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Relativity, LET and Reality

  1. Oct 19, 2006 #1

    JesseM

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    [Mentor's note: This thread was extracted from another thread, SR transforms of matter/light interactions at the request of some of the participants because it drifts significantly from the original topic of that thread. You may want to edit some of your postings to reflect the changed context.]
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    No, SR is just a statement about the fundamental laws of physics being Lorentz-symmetric. This is still true even if you choose not to use the Lorentz transformation to define your set of inertial coordinate systems. (Also, the choice of what coordinate system to use is not in itself an 'interpretation of the laws of physics', any more than your choice of where to place the origin of your spatial coordinate axes is an interpretation of the laws of physics--it seems to me that the only way the LET can count as a distinct 'interpretation' is if it postulates some unobservable physical entities which are governed by non-Lorentz-symmetric laws.)
     
    Last edited by a moderator: Oct 24, 2006
  2. jcsd
  3. Oct 19, 2006 #2
    Why not do the honest thing and admit that you put up a silly post?
     
    Last edited: Oct 19, 2006
  4. Oct 19, 2006 #3

    Aether

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    Ok, first let me say that JesseM, pervect, Hurkyl (and a few others) are my teachers, so what I'm about to say shouldn't be construed as an argument against what JesseM is saying but rather as my exploration of a potential opportunity to learn something new.
    When I said "SR" I was referring to the two postulates of SR + what follows from them. So, I am distinguishing between the reality of local Lorentz symmetry vs. the coordinate-system dependent interpretation following from the two postulates.
    I am distinguishing the different conclusions that can be reached by application of the various simultaneity conventions as "interpretations" vs. the reality of local Lorentz symmetry which is invariant over a change of simultaneity convention.
    If JesseM and pervect both say that I put up a silly post, then I will admit that I did so. Otherwise, I will try to learn anything new that I can while we are on this subject and not admit to such a thing unless my mind is changed about something.
     
  5. Oct 19, 2006 #4

    JesseM

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    Ah, but the two postulates are not coordinate-dependent, they are physical postulates about what will be measured on physical systems of rulers and clocks constructed according to Einstein's specifications. When answering the question of what they will measure, you have no obligation to use a coordinate system that corresponds to their measurements! You could just as well use some other set of coordinate systems like the ones determined by coordinate transformation that Mansouri and Sexl give in their paper, and as long as you make sure to use the correct equations of the laws of physics to go with whatever coordinate system you use, you will still end up predicting that the different systems of rulers and clocks described by Einstein will measure identical results when they do identical experiments in their rest frame.
    Well, I would argue that the theory known as "SR" deals only with physical predictions like the ones described above, it is conventional to use coordinate systems which are based on these systems of rulers and clocks but that isn't a part of the physical theory.
    I think that's a good attitude. I do think your original post showed confusion about which ideas are a core part of the "theory of SR" and which are just commonplace conventions used in solving SR problems, but these issues are somewhat subtle so this kind of confusion is understandable.
     
  6. Oct 20, 2006 #5

    Aether

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    You can take two-way light speed isotropy for granted because Michelson interferometers confirm that, but you can not in general take one-way light speed isotropy for granted because there is no experiment that can measure that in a coordinate-system independent way. This is because there is currently no way to synchronize two clocks at different locations other than to make some coordinate-system dependent assumption. For red-shifts, there is no ambiguity of interpretation due to the conventionality of clock synchronization conventions because the isotropy of v and c are both affected in the say way by an arbitrary choice of clock synchronization conventions.
    This page shows an example calculated using the one-dimensional Lorentz transformation. I may come back to this later to show a counter-example using the one-dimensional LET/GGT transformation, but first let me have this discussion with JesseM to be sure that I am not really confused about something first. However, if you want to go ahead and do the calculations yourself then I will discuss the results with you.
    The two postulates are not physical. They define a set of coordinate systems wherein relative simultaneity is implied. I can use a different set of postulates to construct an equally valid set of coordinate systems wherein absolute simultaneity is implied. Maybe you can say that the postulates themselves are not coordinate-dependent, but their sole purpose is to construct a particular set of coordinate systems; and at least some of the conclusions drawn from their application are coordinate-system dependent interpretations of physical effects.
    If we express in tensor notation the (currently accepted) equations for the laws of physics within an (preferred) inertial frame, then these equations will correctly predict the results of all experiments (to date) carried out in that frame. There is no question of different "equations for the laws of physics to go with whatever coordinate system you use" for any other frame, the same set of equations for the laws of physics can be used regardless of the coordinate system chosen as long as we do all of the coordinate transformations correctly.
    Hurkyl, pervect, and possibly coalquay4004 all said that LET is a formulation of SR in a different coordinate system, and that the two postulates don't define SR per se but only one formulation of SR in a particular coordinate system. They didn't provide any reference for this though, and I have never seen a statement like that anywhere else. Can you provide a reference to show how SR is generally defined without necessarily implying the relativity of simultaneity?
    Which statement of mine is it that you think showed confusion exactly?
     
