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About interpretations and logic

  1. May 6, 2007 #1
    Hello everyone !
    I want to ask you something and I hope you think your answer and not just reply with an orthodox foundation. I'm not another Einstein's enemy, I believe in SR but sometimes I just can't imagine some situations...
    Look at this:
    I will use the famous twin paradox because it is known for all... but I won't answer who is younger at the end, we know "Earth-Twin" is older, now... WHEN "Traveler-Twin" get this difference? was it during his acceleration? was it during his inertial movement (outbound or inbound travel?).
    Even more... let me modify our paradox:
    Now the "Traveler-Twin" never returns to the Earth. Does he remain younger?
    And if we don't know WHO accelerates? who is younger?
    I hope you can understand my doubt. To me, THERE is the real paradox... and I don' think relativity of simultaneousness solves it...
    Someone told me once:
    If nobody is accelerating and nobody turns back, then, they cross at maximum ONE time, and then is not relevant who is younger...
    I can understand that answer in a practical way, but I think it's not acceptable from a theoretic point of view.
    I think SR, with the current interpretation, can't solve this.
    But look at this:
    I we assume there's a preferential frame of reference, if we assume the nature of universe is NOT the same for all inertial observers, BUT:
    every physical theory should look the same mathematically to every inertial observer, and the laws of the universe are the same regardless of inertial frame of reference, so, we left the equations of our SR unbroken, and we save our "logic", because now, like before, we can't answer WHO is younger... but we KNOW that one of them is younger... I think there's an important difference, because again, we can't save our practical problem, but yes the theoretic one.
    Now, why the science community choose the first interpretation of SR, which is so cruel with our logic if the second interpretation take us the SAME equations and preserves our logic?
    Is there some problem with this second interpretation?
    Please, again, I'm not trying to break up the SR or something similar, I'm just trying to solve this logic paradox...

    Thanks for read!
    (and thanks a lot if you reply...)

  2. jcsd
  3. May 6, 2007 #2

    Chris Hillman

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  4. May 6, 2007 #3


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    enridp you might also want to read Barrow and Levin's paper: The twin paradox in compact spaces.
    I argue that the topology of the space is determined by the matter within it and the 'stationary' twin thereby identified to be in the frame of reference of the centre of momentum of that distribution of matter in motion as per Mach's Principle.

    Last edited: May 6, 2007
  5. May 6, 2007 #4

    Chris Hillman

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    Which makes the same points as the much older discussion in sci.physics.relativity by Nathan Urban and others. I believe there is also an eprint by Jeffrey Weeks on this topic. Curiously enough, this is part of the vast background for the Ehrenfest paradox discussion.
  6. May 6, 2007 #5


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    But why not? The question of "who is younger" in this case depends on simultaneity between distant events, why do you think it's not acceptable that simultaneity is a coordinate-system-dependent concept which has no single "objectively true" answer? Do you think it's acceptable that there's no objective truth about which one has a larger velocity, or which one has a greater x-coordinate? If you find it acceptable that velocity and x-coordinate are dependent on your choice of coordinate system, why not simultaneity too?
  7. May 6, 2007 #6
    Hello again !
    First, thanks for your replies.
    Now, I think I'm not explaining well, maybe it's due my poor english, sorry for that, I'll try to do it better now:
    But look at this situation:
    Two ships (A and B) in middle of the universe, they meet in a moment, call it t=0. Both are perfect inertial frames. Now A will say: "B's time is going slow", and B will say: "A's time is going slow".
    So who is right?
    Many people accept the answer:
    *both AND nobody
    And it really breaks my logic. But if we now say something like:
    OK, every physical theory should LOOK the same mathematically to every inertial observer, and the laws of the universe LOOK the same regardless of inertial frame of reference, BUT EXISTS a preferential frame, somewhere, although we can not detect it. Now we still without knowing who is right, A or B, but we know they can't be right at the same time.
    SR is not changed, only its interpretation, at least I think so... and we save our logic...
    Now, have passed more than 100 years and the original interpretation remains in the science community, then, my question is:
    * What is the problem with the "new" (at really is not new, and of course, not mine...) interpretation of the SR? What is wrong with it? if it preserves all the mathematical structure and it's more logic, why we are not using it?

  8. May 6, 2007 #7


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    Again, why does it break your logic? Consider this analogous scenario: Two ships A and B are moving apart at constant velocity. In A's frame, A is at rest and B has the higher speed, while in B's frame, B is at rest and A has the higher speed. So, who is right? Do you refuse to accept that there could be no objective answer to who is "really" moving faster, that speed is an inherently frame-dependent concept?
  9. May 6, 2007 #8
    I don't know, I think time is different...
    Anyway, therefore are you saying that in the twin paradox, if the "traveler-twin" doesn't returns, then, there's no way to know who is younger?
    And we know the "traveler-twin" is younger... I mean, there is a reallity...
    In my example, A and B are moving at a relative velocity, it's like a twin paradox, but now we don't know WHO accelerated, who is right then?
    I can accept the answer: "we don't know"
    But I can't understand the answer "both and nobody", in the twin paradox we don't say both and nobody... there's a reallity...

    thanks again !
  10. May 6, 2007 #9


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    No, I disagree that there is a reality if they don't reunite. There doesn't need to be, any more than there needs to be a reality about which twin "really" has a greater speed.
    But in the twin paradox, they return to the same spot.

