Why Didn't Einstein FULLY Address Simultaneity-at-a-Distance?

Discussion in 'Alternative Theories' started by Mike_Fontenot, Apr 11, 2021.

  1. Mike_Fontenot Registered Senior Member

    Einstein, in his special relativity, DID fully address simultaneity-at-a-distance according to a perpetually-inertial person (the "PIP"). According to the PIP (she), a distant person who may be accelerating in any way he chooses (the AP), is at each instant ageing slower than the PIP by the well-known gamma factor (which is a function only of the his speed v relative to her, according to her, at that instant). So by integrating those relative ageing rates, the PIP can determine the current age of the AP at each instant of her life. She can thus produce a plot of his age (on the vertical axis), versus her age (on the horizontal axis) ... I call that "the age correspondence diagram" (the ACD), according to her (the PIP).

    But as far as I know, Einstein never addressed the question of simultaneity-at-a-distance, according to the person who sometimes accelerates (the AP). How does the AP produce the ACD that gives the distant person's (the PIP's) age at each instant in the life of the AP? And why did Einstein never address the question?
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  3. James R Just this guy, you know? Staff Member

    The Earth orbits the Sun. If we want to calculate the Earth's orbit, approximately, we assume that the Sun is stationary and the Earth is moving, approximately in a circle around the Sun.

    But that's not the only possible choice of reference frame. In principle, we could designate the Earth as "stationary" and have the entire universe, Sun included, revolve around it. The problem is then to determine the apparent motion of the Sun around the Earth in this constantly accelerating reference frame.

    Clearly, one of these two points of view makes for easier analysis than the other. If we consider the Sun to be stationary, then the reference frame is approximately inertial and all the usual laws of physics will work in the ordinary way. If, on the other hand, we insist that the Earth is stationary and the Sun revolves around it, then to make the laws of physics work correctly we need to introduce some inertial ("imaginary") forces, and the problem becomes significantly harder to solve.

    The situation in the opening post is the same kind of thing. The so-called PIP is an inertial frame, in which all the laws of physics work normally. But the AP is a frame whose acceleration is constantly changing - a potentially very complicated non-inertial frame of reference. In principle, we could use that frame, but to do the relevant calculations would be a very complicated matter. It would be far simpler for the AP to use his knowledge that the PIP is inertial and do the calculations the simple way.
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  5. phyti Registered Senior Member


    From the 1905 paper, par. 4:
    "From this there ensues the following peculiar consequence. If at the points A and B of K there are stationary clocks which, viewed in the stationary system, are synchronous; and if the clock at A is moved with the velocity v along the line AB to B, then on its arrival at B the two clocks no longer synchronize, but the clock moved from A to B lags behind the other which has remained at B by tv^2/2c^2 (up to magnitudes of fourth and higher order), t being the time occupied in the journey from A to B."
    "If we assume that the result proved for a polygonal line is also valid for a continuously curved line, we arrive at this result: If one of two synchronous clocks at A is moved in a closed curve with constant velocity until it returns to A, the journey lasting t seconds, then by the clock which has remained at rest the travelled clock on its arrival at A will be tv^2/2c^2 second slow."

    [The key requirement in both cases is a closed path. The issue is accumulated time for each clock starting frm a common location, moving independently of the other, and reuniting at a common location. The deciding factor is a comparison of accumulated time for each path at a common location.

    While the clocks are moving on each path, mutual observations only indicate clock rates, which are affected by observer motion. As the PDF showed, while both have inertial motion, they only observe doppler effects. Slow rates while diverging and fast rates while converging.

    With programmed speed profiles (paths) the outcome can be calculated in advance. With random real world profiles, the outcome is decided after the motions are completed. Since the profiles are independent, there is no functional relation, and it's not possible to observe aging over a distance. The graphic explains why.

    When A sends a signal to B which returns a time t'1, A does not know this until t2. At t2 A does not know the time on the B-clock, since B may have changed speed. This is the meaning of 'there is no instant knowledge', based on the finite speed of light.]

