# Special Relativity Clocks

by JM
Tags: clocks, relativity, special
P: 231
 Quote by lugita15 Einstein was able to make a simpler theory which explained the same empirical results, but discarded the need for an aether by saying that the speed of light is genuinely the same in all inertial reference frames.
lugita, thanks for the clarification. Apparently we agree that Einsteins theory is based on experience. Somewhere I got the idea that some people disagree.
JM
P: 231
DaleSpam:
 Quote by DaleSpam I don't know why you would claim that. Isn't t the time according to clocks in the moving frame?
Einstein provided clocks that are stationary in each frame. Initially he said only that they are synchronized among themselves and with a "specified stationary clock'. The specified clock is not specified for the moving frame, so these clocks are, so to speak, idly waiting for instructions as to what clock they are to synchronize with. The analysis you quoted leads to a definition of the time of the moving frame t based on the X and T of the stationary frame. ( Actually it is Einstein's rigorous analysis, the quoted analysis is only to demonstrate principles.) The moving clocks can now synchroneze with t. In section 4 of part 1 Einstein identifies a clock "located at the origin of the co-ordinates of k ( the moving frame), and so adjusted that it marks the time t (my notation)". The adjustment appears to be the instruction to the moving clocks to use the values of X and T ( and v and c) and the relation for t = gamma(T-vX/c2) to produce a specific value of t.
I hope this clarifies my understanding.
JM
P: 231
Quote by harrylin
Do you claim that the rotation of the Earth and the seasons do not function as natural clocks?
 My point is that we can do little to change the things in nature that awaken us to the existence of time. But we can do what we like with the clocks we make, and what we do is arbitrary and suited to our particular need.
No, that would lead to self contradiction; light is simply defined to be isotropic wrt to the chosen reference system.
 You are right, Einstein defined the light speed to be the same in both directions. Then the relation between the clocks A and B became the starting point for his derivation of the transforms.
I think that that is quite right.
JM
P: 1,583
 Quote by JM lugita, thanks for the clarification. Apparently we agree that Einsteins theory is based on experience. Somewhere I got the idea that some people disagree. JM
JM, the point I was trying to make is that Einstein's theory is not the only theory that explains the experimental facts at hand. Lorentz's theory is also based on these same facts, but Einstein's is simpler, so it's preferred.
P: 231
 Quote by harrylin * Einstein distinguished these things better in his formulation of the second postulate in 1907, as follows (emphasis mine): "We [...] assume that the clocks can be adjusted in such a way that the propagation velocity of every light ray in vacuum - measured by means of these clocks - becomes everywhere equal to a universal constant c, provided that the coordinate system is not accelerated. [..this] "principle of the constancy of the velocity of light" PS. I forgot to add this link of Einstein's illustration of the train and the embankment: http://www.bartleby.com/173/9.html
Thanks for your comments. Can you tell me where the 1907 info is published?
JM
P: 231
 Quote by lugita15 JM, the point I was trying to make is that Einstein's theory is not the only theory that explains the experimental facts at hand. Lorentz's theory is also based on these same facts, but Einstein's is simpler, so it's preferred.
I accept this. I like Einsteins theory because the math is tractable and the physical principles are clear.
JM
P: 255
 Quote by lugita15 JM, the point I was trying to make is that Einstein's theory is not the only theory that explains the experimental facts at hand. Lorentz's theory is also based on these same facts, but Einstein's is simpler, so it's preferred.
Perhaps more importantly, GR is (AFAIK) the only working theory of gravity and it reduces to the Minkowski Metric as mass tends to zero. There is no equivalent approach that allows one to derive LET.
P: 231
 Quote by ghwellsjr OK, fine. Now do you accept Einstein's calculation for τ (tau), the rate at which a moving clock ticks in your stationary frame as a function of t, the rate at which the stationary coordinate clocks tick in your stationary frame and v, the velocity of the moving clock?τ = t√(1-v2/c2)
George: This formula comes directly from the transform equation t = ( T-vX/c2)/√(1-v2/c2), with the assumption that X=vT.
But is the formula intended as an example, or as a universal truth? Consider.....
All theclocks are synchronized, so that all clocks of K read T, not just the clock at X=vT,and all the clocks of k read t, not just the one at x=0. If X=0, thus 'pointing at the origin of K', t = T/√ ( 1- v2/c2), and t>T. Because of synch. this result applies also to the theclocks at the origin of k. The conclusion, seemingly, is that the moving clock at the origin of k can run slow or fast depending on the value of X.
So is 'slow clocks' a universal truth? I'm looking for help, yes or no, and why.
JM
PF Gold
P: 4,087
 Quote by JM lugita, thanks for the clarification. Apparently we agree that Einsteins theory is based on experience. Somewhere I got the idea that some people disagree. JM
Can JM ( or Lugita if he agrees with the above) state what experience it was that convinced Einstein that the speed of light must be constant ?
PF Gold
P: 4,737
Quote by JM
 Quote by ghwellsjr OK, fine. Now do you accept Einstein's calculation for τ (tau), the rate at which a moving clock ticks in your stationary frame as a function of t, the rate at which the stationary coordinate clocks tick in your stationary frame and v, the velocity of the moving clock?τ = t√(1-v2/c2)
George: This formula comes directly from the transform equation t = ( T-vX/c2)/√(1-v2/c2), with the assumption that X=vT.
But is the formula intended as an example, or as a universal truth? Consider.....
All theclocks are synchronized, so that all clocks of K read T, not just the clock at X=vT,and all the clocks of k read t, not just the one at x=0. If X=0, thus 'pointing at the origin of K', t = T/√ ( 1- v2/c2), and t>T. Because of synch. this result applies also to the theclocks at the origin of k. The conclusion, seemingly, is that the moving clock at the origin of k can run slow or fast depending on the value of X.
So is 'slow clocks' a universal truth? I'm looking for help, yes or no, and why.
JM
Yes, slow clocks is a universal truth in Special Relativity.

