdV View Post
    Well then what is simultanity? In how many ways can it be defined?
    Simultaneity is the question as to whether two events separated by space occur at the same time, or not.

    The answer is frame dependant - it depends on the frame of reference of the observer.
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    Quote Originally Posted by SpeedFreek View Post
    Quote Originally Posted by space at the centre View Post

    We have seen that A and B are simultaneous, meet Einstein's test for simultaneity, in two separate Frames and we can go on to prove that they will meet that test in any Frame, in each and every Frame. Not in any one Frame but in all Frames.

    Not at all. Try it without flitting instantaneously between frames. Just stick to finding one frame from which the events are simultaneous in all other frames. After all, the laws of physics, and causality, have to apply in that frame.

    To the laws of physics, no Gods-eye view is allowed. You will never find a frame of reference from which events are simultaneous in all other frames.

    and
    Quote Originally Posted by SpeedFreek View Post
    Quote Originally Posted by sigurdV View Post
    Well then what is simultanity? In how many ways can it be defined?
    Simultaneity is the question as to whether two events separated by space occur at the same time, or not.

    The answer is frame dependant - it depends on the frame of reference of the observer.
    Consider: three points in space A,M,B. AM = MB, M is physically midway between A & B.

    Add two events, E1 and E2: Flashes light propagated at A and B, the light from these events arrive at M simultaneously. This event E3.

    E1 and E2 are therefore simultaneous. Oh, but sorry, this is taking the God view; so let us take a Frame of Reference - any Frame of Reference, and the Points in space A,M B will exist in that Frame. Oh, and so will the events E1,E2,E3.

    For any Frame of Reference may be considered at rest in Spacetime, where movement is only relative.

    Therefore we can conclude that in ANY, that is in each and every, Frame of Reference there will be a point in space, M, midway in space between points A and B where the lights will arrive simultaneously.

    Note that because an Event is a specific point in Time at a specific point in Space, ie at a particular Spacetime Location it cannot moving.

    Therefore points A & B are proven, by Einstein's test to be simultaneous in all Frames of Reference.

    But how can that be?

    Well the Spacetime point M maps to different coordinates in each Frame of reference: in Einstein's Embankment Frame it is point M on the embankment, while in his Train's Frame of Reference it is the point M'.

    Einstein's M and M' meet at E3 when the lights arrive there, but follow different Spacetime paths therefrom.

    Spacetime exists, while Frames of Reference are only vies of it. Maps created with different origins and orientations.
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    Quote Originally Posted by SpeedFreek View Post
    Tell that to those famous identical twins, who end up having different ages at the end of the thought-experiment.
    On the traveller's arrival back at base, their ages, measured by each other, will each be transformed by the Lorentz factor for their relative velocity, While they are travelling.

    t' = gamma.t
    But once the twins are once again at rest with one another, what are those transformed ages - gamma is now = 1?

    they are the same!


    Time dilation - and length contraction - are effects of measuring one frame from another, moving frame, when the frames are not in relative motion their measurements will be the same.

    It is like looking through a microscope - it doesn't matter how long you look, when you take the slide out the object is still the same size as it was before you magnified it!

    I leave you to draw your own conclusions about the rigour of those muon experiments!
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    Quote Originally Posted by space at the centre View Post
    On the traveller's arrival back at base, their ages, measured by each other, will each be transformed by the Lorentz factor for their relative velocity, While they are travelling.

    t' = gamma.t
    But once the twins are once again at rest with one another, what are those transformed ages - gamma is now = 1?

    they are the same!
    The twin experiment is about proper time, and the crucial difference here is that one of the twins undergoes acceleration. The SR relation does not apply here, you need to use the full definition for proper time :



    wherein the metric tensor encapsulates the acceleration information. Now, the stationary twin moves only in time but not in space, thus his measured proper time is simply



    The travelling twin on the other hand moves through time and space along a different curve, so his proper time is measured as



    which is obviously less than the stationary twin. What this shows us is that for any given path through space-time, a stationary one is always the longest one in terms of proper time. Or, to put it differently, an observer travelling through space experiences less proper time than a stationary observer, and thus will have aged less when they are brought together back into the same frame of reference.

    Time dilation - and length contraction - are effects of measuring one frame from another, moving frame, when the frames are not in relative motion their measurements will be the same.
    That is correct - from the point in time at which the twins are back in the same frame of reference onwards, they once again measure the same proper time for any given interval. However, for the period when one of the twins was in accelerated motion, their proper times differ.

    I leave you to draw your own conclusions about the rigour of those muon experiments!
    The muon situation is very simple. The average lifetime of a muon is about 2.2ns, which is by far not enough for a cosmic ray muon to reach the earth's surface. However, muons move at relativistic speeds - from the point of view of a stationary observer on earth the muon experiences time dilation, thus extending its lifetime before it decays. From the point of view of the muon, the thickness of the earth's atmosphere is reduced due to length contraction along the trajectory of motion. Both observers agree as to the outcome - that the muon can reach the earth's surface.
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    Thank you Markus.

    Sorry space at the centre, but you just aren't getting it.

    It doesn't matter if M is equidistant between the events or not. What matters is if the timing of those events, as measured by M, shows M that the events occurred at the same time after subtracting the light-travel time from the event to the observer, with the observer knowing the distance to those events in their own frame. That distance is not the same in both frames, due to relative motion. Einstein only set up his scenario to be equidistant to simplify the calculation so that light-travel time did not need to be calculated. But in doing so, and as he clearly stated, he is basing the frame of the experiment in the embankment frame.

    To all observers, at rest anywhere along the embankment, even if they are not between the two events, those events occurred simultaneously if we take Einsteins example.

    Let's look at this another way, using length contraction.

    Let's say, from the frame of the embankment, the train is the same length as the embankment as it passes through. As the train is in motion, this means it is length contracted from the frame of the embankment. If it is the same length as the embankment whilst in motion, this means it must be longer than the embankment when at rest.

    So, from the frame of the embankment, the ends of the train and the ends of the embankment line up simultaneously. A simple scenario. The right hand end of the train lining up with the right end of the embankment is one event. The left hand end of the train lining up with the left hand end of the embankment is another event.

    Let's say that a light flashes at that position when each end of the train lines up with each end of the embankment.

    So, if whilst the train is in motion, it is same length as the embankment, from the frame of the embankment, then those events must be simultaneous from the frame of the embankment. The lights will flash at the same time, from the frame of the embankment.

    But from the frame of the train, the embankment is shorter than the train, due to length contraction! The embankment is in motion in relation to the train, after all. When at rest, the train is already longer than the embankment, but when the embankment is in motion it is even shorter still! So, from the frame of the train, the ends of the train cannot possibly line up with the ends of the embankment simultaneously. The lights will flash at different times, from the frame of the train.

    Only from the frame of the embankment, when the train is motion, are the events simultaneous. But they are not simultaneous from the frame of the train.

    QED.

    By arguing against the time-dilation we have measured and confirmed in muon experiments, you are proposing a view that goes against the scientific consensus, which was obtained through experiment.
    Last edited by SpeedFreek; January 5th, 2013 at 07:57 AM.
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    Thank you for shewing us that description. What has it to do with Einstien's theory of Relativity?

    His theory does not mention Proper time!

    The very idea of time dilation and length contraction being real Physical changes is logically confusing if not downright impossible!

    Consider:
    Body A is at rest in Spacetime and has properties - length L and duration T

    Then add Body B moving at 0.8667c.
    An observer in B will measure those properties as L/2 and 2T (Lorentz factor = 2).

    Add another body C moving at 0.6c and an observer on C will measure those properties as 0.8L and 1.25T (Lorentz factor = 1.25)

    So what are the physical Properties now?

    Are those properties really different in the two Frames?
    Yet still the original values in Frame A?

    And so on for very differently moving body in the whole of Spacetime?

    I don't think so!

    How are those transformations determined? By measurement? So the measurements differ according to the relative speed of the observer while in A they haven't changed?

    Welcome to the Perspective of Relativity.

    Just as in optical perspective, only the apparent/measured dimensions are a function of the relative speed rather than their separation.

    And how can the speed of light still be c? (c = L/T = L/γ .1/γT = L/γ2T)

    It is because in length contraction we are contracting the unit size; whereas in time dilation we are dilating the unit quantity by the same Lorentz factor. So the absolute dimensions of the said properties ie. unit size x unit quantity will remain constant.

    The Body's property dimensions remain the same, while the measurements made by a moving observer are transformed.

    This way it all makes plain and simple sense with out any of that 'wibbly-wobbly timey-wimey stuff'
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    Markus' equations come from General Relativity. SR is just a subset of GR and GR simplifies to SR in the appropriate conditions. Markus is showing you the most rigorous proof possible.

    We have confirmed the "wibbly-wobbly timey-wimey stuff" in many experiments. The GPS system in your car would not work without it. The internal clocks in GPS satellites were set to run at a different rate to clocks on the ground before take off, to ensure they remained synchronised with clocks on the ground once in orbit, due to both the relative motions of the GPS satellites in orbit and the difference in gravitational potential, in relation to the surface of the Earth. If they had not adjusted those clocks, your GPS would lose accuracy at around 10km per day.
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    Quote Originally Posted by SpeedFreek View Post

    To all observers, at rest anywhere along the embankment, even if they are not between the two events, those events occurred simultaneously if we take Einsteins example.
    Yes they were simultaneous in that frame, however M was the only place where an observer could prove that.
    Let's look at this another way, using length contraction.
    I don't recall that being relevant in Einstein's Description, he states that AB is the length of the train, not the contracted length - after all his drawing was God's view - I really don't see why you have a problem with that when Albert didn't!

    Read Post 42 to see how it really works, that simultaneity HAS to be universal! Relativity of Simultaneity is how simultaneity appears in different frames. It is there because the observer in one frame cannot prove simultaneity in another frame.
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    Quote Originally Posted by space at the centre View Post
    Quote Originally Posted by SpeedFreek View Post

    To all observers, at rest anywhere along the embankment, even if they are not between the two events, those events occurred simultaneously if we take Einsteins example.
    Yes they were simultaneous in that frame, however M was the only place where an observer could prove that.
    Nonsense. Any observer on the embankment, knowing the distance from himself to A and B, can prove that.

    Quote Originally Posted by space at the centre View Post
    I don't recall that being relevant in Einstein's Description, he states that AB is the length of the train, not the contracted length - after all his drawing was God's view - I really don't see why you have a problem with that when Albert didn't!
    No, his drawing is NOT from a god's-eye view! It is impossible to draw the situation from both views at the same time. Any graph or illustration has to define a rest frame.

    "Now in reality (considered with reference to the railway embankment)"
    "Just when the flashes 1 of lightning occur, this point M' naturally coincides with the point M"

    Note 1.As judged from the embankment.

    Quote Originally Posted by space at the centre View Post
    Read Post 42 to see how it really works, that simultaneity HAS to be universal!
    Nope. Simultaneity is relative. Hence the title of the chapter.

    Quote Originally Posted by space at the centre View Post
    Relativity of Simultaneity is how simultaneity appears in different frames. It is there because the observer in one frame cannot prove simultaneity in another frame.
    Nope. It is there because if events are simultaneous in a rest frame, they are not always simultaneous as judged from a frame in motion relative to that rest frame.
    Last edited by SpeedFreek; January 5th, 2013 at 09:21 AM.
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    Quote Originally Posted by space at the centre View Post
    His theory does not mention Proper time!
    I must say it is very disappointing to witness your lack of knowledge on this well established and empirically verified area of physics. I suggest you go and study up on this first - at present you simply do not possess the required expertise to attack an idea which you really do not understand in the first place.
    Proper time is the geometric distance between two events in space-time, and as such very much a basic and integral concept of the theory of relativity.

    Body A is at rest in Spacetime
    At rest with respect to what ?