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  7. Mike_Fontenot Registered Senior Member

    I'm now thinking that Einstein DID address the question of simultaneity-at-a-distance, according to a person who sometimes accelerates. I remember that Einstein predicted that for two clocks stationary in a gravitational field, the clock higher in the field (farther from the source of the field) will run faster than the clock lower in the field. He got this result long before he published his paper on his GR theory (and long before he arrived at his GR theory). He got it by solving an SR problem, and then invoking his "principle of equivalence" between acceleration and gravitation.

    The SR problem he solved was for a rocket, not in the presence of any gravitation field, with a clock at the front and a clock at the back, that is undergoing a constant acceleration. He determined that the clock in front will run faster than the clock at the back. So he DID determine what an accelerating observer at the rear of the rocket will conclude about the current time at the front of the rocket.

    I've heard that Einstein wrote a paper in 1907 (2 years after his SR paper, and 8 years before his GR paper) that may have discussed the above result. I'm currently trying to find that 1907 paper (translated into English, of course). I'd like to know if he used CMIF (co-moving inertial frame) simultaneity in getting his result, and whether he made any assumptions in justifying that choice.
  8. mikelizzi Registered Senior Member


    Horay for you Mike_Fontenot!!

    I have been trying to tell people for years that the behavior of clocks for an accelerating observer is covered under the regime of SR.
    I even have a textbook
    Basic Relativity
    by Richard A. Mould
    copyright 1994
    that derives the relavant transformation in Chapter 8 "Uniformaly Accelerated Coordinates". You can't use the Lorentz Transformation obviously. Chapter 8 is the last of the material on SR just before the author starts on GR. Unfortunately my math is not good enough to follow it. But I did understand one conclusion,

    If you define clock rate as dt'/dt (the change of the other guys clock per the change of your own), then to an accelerating observer, the clock rate of an inertialy moving object is a function, not only of its relative velocity, but also of its relative position and the observer's absolute acceleration.

    And that means that, to an accelerating observer, the other guy's clock can sometimes run faster.

    P.S. Here is my summary of a simplified version as I read it.

  9. Mike_Fontenot Registered Senior Member

    And it can run BACKWARDS ... i.e., the other guy can get YOUNGER. That's according to CMIF (co-moving inertial frame) simultaneity.

    Thanks for those references. I didn't know anything about Richard A. Mould. Both of his books are on Amazon.
  10. mikelizzi Registered Senior Member

    Outside of Thermodynamics, all the laws of Physics allow for someone to get younger. Just run time backwards. But then everybody gets younger.
    I don't see any way the formulas of SR allow one clock to run backwards (get younger) while the others continue to go forward.
    It would require dt'/dt to have negative value. That's crackpot physics as far as I am concerned.
    And I don't want any part of a conversation where that behavior is even considered.
  11. Write4U Valued Senior Member

    It is really much simpler than that.
    You cannot travel back in time except via a wormhole. But wormholes have enormous gravitational properties and your body would begin to stretch and eventually rip you apart into fundamental particles (plasma)


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    Wormholes. Wormholes are hypothetical areas of warped spacetime. The high energy contained in a wormhole could create tunnels through spacetime. If possible, wormholes would allow a traveler to move through time.


    No, they would not allow a traveler to move through time, except perhaps as plasma.

    Are some black holes wormholes in disguise? Gamma-ray blasts may shed clues.

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    Unusual flashes of gamma rays could reveal that what appear to be giant black holes are actually huge wormholes, a new study finds.

    Last 500 years around Milky Way's supermassive black hole

    Theory identifies possibility. Practice teaches us that you cannot travel to another spacetime coordinate as an object. You just revert back into energy.
  12. CptBork Valued Senior Member

    Plus in classical GR a wormhole can only exist if it's built into the structure of the universe, it can't be created by collapsing stars. Furthermore if you attempted to send any quantity of matter or energy through, its own gravity would destroy the wormhole and nothing would actually make it inside. Factoring in quantum mechanics though, who knows?

    Simultaneity is a relative concept in Relativity, the idea of two things happening at the same time depends strictly on the reference frame used to observe them. Meaningful comparisons about ages and clocks can only be made when objects are brought into direct contact or they're at least able to exchange and/or reflect signals.
  13. phyti Registered Senior Member


    [No. What it was then. Her (knowledge of his time) is not simultaneous with (his time).

