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Lorentz Transforms Rule

  1. Dec 5, 2006 #1

    JM

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    It's my impression that the derivation and use of the Lorentz transform can be explained clearly and completely using ordinary math and physics of the college level. What then is the reason for the emphasis on the mysteries of slow clocks, shrinking rulers, and the twin paradox?
     
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  3. Dec 5, 2006 #2

    robphy

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    While the mathematics is relatively simple, the physical interpretation by way of observations and thought-experiments is highly-nonintuitive [for us]. (Mathematics is probably too abstract for the general audience.)
     
  4. Dec 5, 2006 #3

    JM

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    Thank you for your response, robphy. Part of ordinary physics is the interpretation of Lorentz transform results as describing the physical behavior of light waves. This interpretation seems to me to be sufficient. Is there some reason to follow a different interpretation? Could you elaborate on what observations and thought-experiments you have in mind?
     
  5. Dec 5, 2006 #4
    I think that clock synchronization is the first step each learner should go through. Combined with the concept of space-time coordinates of the same event in two inertial reference frames in relative motion a combination of math and phys leads to the Lorentz-Einstein transformations.
    sine ira et studio
     
  6. Dec 5, 2006 #5

    JM

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    Do you find that you need to follow any interpretation other than the ordinary physics view that the results represent the behavior of the light waves? Can you direct me to your derivation?
     
  7. Dec 5, 2006 #6
    The results represent the behavior of all physical objects and fields. Do I misunderstand the question? That the math is simple doesn't mean that the results aren't weird.
     
  8. Dec 5, 2006 #7

    robphy

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    The behavior of light rays [which have finite speed] under the Lorentz transformation has implications for the non-intuitive notion of time in relativity. [Radar experiments are the probably the best ways to see them.] I think that various effects are emphasized in introductions to relativity in order to challenge the Newtonian common sense of students... which unfortunately [in many standard treatments] just seems to leave most of them confused.
     
  9. Dec 6, 2006 #8
    Let

    I think that it is not the behaviour of of the light wave but the behaviour of a light signal what is essential. That is why many instructors consider that the radar detection procedure of the space-time coordinates of the same event is a transparent way to derive the LET.
    Please have a critical look at


    arXiv.org > physics > physics/0602054
    abstract

    Starting with a thought experiment proposed by Kard, which derives the formula that accounts for the relativistic effect of length contraction, we present a "two line" transparent derivation of the Lorentz-Einstein transformations for the space-time coordinates of the same event. Our derivation make uses of Einstein's clock synchronization procedure.

    Thanks for answering my thread.
    the best things a physicist can offer to another one are information and constructive criticism
     
  10. Dec 6, 2006 #9

    JM

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    The Lorentz transforms are derived for the physics of light (electrodynamic) waves. By what reasoning are these equations applicable to solid bodies?
     
  11. Dec 6, 2006 #10

    JM

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    Examination of the physics of light implicit in (Einsteins) derivation of the LET reveals the mechanisms required to satisfy the Light Speed Postulate. Each term of the LET is related to these mechanisms. The procedure uses the same principles a student of physics already knows. Results calculated by LET for a spherical wave of light reduce to known results for an ordinary wave. I think this approach is less confusing than others.
    Can you suggest a reference for the radar experiments?
     
  12. Dec 6, 2006 #11

    JM

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    Prof. Rothenstein, Thank you for your information. I will look into your derivation.
     
  13. Dec 6, 2006 #12
    .
    Can you suggest a reference for the radar experiments?[/QUOTE]
    Please have a critical look at


    arXiv.org > physics > physics/0409121

    Physics, abstract
    physics/0409121


    Three levels of understanding physical relativity: Galileo's relativity, Up-to-date Galileo's relativity and Einstein's relativity: A historical survey


    We present a way of teaching Einstein's special relativity. It starts with Galileo's relativity, the learners know from previous lectures. The lecture underlines that we can have three transformation equations for the space-time coordinates of the same event, which lead to absolute clock readings, time intervals and lengths (Galileo's relativity), to absolute clock readings but to relative time intervals and lengths (up-to-date Galileo transformations) and to relative clock readings time intervals and lengths.
    a paradox is that in our era there are more Authors then readers
     