    Then add Body B moving at 0.8667c.
    Moving at 0.8667c with respect to what ?

    An observer in B will measure those properties as L/2 and 2T (Lorentz factor = 2).
    With respect to what ?

    Add another body C moving at 0.6c
    With respect to what ?

    So what are the physical Properties now?
    They are what each observer measures them to be. There is no requirement for observers to agree on measurements, only on outcomes. Take for example the aforementioned muon - both observers always agree on the outcome ( the muon reaching earth's surface ), but they do not agree how or why the outcome takes place, because they are not in the same frame of reference.

    Are those properties really different in the two Frames?
    Yes.

    So the measurements differ according to the relative speed of the observer while in A they haven't changed?
    You are not getting this at all. For A, frame B is moving. However, if you go to B then it is frame A that is moving. Who is right and who is wrong ? Who decides ?

    And how can the speed of light still be c?
    Because it is invariant under Lorentz transformations. If you go from one frame to another you perform a Lorentz transformation, which leaves the numerical value of c untouched in both frames.

    So the absolute dimensions of the said properties ie. unit size x unit quantity will remain constant.
    There are no "absolute" dimensions. Only observers in the same frame of reference will agree on the measured dimensions of an object.

    The Body's property dimensions remain the same, while the measurements made by a moving observer are transformed.
    Moving with regards to what ? Transformed as compared to what ?

    This way it all makes plain and simple sense with out any of that 'wibbly-wobbly timey-wimey stuff'
    No, it is just wrong. Plain and simple.
    Last edited by Markus Hanke; January 5th, 2013 at 11:18 AM.
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    Read Post 42 to see how it really works, that simultaneity HAS to be universal!
    Simultaneity is observer dependent, and the term "universal" is without meaning in the theory of relativity.
    The observer dependence does not just entail the state of relative motion of the observers, but also the geometry and topology of the space-time between them; this is why I used the metric tensor in my previous calculation, since it contains just that information.
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    Since it is apparent that space at the centre's purpose here is not to discuss or learn about Relativity, but to dismiss it, I'm booting this thread to pseudoscience.
    "Men are apt to mistake the strength of their feelings for the strength of their argument.
    The heated mind resents the chill touch & relentless scrutiny of logic"-W.E. Gladstone


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    Quote Originally Posted by SpeedFreek View Post
    Quote Originally Posted by space at the centre View Post
    Quote Originally Posted by SpeedFreek View Post

    To all observers, at rest anywhere along the embankment, even if they are not between the two events, those events occurred simultaneously if we take Einsteins example.
    Yes they were simultaneous in that frame, however M was the only place where an observer could prove that.
    Nonsense. Any observer on the embankment, knowing the distance from himself to A and B, can prove that.
    Not using Einstein's test: "By measuring along the rails, the connecting line AB should be measured up and an observer placed at the mid-point M of the distance AB. This observer should be supplied with an arrangement (e.g. two mirrors inclined at 90°) which allows him visually to observe both places A and B at the same time. If the observer perceives the two flashes of lightning at the same time, then they are simultaneous."

    Quote Originally Posted by space at the centre View Post
    I don't recall that being relevant in Einstein's Description, he states that AB is the length of the train, not the contracted length - after all his drawing was God's view - I really don't see why you have a problem with that when Albert didn't!
    No, his drawing is NOT from a god's-eye view! It is impossible to draw the situation from both views at the same time. Any graph or illustration has to define a rest frame.
    No, I am sorry to disagree but we can take Spacetime as the system we are viewing.[quote]

    "Now in reality (considered with reference to the railway embankment)"
    "Just when the flashes 1 of lightning occur, this point M' naturally coincides with the point M"

    Note 1.As judged from the embankment.

    Quote Originally Posted by space at the centre View Post
    Read Post 42 to see how it really works, that simultaneity HAS to be universal!
    Nope. Simultaneity is relative. Hence the title of the chapter. [quote]
    Exactly! It is relative to where it is viewed from but that does not change the fact that two events are simultaneous in Spacetime and from any frame if measured in the right way.

    Quote Originally Posted by space at the centre View Post
    Relativity of Simultaneity is how simultaneity appears in different frames. It is there because the observer in one frame cannot prove simultaneity in another frame.
    Nope. It is there because if events are simultaneous in a rest frame, they are not always simultaneous as judged from a frame in motion relative to that rest frame.
    Exactly - not simultaneous as judged, yet simultaneous in fact!
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    Quote Originally Posted by Markus Hanke View Post
    Quote Originally Posted by space at the centre View Post
    His theory does not mention Proper time!
    I must say it is very disappointing to witness your lack of knowledge on this well established and empirically verified area of physics. I suggest you go and study up on this first - at present you simply do not possess the required expertise to attack an idea which you really do not understand in the first place.
    Proper time is the geometric distance between two events in space-time, and as such very much a basic and integral concept of the theory of relativity.
    I'm afraid that you may be a little precipitate in making such a sweeping judgement.
    Body A is at rest in Spacetime
    At rest with respect to what ?
    Minkowski wrote: "The substance existing at any world point can always be conceived to be at rest, if time and space are interpreted suitably" -- ref:Space and Time (1920) by Hermann Minkowski, Space and Time - Wikisource, the free online library
    Then add Body B moving at 0.8667c.
    Moving at 0.8667c with respect to what ?
    With respect to body A

    An observer in B will measure those properties as L/2 and 2T (Lorentz factor = 2).
    With respect to what ?
    Sorry, did you miss this line: Body A is at rest in Spacetime and has properties - length L and duration T

    Add another body C moving at 0.6c
    With respect to what ?
    with respect to A

    So what are the physical Properties now?
    They are what each observer measures them to be. There is no requirement for observers to agree on measurements, only on outcomes. Take for example the aforementioned muon - both observers always agree on the outcome ( the muon reaching earth's surface ), but they do not agree how or why the outcome takes place, because they are not in the same frame of reference.
    I am sorry but now you are talking nonsense. If time dilation and length contraction are physical effects that change the measurements in the observed frame, then how can that be for multiple cases at the same time? are those changes cumulative or only appliccable to the observer's frame - for if so it is only that observer's measurements that are transformed not the Physical measurements in the observed.
    Are those properties really different in the two Frames?
    Yes.

    So the measurements differ according to the relative speed of the observer while in A they haven't changed?
    You are not getting this at all. For A, frame B is moving. However, if you go to B then it is frame A that is moving. Who is right and who is wrong ? Who decides ?
    no it is you who are twisting it round. we are not talking of A viewing B compared to B viewing A.
    We are comparing A viewed by B with A viewed by C. If it is only the way they are viewed that changes - fair enough - but to say that they are Physically changed is nonsense, for if A is contracted by being viewed by B then surely it must be that that contracted measure is contracted again by C.

    And how can the speed of light still be c?
    Because it is invariant under Lorentz transformations. If you go from one frame to another you perform a Lorentz transformation, which leaves the numerical value of c untouched in both frames.
    Oh very good, very good. Yes of course that is true - spoken like a true politician! Now how about explaining the point: And how can the speed of light still be c? (c = L/T = L/γ .1/γT = L/γ2T)
    So the absolute dimensions of the said properties ie. unit size x unit quantity will remain constant.
    There are no "absolute" dimensions. Only observers in the same frame of reference will agree on the measured dimensions of an object.
    Again I apologize, by absolute I mean the magnitude regardless of units of measurement for the number of units multiplied by the size of a unit gives the true size. Just stating the number of units is meaningless when those units are being transformed by the Lorentz equations.
    When t' = t/γ t' and t are not the same units

    The Body's property dimensions remain the same, while the measurements made by a moving observer are transformed.
    Moving with regards to what ?
    I do not believe this question is necessary! A mobving observer is moving with regards to what he is observing!
    Transformed as compared to what ?
    as compared to those measurements in the observed frame!

    This way it all makes plain and simple sense with out any of that 'wibbly-wobbly timey-wimey stuff'
    No, it is just wrong. Plain and simple.
    There is so much here that no one ever questions because they just repeat what they were taught!
    If one examines it is full of holes ,fudges and inconsistencies. Have any of you actually worked through it and checked it? NO!
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    [QUOTE=space at the centre;381964]
    Quote Originally Posted by SpeedFreek View Post
    Quote Originally Posted by space at the centre View Post
    Quote Originally Posted by SpeedFreek View Post

    To all observers, at rest anywhere along the embankment, even if they are not between the two events, those events occurred simultaneously if we take Einsteins example.
    Yes they were simultaneous in that frame, however M was the only place where an observer could prove that.
    Nonsense. Any observer on the embankment, knowing the distance from himself to A and B, can prove that.
    Not using Einstein's test: "By measuring along the rails, the connecting line AB should be measured up and an observer placed at the mid-point M of the distance AB. This observer should be supplied with an arrangement (e.g. two mirrors inclined at 90°) which allows him visually to observe both places A and B at the same time. If the observer perceives the two flashes of lightning at the same time, then they are simultaneous."
    He determines that they are simultaneous because he is both halfway between and see then at the same time. However, this does not mean that he judges the flashes to have occurred at the time that he sees them; he judges them to have taken place at some time in the past. Putting him at the midpoint just allows him to make this judgement without knowing the speed of light or the actual distance from A to B. If however, he knows both and his relative position between A and B he would be able to judge that the flashes where simultaneous by noting the time delay between his seeing the flashes.[quote]



    Quote Originally Posted by space at the centre View Post
    I don't recall that being relevant in Einstein's Description, he states that AB is the length of the train, not the contracted length - after all his drawing was God's view - I really don't see why you have a problem with that when Albert didn't!
    The reason he does not bring in length contraction here is because he hasn't introduced the concept yet. He actually touches on it in the next section. He starts out by describing how one would go about measuring the length of the Train (from `A to B`) from within the train and from the embankment. He then concludes:

    A priori it is by no means certain that this last measurement (from the embankment) will supply us with the same result as the first(from the train). Thus the length of the train as measured from the embankment may be different from that obtained by measuring in the train itself.

    He then in the next sections goes on to show that this is indeed the case; the distance `A-`B is different when measured from the embankment than it is as measured from the train.
    [quote]

    No, his drawing is NOT from a god's-eye view! It is impossible to draw the situation from both views at the same time. Any graph or illustration has to define a rest frame.[quote]
    No, I am sorry to disagree but we can take Spacetime as the system we are viewing.

    "Now in reality (considered with reference to the railway embankment)"
    "Just when the flashes 1 of lightning occur, this point M' naturally coincides with the point M"

    Note 1.As judged from the embankment.
    And? What this means that in the embankment frame M and M' are next to each other when the lightning strikes occur. (when the lightning strikes occur, not when M sees them), however it does follow that M and M' are next to each other when either of the strikes occur in the frame of the train. In fact, when we take what is covered in the sections into account, we see that this cannot be the case. If A'-B' and A-B are equal distances in the embankment frame (as shown in the diagram), then A'-B' cannot be equal to A-B in the train frame. Thus A cannot coincide with A' nor B with B' when M and M coincide in the Train frame. We can also conclude that when A and A' coincide B and B' do not (and conversely when B and B' coincide, A and A' do not) Since the one lighting strike occurs at AA' when A and A' coincide (in both frames) and the other at BB' when B an B' coincide (again in both frames), The two strikes cannot occur at the same time in the train frame.[quote]

    Quote Originally Posted by space at the centre View Post
    Read Post 42 to see how it really works, that simultaneity HAS to be universal!
    Nope. Simultaneity is relative. Hence the title of the chapter.
    Exactly! It is relative to where it is viewed from but that does not change the fact that two events are simultaneous in Spacetime and from any frame if measured in the right way.

    Quote Originally Posted by space at the centre View Post
    Relativity of Simultaneity is how simultaneity appears in different frames. It is there because the observer in one frame cannot prove simultaneity in another frame.
    Nope. It is there because if events are simultaneous in a rest frame, they are not always simultaneous as judged from a frame in motion relative to that rest frame.
    Exactly - not simultaneous as judged, yet simultaneous in fact!
    In this case, as "judged" by a frame is the same thing as "in fact" in that frame.

