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Time dilation #3

  1. Apr 21, 2009 #1

    cos

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    I seek information in relation to my attempts to understand an aspect of special theory.

    I recently read the comment - "SR says that the measured speed of light is constant."

    In his book 'An Introduction to the Special Theory of Relativity' Robert Katz asks (36, Affiliated East-West, 1964) -

    "Is the moving rod really contracted in its direction of motion? Is time really dilated? These questions depend on what is meant by 'really'. In physics what is real is identical with what is measured."

    In his article 'The Twin Paradoxes of Special Relativity: Their resolution and Implications' S J Prokhovnik wrote (548, Foundations of Physics, Vol 19, No 5, May 1989) that (in space) light travels isotropically away from its source but that if an observer is moving past that source it's emissions will not be isotropic relative to him however on page 550 Simon points out "It is well known that the contraction effect is sufficient to conceal the light-speed anisotropy [from that observer].

    Is this correct? Does the idea that his rule is contracted conceal the light's anisotropy relative to the moving observer ergo he measures it to be c?
     
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  3. Apr 21, 2009 #2

    atyy

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    I'm not sure specifically about anisotropy, but the constancy of the speed of light in different inertial reference frames has 2 interpretations
    (i) matter contracts, etc in strange ways to make it so
    (ii) spacetime itself has strange properties

    Variations of the first point of view are nowadays often called "Lorentzian", and you can find an exposition of it in John Bell's book "Speakable and Unspeakable". Variations of the second point of view are often called "Einsteinian", and are descended from Minkowski. If I remember right, Clifford Will's book, for example, usually takes the second point of view. For established theory, one just uses the point of view most congenial to one's mode of thinking, and the problem at hand. There are no differences in experimental predictions.
     
    Last edited: Apr 21, 2009
  4. Apr 21, 2009 #3

    JesseM

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    In a "Lorentz ether" interpretation of SR, there's some preferred frame (often called the 'ether frame' although it's not necessary to believe in an actual physical ether), and rulers moving relative to this frame shrink objectively, and clocks moving relative to this frame slow down objectively. So in this interpretation, light "really" only moves at c in the ether frame, while observers moving relative to the ether frame only think light is moving at c relative to themselves because of their distorted rulers and clocks.

    The thing is, all the known fundamental equations of physics are Lorentz-symmetric, which means that they're guaranteed to obey exactly the equations in every inertial coordinate system (general relativity is locally Lorentz-symmetric in the neighborhood of every point in spacetime, although it isn't possible to define inertial frames in a global sense in GR). So, any possible experiment you do in different inertial frames will give identical results in all these frames, according to the known laws of physics. This means even if there is a preferred ether frame, there is no possible way for any observer to determine which frame this is experimentally, so the idea of such a frame is more like a metaphysical speculation than a physics theory.
     
  5. Apr 22, 2009 #4

    cos

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    Thanks for that input but I would prefer it if we could only talk about Einsteinian applications and not refer in any way to Lorentzian ideas which, in my opinion, only tends to confuse matters and is not relevant to Prokhovnik's or Katz's presentations as they both only refer to STR.

    An observer is stationary some distance from a light source and, (hypothetically - using a rule and two clocks) measures the speed of light emitted by that source to be c; he accelerates then moves past that source with uniform velocity.

    Is his (1 meter) rule then shorter than it was before he started moving or is it merely measured by an observer alongside the source to be shorter than his (1 meter) rule?

    I.e. does the traveler's rule physically incur length contraction?

    Or as Katz put it "Is the moving rod really contracted in its direction of motion?"
     
  6. Apr 22, 2009 #5

    JesseM

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    The difference between the Einstein interpretation and the Lorentz interpretation is purely a matter of how relativity is interpreted conceptually, both make exactly the same experimental predictions in all cases. But the Einstein interpretation says all inertial frames are on equal footing, and that there is no single "real truth" about frame-dependent questions. And of course the laws of physics obey the same equations in all inertial frames (this is true regardless of which interpretation you use), including the fact that in any frame, a ruler moving relative to that frame will be shrunk relative to a ruler at rest relative to that frame.
    It depends what you mean by "really" or "physically". The rod is contracted relative to the observer's ruler in the coordinates of the observer's rest frame, but it's not contracted in any frame-independent sense, there'd be another frame where the observer's ruler is contracted relative to the rod, and in Einstein's interpretation all inertial frames are considered equally valid.
     
  7. Apr 22, 2009 #6

    jtbell

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    "Physical" is a slippery word. There have been many debates on this forum that ultimately reduce to disagreements about its meaning. You need to define very carefully and very explicitly, in operational terms, what you mean by "physical," for the purposes of this thread.
     
    Last edited: Apr 22, 2009
  8. Apr 22, 2009 #7

    jtbell

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    "Sniping" type posts have been deleted. Let's give this thread a chance, and not jump to conclusions about its outcome. If it does end up going round in circles like certain other threads, then it will be locked.
     
  9. Apr 22, 2009 #8

    atyy

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    Perhaps the most famous toy problem to do with this is Bell's spaceship paradox. I've got to go quickly, and actually I've never studied it myself, so I'm outlining my guess as to what happens, and relying on the usual experts to correct my guess.

    Does the string really break? Yes.
    Did the string really get shorter or did the distance between the spaceships increase? The string really got shorter with respect to one particular lattice of rods and clocks (reference frame), but the distance between the spaceships really increased with respect to another lattice of rods and clocks.
     