Einstein's derivation of the Proper Time on a clock moving at speed v as a function of t, Coordinate Time, in a frame comes from section 4 of his 1905 paper. Remember, Coordinate clocks always remain fixed at the locations at which they were synchronized within a particular Frame of Reference. If you look at his derivation, he starts off talking about "one of the clocks which are qualified to mark time t when at rest relatively to the stationary system". What he means is that there is a second synchronized clock located at the spatial origin of one reference frame prior to time zero which then becomes stationary in a second reference frame moving at v with respect to the first reference frame after their mutual time zero. He asks the question, "What is the rate of this clock, when viewed from the stationary system?"

So τ is the Proper Time of a single clock put in motion at time zero compared to the infinite number of Coordinate Clocks that remain stationary. We are comparing the time on this moving clock to the times on the adjacent clocks as it passes by them. The moving clock will always run slower than the stationary clocks. But remember, we are comparing one clock to a bunch of different clocks that have been previously synchronized.

So we always know the tick rate of a clock moving in a Frame of Reference by the simple formula expressed above.
P: 1,583
 Quote by GeorgeDishman Perhaps more importantly, GR is (AFAIK) the only working theory of gravity and it reduces to the Minkowski Metric as mass tends to zero. There is no equivalent approach that allows one to derive LET.
Yes, I was just talking about the facts underlying special relativity.
Mentor
P: 17,226
 Quote by JM The analysis you quoted leads to a definition of the time of the moving frame t based on the X and T of the stationary frame.
So then the analysis clearly did make use of clocks in both the moving and stationary frames.
P: 3,187
 Quote by JM See also my clarification in a later post. JM
I saw all your later posts, but no clarification that would affect my comments (or that of others).

 Quote by JM Thanks for your comments. Can you tell me where the 1907 info is published? JM
Sure, you can find it here: http://physicsforums.com/showthread.php?t=575526
With an illegal copy of a not-so-perfect translation linked in post #2.
P: 231
 Quote by DaleSpam So then the analysis clearly did make use of clocks in both the moving and stationary frames.
Are we talking semantics here?
Einsteins mathematical derivation of the transform of time begins with the equation defining the synchronization of the moving clocks. The light postulate is then used with geometry to develop the transform. The only feature of the moving clocks used in this analysis is the synch. relation. He later speaks of clocks qualified to mark the time of the moving frame. Since the time of the moving frame is defined by the transform, doesnt 'qualified' mean the clocks display the time given by the transform?
At this point there seems to be a choice. Either the clocks originally placed in the moving frame are 'programed' to display t, or additional clocks are supplied ( as we would use stop watches) to display t.
JM
P: 231
 Quote by ghwellsjr Yes, slow clocks is a universal truth in Special Relativity. So we always know the tick rate of a clock moving in a Frame of Reference by the simple formula expressed above.
George: I believe I understand your explanation. I have studied section 4 and my questions are:
Einstein refers to a clock qualified to mark the time t (my notation) when at rest relativily to the moving system and so adjusted that it marks the time t. This adjustment seems to mean that the moving clock displays the time t given by the transform, doesn't it?
Then he says "Between the quantities x,t,and τ, which refer to the position of the clock,..." (his notation), x and t being the coordinates of the stationary frame and τ being the time of the moving frame. By what justification does x refer to the position of the clock? In the transforms, as they are usually viewed, x and t are independent variables allowed over the range -∞ to +∞. If slow clocks is universal then x must be permanently restricted to the values x=vt. If x is an independent variable then there is no significance to where x is 'pointing' because all clocks read the same value wherever located.

JM
Mentor
P: 17,226
 Quote by JM Since the time of the moving frame is defined by the transform, doesnt 'qualified' mean the clocks display the time given by the transform?
"Qualified" just means that the clock keeps correct time. I.e. if it is at rest wrt some process that takes exactly 10 s then it measures 10 s as opposed to something like 11 s or 9 s.
 P: 231 George and DaleSpam, Are we done here? The discussion here leads to the suggestion that the 'slow clock' idea, with τt for x=0. Synchronization means that the result applies to all the moving clocks, including the one at the origin of the moving frame. Do you all accept this idea, or do we have some more to talk about? JM
Mentor
P: 17,226
 Quote by JM Do you all accept this idea, or do we have some more to talk about?
No, I don't accept the idea.

If you have a clock which is moving in an arbitrary fashion (including, but not limited to, x=vt) you use the following formula to calculate the time displayed on the clock:
$$\tau = \int \sqrt{1-v(t)^2/c^2} dt$$
http://en.wikipedia.org/wiki/Proper_...ial_relativity

The integrand is always less than or equal to 1, so you never get $d\tau>dt$ where t is the time coordinate in an inertial frame and v is the clock's velocity in that frame.

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