    Events according to the embankment frame (according to anyone located anywhere at rest with respect to the embankment):



    Same events according to the train( according to anyone on the train):

    "Men are apt to mistake the strength of their feelings for the strength of their argument.
    The heated mind resents the chill touch & relentless scrutiny of logic"-W.E. Gladstone


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  54. #53  
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    Quote Originally Posted by space at the centre View Post
    True, there is no Frame of Reference that has any more than one view of Spacetime.
    Yet that does not mean that Spacetime does not exist as a homogeneous and isotropic entity, the same everywhere in every direction.
    Quote Originally Posted by space at the centre View Post
    A Frame of Reference is a particular view of Spacetime.

    This understanding comes directly from Mikowski's Spacetime.
    You seem to think Minkowski spacetime exists as a real entity in which the ordering of events is real!

    Quote Originally Posted by space at the centre View Post
    Exactly! It is relative to where it is viewed from but that does not change the fact that two events are simultaneous in Spacetime and from any frame if measured in the right way.
    It is relative to where it is viewed? Do you now agree that the train frame views the events the events not to be simultaneous then? In Einstein's example?

    You say the events would be simultaneous from any frame if measured in the right way. Do you mean if the train frame chooses the embankment frame to be the "real" frame? That is all you can possibly mean, as the train frame definitely measures the events not to be simultaneous in its own frame, using its own ruler and clock.

    Quote Originally Posted by space at the centre View Post
    Exactly - not simultaneous as judged, yet simultaneous in fact!
    Where did you forget the part about there being no preferred frame where the laws of physics are any more "real" than anywhere else?

    If you now agree that the train does not measure the events to be simultaneous in its own frame, then what we have here folks... is a some version of Lorentzian Ether Theory, by any other name.

    What that means is that spacetime is a real entity which represents a "hidden" frame of reference, where the ordering of events are real, and time and distance are not dilated. All other frames are time-dilated and length contracted in relation to that "hidden" frame, but they cannot know it, as their rulers and clocks are also affected.

    Unless, that is, you are still thinking that the train observer calculates the events to be simultaneous, using their own ruler and clock, which is definitely not what Einstein was saying in Chapter 9. He was simply illustrating the problem from the view of the embankment, and showing how the observer on the embankment measures the events not to be simultaneous on the train.

    We have already established by this point that the other frame can consider themselves to be the rest frame, in which case (the "vice-versa) IF they are simultaneous on the train then they are NOT simultaneous on the embankment (which would be a different set of events). But he is not saying they are simultaneous in both frames. Unless, you think all other texts published on this subject by respected authors since are wrong (which includes many texts published during his lifetime - surely he would have sought to correct all these misconceptions about his theory!).

    So which is it? Everyone is wrong about what Einstein said but he never bothered to point this out, or the events are calculated to be not simultaneous in the train frame, but are simultaneous in the embankment frame?

    (and are simultaneous in the "hidden" frame of spacetime itself, which apparently is real, rather than a concept conceived as a framework to show how SPACE AND TIME ARE RELATIVE, rather than absolute?)

    I will leave you with a Minkowski diagram showing two events that are simultaneous in the green frame, but not simultaneous in either the red or blue frames.

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    Hi! I thank you for trying to explain things instead of telling me that I am stupid and ignorant.
    I notice you make use of Einsteins definition:

    The events a and b are simultaneous if and only if lightrays from a and b arrives simultaneously at the midpoint of the segment ab.
    Quote Originally Posted by space at the centre View Post
    Quote Originally Posted by SpeedFreek View Post
    Quote Originally Posted by sigurdV View Post
    Well then what is simultanity? In how many ways can it be defined?
    Simultaneity is the question as to whether two events separated by space occur at the same time, or not.

    The answer is frame dependant - it depends on the frame of reference of the observer.
    Consider: three points in space A,M,B. AM = MB, M is physically midway between A & B.

    Add two events, E1 and E2: Flashes light propagated at A and B, the light from these events arrive at M simultaneously. This event E3.

    E1 and E2 are therefore simultaneous. Oh, but sorry, this is taking the God view; so let us take a Frame of Reference - any Frame of Reference, and the Points in space A,M B will exist in that Frame. Oh, and so will the events E1,E2,E3.

    For any Frame of Reference may be considered at rest in Spacetime, where movement is only relative.

    Therefore we can conclude that in ANY, that is in each and every, Frame of Reference there will be a point in space, M, midway in space between points A and B where the lights will arrive simultaneously.
    Hopefully I made no quotational error here... if so its not intentional. Lets get to business then:

    How is it determined if something happens simultaneously? I took the liberty of underlining the word wherever it occured.
    (And also the concept "at the same time" at the same time.)

    I notice it occurs already in Einsteins definition: The concept " simultaneous" is defined using the concept "simultaneously".

    It seems to me that we should use some OTHER concept than "simultaneously" in understanding
    the concept "simultaneous". Otherwise we seem to define a concept with itself.
    Perhaps not a quite safe and healthy procedure in erecting the foundation of a scientific theory?

    Why did Einstein introduce the definition?
    Cant we be satisfied with the concept "at the same time" or is that concept in need of explanation as well?

    I hope you excuse my for asking questions?

    But I am only a poor layman of Relativity trying to understand what you experts do and say.
    I can not follow your arguments unless I may check each step. And I got stuck on "simultaneity".
    It surely means "being simultaneous" or "happens at the same time". What can be done?
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    Quote Originally Posted by space at the centre View Post
    I'm afraid that you may be a little precipitate in making such a sweeping judgement.
    No, it is simply based on what you have presented thus far.

    The substance existing at any world point can always be conceived to be at rest, if time and space are interpreted suitably
    Precisely - what that means is that you have to choose a reference point. There is no absolute frame of reference. You can interpret frame A to be at rest, then B moves. You can also consider B to be at rest, then it is A that moves. The connection between the two is the Lorentz transformation.

    Sorry, did you miss this line: Body A is at rest in Spacetime and has properties - length L and duration T
    Space-time is not a frame of reference. A can be at rest only with respect to some other frame. This is where your entire argumentation falls down; there is no absolute frame of reference, things are not at rest or in motion with regards to space-time, but only with regards to some other frame.

    I am sorry but now you are talking nonsense. If time dilation and length contraction are physical effects that change the measurements in the observed frame, then how can that be for multiple cases at the same time? are those changes cumulative or only appliccable to the observer's frame - for if so it is only that observer's measurements that are transformed not the Physical measurements in the observed.
    I have no idea what you mean by this. Multiple observers in the same frame will make the same measurements; if they are not in the same frame then their measurements will differ. You are still holding on to the idea that there must be some intrinsic reality to this subject, something which is independent of what is and can be observed. You appear to be under the impression that length contraction and time dilation are only apparent effects. They are not, they are very physically real. You can test this directly via particle acceleration experiments; for example, if you accelerate two heavy ions ( like gold or lead, which are normally spherical in shape ) to relativistic speeds and let them collide, you measure collision dynamics not of spheres, but of flattened obloids. That is because the normally spherical ions are length contracted along their trajectory of motion with respect to the stationary particle collider. Refer here :

    RHIC | Physics of the Relativistic Heavy Ion Collider

    And how can the speed of light still be c?
    I would advise you against refusing to acknowledge explanations already given. The moderators here do not take kindly to this kind of conduct.
    So once again - Lorentz transformations leave the speed of light invariant. Pick an arbitrary frame - the observer in that frame measures exactly c. Now pick another arbitrary frame which is in uniform motion with respect to the first frame - you go into that one by performing a Lorentz transformation. Once again, you arrive at c.
    If you like you can think of it this way - the speed of light is a function of vacuum permittivity and permeability :



    Since both of these are universal constants of a medium/vacuum, and thus observer independent, all observers necessarily see the same speed of light, and the Lorentz transformations ensure that this is indeed the case. You don't even need to know anything about relativity to realize that.

    Again I apologize, by absolute I mean the magnitude regardless of units of measurement for the number of units multiplied by the size of a unit gives the true size.
    And who determines the "size" of a unit ?

    I do not believe this question is necessary! A mobving observer is moving with regards to what he is observing!
    Exactly. He is moving with regards to another frame of reference. There is no absolute rest or absolute motion.

    There is so much here that no one ever questions because they just repeat what they were taught!
    Typical crackpot argument.
    This is all very logic and straightforward stuff, but of course you need to understand it first.

    If one examines it is full of holes ,fudges and inconsistencies.
    Again, that is because you do not understand it. You may wish to also take a look here :

    Modern Tests of Relativity

    Have any of you actually worked through it and checked it?
    Yes, for the past several decades, maths and empirical experiments. Have you ? Judging by your lack of understanding the answer seems obvious - no you haven't. You just come on here asserting that relativity is wrong, and once we try and explain things to you, you refuse to acknowledge those explanations.
    Or is it a case that you do not want to understand it ? We have had plenty of cranks like that here, for sure !
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    Quote Originally Posted by Janus View Post
    He determines that they are simultaneous because he is both halfway between and see then at the same time. However, this does not mean that he judges the flashes to have occurred at the time that he sees them; he judges them to have taken place at some time in the past. Putting him at the midpoint just allows him to make this judgement without knowing the speed of light or the actual distance from A to B.
    Yes, of course.
    If however, he knows both and his relative position between A and B he would be able to judge that the flashes where simultaneous by noting the time delay between his seeing the flashes.
    yes, true, yet much more complicated and requiring more measurements and data than Einstein's simple test.


    Quote Originally Posted by space at the centre View Post
    I don't recall that being relevant in Einstein's Description, he states that AB is the length of the train, not the contracted length - after all his drawing was God's view - I really don't see why you have a problem with that when Albert didn't!
    The reason he does not bring in length contraction here is because he hasn't introduced the concept yet. He actually touches on it in the next section. He starts out by describing how one would go about measuring the length of the Train (from `A to B`) from within the train and from the embankment. He then concludes:

    A priori it is by no means certain that this last measurement (from the embankment) will supply us with the same result as the first(from the train). Thus the length of the train as measured from the embankment may be different from that obtained by measuring in the train itself.

    He then in the next sections goes on to show that this is indeed the case; the distance `A-`B is different when measured from the embankment than it is as measured from the train.
    Exactly, it is the measurements made under different conditions, ie. by a movingobserver, that are different; Not the distances them selves; for as Einstein states: "But the events A and B also correspond to positions A and B on the train."


    Quote Originally Posted by space at the centre View Post
    Read Post 42 to see how it really works, that simultaneity HAS to be universal!
    Nope. Simultaneity is relative. Hence the title of the chapter. [/quote]
    Then tell me what is wrong with the logic in post 42!


    Quote Originally Posted by space at the centre View Post
    Relativity of Simultaneity is how simultaneity appears in different frames. It is there because the observer in one frame cannot prove simultaneity in another frame.
    Nope. It is there because if events are simultaneous in a rest frame, they are not always simultaneous as judged from a frame in motion relative to that rest frame.[/quote]Exactly - not simultaneous as judged, yet simultaneous in fact![/quote]

    In this case, as "judged" by a frame is the same thing as "in fact" in that frame.

    Events according to the embankment frame (according to anyone located anywhere at rest with respect to the embankment):



    Same events according to the train( according to anyone on the train):

    [/quote]

    No, the second one is according to how the observer on the embankment will conclude that the observer on the train will see it.
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    Quote Originally Posted by SpeedFreek View Post
    Quote Originally Posted by space at the centre View Post
    True, there is no Frame of Reference that has any more than one view of Spacetime.
    Yet that does not mean that Spacetime does not exist as a homogeneous and isotropic entity, the same everywhere in every direction.
    Quote Originally Posted by space at the centre View Post
    A Frame of Reference is a particular view of Spacetime.