    Here's an analogy--on a 2D sheet of paper, draw two points, a "starting point" A and a "finishing point" B, and then draw two paths between them, one a straight line and the other a bent line. Now draw x and y coordinate axes, with the y axis parallel to the the straight line. To get some specific numbers, let's say the starting point A is at x=0, y=0 and the finishing point B is at x=0, y=8, and the bent path consists of two straight line segments at different angles, the first of which of which goes from A to a point C at x=3, y=4, while the second line segment goes from C to B. Note the y-coordinates of the two points A and B, in this case y=0 and y=8, and then for any y-coordinate in between these two values, like y=4, there will be a unique point on each path with this y-coordinate. So you can ask about the distance along each path that you'd need to travel to get to the point on the path that has that y-coordinate; let's invent a term for that distance, like "partial path length". For example, at coordinate y=4, the "partial path length" along the straight path would have to be 4, while the "partial path length" on the bent path would larger, in this case 5 (the distance from point A to point C). If you look at the y-coordinate of the finishing point B, y=8, then the "partial path length" at y=8 would just be equal to the total length of the path from the starting point to the finishing point. In this case the "partial path length" for the straight path at y=8 would be 8, while the "partial path length" for the bent path would be 10.

    Now, keep the same two paths between the same two points, but redraw your x and y axes so the y-axis is no longer parallel to the straight path--for example, we might draw the y-axis so it's parallel to the line segment joining A and C. Now the coordinates of the starting point A and the finishing point B for each path won't be the same--if we place the origin so that A still has coordinatex x=0, y=0, then the finishing point B will now have coordinates x=0, y=5.12. It's still true that "partial path length" for each path at the y-coordinate of the finishing point, y=5.12, must just be the total length of each path, which won't have changed just because we picked a different coordinate system, so it'll still be 8 for the straight path and 10 for the bent path. But at some earlier y-coordinate, since the lines of constant y are now at different angles, they'll intersect the two paths at different points so the "partial path length" at this y-coordinate will be different--for example, at y-coordinate y=2.56 in this coordinate system, the "partial path length" on the straight path would be 4 (just like the partial path length at y=4 in the previous coordinate system), while the "partial path length" on the bent path would be 2.56. Notice that while in the previous coordinate system the "partial path length" of the straight path was always smaller than the bent path at a given y-coordinate, in this coordinate system the "partial path length" of the straight path can actually be larger for certain values of y, although both coordinate systems agree that the total path length between A and B is shorter for the straight path.

    All of this is pretty closely analogous to the situation in relativity, with different coordinate systems on the paper being analogous to different inertial reference frames in relativity, the y-coordinate being analogous to the coordinate time t in a given frame, and the "partial path length" at a given y-coordinate being analogous to the proper time T accumulated by a particular clock at a given coordinate time t. Just as both coordinate systems agreed on the value of the "partial path length" at the y-coordinate of point B where the two paths reunite, so different frames in relativity will always agree on the value of the proper time read by each twin's clock at the t-coordinate where they reunite at a single point in space. But hopefully you would agree that there is no single true answer to the question of which path is accumulating "partial path length" faster before they reach point B--this is entirely coordinate-dependent, you can get different answers depending on how you orient your y-axis and none is more "objectively true" than any other. In the same way, I'd say there's no single true answer to the question of which twin is accumulating proper time faster (or 'aging faster') before they reunite at a single point in space.
    Last edited: May 6, 2007
  11. May 6, 2007 #10
    I suggest you give up on this line. You will never get a satisfactory answer to that question under current theory.
  12. May 6, 2007 #11


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    Note that current theory has an answer - it's just that some people may judge it to be "unsatisfactory.
  13. May 6, 2007 #12
    That is exactly right.

    In the pre-relativity physics space and time were separate entities. Specifications of time were independent of the choice of the space of reference. The Newtonian mechanics was relative with respect to the space of reference, so that, e.g. the statement that two non-simultaneous events happened at the same place had no objective meaning (that is, independent of the space of reference). But this relativity had no role in building up the theory. One spoke of points of space, as of instants of time, as if they were absolute realities. It was not observed that the true element of the space time specification was the event specified by the four numbers x1, x2, x3, t. The conception of something happening was always that of a four-dimensional continuum; but the recognition of this was obscured by the absolute character of the pre-relativity time. Upon giving up the hypothesis of the absolute character of time, particularly that of simultaneity, the four-dimensionality of the time-space concept was immediately recognized. It is neither the point in space, nor the instant in time, at which something happens that has physical reality, but only the event itself. There is no absolute (independent of the space of reference) relation in space, and no absolute relation in time between two events, but there is an absolute (independent of the space of reference) relation in space and time, as will appear in the sequel.
    - Einstein, Stafford Little Lectures
  14. May 6, 2007 #13
    My apologies. I should have said that enridp will not get an answer that will satisfy him.