    [Then he is analyzing the problem in a gravitational environment or GR.]

    [In the graphic, the ship accelerates in the U frame until Ut=t.
    At Bt=0, a signal is sent to F at the front, arriving at F at t'1, returning to B at tb1. Without td corrections, Δ is the difference in clock readings for F and B per the axis of simultaneity (green). B cannot assign a corresponding time for t'1 until tb1, which is later by d, and not simultaneous.

    At Bt=t, a signal is sent to F at the front, arriving at F at t'2, returning to B at tb2. Without td corrections, Δ is the difference in clock readings for F and B per the axis of simultaneity (green). B cannot assign a corresponding time for t'2 until tb2, which is later by d, and not simultaneous. Inertial or non-inertial motion makes no difference. Even with coordinate transformations, you can only form corresponding event times after the fact. All your information is historical!]

    [Your idea would have been acceptable in the Newtonian era, with absolute universal time and simultaneity, but has been laid to rest with the principle of relativity.]
    You can research any of Einstein's papers at einsteinpapers.press.princeton.edu

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  14. Write4U Valued Senior Member

    Question; Doesn't the law of falling bodies explain the results of both gravity and acceleration?
  15. Mike_Fontenot Registered Senior Member

    Thanks for sending that. I found out about that link from Tom Roberts on the relativity "usenet" forum a week or so ago. I found the article to be hard to understand, but it does confirm my conjecture that Einstein got his result about clocks running faster the farther they are from the source of the gravitational field by determining that a clock in the front of an accelerating rocket will run faster than a clock in the tail of the rocket (with no gravitational field present). And I THINK he uses CMIF simultaneity in that analysis, although I found his presentation difficult to understand, so I'm not sure yet. And I'm not sure yet if he justifies his use of CMIF simultaneity by arguing that it is reasonable that the accelerating observer should always agree with the perpetually-inertial observer with whom he is currently momentarily stationary ... i.e., that that IS an assumption, not a fact.
  16. Mike_Fontenot Registered Senior Member

    For a given perpetually-inertial observer (the "home twin", her), there is only one answer to the question, "How old is that distant person right now?", that agrees with her own measurements. The way she can make those measurements was described in detail by Einstein: a collection of equally-spaced clocks are laid out that are stationary with respect to her (and with respect to her perpetually-inertial mother or grandmother), and all those clocks are synchronized via light signals. There is a perpetually-inertial observer at each clock. Those observers keep a record of every person who goes flying past them, recording the time on that person's clock, and what their own clock shows at that instant. They then send that information to the home twin (which she receives after a long delay) . For the case where she and the traveler (he) were born simultaneously when they were momentarily co-located, and were both perpetually inertial with a relative speed of 0.866 ly/yr (giving gamma = 2.0), those measurement results tell her that when she was 80 years old, he was 40 years old. That result is exactly what the time dilation equation (the TDE) told her, long ago. The TDE told her that result immediately, without the long delay that the measurements took. ANY other answer will disagree with what the measurements say. There is only one correct answer to that original question.
  17. phyti Registered Senior Member


    The question is 'What is his age now at a distance?'
    She doesn't have the answer until later (after a long delay).
    The TDE predicts the time dilation with the condition that he follows the specified speed profile, which is not a certainty.
    Agreement only implies he followed the profile. It did not answer the question.
  18. Mike_Fontenot Registered Senior Member

    She has the answer immediately if she knows (and believes) the Time Dilation Equation (TDE), assuming she knows that they ARE both perpetually inertial, with a relative speed of v.

    And, as I've described before, she can set up a grid of clocks, stationary wrt her, and synchronized via light signals, with each clock manned by a helper observer (always having her same age) who can send her a message giving that helper's age and the other twin's age when the other twin goes flying by that helper. That message she receives will always agree with what the TDE equation told her when she asked the question.
  19. phyti Registered Senior Member


    The TDE requires knowing v/c is constant for his distant clock.
    The predicted result will only agree with the message from the distant time keeper IF his speed does not vary. Believing it will happen is not equivalent to it does happen, nor will it influence the outcome.
    The second issue is the ideal system of synchronized clocks. The local GPS system requires periodic corrections to make it work. An extended system is not realistic or logistically possible.
    Don't waste your time trying to bypass the fact of finite light speed. All awareness of distant events is historical. You cannot know of an event until after it happens.
  20. Neddy Bate Valued Senior Member


    So, keeping with your example, v=0.866c (gamma = 2.0)...