    This understanding comes directly from Mikowski's Spacetime.
    You seem to think Minkowski spacetime exists as a real entity in which the ordering of events is real!
    Yes Spacetime is real, it exists - or are you saying it is imaginary?

    I will leave you with a Minkowski diagram showing two events that are simultaneous in the green frame, but not simultaneous in either the red or blue frames.

    As seen from the green frame!

    If viewed from the red frame or the blue frame then they would be the ones drawn square and seeing simultaneity!

    My goodness that is such an Obvious error!
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    If viewed from the red frame or the blue frame then they would be the ones drawn square and seeing simultaneity!

    My goodness that is such an Obvious error!
    Man, what are you talking about ? Going into the red or blue frame would mean a rotation of the entire grid, including the event points. Of course the red or blue grid would then be the ones with squares drawn, but A and B would no longer lie along the same grid line.
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    Quote Originally Posted by Markus Hanke View Post
    Quote Originally Posted by space at the centre View Post
    The substance existing at any world point can always be conceived to be at rest, if time and space are interpreted suitably
    Precisely - what that means is that you have to choose a reference point. There is no absolute frame of reference. You can interpret frame A to be at rest, then B moves. You can also consider B to be at rest, then it is A that moves. The connection between the two is the Lorentz transformation.
    If one considers a single body in spacetime, then that body is 'at rest' as their is nothing in relation to which it can be moving!

    Sorry, did you miss this line: Body A is at rest in Spacetime and has properties - length L and duration T
    Space-time is not a frame of reference. A can be at rest only with respect to some other frame. This is where your entire argumentation falls down; there is no absolute frame of reference, things are not at rest or in motion with regards to space-time, but only with regards to some other frame.
    If you are trying to deliberately misunderstand everything I write, try to do so logically!
    I will repeat: a body is at rest in spacetime unless there is something else that it can be moving relative to. AND if "things are not at rest or in motion with regards to space-time, but only with regards to some other frame" then you are saying that one cannot consider a single frame in spacetime!

    I am sorry but now you are talking nonsense. If time dilation and length contraction are physical effects that change the measurements in the observed frame, then how can that be for multiple cases at the same time? are those changes cumulative or only appliccable to the observer's frame - for if so it is only that observer's measurements that are transformed not the Physical measurements in the observed.
    I have no idea what you mean by this.[/quote]Sigh.
    If a body is physically length contracted - to only half its original length (L), (0.8667c - gamma = 2) by the motion of one observer, then what is its physical length if there is another observer moving at 0.6c - gamma = 1.25 ?

    Is it 0.8L - but no it is already contracted to 0.5L so is it 0.4L? - but no for if that were accumulative, and there being no distance beyond which the effect is no longer felt, no if it were accumulative there are so many moving bodies in the universe everything would become so small they would vanish!
    Or perhaps you would say the effect is only within that observer's frame - so in one frame it is 0.8L while in another it is 0.5L, but how can one body possess different lengths according to how it is observed??
    Almost like perspective where the body doesn't change but the size it is measured at depends on the distance - but no that can't be either because you insist that the observed body really becomes physically shorter. . .

    Can you please explain this?


    Multiple observers in the same frame will make the same measurements; if they are not in the same frame then their measurements will differ.
    Yes! the Measurements differ! I can agree with that.
    You are still holding on to the idea that there must be some intrinsic reality to this subject, something which is independent of what is and can be observed. You appear to be under the impression that length contraction and time dilation are only apparent effects. They are not, they are very physically real. You can test this directly via particle acceleration experiments; for example, if you accelerate two heavy ions ( like gold or lead, which are normally spherical in shape ) to relativistic speeds and let them collide, you measure collision dynamics not of spheres, but of flattened obloids. That is because the normally spherical ions are length contracted along their trajectory of motion with respect to the stationary particle collider. Refer here :

    RHIC | Physics of the Relativistic Heavy Ion Collider
    And if the measurements of a relativistic heavy ion are length contracted would not that same effect be measured throughout the experiment?
    And how can the speed of light still be c?
    I would advise you against refusing to acknowledge explanations already given. The moderators here do not take kindly to this kind of conduct.[/quote]
    I am NOT refusing to acknowledge explanations I am questioning them! I have spent a long time going over these explanations and there appear to be so many things that are merely glossed over with a 'this is what you should think'.
    Contrary to what I was told when I started this, I do not believe that 'relativity is a question of faith - that one has to believe in it rather than understand it'!
    So once again - Lorentz transformations leave the speed of light invariant. Pick an arbitrary frame - the observer in that frame measures exactly c. Now pick another arbitrary frame which is in uniform motion with respect to the first frame - you go into that one by performing a Lorentz transformation. Once again, you arrive at c.
    If you like you can think of it this way - the speed of light is a function of vacuum permittivity and permeability :



    Since both of these are universal constants of a medium/vacuum, and thus observer independent, all observers necessarily see the same speed of light, and the Lorentz transformations ensure that this is indeed the case. You don't even need to know anything about relativity to realize that.
    There you go again! but I will not be annoyed by such coments.
    I do understand exactly how the Lorentz transfomations work and can draw diagrams to shew it, but that is not the point here.

    What I am querying is if c is a measure of distance divided by time, and you contract the distance while dilating the time in a moving frame, then how on Earth can it still be c?

    Again I apologize, by absolute I mean the magnitude regardless of units of measurement for the number of units multiplied by the size of a unit gives the true size.
    And who determines the "size" of a unit ?
    sigh; that is defined by the scale against which it is measured

    I do not believe this question is necessary! A moving observer is moving with regards to what he is observing!
    Exactly. He is moving with regards to another frame of reference. There is no absolute rest or absolute motion.
    so if you know that why ask?

    There is so much here that no one ever questions because they just repeat what they were taught!
    Typical crackpot argument.
    This is all very logic and straightforward stuff, but of course you need to understand it first.

    If one examines it is full of holes ,fudges and inconsistencies.
    Again, that is because you do not understand it. You may wish to also take a look here :

    Modern Tests of Relativity

    Have any of you actually worked through it and checked it?
    Yes, for the past several decades, maths and empirical experiments. Have you ? Judging by your lack of understanding the answer seems obvious - no you haven't. You just come on here asserting that relativity is wrong, and once we try and explain things to you, you refuse to acknowledge those explanations.
    Or is it a case that you do not want to understand it ? We have had plenty of cranks like that here, for sure !
    There you go again! A constant barrage of insults and doubts about my integrity! - but no matter.

    I have no problem with relativity as described by Einstein. It is a beautiful, simple, elegant theory and it obviously works very well, as seen in GPS etc were its application has been proved over and over.

    It is some of the more esoteric bits that have been added to it to try and explain by torturous logic, what is simple and straightforward yet not fully grasped.
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    Muon experiment. If one also applies length contraction then the distance travelled by the muons will be length contracted by the factor gamma, the same factor by which the time is dilated. So they will not travel further.
    That experiment seems to assume that all cosmic rays generate muons at some set distance from the planet surface. Surely most will continue down through the atmosphere until they eventually strike a molecule?
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    Looking at this debate one might think the subject is religion.
    The argument proceeds fast and predictable,
    no errors is ever admitted from any side, holy text is recited?
    What can we onlookers do? Ask if there is anything both parties agree on?
    I bet the only thing they will agree on is that we should be quiet and let them fight in peace!
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  63. #62  
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    Quote Originally Posted by space at the centre View Post
    If one considers a single body in spacetime, then that body is 'at rest' as their is nothing in relation to which it can be moving!
    The notion of "speed" is not defined for a single, isolated frame of reference, and neither are time dilation and length contraction.

    I will repeat: a body is at rest in spacetime unless there is something else that it can be moving relative to. AND if "things are not at rest or in motion with regards to space-time, but only with regards to some other frame" then you are saying that one cannot consider a single frame in spacetime!
    See above. Of course you can consider a single frame of reference, but then its speed is not defined. Likewise, time dilation and length contraction wouldn't be defined, because there would not be anything to compare your single frame against.

    If a body is physically length contracted - to only half its original length (L), (0.8667c - gamma = 2) by the motion of one observer, then what is its physical length if there is another observer moving at 0.6c - gamma = 1.25 ?
    Once again - the "physical length" is what the observer performing the measurement determines. There is no absolute length, it depends on the observer.

    Is it 0.8L
    Only for one observer, but not for anyone else. Again, there is no absolute length, it depends on the observer.

    Or perhaps you would say the effect is only within that observer's frame - so in one frame it is 0.8L while in another it is 0.5L
    Yes, exactly.

    but no that can't be either because you insist that the observed body really becomes physically shorter. . .
    Yes, it "really" becomes shorter as measured by an outside frame. Refer to the RHIC experiment which I referenced earlier.

    And if the measurements of a relativistic heavy ion are length contracted would not that same effect be measured throughout the experiment?
    I don't know what you mean by that. The important bit is once again the outcome - at the time of collision the ions behave as flattened obloids, not as spheres. If you were to go into the frame of one of the ions, then the accelerator would appear contracted, and also the other ion coming at you. It would also see a different configuration of EM fields. The outcome itself however would once again be the same.

    What I am querying is if c is a measure of distance divided by time, and you contract the distance while dilating the time in a moving frame, then how on Earth can it still be c?
    Because they are equal and opposite effects, so if you want both length contraction and time dilation at the same time, you need to look from a stationary frame onto a moving one that contains a clock, from the "outside" so to say. You will then see that the moving clock is dilated, while that moving frame itself is length contracted. You are now using the moving clock and ruler to measure a shorter distance in less time, from your own point of view - the ratio ( speed of light ) remains the same. In the moving frame itself neither length contraction nor time dilation are measured, so again the ratio is just c.
    Why is this even an issue for you ? It is completely logic, even without any maths, so long as you are clear who measures what and in which frame.

    sigh; that is defined by the scale against which it is measured
    You can *sigh* yourself, because "scale" is also observer dependent. There are no absolute scales.

    so if you know that why ask?
    To show you that there is no absolute frame.

    I have no problem with relativity as described by Einstein. It is a beautiful, simple, elegant theory and it obviously works very well, as seen in GPS etc were its application has been proved over and over.
    What are you talking about ? Nothing at all was added since Einstein published the theory. It is based on Lorentz transformations now just as it was back then. And if you agree with this theory, why are you arguing it so vigorously ?
    Last edited by Markus Hanke; January 6th, 2013 at 11:43 AM.
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    Quote Originally Posted by space at the centre View Post
    Muon experiment. If one also applies length contraction then the distance travelled by the muons will be length contracted by the factor gamma, the same factor by which the time is dilated. So they will not travel further.
    No, because in the muon's frame no time dilation is observed, only length contraction of the atmosphere. Likewise, the stationary Earth-bound observer does not see length contraction, only time dilation. Be careful that you don't mix who sees which effect from what frame. That is where most misunderstanding about relativity come from.

    Surely most will continue down through the atmosphere until they eventually strike a molecule?
    Muons originate through the interaction of cosmic rays with the upper atmosphere, so there is well defined height at which those reactions occur. A muon has a lifetime of about 2.2ns, which would not nearly be enough to traverse the entire thickness of the atmosphere, yet we detect very many of those muons down here.
    Also, the whole thing can be done under controlled conditions in particle accelerators as well - with the same results.
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    Quote Originally Posted by sigurdV View Post
    Looking at this debate one might think the subject is religion.
    The argument proceeds fast and predictable,
    no errors is ever admitted from any side, holy text is recited?
    What can we onlookers do? Ask if there is anything both parties agree on?
    I bet the only thing they will agree on is that we should be quiet and let them fight in peace!
    I find it disappointing that even a century later people still argue against relativity, despite all experimental and observational evidence. It always reminds of this crowd :

    The Flat Earth Society
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    Quote Originally Posted by space at the centre View Post
    Quote Originally Posted by SpeedFreek View Post
    You seem to think Minkowski spacetime exists as a real entity in which the ordering of events is real!
    Yes Spacetime is real, it exists - or are you saying it is imaginary?
    Of course it is imaginary - it is a mathematical concept conceived as a framework against which to do calculations of how different observers experience space and time in different ways, because space and time are both relative, rather than absolute. That was the whole point of Special Relativity in the first place!