    Last edited: Oct 20, 2006
  7. Oct 20, 2006 #6
    While the formulas are identical between LET and relativity their interpretations of reality are very different.
    In relativity distance and duration are dynamic and depend on the relative speed of the measured object while in LET distance and duration are static and contraction and dilation are caused by objects moving relative to the ether.
    In LET there is absolute space and time, in relativity there is not.
     
  8. Oct 20, 2006 #7

    Aether

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    Yes, my point is to beware of such interpretations of reality because they aren't based on observation, and therefore they are outside of the domain of science. I am particularly alarmed by such interpretations of reality because they can fool us into ruling-out theories that we think are contrary to observed facts when they really aren't.
     
  9. Oct 20, 2006 #8
    Actually I agree with you. :smile:

    So then that is why I responded to your earlier statement saying:
    There is no experimental evidence for this assertion.
    In LET it is believed to be true but not in relativity.
    :smile:
     
  10. Oct 20, 2006 #9

    Aether

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    Well, I don't disagree with you either. :smile:

    That's why I said that I don't want to argue over the semantics of this, although if I can find a more precise way to say what I mean in a coordinate-system independent way that would be nice. Poor nakurusil is over there insisting that there is no physical difference between objects in relative motion to one another....:rolleyes:...I got hit by a baseball one time, and it sure felt real to me.
     
  11. Oct 20, 2006 #10
    What I objected to is this statement:

    Your statement was wrong in first place and is still wrong, you are trying to take us through some metaphysical detour of LET vs SR. I explained to you that you picked a wrong example, i.e. you do not understand the fact that you are operating outside SR already. Very simple.
     
  12. Oct 20, 2006 #11

    JesseM

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    This is the part of your argument that I was referring to as "confused". Of course the postulates are physical--they are a statement that if you build measuring-devices of the type Einstein specified, the laws of physics will be measured to work the same way in each one. Again, this would be true even if you used a different set of coordinate systems (with a different notion of simultaneity) to actually analyze this problem and make predictions about what each of these measuring-devices will measure. How do you think that isn't a physical prediction? And if you agree "the laws of physics are Lorentz-symmetric" is a physical statement, what difference do you imagine there is between that statement and the statement "the laws of physics will work the same way in different measuring-systems whose measurements are related by the Lorentz transform"? How would you express the fact that the laws of physics are Lorentz-symmetric if you were working in some other set of coordinate systems?
    That's true, but I wasn't talking about the laws of physics expressed in tensor notation, since any law of physics (including Newtonian mechanics) can be expressed in tensor notation and it will then work the same in all coordinate systems. The easiest and least technical way to understand the concept of Lorentz-symmetry is to say that if you express the laws of physics in terms of algebra/calculus equations (like expressing the equation for time dilation as [tex]t = t_0 / \sqrt{1 - v^2/c^2}[/tex]), then the equations will be the same for each of the inertial measuring-systems described by Einstein which define the coordinate systems of the Lorentz transformation, while they will not be the same (again, assuming you are expressing them in non-tensor notation) in other types of coordinate systems.
    Again, SR is defined by the statement that the laws of physics have a particular symmetry, namely Lorentz-symmetry. I'm sure there are mathematically more advanced ways of expressing this symmetry than the one I give above, probably involving group theory, but the way of defining it above is a perfectly valid one that's easy to understand without knowing a lot of advanced math, and it is a physical definition that doesn't require that you yourself use the coordinate systems defined by the Lorentz transformation, you can use whatever coordinate system you like to predict what would be measured in the type of physical ruler-clock system described by Einstein.
    The way I defined it above does not "imply the relativity of simultaneity", since you are free to analyze those different ruler/clock systems from the perspective of a set of inertial coordinate systems which all agree on simultaneity, like the ones defined in the Mansouri-Sexl paper.
    You seem to be rather confused about the difference between coordinate-dependent statements and "physical" or coordinate-independent ones. The fact that you don't understand that the question "what would be measured by a system of physical rulers and clocks constructed according to Einstein's specifications in his 1905 paper" is a physical question, not a coordinate-dependent one, is the prime example of this confusion.
     