    She has an array of helper-clocks synched to her own. So everyone at rest in that reference frame agrees that all of these clocks display a time that is the same as her age.

    When he passes one of those clocks, his age is half the age on the helper-clock. So he might be 20 years old, and he might be passing one of her helper clocks which displays 40 years, even though he calculates that she is only 10 years old at that time.

    So let's say he stops there. He is now standing still relative to the helper clock, and he is also standing still relative to her. He knows he himself is currently 20 years old, and he knows that the helper clock indicates that she is currently 40 years old. According to your own argument, there is no reason for him to wait for any light signals to travel from her to him. And so he can immediately abandon his prior belief that she was 10 years old, and accept that as he decelerated quickly and stopped, she must have changed from 10 to 40 years old. Correct?

    (If you say no, I will be going on a long vacation, lol...)
  21. Mike_Fontenot Registered Senior Member

    OK, up to this instant, he and she have never accelerated, so they are effectively both perpetually inertial. So we don't have to specify a simultaneity method in that case, because we know that in the perpetually-inertial case, the only correct simultaneity is that given by the Lorentz equations and/or the Time Dilation Equation (TDE) You have specified that he is 20 at the instant immediately before he changes his speed to zero. And we are assuming they were each zero years old when they were momentarily co-located. Therefore, by the TDE, he says she is 10 when he is 20. She says she is 40 when he is 20.

    OK. Now you have specified that he has accelerated (with a Dirac delta acceleration that instantaneously reduces his speed relative to her to zero). So now you DO have to specify which simultaneity method you want to use. You can't say anything now about simultaneity until you've chosen a simultaneity method. From your conclusions about what happens at that instant (when he changes their relative speed to zero), you have clearly chosen the CMIF (Co-Moving Inertial Frames) simultaneity method. The defining assumption of the CMIF method is that the observer ALWAYS agrees with the perpetually-inertial observer (the PIO) with whom he is currently co-stationary and co-located at that instant. The PIO says that she is 40 at that instant (when he is 20).

    He doesn't abandon his prior belief. I.e., he doesn't say "I must have been wrong before". What he says is that she instantaneously aged by 30 years, from 10 years old to 40 years old. (And if, instead of changing their relative speed to zero, he had instantaneously increased his speed, the CMIF method would say that her age had instantaneously DECREASED by some amount ... i.e., she had instantaneously gotten YOUNGER).

    But if, instead of choosing the CMIF simultaneity method to get your answer, you had chosen my simultaneity method, then he would NOT conclude that her age changed instantaneously when he changed their relative speed to zero. He would NOT agree with the PIO for some (determinable) time after his speed change. That amount of time in his life when he disagrees with the PIO is called the Disagreement Interval (DI). The magnitude of the disagreement is largest immediately after his speed change, and decreases after that until it reaches zero at the end of the DI.

    And in the alternative scenario above where he instantaneously increases his speed (rather that instantly making it zero), my simultaneity method gives NO instantaneous decrease in her age. In fact, it never gives ANY decrease in her age at all, not even a gradual decrease.

    If you plot an Age Correspondence Diagram (ACD) for your scenario, using the CMIF simultaneity method, it will look like this:

    (I recommend either drawing all these diagrams I'm going to describe below very accurately, or at least sketching them well enough to see what's going on ... otherwise, the words alone are hard to follow.)

    The ACD always just plots her age "tau" according to him, on the vertical axis, versus his age "t" on the horizontal axis. So during the initial segment, the line starts at the origin, and rises linearly with slope 1/2, until it reaches the point (t = 20, tau = 10).

    Then, when he instantaneously changes his speed to zero, the plot rises vertically from tau = 10 to tau = 40. That vertical piece of the plot is the second segment of the plot.