    Consequently, there is no way to separate space from time in any absolute manner. This is why simultaneity cannot be absolute. We take the concepts of space and time and combine them into one concept - spacetime - and we find that space and time break down differently, depending on the frame of the observer.

    Quote Originally Posted by space at the centre View Post
    Quote Originally Posted by SpeedFreek View Post
    I will leave you with a Minkowski diagram showing two events that are simultaneous in the green frame, but not simultaneous in either the red or blue frames.

    As seen from the green frame!

    If viewed from the red frame or the blue frame then they would be the ones drawn square and seeing simultaneity!

    My goodness that is such an Obvious error!
    My goodness, what an ignorant statement!

    If the red frame was drawn square, event B would still be 3/4 of a unit ABOVE the red x avis.
    If the blue frame was drawn squre, event B would still be 1.5 units BELOW the blue x axis.
    In either case, event B would still be on the x axis in the green frame - the same axis as event A in that frame.
    The green frame is the only frame where events A and B both occur at the same place on the time axis.

    Surely anyone can see this. Especially if, as they claim, they are basing their view in Minkowski spacetime.
    Last edited by SpeedFreek; January 6th, 2013 at 09:30 AM.
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    Quote Originally Posted by Markus Hanke View Post
    Quote Originally Posted by sigurdV View Post
    Looking at this debate one might think the subject is religion.
    The argument proceeds fast and predictable,
    no errors is ever admitted from any side, holy text is recited?
    What can we onlookers do? Ask if there is anything both parties agree on?
    I bet the only thing they will agree on is that we should be quiet and let them fight in peace!
    I find it disappointing that even a century later people still argue against relativity, despite all experimental and observational evidence. It always reminds of this crowd :

    The Flat Earth Society
    I understand your point..but it seems to me your side of the argument tries to reach out too far.
    It seems you think the theory of relativity applies everywhere: On the universe as a whole down to the inside of a point!
    Does it? What has it to say about our universe thought of as an existing object? Or about objects below the Planck limit? And how is what it says then verifiable?
    I enjoy your discussion but it is with the speed of a snail I follow it.
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    Quote Originally Posted by sigurdV View Post
    I understand your point..but it seems to me your side of the argument tries to reach out too far.
    It seems you think the theory of relativity applies everywhere: On the universe as a whole down to the inside of a point!
    Does it? What has it to say about our universe thought of as an existing object? Or about objects below the Planck limit? And how is what it says then verifiable?
    I enjoy your discussion but it is with the speed of a snail I follow it.
    No, I am not saying that GR applies everywhere - there are limits to the domain of applicability of the theory, and in that sense it is incomplete. For example, GR does not incorporate any quantum effects, so for length/energy scales where such effects can no longer be neglected, GR is clearly not a good model. As to whether GR applies to the universe as a whole is a matter of debate; mathematically it is easy to get cosmological solutions to the field equations, but those solutions are based on certain assumptions which cannot be proven without doubt.
    At the end of the day the situation is just this - GR is not perfect, is not complete, but at this point in time it is the best model we have. What is a certainty is that in the future there will be amendments and extensions made to the theory.
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    Quote Originally Posted by space at the centre View Post
    That experiment seems to assume that all cosmic rays generate muons at some set distance from the planet surface. Surely most will continue down through the atmosphere until they eventually strike a molecule?
    here's how the experiment is set up: You set up a detector to measure muon flux at an altitude of 10 km. You then compare this to the muon flux at sea level. The half life of a muon is 1.56 microseconds, meaning that without time dilation, half the muons detected at 10 km will have decayed after traveling a distance of 0.468 km at 0.98c. After traveling for another 0.468 km, half of the remaining muons will have decayed, and so on for ~21 reductions by a half of the muons over the 10 km. This means that for every 1,000,000 muons detected at 10 km, only 0.3 would reach the surface.

    The time dilation factor at .98c increases the muon half-life to 7.8 microseconds, meaning they travel 2.34 km before half of the muons decay. This means that the number of muons halve only ~4 times while traveling the 10 km, leaving 49,000 muons detected at sea level for every 1,000,000 detected at 10 km altitude. This is a factor of 163,333 time greater than that expected without time dilation.

    In order for cosmic rays penetrating deeper into the atmosphere to be able to account for large of an increase, the cosmic ray flux at even moderate elevation would have to be 10's of thousands of times greater than what we measure.

    In addition, we know how much cosmic radiation strikes the upper atmosphere. We can also calculate the mean free path of a cosmic ray in the upper atmosphere and thus the opacity of the atmosphere to cosmic rays. Thus it is easy to show that the number of cosmic rays that could penetrate deeply enough to produce low elevation muons is statistically insignificant.
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    I do not appreciate the tone of this thread; it is unhelpful both for myself and anyone reading it. I know I have to bare some of the responsibility yet all I am seeking is elucidation of some of the less obvious conclusions.

    Let me say once again that I am an ardent follower of Einstein and his theory; it is some of the conclusions that have been drawn from it that seem a bit of a stretch.

    Constant repetition of those conclusions without explanation of them is most unhelpful, leading to me sounding as if I am questioning Relativity itself.

    I am not; I am trying to understand how those conclusions are justified.

    For instance; to me Spacetime is not imaginary. It is a mathematical description of the way we view our Universe. It is a description of something real, of the way that Space and time work.

    Frames of Reference are how we model, mathematically, different 'views' of Spacetime from different Points in Spacetime.

    It is still the same Space and Time, the same Spacetime, that is being modelled.

    So rather than flying off in different directions let's try and answer one thing at a time without the endless quibbling over language and semantics for I have found that due to the flexibility of the English Language, that however I phrase a point, someone will read a different shade of meaning and go off to quibble about how I said it rather than what I said.

    Honestly, it is at times, like talking to a politician!
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    I will give one more example of the confusing nature of how things are argued:
    Quote Originally Posted by Markus Hanke View Post
    Quote Originally Posted by space at the centre View Post
    If a body is physically length contracted - to only half its original length (L), (0.8667c - gamma = 2) by the motion of one observer, then what is its physical length if there is another observer moving at 0.6c - gamma = 1.25 ?
    Once again - the "physical length" is what the observer performing the measurement determines. There is no absolute length, it depends on the observer.

    Is it 0.8L
    Only for one observer, but not for anyone else. Again, there is no absolute length, it depends on the observer.

    Or perhaps you would say the effect is only within that observer's frame - so in one frame it is 0.8L while in another it is 0.5L
    Yes, exactly.



    So how can one be 0.8L and one 0.5L if there is no absolute length (L)?
    Without an absolute length, without the body having a length of its own, how can it be shortened?
    Shortened compared to what?
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    Quote Originally Posted by space at the centre View Post
    So how can one be 0.8L and one 0.5L if there is no absolute length (L)?
    Without an absolute length, without the body having a length of its own, how can it be shortened?
    Shortened compared to what?
    Length contraction and time dilation are relational laws. What they do is relate the measurements in two frames of reference to one another - that is why there are no absolute measurements. One can only determine how something is contracted or dilated in relation to something else. If we only consider a single frame of reference in isolation, then neither speed nor contraction/dilation are defined. Locally, within the same frame, none of these effects are observed, however, any measurements made are then only valid in that same frame, not in any other, which is why no measurement is ever absolute. So for example, the heavy ion is length contracted in relation to the stationary particle accelerator, and the muon's lifetime is dilated in relation to the Earth's surface. However, these relations are not just apparent, they are physically real, because they effect the outcome of physical processes, as shown previously.
    In short - there is no reality apart from the one experienced by an observer, and that experience may vary from one observer to another. Compare that to electromagnetism : depending on how you look at it you may see an electric field, a magnetic field, or a mixture of both, but these are all just facets of the same electromagnetic field. Space-time with its observers is much the same.

    Let me say once again that I am an ardent follower of Einstein and his theory;
    I am sorry to tell you this, but that was not how you came across.

    Frames of Reference are how we model, mathematically, different 'views' of Spacetime from different Points in Spacetime.
    It is still the same Space and Time, the same Spacetime, that is being modelled.
    That is true, but you need to realize that this space-time is not Euclidean. It is a Minkowski space-time, so to go from one frame to another we use not linear Gallilean transformations, but Lorentz transformations. This is where some of the less intuitive effects come in.
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    Quote Originally Posted by space at the centre View Post
    So how can one be 0.8L and one 0.5L if there is no absolute length (L)?
    That is because there is no absolute length.

    Shortened compared to what?
    Shortened relative to its "proper length"; i.e. the length measured in its own frame of reference.

    In other words, measure it when it is stationary relative to you then set it in (relative) motion and measure it again.
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    Quote Originally Posted by space at the centre View Post
    I do not appreciate the tone of this thread; it is unhelpful both for myself and anyone reading it. I know I have to bare some of the responsibility yet all I am seeking is elucidation of some of the less obvious conclusions.

    Let me say once again that I am an ardent follower of Einstein and his theory; it is some of the conclusions that have been drawn from it that seem a bit of a stretch.

    Constant repetition of those conclusions without explanation of them is most unhelpful, leading to me sounding as if I am questioning Relativity itself.
    But those conclusions are Einstein's own. The problem is that you've come into this with some preconceived notions; notions that are in conflict with Relativity. Then, rather than abandon them, you have tried to reinterpret Relativity to be consistent with those preconceptions. IOW, the "Relativity" of which you are such an ardent follower of is not Einstein's theory, but a bastardized version of your own creation.



    I am not; I am trying to understand how those conclusions are justified.
    We've been trying to explain it to you, however, no matter how hard we try, we cannot understand it for you.

    For instance; to me Spacetime is not imaginary. It is a mathematical description of the way we view our Universe. It is a description of something real, of the way that Space and time work.

    Frames of Reference are how we model, mathematically, different 'views' of Spacetime from different Points in Spacetime.

    It is still the same Space and Time, the same Spacetime, that is being modelled.
    Yes, and no.

    I'll try to explain what I mean by that by way of analogy. Let's imagine space-time as a grid with the space axis and a time axis at right angles to each other. Now, imagine that the grid is laid out that the time axis runs North and South and the Space axis East and West. Thus two events in space-time can be described by their North-South(time_ and East-West(space) relative positions to each other. Now imagine two observers on this grid, each facing different direction from each other. Now, how these two events "look" like to these observers might be very different. The left-right separation between the events might be small for one and larger for the other. This is how they might look, but the North-South and East-West separation is unchanged. This seems to be the way that you think of space-time. Things may "appear" different from different frames, but there is still and underlying "reality" that defines the spatial and temporal relationship between the events.

    In Relativity, however this is not the case. We retain the concept of the Space-time grid, however, we throw out the ideas of North-South and East-West, and instead we use Left-Right and front-back. If Front-back is the time axis, then Left-Right is the space axis. Thus in this analogy, the time separation and space separation of our two events does depend on which way the direction our observer faces. The time axis and space axis "turn" with him as he changes directions. In this sense space-time is different for the two observers in different frames.

    But above I said, "Yes and no", where does the "yes" come in.

    If we plot out our two event by their space and time coordinates, they can be drawn as two legs of a right triangle, the hypothenuse of this triangle is known as the space-time interval. Now someone else plotting the same events from a different frame will draw out a different triangle, but the hypothenuse will be the same. Thus the space-time interval is the same, even if the separations in time and in space differ. It is the space-time interval that is the same across frames.