  13. Oct 20, 2006 #12

    Aether

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    I think that by building measuring-devices of the type Einstein specified that you have necessarily embedded a coordinate-system dependency into many of the "measurements" that you could make with them.
    I agree that the known laws of physics are Lorentz-symmetric is a physical statement, but also seek-out possible observable violations of this which may define a locally preferred frame. I dont mind ignoring a potential locally preferred frame by using the Lorentz transforms, but I do object to ruling-out the possible existence of one by other than observational means.
    I would express the laws of physics in tensor (spinor) notation, note that they agree with all experiments in at least one (locally preferred) inertial reference frame, and then transform to the other set of coordinate systems; requiring that any transformations preserve an invariant line-element may be the key step in expressing Lorentz symmetry. I would go to this trouble only because I am trying to examine the fundamental laws of physics themselves while trying to avoid costly coordinate-system dependent detours when designing experiments and writing-up results/predictions.
    I have stipulated in other thread(s) that Einstein's simultaneity convention simplifies many practical calculations by collapsing the tensor notation into a simpler notation. I don't have any objection to that until it leads someone to a belief that relativity of simutaneity is an empirically established fact, for example.
    But it embeds a conventional clock synchroinzation choice that leads people to a belief that the relativity of simultaneity is "real", and that isn't necessarily so.
    The way you defined it above (actually, there is an ambiguity here because you have talked about several things above) does not imply the relativity of simultaneity because that isn't the Lorentz tranform for the time coordinate, but rather it is the LET transform. The way you defined it above is insconsistent with the two postulates of SR.
    Ok, if you will bear with me I would certainly like to dispell any confusion that may be lurking.
     
    Last edited: Oct 20, 2006
  14. Oct 20, 2006 #13

    Aether

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    My statement may or may not be viewed as "wrong" depending on which coordinate system that you choose to work in; so it is not wrong in reality, though I may learn to phrase it more effectively I'll admit. My reference to the LET transforms as a counter-example to the Lorentz transforms follows their use by Mansouri & Sexl. This is standard mainstream physics, although it is unfamiliar to many in the field. If you do not have access to their papers, I could make them available to you. You can also search this forum for an extensive discussion of them.
    Ok, I accept the validity of SR within its narrowly defined domain of applicability. Do you accept that LET (aka GGT) is empirically equivalent to SR?
     
    Last edited: Oct 20, 2006
  15. Oct 20, 2006 #14

    JesseM

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    Not if I don't use these measuring-devices to define my coordinate system! I am simply treating them as a physical system to be analyzed, no different than the clocks in the twin paradox or any other physical system. Are you really saying that if I analyze any other physical system using, say, the coordinate systems provided by the Mansouri-Sexl, everything is fine and dandy, but if I analyze that particular physical systems consisting of a grid of rulers and clocks constructed according to Einstein's specifications, I am magically forced to abandon the coordinate system I'd been using and adopt the coordinate system defined by these rulers and clocks? How could that possibly make any sense? This is why I said you were confused!
    OK, SR is simply the theory that all fundamental laws are Lorentz-symmetric, if a law is found that falsifies this, then SR will be falsified. However, the Lorentz Ether theory does not predict that there will be any measurable violations of Lorentz-symmetry, although it may be an interpretation which imagines fundamentally unmeasurable entities which violate it, in the same way that Bohm's interpretation of quantum mechanics imagines fundamentally unmeasurable precise positions for particles at all times.
    Yes, you're free to imagine whatever you want for future laws of physics. But this is not what we were debating; we were debating whether Einstein's two postulates are purely physical ones, or whether they commit you to using a particular coordinate system and thus would be violated by a restatement of the laws of physics in a different set of coordinate systems which nonetheless made no distinct physical predictions.
    I don't know enough about tensor notation to say if "requiring that any transformations preserve an invariant line-element" would be equivalent to the assumption of Lorentz-symmetry, but regardless, you are still confused if you think the mathematically less sophisticated statement that "the laws of physics expressed in non-tensor form will obey the same equations in all the inertial measuring-systems constructed according to Einstein's procedure" is itself a coordinate-dependent statement. This statement could be verified in any arbitrary coordinate system or set of coordinate systems, it's a physical statement about the results of physical measurements made using physical devices.
    My statement above does not in any way commit you to using Einstein's simultaneity convention, you are free to view the physical clocks in the measuring-devices you're analyzing as being out-of-sync in the coordinate system which you define as their rest frame.
    This seems to be some sort of pedagogical argument, not an argument against the only thing I am claiming here, that Einstein's postulates are physical ones which are equivalent to the postulate that the laws of physics should be Lorentz-symmetric.
    I don't think there is any ambiguity--where in that quote do you see it?
    False, the postulates of SR only involve predictions about physical measurements on physical systems of rulers and clocks. If you want to analyze those rulers and clocks from the perspective of some other set of coordinate systems besides the ones defined in terms of their measurements, nothing is stopping you. In much the same way, we could use the conventional coordinate systems normally used in SR to analyze the behavior of a set of ruler/clock systems whose clocks were "synchronized" using some other convention besides the Einstein synchronization convention, with the consequence that the clocks will appear out-of-sync from the perspective of the coordinate system we are using--this is no different from the idea that you can use these conventional coordinate systems to analyze the accelerating clock in the twin paradox, which will not stay synchronized with the inertial clock in this coordinate system. Analyzing a particular set of physical clocks does not commit you to using a coordinate system in which they are in sync!
     
