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Einstein simultaneity: just a convention?

  1. May 5, 2008 #1

    Ken G

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    I'm curious about how people here view Einstein's prescription for determining simultaneity in an inertial frame, and how the extension of that approach to other inertial frames spawns the Lorentz transformation. It seems to me the competing pictures here are that this is an arbitrary way (in the sense of, not physically forced, even if convenient) to coordinatize time, and hence the Lorentz transformation is an arbitrary mapping between the coordinates of different reference frames, versus saying that the Einstein convention is fundamental to what we mean by time, and the Lorentz transformation is fundamental to what we mean by motion. I am rather of the former school, that what is physically fundamental is a deeper symmetry that allows the Einstein convention to be a particularly convenient coordinate choice, but that its physical significance comes entirely from how it simplifies the coordinatizations when we apply the laws of physics. But others might argue that the simplification is so fundamental that it would be foolish for us to imagine that "reality itself" could be doing anything different, even if just a means for recognizing equivalent possibilities.

    Note, in particular, that the isotropic and constant speed of light in an inertial frame is a ramification of Einstein's coordinatization prescription, so an equivalent way to ask this is, is the isotropic speed of light a law of nature or just the proof that there exists a particularly elegant coordinate possibility? As the former is often taken as a postulate of special relativity, are we messing up the proper axiomatic structure of our art here?
     
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  3. May 5, 2008 #2
    I think I can't understand what you are asking for!
    As I have understood it, my answer would be, there is nothing fundamental in Einstein's definition of time (or for that matter simultaneity) or Lorentz transforms, and they are just arbitrary (and convenient, as u said) ways to understand the 'mnemonics' of 'motion'. We will keep on refining them until we have matched the ultimate way of understanding everything. However, It's just me, others may (and should, will) differ.
     
  4. May 5, 2008 #3

    Ich

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    It is the mere "coordinate possibility", which makes not only the speed of light but also the electromagnetic and mechanical laws isotropic, that lets us assume that this symmetry is a law of nature.
     
  5. May 5, 2008 #4

    Ken G

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    Both of the responses so far seem more in keeping with "the former" answer, in that mitesh9 echoes my use of "convenience", and Ich cautiously inserts "lets us assume" that the speed of light is isotropic. Probably Ich is straddling the line a bit, and likely identifies more with "the latter" camp from the OP, but only in a kind of "Occam's Razor" sort of way. To be a full-fledged member of "the latter" camp, someone would need to interpret the one-way speed of light itself, not the symmetry that "permits the assumption", to be a constant of nature. I'm wondering if anyone else sees it more firmly in "the latter" camp, and if that's not our understanding, why do we teach it that way?
     
  6. May 5, 2008 #5
    You will notice Sir, that the teachings are not working for some reason, else, you would have found the answers with second flavor!!!
     
  7. May 5, 2008 #6

    Ken G

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    I tend to agree, though I am not familiar with your colorful use of the expression "second flavor"!
     
  8. May 5, 2008 #7

    Hurkyl

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    For the record, axioms are not an intrinsic part of a theory. They are more like a spanning set for a vector space; axioms are simply a 'computationally' convenient way for working with a theory.
     
  9. May 5, 2008 #8
    Using the 2nd postulate, c is constant..., you can derive the same results in SR, with one exception. Time dilation is physically real, length contraction is an interpretation.
    The 1st postulate was a philosophical preference.
     
  10. May 5, 2008 #9

    Ken G

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    I'm not at all sure what you mean by that, or if you are distinguishing axioms from postulates (I should have used the latter term, as I believe postulates are chosen optionally to test their ramifications whereas some view axioms as kind of self-evident truths). But nevertheless, this is very much the question I'm asking-- is the isotropic speed of light truly a postulate of relativity, or has it been misnamed, as it is instead an assumption of convenience that is deeply related to a particular choice of coordinates?
     
  11. May 5, 2008 #10

    Ken G

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    This is also right at the heart of what I'm asking, i.e., the difference between a physical principle and a philosophical preference. But I don't understand what you are saying-- if you had to clarify more clearly what is a physical postulate, what is a philosophical preference, and what is a coordinate choice, how would you recast the description of special relativity?
     