    I hope that this sheds some light(no pun intended) on the subject.
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    Quote Originally Posted by space at the centre View Post
    Quote Originally Posted by Janus View Post

    Events according to the embankment frame (according to anyone located anywhere at rest with respect to the embankment):



    Same events according to the train( according to anyone on the train):

    No, the second one is according to how the observer on the embankment will conclude that the observer on the train will see it.
    That makes no sense.

    Exactly according to you does the train observer see? Are you claiming that he sees the flashes simultaneously? In which case, you are violating the first postulate. Or are you claiming that he sees them at different times, but from that concludes that the strikes occurred simultaneously? In which case you are violating the second postulate.

    To demonstrate what I mean, let's rig our experiment thusly: Instead of lightning flashes, we will have lasers which are mechanically triggered when each end of the train reaches its respective red dot. with each observer are two paint balloons, one with red paint and one with green paint. The lasers are powerful enough to pop each balloon in an infinitesimal amount of time. One laser is aimed at the red balloons and the other at the green.

    Now according to the embankment observer the laser arrive simulataneously popping both balloon, splattering red and green paint on both the observer and the second from the last car. In addition, the laser coming from the right hits one balloon (say red) on the train when it is about four railway ties from the embankment observer, splattering red paint on the embankment there. The other laser then hits the green balloon when it is just about even with the right red dot, splattering it with green paint. This leaves two different points on the track splattered with different colored paint and one car of the train splattered with two colors as a permanent record.

    Now we go to the train frame. If you claim that the train observer sees both lasers simultaneously, then according to him his balloons pop simultaneously and leave a mixed paint splatter at a single point of the embankment. And in turn, the lasers would hit the embankment observer at different times when he was next to different cars, so one would get two separate cars splattered each with a different colored paint. Again, this is a permanent physical record. So what happens if you stop the train and bring the observers back to together? Do separate paint splashes magically merge together or mixed ones separate apart? That would be a good trick.

    The only way we can remain consistent between frames as to what happens where, relative to the track and train and also staying true to the postulates of Relativity is for the second animation to represents what happens in the train frame as seen from the train frame.
    "Men are apt to mistake the strength of their feelings for the strength of their argument.
    The heated mind resents the chill touch & relentless scrutiny of logic"-W.E. Gladstone


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    Yes I can understand what you are saying and that works fine, except that it gives preference to the embankment frame.
    The problem here for me is giving that preferment to the embankment frame.

    Remember what Einstein said: "People travelling in this train will with advantage use the train as a rigid reference-body (co-ordinate system); they regard all events in reference to the train. Then every event which takes place along the line also takes place at a particular point of the train. Also the definition of simultaneity can be given relative to the train in exactly the same way as with respect to the embankment."

    He then goes on to give a complete description of simultaneity as seen by the observer on the Embankment; and finishes by saying and vice versa; if that is not referring to how it is seen from the train, then what does it refer to.

    I can look at it differently:

    A and B are two events in Spacetime. As events they can have no movement, each being a point in space at a point in time.
    Light from those events meet at event L, a point in space S, midway between A and B, at a particular time t.
    M and M' are colocated at location S at the same time point as events A and B.

    In the embankment frame, the train, and hence the point M', is moving; while the Point M is at rest, at location S, midway between A and B; so in that embankment frame the lights meet at point M on the Embankment, at event L. Therefore A and B are simultaneous in the Embankment Frame.

    In the train frame it is the embankment, and hence point M, that is moving; while the point M', is at rest, at location S, midway between A and B; so in that train frame the lights meet at point M' on the Train, at event L. Therefore A and B are simultaneous in the Train Frame.

    Yet in each case for the moving frame, M or M' in that moving frame cannot be simultaneous.


    So I have to agree that there is nothing absolute about what is seen. It is different relative to each frame.

    We know that the distance AB is the same in each frame as it is measured within that frame as a proper length.
    That the Spacetime interval AB is the same in each frame and that having the same spatial component, the time components must also be equal and be zero - for if it is zero in one it must be in the other.

    We know that in the embankment frame AM = BM both as times, distances and Spacetime intervals. This also gives us the same time points for A and B in each case.

    Note that I am seeing Relativity of Simultaneity; that Simultaneity is relative to where it is seen from - in the local (stationary) frame we see it, in the moving frame we don't. Einstein's 'vice versa'.


    I am not saying I am right and you are wrong! I am asking for you to shew me what is wrong with the above reasoning.


    This view is arrived at by logical reasoning, so please shew me where that falls down, and that is not done by pointing out that someone says differently, it is done by simple maths and logic.
    I refer you to posts 17 and 18 where SpeedFreek agreed with my reasoning.I came to Einstein's simple guide with an open mind, knowing nothing and that is how I read it.
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    Quote Originally Posted by space at the centre View Post
    Yes I can understand what you are saying and that works fine, except that it gives preference to the embankment frame.
    The problem here for me is giving that preferment to the embankment frame.
    No it doesn't. All it is doing is saying that events that occur at a particular point of the train or embankment have to occur at the same point according to both frames. this does not give preference to one frame over the other, because they both agree on these events. The fact that we chose one frame as the starting point has no bearing on this.

    Remember what Einstein said: "People travelling in this train will with advantage use the train as a rigid reference-body (co-ordinate system); they regard all events in reference to the train. Then every event which takes place along the line also takes place at a particular point of the train. Also the definition of simultaneity can be given relative to the train in exactly the same way as with respect to the embankment."

    He then goes on to give a complete description of simultaneity as seen by the observer on the Embankment; and finishes by saying and vice versa; if that is not referring to how it is seen from the train, then what does it refer to.
    What is meant here is that in order to determine simultaneity for the train you perform the same type of test as you would for the embankment. IOW, you take two points, A' and B' which are at rest with respect to M' ( in other words affixed to the train) and if the observer at midpoint M' were to see flashes of light arriving from these two point at the same time, then M' concludes that the light left A' and B' simultaneouly.

    What it does not mean is that because M determines that the events at A and B are simultaneous by this test that M' must conclude the same for the same events. That is whole point behind this exercise, to determine whehter or not this is the case.

    I can look at it differently:

    A and B are two events in Spacetime. As events they can have no movement, each being a point in space at a point in time.
    Light from those events meet at event L, a point in space S, midway between A and B, at a particular time t.

    [/b]M and M' are colocated at location S at the same time point as events A and B.[/b]
    According to the embankment frame. whether or not this is true in the train frame is as yet to be determined.



    In the embankment frame, the train, and hence the point M', is moving; while the Point M is at rest, at location S, midway between A and B; so in that embankment frame the lights meet at point M on the Embankment, at event L. Therefore A and B are simultaneous in the Embankment Frame.

    In the train frame it is the embankment, and hence point M, that is moving; while the point M', is at rest, at location S, midway between A and B; so in that train frame the lights meet at point M' on the Train, at event L. Therefore A and B are simultaneous in the Train Frame.
    No. You cannot just assume that M' is midway between A and B when the lightning strikes these points according the train frame. As at this point, we have only established that this is true in the embankment frame. You are assuming the conclusion
    We know that the distance AB is the same in each frame as it is measured within that frame as a proper length.
    No we do not. AB is at rest in the embankment frame, so the only frame in which we measure its proper length is the embankment frame. Conversely, the proper distance between A' and B' can is measured in the train frame. And, as I pointed out in an earlier thread, Einstein then goes on in later sections to show that lengths lengths measured in one frame will not measure the same from another.

    That the Spacetime interval AB is the same in each frame and that having the same spatial component, the time components must also be equal and be zero - for if it is zero in one it must be in the other.
    But the spatial component is not the same between frames.

    We know that in the embankment frame AM = BM both as times, distances and Spacetime intervals. This also gives us the same time points for A and B in each case.

    Note that I am seeing Relativity of Simultaneity; that Simultaneity is relative to where it is seen from - in the local (stationary) frame we see it, in the moving frame we don't. Einstein's 'vice versa'.


    I am not saying I am right and you are wrong! I am asking for you to shew me what is wrong with the above reasoning.


    This view is arrived at by logical reasoning, so please shew me where that falls down, and that is not done by pointing out that someone says differently, it is done by simple maths and logic.
    I refer you to posts 17 and 18 where SpeedFreek agreed with my reasoning.I came to Einstein's simple guide with an open mind, knowing nothing and that is how I read it.

    It downs when you make erroneous assumptions about the scenario described.

    Very simply, its goes like this. in the embankment frame we note that lightning strikes point A on the embankment when it is next to point A' on the train. We also note that it strikes point B on the embankment when it is next to point A' . We purport that these strikes occur simultaneously in this frame and while M who is midway between A and B is next to M' who is riding the train. This in turn establishes that M' is at the mid point between A' and B'. M then later confirms the simultaneity of the strikes (by his accord) by seeing the light from each strike at the same time.

    It is also noted that M' is moving towards B. Thus it is clear that the flash from B must meet up with M' before it reaches M, and that the Flash from A must reach M before it catches with M'. Thus M must be next to different points of the embankment when the two flashes arrive.

    Any event that happens at a particular part of the embankment or train must happen according to each frame. Thus both frames must agree that Lightning stuck A and A' when they were next to each other and that it Struck B and B' while they were next to each other. If M' were to sneeze while passing mile post 23 on the embankment, both frames will agree that he sneezed while next to post 23.

    Now we can continue to what happens according to the train frame.

    Included in events that will be agreed upon by both frames is where M' is with respect to the embankment when he see the flash from each strike. We have already established that he was at two different points of the embankment upon seeing each in the embankment frame. It then follows that he sees the flashes while passing the same points according to the train frame. Since he cannot see the flashes at different points of the embankment without seeing them at different times, he does not see the flashes simultaneously.

    Now applying the test of simultaneity, we note that the lightning struck points A' and B' of the train. As we already established, M' is at the midpoint of these two points. Thus if the strikes occurred simultaneously in the train frame, M' would see the flashes from these strikes at the same time. He does not, and this causes us to conclude that the strikes did not occur simultaneously in the train frame.

    Again please note that at nowhere do you treat the embankment frame as a preferred frame it just happens to be the frame we chose to start from. We could have chosen the train frame and picked two events that were simultaneous in it and showed that they were not so in the embankment frame, but, and this is important, they could not have been the same lightning strokes that we used in the last example.

    So when Einstein said:
    "Events which are simultaneous with reference to the embankment are not simultaneous with respect to the train, and vice versa (relativity of simultaneity)."
    He means that:
    If we pick two event that are simultaneous for the embankment frame, they will not be simultaneous according to someone on the train, and if we pick two events that are simultaneous for someone on the train, they will not be so for for the embankment frame. But he not talking about the same set of events in both cases. It is a different set of events that are simultaneous in the embankment frame than the set of events that are simultaneous in the train frame.
    SpeedFreek and Markus Hanke like this.
    "Men are apt to mistake the strength of their feelings for the strength of their argument.
    The heated mind resents the chill touch & relentless scrutiny of logic"-W.E. Gladstone


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  78. #77  
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    Quote Originally Posted by space at the centre View Post
    I refer you to posts 17 and 18 where SpeedFreek agreed with my reasoning.I came to Einstein's simple guide with an open mind, knowing nothing and that is how I read it.
    Sorry, I just re-read it and realised I made a gross mistake in post 18, which might well have confused you. I wrote the "vice-versa" example the wrong way around! I don't know what I was thinking there. But I got it right in all my other posts, which contradict what I said in post 18. So, ignore post 18 - I will leave it as it is, but with an edit to say what is wrong with it.

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    Dear Janus, Speed freek and Marcus Hanke
    I find myself in a difficult position here; that the system that I am determined to build a working knowledge of, persists in presenting aspects that seem to sit uneasily together.
    If I knew no better, I might almost say that those facts and formulae that comprise the theory have been chosen somewhat selectively, promoting a particular slant in the understanding of the particulars.