  10. Apr 22, 2009 #9
    I think Einstein would say that "the distinction real - unreal is hardly helpful" and "rather than distinguishing between "real" and "unreal" we want to more clearly distinguish between quantities that are inherent in the physical system as such (independent from the choice of coordinate system), and quantities that depend on the coordinate system."

    So the "Einsteinian" answer would be that whether or not the rod contracted depends on the choice of coordinate system, ie it's frame dependent.

    Edit: Even if there were a preferred reference frame in which measured length is "real" and measurements in other frames were "not real", it would still just be a matter of semantics, since the operational definition of "real" would be "with respect to the preferred frame".

    Maybe a better question is - Is "actual length" a different concept than "measured length"? Is there a concept of length that would differ from measured length?
     
    Last edited by a moderator: Apr 22, 2009
  11. Apr 22, 2009 #10
    Hello cos.

    Real or unreal, some authors, such as Rindler, comment that it is in principle detectable. The words "real in every sense of the word" are also used. One point to note is that we may not be able "see" such a contraction because of Terrell rotation, an effect more noticeable at high relative velocity but not a relativistic effect, but perhaps for the purposes of deciding on the reality, this effect should be ignored. My personal opinion is probably pretty unhelpful, but it quite common--It depends what you mean by real. Of course this is a discussion whuich has taken place many times and by its nature cannot reach an outcome that will satisfy everybody.

    Matheinste.
     
  12. Apr 22, 2009 #11

    Mentz114

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    If some people look at a lamp through a sheet of distorting glass and they are asked to point in the direction of the lamp, they may well point in diverging directions. Who is right ? They all are. Each person's experience is as real as the others. They might argue about the direction of the lamp but only until they discover the glass.

    In the case of inertial observers who are not at rest relative to each other, they may experience perceptual distortions relating to distances and clock rates which to them are real ( in the sense that they actually see them ).

    The question 'is the rod actually contracted' does not have meaning for any observer who is not at rest wrt to the rod, because 'the length of the rod' has been defined only for someone colocated and at rest wrt to the rod. In order to define the 'length' of the rod for a distant observer who is moving relative to the rod, one must specify exactly what procedures are used to measure the rod. Radar ? Lasers ? How will clocks in different locations be synchronised ? etc.

    Until terms like 'length' and 'contraction' are operationally defined, this discussion can't be expected to resolve anything.
     
  13. Apr 23, 2009 #12
     
  14. Apr 23, 2009 #13
    Hello phyti.

    Surely time dilation and length contraction are on a par. If one is "real" so is the other.

    Matheinste.
     
  15. Apr 23, 2009 #14
    evening matheinst

    The SR theory has one specific condition in its formation, preserving the constant speed of light. The transformation equations must satisfy this condition, even if it requires altering time, space, mass, etc.
    If you form the theory without this condition, only using constant speed of light where necessary, you discover reasons for the transformations. The reasons for each are not the same.
     
  16. Apr 24, 2009 #15
    Your statement does not seem logical or consistent.

    If we accept the speed of light as being constant and the same for all observers in relative inertial motion then the transformation equations must reflect this and we must accept the logical consequences whatever they are. If the consequences do not agree with observation then either the light axiom is wrong or the transformations are wrong. I have not come across a probelm with this yet.

    We accept the light axiom or we do not. We cannot just choose to accept it when it "where necessary". Perhaps I misinterpret what you meant by this.

    -----If you form the theory without this condition, only using constant speed of light where necessary, you discover reasons for the transformations. The reasons for each are not the same-----

    I assume you are saying that the reasons for the transformations are not the same for time dilation and light contraction when "only using constant speed of light where necessary ". I will not argue with this because I do not know why you say this. The words "If you form the theory without this condtion" I assume by this that you mean the condition of preserving the constancy of light speed. Could you, or perhaps anyone else, explain the meaning of these words.

    Thanks.

    Matheinste
     
  17. Apr 24, 2009 #16
    Form the theory using only the constancy of light, and without the condition of total symmetry, and see if the symmetry actually developes. Time dilation is the result of constant light speed. The length contraction is required because the moving observer calculates distances too long by a factor of gamma. This is because the assumed rest frame for the moving observer is not equivalent to a relative rest frame.
     
  18. Apr 24, 2009 #17

    JesseM

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    What do you mean by "form the theory"? Can you elaborate on what kind of derivation you're thinking of? For example, are you starting with the light clock thought-experiment?
     
  19. Apr 24, 2009 #18
    You wouldn't believe it if I showed you.
     
  20. Apr 24, 2009 #19

    JesseM

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    Uh, it's not a matter of "belief", a derivation is either valid or it isn't; if you could show a way for rulers and clocks to behave such that everyone would measure the speed of light to be c but rulers didn't shrink symmetrically in different frames, I'd certainly accept that. And if I didn't accept that I'd have to show a detailed scenario where all observers don't measure the speed of light to be c even if we adopt your assumptions about how rulers and clocks behave.

    One possibility that occurs to me is that we might try dropping the assumption that rulers don't change length if they're oriented perpendicular to the direction of motion; if we assume rulers do change length in the perpendicular direction when moving relative to some preferred "aether" frame, then it might be possible to have the first postulate of SR be false but the second be true.
     
  21. Apr 25, 2009 #20
    It seems you can't have a discussion about anything wihout defining words!
    Anyway here's hint. Referring to the MM experiment, the radial dimension perpendicular to the direction of motion (x) is dg (gamma). The x dimension is dgg. What do you make of it?
     
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