    Then, from there, the third segment rises linearly with the slope 1.0, because they are now ageing at the same rate, according to him (and also according to her in this case).

    In my simultaneity method, the first segment of the plot is the same as for the first segment of the CMIF plot: a straight line rising from the origin with a slope of 0.5, until the point (t = 20, tau = 10) is reached. And we know that, for my method, immediately after his speed change, there is NO change in her age ... i.e., there is no discontinuity. This is the beginning of the disagreement interval (the DI), where he disagrees with the PIO. But before we can do anything further, we have to determine the end of the disagreement interval (the DI), where he once again agrees with the PIO. To do that, we need to draw a Minkowski diagram, which plots her age, tau, horizontally, and their separation X (according to her), vertically.

    The first segment of the diagram is a straight line rising from the origin, with a slope of 0.866. When she is 40, he is (40)(0.866) = 34.64 ly from her, according to her. So the coordinates of the end of that first segment on the Minkowski diagram are (tau = 40, X = 34.64).

    The second (and final) segment of the Minkowski diagram is just a horizontal line, because their relative speed is zero from then on, so their separation doesn't change any more.

    To determine the end of the disagreement interval, we draw a straight line on the Minkowki diagram, starting from tau = 40 on the horizontal axis, rising to the right with slope 1.0 (an angle of 45 degrees wrt the horizontal axis). That line represents a light pulse that she emits toward him when she is 40. Extend that line upward to the right until it intersects the horizontal segment of his worldline. Consider the right triangle formed by that light pulse line, together with the segment of the horizontal axis to the right of the point tau = 40, together with the vertical line going upward from that point. The two equal sides of that right triangle each have a "length" of 34.64. Therefore her age increases by 34.64 years, according to her, while the pulse is in transit. So she is 74.64 years old when the pulse reaches him (according to her, and in this particular case, also according to him). And since their relative speed is zero during the transit of the pulse, he likewise ages by 34.64 years during the pulse transit, so he is 54.64 years old when he receives the pulse. (They both agree about that, because the arrival of the pulse is an event.)

    The end of the disagreement interval (the DI) occurs when he receives the pulse. (And the DI started when he changed his speed). So we now have enough information to finish the age correspondence diagram. The DI ends when he is 54.64 years old, and she is 74.64 years old. WARNING: Note that, if he had changed their relative speed to anything other than zero, we would need to do a little work at this point to determine his line of simultaneity (LOS) that passes through his worldline where he receives the pulse, and then determine where that LOS intersects the horizontal axis. That point of intersection is her age when he is 54.64, according to him. That's what is needed for the ACD. But in this simple case, because their relative speed is zero, his LOS is just a vertical line, and so she and he both agree that when he is 54.64 years old, she is 74.64 years old.

    SO, to complete the ACD for my method, we just find the point on the ACD for the CMIF method where he is 54.64 years old and she is 74.64 years old (which denotes the the end of the DI), and then draw a straight line between that point and the point where he is 20 and she is 10 (the beginning of the DI), because that beginning point gives their ages immediately after he changed his speed, and her age didn't change there, according to my method).

    The reason it's fairly easy to draw that middle segment in my method is because it's always a straight line, so we only need to determine its two end points. If it were a curved line, it would still be possible to determine it (as described in my monograph in the definition of my method), but it would be MUCH more time-consuming. Sometimes you get lucky.

    So, we now have the solution for your scenario for both the CMIF simultaneity method and for my simultaneity method. Which one do we choose? Obviously, we want to choose the correct one. And I'm convinced (for philosophical reasons) that there IS a single correct answer. But there doesn't seem to be any way to experimentally determine the correct answer. So there seems to be no way to tell what the correct simultaneity method is. It may be the CMIF simultaneity method, or it may be my method, or it may be neither. I don't like that situation, but I think we're stuck with it. I would prefer that the CMIF method be the correct one, because it is simpler, and because I don't have a problem with negative ageing. But many people can't accept the negative ageing implied by the CMIF method, so for them, my method may be more comforting.
  22. Beaconator Valued Senior Member

    Is he older than her or younger!
  23. Beaconator Valued Senior Member

    That makes sense

    the origin of energy has shifted so far away from its physical counterpart... a

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