    I would very much like to put away such thoughts, that could prompt one to think that the arguments contain certain, fudges, omissions and half-truths, somewhat distorting their true relationship.


    So let me try by stating what we are dealing with:


    In Relativity we are dealing, principally, with two situations:
    • that of an inertial Frame of Reference and the measurements obtained from within that Frame;
    • and how those measurements are transformed to become relative to an observer moving with respect to that Frame of Reference.

    The first of these situations applies to each and every Inertial Frame of Reference and those measurements made by an observer, at rest, within that frame of reference.

    Principally by an observer at rest at the Origin of that frame holding a standard clock; which therefore becomes a measure of the time axis of that frame.

    Now in relativity, proper time is the elapsed time between two events, as measured by a clock that passes through both events and as this applies in respect of the clock held by our observer it is, it has to be, recording proper time.

    In the same way distances along the x axis are those that would be measured between synchronised clocks placed at rest at appropriate points along that axis.

    And in special relativity, the proper length between two spacelike-separated events is the distance between the two events, as measured in an inertial frame of reference in which the events are simultaneous and as, once again, this applies in respect of the distances measured along the x axis in our frame, the scale of that axis has to be measuring proper lengths.

    Therefore all inertial frames measure the same, Proper, times and distances within their own frames.

    In the second circumstance, where those measurements are transformed to make them relative to a moving observer, we have to use a function that incorporates the relative velocity of the observer into those measurements; that function comprises the Lorentz Transformation Equations.

    Yet these Lorentz equations are not mere formulae that are applied; no,they are the mathematical description of a real process whereby the observed Frame of Reference is rotated, leading to the contraction and dilation of those measurements.

    (Yes I have now understood how those measurements do physically change for the moving observer - that the muons do reach the Earth)

    Be patient with me.
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    Quote Originally Posted by space at the centre View Post
    Dear Janus, Speed freek and Marcus Hanke
    I find myself in a difficult position here; that the system that I am determined to build a working knowledge of, persists in presenting aspects that seem to sit uneasily together.
    If I knew no better, I might almost say that those facts and formulae that comprise the theory have been chosen somewhat selectively, promoting a particular slant in the understanding of the particulars.


    I would very much like to put away such thoughts, that could prompt one to think that the arguments contain certain, fudges, omissions and half-truths, somewhat distorting their true relationship.


    So let me try by stating what we are dealing with:


    In Relativity we are dealing, principally, with two situations:
    • that of an inertial Frame of Reference and the measurements obtained from within that Frame;
    • and how those measurements are transformed to become relative to an observer moving with respect to that Frame of Reference.

    The first of these situations applies to each and every Inertial Frame of Reference and those measurements made by an observer, at rest, within that frame of reference.

    Principally by an observer at rest at the Origin of that frame holding a standard clock; which therefore becomes a measure of the time axis of that frame.

    Now in relativity, proper time is the elapsed time between two events, as measured by a clock that passes through both events and as this applies in respect of the clock held by our observer it is, it has to be, recording proper time.

    In the same way distances along the x axis are those that would be measured between synchronised clocks placed at rest at appropriate points along that axis.

    And in special relativity, the proper length between two spacelike-separated events is the distance between the two events, as measured in an inertial frame of reference in which the events are simultaneous and as, once again, this applies in respect of the distances measured along the x axis in our frame, the scale of that axis has to be measuring proper lengths.

    Therefore all inertial frames measure the same, Proper, times and distances within their own frames.

    In the second circumstance, where those measurements are transformed to make them relative to a moving observer, we have to use a function that incorporates the relative velocity of the observer into those measurements; that function comprises the Lorentz Transformation Equations.

    Yet these Lorentz equations are not mere formulae that are applied; no,they are the mathematical description of a real process whereby the observed Frame of Reference is rotated, leading to the contraction and dilation of those measurements.

    (Yes I have now understood how those measurements do physically change for the moving observer - that the muons do reach the Earth)

    Be patient with me.
    Do not be discouraged, SATC ( allow me to abbreviate your name in that way ). Relativity does not come easy, and every student of the subject will have his/her struggles and moments of doubt. Our subjective experience of the everyday world we live in is one of a simple, 3-dimensional Euclidean space. Relativity on the other hand assumes Minkowski ( SR ) or pseudo-Riemannian ( GR ) space-time, which has a different causal structure to what we are used to. This is a paradigm shift which takes time getting acquainted with. So long as you have a genuine desire to learn we will do our utmost to try and help you in any way we can, and yes, we will be patient.

    I agree with the gist of what you have written above. Just think of SR as a model which relates inertial frames of reference in Minkowski space-time to one another, regardless of their state of relative motion. A proper measurement is one performed by an observer in his own frame of reference; so, for example, proper time is the time an observer himself measures in his own frame with his own clock, and proper distance is the distance an observer measures in his own frame with his own ruler, and so on. You go from one frame to another frame by performing a Lorentz transformation ( as opposed to a Gallilean transformation in Euclidean space ), and it so happens that this transformation leaves some values invariant, e.g. the speed of light. The other really important thing to know is what is a valid inertial frame, and what is not; specifically, you need to know that "the universe" is not a valid inertial frame, and neither is a photon. An observer experiencing significant acceleration is also not an inertial frame; you can still treat such frames with the tools of SR, but because these frames aren't inertial ones, care must be taken when doing the maths.

    I would also recommend reading Janus's excellent sticky "Special Relativity Primer" in the physics section.
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    Thank you Marcus.

    Now, as an example of the sort of issue that disturbs my logic, let me now put before you the experiment made by SpeedFreek in post #6. Viz:

    Quote Originally Posted by SpeedFreek View Post
    Let's take a simpler experiment:
    A is sitting in the centre of a train carriage and there is a bulb above his head. This bulb lights up, and the light propagates at c in both directions, up and down the carriage. The light will reach each end of the carriage at the same time, in the frame of A, regardless of whether the train is moving or not.



    Now we move to the frame of B, standing on the embankment. Just as the train passes B, and the centre of the train is directly in front of B, the bulb turns on in the centre of the carriage. The light propagates up and down the carriage at c, in relation to the rest frame of B, on the embankment. But the train is also moving in relation to B, moving across his view. So this is what happens in the frame of B:

    The light reaches the back of the carriage before it reaches the front. It does not reach the ends of the carriage at the same time, from the frame of B.

    So, did the light reach the ends of the carriage at the same time, or did it reach the back of the carriage before it reached the front?

    The answer is.... both options.
    The problem is that this leaves us with an unanswered paradox; two incompatible scenarios, yet both apparently true.

    So how do we resolve this without departing from our theory?

    May I humbly suggest that we start by examining the two Frames Separately?

    So, in the frame of the train carriage we know that the light reaches the ends of the carriage simultaneously. The first set of diagrams.

    Similarly we know that light from the carriage, shining through the windows and therefore in the frame of the embankment will travel as shown in the second set of diagrams.

    In each case simple mechanics.

    The important thing I notice here is that in each case the light does one or the other depending on which frame it is in.

    It is when we put those frames together in one diagram that we have a problem.

    Why?

    Because we know that the light travelling to the ends of the carriage in the first diagrams MUST also travel at c with respect to the embankment observer.

    Yet simple mechanics already shows us exactly where that light goes, so how can it do that and still travel at c with respect to the embankment?

    The answer is the Lorentz Transformation equations, for by applying them to the measurements made in the carriage, those measurements are transformed to make them relative to the embankment and preserve the speed of light.

    The Lorentz equations allow us to measure the light moving at c with respect to the carriage, in those first diagrams AND to travel along those same paths at c relative to the embankment. And of course the reverse with respect to the light travelling from the carriage along the embankment.

    It seems to me that that is precisely what the Lorentz equations give us. The resolution of that paradox.
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    Quote Originally Posted by space at the centre View Post

    The problem is that this leaves us with an unanswered paradox; two incompatible scenarios, yet both apparently true.

    So how do we resolve this without departing from our theory?

    May I humbly suggest that we start by examining the two Frames Separately?

    So, in the frame of the train carriage we know that the light reaches the ends of the carriage simultaneously. The first set of diagrams.

    Similarly we know that light from the carriage, shining through the windows and therefore in the frame of the embankment will travel as shown in the second set of diagrams.

    In each case simple mechanics.

    The important thing I notice here is that in each case the light does one or the other depending on which frame it is in.

    It is when we put those frames together in one diagram that we have a problem.

    Why?

    Because we know that the light travelling to the ends of the carriage in the first diagrams MUST also travel at c with respect to the embankment observer.

    Yet simple mechanics already shows us exactly where that light goes, so how can it do that and still travel at c with respect to the embankment?

    The answer is the Lorentz Transformation equations, for by applying them to the measurements made in the carriage, those measurements are transformed to make them relative to the embankment and preserve the speed of light.

    The Lorentz equations allow us to measure the light moving at c with respect to the carriage, in those first diagrams AND to travel along those same paths at c relative to the embankment. And of course the reverse with respect to the light travelling from the carriage along the embankment.

    It seems to me that that is precisely what the Lorentz equations give us. The resolution of that paradox.
    Yes, I think you are pretty much spot on. I personally would not even have bothered with mechanics, all I'd have said is that both outcomes are equally valid, but only in their own respective frames. The important thing is to realize that you can go from the embankment to the train ( and vice versa ) by performing a simple Lorentz transformation, and by doing so you introduce time dilation and length contraction as required to keep c constant at all times and for all observers.
    Like I said, it needs getting used to, but once understood it is actually pretty straightforward ( at least for simple scenarios like this one ).
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    Right So in the second set of the said diagrams the path(s) of the light should be drawn outside the carriage, not within it?

    Indeed one could then combine the two drawings. To shew the light path from the first drawing, going to the ends of the carriage and the light path from the embankment view, on the outside of the carriage, as long as one noted that it was the two views superimposed?
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  84. #83  
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    Quote Originally Posted by space at the centre View Post
    Right So in the second set of the said diagrams the path(s) of the light should be drawn outside the carriage, not within it?

    Indeed one could then combine the two drawings. To shew the light path from the first drawing, going to the ends of the carriage and the light path from the embankment view, on the outside of the carriage, as long as one noted that it was the two views superimposed?
    For me that would be more confusing than anything, since there is supposed to be a detector at both ends of the carriage, so the light ray shouldn't be outside of it.
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    That is why I said if the light were to pass through the windows, then it would be travelling in the embankment frame rather than the carriage Frame - as far as the mechanics of what is happening are concerned.
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    Right. All the light is inside the carriage. Then we can see that by simple mechanics the light reaches both ends of the carriage simultaneously, in the frame of the carriage.

    Nothing happening outside the carriage will change that.

    So in the frame of the embankment the carriage is moving, along with everything in it.

    In order for the light to be measured to be travelling at c relative to the embankment the frame of the carriage is rotated so that the light in the carriage does indeed travel at c as measured from the embankment frame.

    That rotation is exactly what the Lorentz transforms describe.
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    Quote Originally Posted by space at the centre View Post
    Right. All the light is inside the carriage. Then we can see that by simple mechanics the light reaches both ends of the carriage simultaneously, in the frame of the carriage.

    Nothing happening outside the carriage will change that.

    So in the frame of the embankment the carriage is moving, along with everything in it.

    In order for the light to be measured to be travelling at c relative to the embankment the frame of the carriage is rotated so that the light in the carriage does indeed travel at c as measured from the embankment frame.