    Funnily enough I agree with some of the things that seem at first illogical in SR but I do for different reasons. I even thought those reasons might be acceptable to SR but I don't think they are now. However this forum is not the place for discussing anything but respected quotable theory.
  15. May 6, 2007 #14
    I don't see anything wrong here, and I don't see anything "profound" in what you're saying. Sounds like you are having trouble intuitively conceiving of a universe without a preferred frame of reference, and you perhaps confuse intuition for logic. So, you state that if something is counterintuitive to you, it must be the "wrong" interpretation (whatever that means). Look at these statements:

    This isn't founded on any objective reasoning that I can see. It just means you haven't thought about it enough to become comfortable with it.

    Nothing is wrong with it, but it's like adding extra "entities" for no reason, and getting nothing in return. Why are you inventing a "universally preferred" frame of reference? How can we determine what that frame of reference is? If we can't, why even say it exists? Isn't it simpler just to pick your own preferred frame of reference and use that?

    It sounds less logical to me, I think you're just saying it's more intuitive to you personally. And I don't see why we would want to use it. The lack of a preferred frame of reference is, as I understand it, the greatest strength of SR. It means you can use any frame you want.

    Why would the universe care? By the argument of symmetry, any frame is as good as any other frame, so there's no information for the universe to use to pick one over the others (unless you claim it is random). Just like any symmetry argument in physics (albeit a lot less rigorous), I think that suffices to show that the idea of a universally preferred frame is superfluous.
  16. May 7, 2007 #15
    Hi eripd.

    Pre SR it was thought that there was a medium through which light propagated called the Ether. As light was thought to propagate through this medium it was proposed that an experiment should be able to detect a difference in light speed measured at the Earth as the Earth's orbit changed direction relative to the statc? ether. It was the failure to detect this difference that led to the proposed Lorentz-Fitzgerald contraction. Instead of this contraction being the reason the conclusion was reached that the speed of light was the same in all spatial directions and thus UNDETECTABLE by such experiments. Einstein realised that this meant it was the same for all observers whatever their motion and SR was born. So as an indirect answer to your question, it was the undetectability of a preferred frame that led to SR in the first place and proposing a return to an undetectable preferred frame would be a backward and unnecessary step. This of course should not stop anyone continuing to search for such a medium or frame.

  17. May 7, 2007 #16
    First I want (I think I must...) to clarify something:
    I'm not trying to change SR.
    I have not physical arguments to defend the universal frame.
    I'm trying to understand WHY it's not possible the existence of a universal frame.
    At really, I'm one of the "enemies" of that universal frame, and my original thinking about relativity was exactly like Xezlec (but weaker...), but when someone propose to me the possibility of an universal frame I canĀ“t prove he is wrong, and sometimes, like you saw in the previous posts, my logic is crumbled, and I don't know what to think.
    The JesseM's reply was really helpful to me, I think many things go back to the logic part of my brain again...
    But I'm sad because if we can't prove the incompatibility with a universal frame then I think this possibility remains open...
    I found just one physical difference:
    If we accept a universal frame, then the physics allow us to have velocities higher than "c", then will be possible to find where is the universal frame.
    Anyway, now the "orthodox" interpretation is my logic election again, but I'll be really happy if we could banish definitely the universal frame.

    Thanks a lot to everybody.
  18. May 7, 2007 #17


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    The short answer is that you could have a universal frame, or you could have relativity, but you can't have both.

    Relativity is basically the statement that the speed of light is 'c' relative to all observers plus an additional assumption that there is no preferred direction, i.e. that space is isotropic.

    Experimental evidence shows that the universe acts relativistically, and not in the manner that it would if it had a preferred frame.
  19. May 7, 2007 #18
    OK, so you're saying I can't prove that the "one frame is better than the others" interpretation is wrong, so I shouldn't claim that it is?

    I might have to agree with that, except that I'm not sure we need to prove anything about a mathematically equivalent interpretation, do we? We just pick the interpretation we like. Which might also kill my argument... hmm...
  20. May 8, 2007 #19
    Hi Xezlec and Enripd.

    It is perfectly acceptable to believe that there is a preferred frame but to convice others evidence of such a fact must be offered. Scientific evidence, but not thought experiments, to support this possibility would of course be accepted by myself and most others.

    In answer to your point about mathematics I would say that we are free to choose any mathematical tools we wish to describe reality but I believe that there is an objective reality ( some people believe otherwise ) which we cannot pick and choose and that the mathematical description we decide to use does not create this reality but as you say merely interprets it and helps us to understand it and to make testable predictions about it.

    We often use a preferred frame to make life easier when required, for example our own rest frame. A universally preferred frame is another matter and does not depend on any mathematics but the absence of such a thing is an axiom of SR and in theory capable of disproof.

  21. May 18, 2007 #20
    No we shouldn't.

    But which category Relativity belongs? Quite little experimental proof, quite furious arguments pro and contra...
  22. May 18, 2007 #21


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