  14. Dec 9, 2006 #13

    JM

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    I note some comments on radar methods. Checking references I didn't find what I wanted. Consider: Basic radar records the time of emission and return of the reflected signal to obtain position of the reflecting body. Pulses in succession determine velocity. If the body has reflective surfaces on its near and far sides a single pulse will produce two reflected pulses arriving at different times. It seems that these two reflections can be used to determine the length of the body. For a stationary body L=(ct3 - ct2)/2, where ct3 and ct2 are the second and first recieved reflected signals. For a body in motion the calculation is complicated, but if I didn't make a mistake, it shows that the length is the same, i.e. the measured length does not depend on the speed of motion. Has anyone done this already?
     
  15. Dec 9, 2006 #14
    radar detection

    As far as I know the radar detection procedure for the space-time coordinates of the same event leads to the conclusion that depending on the way in which the mirror moves (incoming or outgoing) time and space coordinates transform via the Bondi factor k. Distances and time intervals behave in the same way. Giving google to look for Bondi you will find the papers related to the subject. If I remember well Rosser in his Introduction to Special Relativity treats the problem.
    sine ira et studio
     
  16. Dec 9, 2006 #15
    I don't know if this is helpful for JM, but it's possible to derive the Lorentz transformations without the second postulate but only assuming

    * Principle of Relativity (first postulate)
    * Isotropy of space
    * Homogeneity of space and time
    * Causality

    When you do this, you find there are only two choices for transformations between inertial frames that are consistent with these assumptions

    * Galilean transformations
    * Lorentz transformations

    No discussion of light rays or any other kind of electromagnetic interaction is needed. The Lorentz transformations thus derived will have a parameter with the units of velocity that must be bounded from above for causality to hold (let's call it "c"). You can then use experiment to choose between these transformations and fix the value of the parameter.

    This is done in Doughty, Lagrangian Interaction (section 5.5). He refers to two papers from the 1970s in the American Journal of Physics (vol. 43, pages 434-437 and vol. 44, pages 271-277).

    Rindler, in his book Essential Relativity in a section titled "Special Relativity without the Second Postulate", refers to a paper from 1910 and another from 1921, so it seems to be one of those bits of knowledge that is periodically forgotten and remembered. (This has also come up on the forum before.)
     
  17. Dec 10, 2006 #16
    radar detection

    it is up to jm to decide. have you ever tried to teach SR that way?
     
  18. Dec 10, 2006 #17
    I think the derivation is too lacking in concreteness for a first introduction, but
    it does point up the fact that the LT does not depend on properties of electromagnetic radiation or interaction of any kind. I also find it fascinating that if you make the assumptions above and crank through the logic and math that the Galilean and Lorentz transformations pop out.

    Worth looking up if you have access to a library that carries Am. J. Phys. or the books mentioned above.
     
  19. Dec 10, 2006 #18
    that is my opinion as well and I am fond of simple and special relativity with human face. I know the papers and I think that it is hard to teach them without mnemonic helps i.e. without using notices during the lecture a condition I consider making part from the deontology of teaching. Thanks for your answer and help.
     
  20. Dec 10, 2006 #19

    Doc Al

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    Sure.
    OK.
    Why don't you show what you did that led you to that conclusion.
     
  21. Dec 10, 2006 #20

    JM

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    The focus of this discussion is whether moving objects actually contract or whether the calculated shortening is caused by the method of measurement.Einstein said that the moving object 'appeared to contract'. French says that the contraction is not in the body,but in the measurements. I note in one of your papers is a figure that shows both contraction and dilation. Is there general agreement that physical bodies do not change length?
    The radar methods that I have seen don't appear to use both projected and reflected rays, but use only the projected ray. The quantity of my interest is the length of the moving body, not coordinates. My proposed radar method uses both rays and a single observer to eliminate the moving observer.
    Does this clarify my question posed in my radar comment.
     
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