    That rotation is exactly what the Lorentz transforms describe.
    Yes, correct. You perform a hyperbolic rotation by some angle ( called the rapidity of the moving frame ) to get from a stationary frame to the moving frame. This is completely equivalent to the usual Lorentz transformation.
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    Good.
    So the light n the carriage travels to both ends of the carriage as measured by each frame.
    Only in the embankment frame it is that rotation that ensures that the speed of the light relative-to/as-measured-from the embankment frame is 'c'.
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    Quote Originally Posted by space at the centre View Post
    Good.
    So the light n the carriage travels to both ends of the carriage as measured by each frame.
    Only in the embankment frame it is that rotation that ensures that the speed of the light relative-to/as-measured-from the embankment frame is 'c'.
    Yes. You could also turn it around - fix the light source on the embankment. In the train frame it is now the embankment that is moving - the same principles apply.
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    Kerling: In the information age ignorance is a choice.
    From eaglepass...great observation!
    And, if I may, in the interest of cooperation and sharing, I would like to add a little more to the observation-information does not appear to become knowledge until it is understood by the beholder ....knowledge deems to be the essence of higher ordered powerful thinking skills. However, more complex the information, the less amount of people tend to understand it. Thus, in many a case, lack of understanding of information could be equivalent to ingnorance.

    QUOTE FROM MATTHEW 13:14
    “You will indeed listen, but never understand,
    and you will indeed look, but never perceive.
    15 For this people’s heart has grown dull,
    and their ears are hard of hearing,
    and they have shut their eyes;
    so that they might not look with their eyes,
    and listen with their ears,
    and understand with their heart and turn—
    and I would heal them.”
    16But blessed are your eyes, for they see, and your ears, for they hear. 17Truly I tell you, many prophets and righteous people longed to see what you see, but did not see it, and to hear what you hear, but did not hear it...JC
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    Kerling: In the information age ignorance is a choice.
    From eaglepass...great observation!

    And, if I may, in the interest of cooperation and sharing, I would like to add a little more to the observation-information does not appear to become knowledge until it is understood by the beholder ....knowledge deems to be the essence of higher ordered powerful thinking skills. However, more complex the information, the less amount of people tend to understand it. Thus, in many a case, lack of understanding of information could be equivalent to ingnorance.

    QUOTE FROM MATTHEW 13:14
    “You will indeed listen, but never understand,
    and you will indeed look, but never perceive.
    15 For this people’s heart has grown dull,
    and their ears are hard of hearing,
    and they have shut their eyes;
    so that they might not look with their eyes,
    and listen with their ears,
    and understand with their heart and turn—
    and I would heal them.”
    16But blessed are your eyes, for they see, and your ears, for they hear. 17Truly I tell you, many prophets and righteous people longed to see what you see, but did not see it, and to hear what you hear, but did not hear it...JC
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    Brassica oleracea Strange's Avatar
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    Disappointed. I was expecting something on the Pizza of Simultaneity.
    ei incumbit probatio qui dicit, non qui negat
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    o space at the centeo space at the center....from eaglepassr....from eaglepass
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    To Space at the centre...from eaglepass
    This may be STRANGE, but it looks and sounds like you are thinking out of the box! Have you noticed one thing: according to Einstein's thought experiment, simultaneity on the embankment can only occur at the midpoint M between points A and B. If observers are placed at any point away from the midpoint M, simulaneity can not occur for them when the rays are "fired." Those observers to the "right" of the midpoint will "observe the same thing that M-1 sees when the train is in motion. They will practically conclude the same thing: that Ray B was fired before Ray A. Those observers to the "left" of the midpoint, will conclude that Ray A was fired before Ray B. The only observer(s) that can witness simultaneity is the observer standing stationary at midpoint M on the enmbankment.

    However, simultaneity can be "fixed" for it to occur at midpoint M by modifying the distance and times relating to the light rays and the starting point of M-1, the observer on the moving train. Observer M-1 moving past midpoint M, would witness simultaneity: his arrival at point M and the arrival of the light rays at the same time. I do not believe that Einstein really had to use his thought experiment to show that observer M-1 concluded that the rays were not fired simultaneously. He could have done this in this manner.
    [I am running out of battery power for "now"....I will continue tomorrow...there is more....much more! In the mean time-stay out of the STRANGE BOX!]
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    [QUOTE=space at the centre;374848]
    Quote Originally Posted by SpeedFreek View Post
    May I ask, is it
    Quote Originally Posted by SpeedFreek View Post
    the plane of simultaneity that you are having trouble with, or the concept of the relativity of simultaneity itself?

    Do you understand the reasoning behind Einstein's famous "train and embankment" thought experiment?
    Well yes, I think I do understand exactly how that works, but, to me, that understanding leads to an inevitable paradox.

    It is describing three events: Lightning striking point A, lightning striking point B and the meeting of light reflected from A and B at the midpoint of the line AB.

    FROM eaglepass... Note: These events you are describing are required in order for simultaneity to forcefully exist on the embankment. Note also that the scenario in Einstein's thought experiment mentally situated on a straight line segment AB (This is mportant to note for further discussion).

    The line segment is required to be parallel to the rectilinear path of "a moving vehicle" that will "fit" the geometry of the embankment and its midpoint, and that vehicle, is a train (without specifications as to length.).

    The thought experiment also "requires" that two observers, M-0 and M-1 be present and at rest on the embankment, specifically at midpoint M of line segment AB, during the first firing of the rays. Thus if observers, M-0 ande M-1 are not at rest and standing at mipoint M, these observers will not be able to witness simultaneity on the embankment; thus simultaneity will not occur according to the observers M-0 and M-1 on the embankment.

    Thus it appears that Einstein's definition of simultaneity at mipoint M on the embankment is observer and midpoint dependent. (From my point of view, simultaneity on the embankment, according to the set-up given by Einstein, is midpoint dependent and not observer dependent at all. )

    The light rays will still meet at the midpoint of line segment AB (on the embankment). Simultaneity, regardless where M-0 and M-1 are located on the embankment will still occur.
    Note: if the light rays meet simultaneously at midpoint M, but are not witnessed by the observers, M-0 and M-1, then
    their conclusion regarding the timing of the light rays will be in the form of an illusion: that the rays were not fired simultaneously. This is practically the same conclusion reached by observe M-1 while he/she is riding on the moving train at velocity V.

    ABOUT THE LENGTH OF THE TRAIN...suppose the train is long enought to have two observers M-1 and M-2. Observer M-1 starts with the motion on the train while he/she is aligned with midpoint M on the embankment. And, obsever M-2 is situated at the back of this long train far way from M-1. LONG STORY SHORT: It can be arranged for observer M-2 to reach mipoint M on the embankment
    at the same time the light rays meet there!


    Events are defined by location and time; they do not and cannot have movement. Movement is a change of location between two moments(points) of time.


    Any observer at the origin of their Frame of reference is, by definition at rest in that Frame of Reference.

    Hence, in the Embankment observer's FoR, he is at rest at M, midway between A and B and the reflected lights meet at his location.

    But the reciprocal situation obtains for the observer on the train.

    She is at rest at M', the midpoint between A and B in her FoR. In her Frame of Reference. She is at rest, stationary, unmoving at M', the midpoint of the line AB. (apologies for being repetitive, but this is an important, nay, crucial point).


    Then, as she is at rest in her FoR, she cannot be moving toward one and away from the other lightning strike!


    To her, in her own FoR she is at the midpoint when the reflected lights meet.


    To her, in her Frame of Reference, the two events, the lightning strikes meet Einstein's test of Simultaneity.


    How can they not do?


    To the Embankment observer, however, it will be equally obvious and Provable that, in his Frame of Reference, Einstein's test for simultaneity is not met, for the observer in the train; just as the reciprocal is true, in that the observer on the train will be equally assured that, in her FoR, the Embankment observer's observations do not satisfy Einstein's test.


    So, it seems to me, that the True definition of the Relativity of Simultaneity is that Einstein's test for Simultaneity will be satisfied in any and every Frame of Reference by a suitably located observer, but, such an observer will be equally convinced that the test can only be satisfied in their Frame of Reference.


    Which conclusion is satisfying as it removes the Paradox of the Planes of Simultaneity where each point on a Minkowski Diagram represents two different times in the same FoR!


    Sowhere am I going wrong???!
    [It looks like you are trapped in a STRANGE BOX and you are trying "KNOCK YOUR WAY OUT" to get out of it! ...."Seek and you shall find, ask and you shall be give, knock and the door will open..." JC-The Master of all Masters!]
    Last edited by eaglepass; January 31st, 2013 at 12:42 AM.
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    Quote Originally Posted by eaglepass View Post
    Events are defined by location and time; they do not and cannot have movement. Movement is a change of location between two moments(points) of time.
    Apart from any other errors in your post this is nonsense.
    Movement, by definition, is a change of location in space.
    Things transition through time whether they move or not.
    "[Dywyddyr] makes a grumpy bastard like me seem like a happy go lucky scamp" - PhDemon
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    the lightning reaching the midpoint is the evnt that will happen when it happens, no matter what. it's the result of the lightnings hitting point AB.
    whether someone is there to watch it or not.
    now M happens to be at the embarkment while it happened and reports, both lightnings hit at the same time.(which they did from his point of view)

    then M' comes along saying, he passed the embarkment in a train that time, and the lightning at B occured first.(which is true, from his point of view).

    both observations are correct. so if M' can tell you how much later he observed the 2nd lightning, you then could determine what speed the train had? i.e. if he said, the 2nd lightning was observed 0.5 sec after the 1st one, he travelled with 1/2 c?
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    Quote Originally Posted by eaglepass View Post
    Sowhere am I going wrong???!
    1. Using random fonts, size, colours and block caps.

    2. Where you say:
    Thus it appears that Einstein's definition of simultaneity at mipoint M on the embankment ...
    I think you are missing the point. Einstein is not defining simultaneity at the mid-point. He doesn't need to: it is obvious what that means. He is describing how to define simultaneity for two spatially separated locations. This is necessary because he has previously shown that measurements of time (and space) are dependent on the state of motion of the observer. Therefore there is no universal clock we can use to determine "simultaneous" for events which happen at different locations.

    What he shows is that different observers will disagree on whether two spatially-separated vents are simultaneous or not.

    He places the observers at the mid-points for simplicity. They could be at any location (but the explanation/calculation becomes a little more complicated as they have to tack their position and the speed of light into account).

    3. When you say:
    Any observer at the origin of their Frame of reference is, by definition at rest in that Frame of Reference.
    An observer does not have to be at the origin of their frame of reference. Wherever they are, they are at rest wrt their frame of reference (by definition).
    ei incumbit probatio qui dicit, non qui negat
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    Quote Originally Posted by curious mind View Post
    the lightning reaching the midpoint is the evnt that will happen when it happens, no matter what. it's the result of the lightnings hitting point AB.
    whether someone is there to watch it or not.
    now M happens to be at the embarkment while it happened and reports, both lightnings hit at the same time.(which they did from his point of view)

    then M' comes along saying, he passed the embarkment in a train that time, and the lightning at B occured first.(which is true, from his point of view).

    both observations are correct. so if M' can tell you how much later he observed the 2nd lightning, you then could determine what speed the train had? i.e. if he said, the 2nd lightning was observed 0.5 sec after the 1st one, he travelled with 1/2 c?
    what about me? i got it right?
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    Quote Originally Posted by curious mind View Post
    Quote Originally Posted by curious mind View Post
    the lightning reaching the midpoint is the evnt that will happen when it happens, no matter what. it's the result of the lightnings hitting point AB.
    whether someone is there to watch it or not.
    now M happens to be at the embarkment while it happened and reports, both lightnings hit at the same time.(which they did from his point of view)

    then M' comes along saying, he passed the embarkment in a train that time, and the lightning at B occured first.(which is true, from his point of view).

    both observations are correct. so if M' can tell you how much later he observed the 2nd lightning, you then could determine what speed the train had? i.e. if he said, the 2nd lightning was observed 0.5 sec after the 1st one, he travelled with 1/2 c?
    what about me? i got it right?
    Looks good to me. But calculating the speed from the difference in simultaneity would need to take the Lorentz transformation into account.
    ei incumbit probatio qui dicit, non qui negat
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    that must be that graph in the 1st post, which (sadly) tells me nothing.
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