  12. May 5, 2008 #11

    Hurkyl

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    In formal logic, axioms are nothing more than a means for presenting a theory. There is no intrinsic quality that distinguishes between the chosen axioms and the other statements in that theory. To wit, any mathematical theory can be axiomatized in infinitely many different ways. (including the "every statement of the theory is an axiom" axiomization)

    The main point I'm trying to make is that there is no mathematical content in your question -- it's purely a question of pedagogy. (or possibly of philosophy)
     
    Last edited: May 5, 2008
  13. May 5, 2008 #12

    Ken G

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    I see what you are saying, the theory is essentially every prediction it makes of the invariants, and the paths used to arrive at the prediction is a particular choice of axiomatization. That's a helpful insight, bringing into better focus some of the things bouncing around in my head, and gibes with what I was calling "the former" presentation of the axiomatic structure of relativity. So I should not have asked if we are messing up the axiomatization itself, I should have asked are we messing up the way we describe the meaning of that axiomatization. Because the way relativity is taught is invariably "at first we thought there was an ether but then Michelson-Morely proved there wasn't", when it should be said that "at first we thought the basic symmetry was built around a preferred frame, but found the symmetry supports an elegant coordinatization that doesn't require that concept". Ironically, cosmology returns us to something closer to the former position, which is why the way special relativity gets taught could be viewed as counterproductive.
    That's how I tried to frame it, yes. But I see that the "messing up" comment suggested otherwise-- what I meant was that we may be messing up the proper pedagogy. I'm still interested if there is anyone who doesn't see it that way, before I conclude that we are.
     
  14. May 6, 2008 #13

    Ich

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    I'm not sure whether our pedagogy is fundamentally flawed in this aspect. Do people actually say that the ether ist disproved? There are other things to worry about, like the teaching of SR in ether terms, which is quite common.
    But I think it is right that it is not common knowledge that there are infinitely many theories which are experimentally indistinguishable from SR. It is also quite hard to explain at an introductory level why these theories are nevertheless unacceptable.
     
  15. May 6, 2008 #14
    "Second flavor" meant to depict the second option you gave, amongst the two to choose between... You see, from the given two, we (me and Ich) chose to go with the first one (or first flavor?)!
     
  16. May 6, 2008 #15

    Dale

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    I think the pedagogy is fundamentally flawed. Students are famously unsuccessful at learning the relativity of simultaneity, and based on my own experience I would strongly favor introducing 4-vectors and the Minkowski norm as early as possible.

    However, as to the OP's Q: There is a physical significance to the Einstein synchronization convention, namely the isotropy of the one-way speed of light. There is also a mathematical significance, namely that synchronization gives an orthogonal basis set. That said, the physical significance does seem somehow "less" since there seems to be no physical significance to the fact that two events are simultaneous in some frame since they cannot be causally related.
     
  17. May 6, 2008 #16

    Ken G

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    In my experience, yes.
    I haven't seen that. Perhaps there is more than one problem going around.
    Why are they unacceptable? Also, stimulating that kind of question may be as important to a student of science as relativity itself.
     
  18. May 6, 2008 #17

    Ken G

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    Ah, I see. Frankly it surprised me how preferred that flavor is-- among the scientists I know, that flavor comes close to being blasphemous.
     
  19. May 6, 2008 #18

    Ken G

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    It sounds like you are saying that because people have problems with the physical significance of the Einstein simultaneity convention, it is best to move right to its ramifications (the Minkowski norm) and avoid confusion in applying it. But are we not covering our tracks a bit too much with that approach? In other areas of physics, we teach that multiple coordinate systems are equally valid, it's just that some conform better to the symmetries so are more convenient.
    But not a unique one, correct?
    That's very much a key point, I would say.
     
    Last edited: May 6, 2008
  20. May 6, 2008 #19
    Sure! But why only the scientists? It is equally "blasphemous" here on PF as well!
    Ironically enough, if you do not accept SR and GR, you are not fit to be scientist. Logic is no absolute either, It is relative indeed (i.e. if it matches with SR, it's true, else not)!
    But yes, It surely (fortunately and thankfully) disqualifies me to be a scientists.
     
    Last edited: May 6, 2008
  21. May 6, 2008 #20

    Ken G

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    Perhaps it would be helpful to distinguish two separate issues, one being whether or not the observational evidence has made the case as to the value of special relativity, and the other is whether we are being true to the lessons of relativity as to what we accept as the most general way to understand that theory.
     
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