Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Time dilation and Lorentz-Einstein transformations

  1. Nov 16, 2006 #1
    :rofl: Discussing with a friend, I was told that using in a derivation the time dilation formula I implicitly use the Lorentz-Einstein transformations.. I mentioned that many Authors derive time dilation without using the LET considering that the transformation equations obscure the physics behind the studied problem. Others derive the addition law of velocities without using LET based on time dilation and length contraction. My oppinion is that as long as we do not perform the transformation of the space-time coordinates of the same event we do not use LET. Your opinion is highly appreciated. Thanks
    At leasts in physics who is right should be right!
     
  2. jcsd
  3. Nov 17, 2006 #2
    To me its more instructive to proceed from the standpoint that all objects move through spacetime at c - and that the spacetime interval is invariant in all inertial frames. From this you get time dilation and length contraction in one step just as you do with the light clock
     
  4. Nov 17, 2006 #3
    time dilation let

    do you mean that the derivation does not involve LET?
     
  5. Nov 17, 2006 #4
    You can derive Lorentz transforms from the requirement that something moving with speed c in any frame must appear to move with speed c in all other frames.

    http://www.mth.uct.ac.za/omei/gr/chap1/frame1.html gives a pretty good outline of what must be done.
     
  6. Nov 17, 2006 #5

    robphy

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Here is an analogous statement:
    using in a derivation the "formula that says, in a right triangle, the length of the adjacent side is equal to cos(included angle)*(the length of the hypotenuse)" I implicitly use the "Euclidean rotation" transformations..
     
  7. Nov 17, 2006 #6
    thank you for your answer but my problem is that if I use in a paper the time dilation formula I use or I do not use explicitly the LET. In my oppinion time dilation has nothing to do with LET because in order to derive the formula that accounts for it it is not compulsory to use the LET. Of course LET accounts for it. I conider that I use LET only when I establish a relationship between the space-time coordinates of the same event.
     
  8. Nov 17, 2006 #7
    LET and time dilation

    Thank you for your answer. I am more interested in your oppinion about the fact that if I use in a derivation the time dilation formula or the length contraction I should use the LET.
    sine ira et studio
     
  9. Nov 18, 2006 #8
    The premise that all objects move at velocity c through spacetime is consequent to Minkowski - it is implied in LET - but not explicitly stated by either Einstein or Lorentz - so for me its an easier starting point than the constancy of light in all frames - better as a tutorial from my perspective since you get the time dilation and length contraction relationships in an easily to visualize diagram. As one goes through the derivation of the Lorentz transforms it is easy to lose track of the physical connection

    Regards

    Yogi
     
  10. Nov 18, 2006 #9

    robphy

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    That "all [massive] objects move at velocity c through spacetime" is merely the statement that we describe their 4-velocities as unit-timelike vectors (conventionally normalized to c).

    However, that in itself does not fully characterize the situation in special relativity [since the same situation is true in a Galilean spacetime]. Somehow, you have to specify the location of all of the tips of those 4-velocities [a hyperboloid for SR, a hyperplane for Galilean], which is almost the same as specifying the metric. Alternatively, one can use the null cone, which is almost the same as the postulating the "constancy of a maximal signal speed".
     
  11. Nov 18, 2006 #10

    Hurkyl

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    I'm confused; there isn't anything to normalize for 4-velocity vectors: they are exactly equal to
    d{coordinate position}/d{proper time}.​
     
  12. Nov 18, 2006 #11

    robphy

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Yes, that's true. Maybe I didn't make my point clearly.
    What I meant to say is that the statement "all [massive] objects move at velocity c through spacetime" by itself is empty without somehow specifying a metric.
     
  13. Nov 18, 2006 #12

    daniel_i_l

    User Avatar
    Gold Member

    one way to derive the time dilation formula is to use the invariance of the ST interval: t^2 - x^2 (assuming that you measure time in meters or distance in seconds - as long as everything is in the same units)is constant in all frames. for example, if there's a tunnel with length x in one frame and in that frame it takes time t for a rocket to go thru it then the ST interval between the first event (entering the tunnel) and the second (exiting) is t^2 - x^2. but in the rocket frame the distance between the events is 0 so: Trocket^2 = Trest^2 - Xrest^2.

    another way to derive it is with the famous paralell mirrors clock.
     
  14. Nov 18, 2006 #13
    time dilation and LET

    Thank you. I figured it out in connection with distant clock synchronization. Please give me some references where interval invariance is used in order to derive time dilation.
    The best things a physicist can offer to another one are information and criticism
     
  15. Nov 18, 2006 #14

    robphy

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    The standard "light clock" uses the invariance of the interval (declaring that a round trip by the light signal in an identically constructed light clock is one unit interval).
     
  16. Nov 18, 2006 #15
    light clock and other clocks

    I think that the light clock involves in its rest frame two clocks located on the two distant mirrors respectively. In the reference frame relative to which it moves, it involves a clock located where the first light signal is emitted, a clock located where the light signal arrives at the upper mirror and a clock located where the reflected light signal returns. Time dilation is the result of the synchronization of the mentioned clocks in theirs reat frames. That fact is not allways mentioned. Do you think that it is worth to mention it in the teaching process?
    sine ira et studio
     
  17. Nov 19, 2006 #16

    robphy

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    A light clock is formed from two inertial mirrors and a light ray that bounces back and forth between them. You may (for consistency) introduce other clocks... but, in my opinion, that is unnecssary for the operation of the light clock as a clock [at its natural resolution].
     
  18. Nov 19, 2006 #17
    light clock

    Thanks. I think that it is good to mention the other clocks when we consider the light clock out from its rest frame.
     
  19. Nov 19, 2006 #18
    It is true you need to be more rigorous to recover the complete transforms - but as a visual tutorial to display time dilation simply draw the t axis vertical, the space axis horizontal and construct a first quadrant arc of length ct centered on the origin. The intercept on the t axis is the spacetime interval ct (which is invarient from one frame to the other) in the frame selected to be at rest, the length vt along the space axis is the distance traveled by a clock in the moving frame during the time t, the vertical line drawn from the point vt to intercept the arc gives the length (ct') logged by the moving clock. The line from the origin to the intercept is the hypotenuse (also ct), therefore

    (ct)^2 = (vt)^2 + (ct')^2
     
  20. Nov 20, 2006 #19
    time dilation and let

    most of the answers did neglect my original question: If I use in a derivation the time dilation formula and I am told that I use implicitly the Lorentz-Einstein transformation, is my discussion partner right or wrong?
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?