  16. Oct 20, 2006 #15

    Aether

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    Ok, you are talking about a physical system of measuring-devices that are set-up by Einstein's procedure(s), and then you are going to examine that system; but in doing so you may set up a second coordinate system that is not set-up by Einstein's procedure(s)? In that case, your first set-up is a physical system and the second set-up isn't. I was only considering the second set-up 'til now.
    No, of course not. I don't prefer LET/GGT over SR or one simultaneity convention over another. I prefer a coordinate-system independent view in the absence of an observational constraint on the simultaneity convention.
    LET/GGT and SR stand or fall together. The only reason that I refer to LET/GGT at all is to understand the coordinate-system dependency of SR; this is how Mansouri & Sexl intended I think.

    I have to run right now, so I will reply to the rest of your comments here later.
     
  17. Oct 20, 2006 #16

    your repeated references to LET/GGT/ETC are nothing but a red herring, your example is non-inertial because of the turnaround involved. Do you get this? You are outside any of the theories that use inertial frames.
    The stuff about coordinate-dependent measurements, one way light speed isotropy, etc is just another red herring, you miss the basic experimental and theoretical stuff. I'll let JesseM set you straight on this subject.
     
    Last edited: Oct 20, 2006
  18. Oct 20, 2006 #17

    Aether

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    Any "measurement" that you can make comparing the elapsed times on the two separated clocks without the turnaround is necessarily coordinate-system dependent because it requires a conventional clock synchronization choice. If JesseM disagrees with this, then let him say so. Otherwise, please feel free to be quiet now and try to learn something.
     
    Last edited: Oct 20, 2006
  19. Oct 20, 2006 #18
    You don't need to be arrogant, let me remind you what you really wrote:

    Apparently you not only have problems with understanding the basics but also with understanding your own posts.
     
  20. Oct 21, 2006 #19

    JesseM

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    I'm not treating the physical system of measuring-devices as a "coordinate system" at all, just as a physical system. You can use whatever coordinate system you like to analyze it, provided you pick the correct form of the laws of physics in that coordinate system. And again, the first and second postulates are physical postulates about what will be measured by such measuring-devices, your predictions about what they will measure should be independent of what coordinate system you choose.
    So you agree that analyzing the type of system of measuring-devices and clocks proposed by Einstein does not commit us to the view that their definition of simultaneity is "correct"? And do you agree that the first and second postulate are simply postulates about what would be measured by such systems?
     
  21. Oct 21, 2006 #20

    Aether

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    LET and SR (e.g., the first and second postulates) are empirically equivalent, so any predictions about actual measurements will agree; so, for predictions on which these two theories agree I would call "physical". It is only on matters where these two theories disagree that I would raise an issue of coordinate-system dependency.
    Let's come back to this and every other issue above after we have examined this statement: "the only thing I am claiming here, that Einstein's postulates are physical ones which are equivalent to the postulate that the laws of physics should be Lorentz-symmetric." Can you (or someone else who is reading along) cite a reference for this along the lines of "I'm sure there are mathematically more advanced ways of expressing this symmetry than the one I give above, probably involving group theory"?
     
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