# Special Relativity Clocks

1. Mar 17, 2012

### JM

Clocks and time are not the same thing. Time is a property of nature observable as changes. Day turns to night, summer follows winter, and rivers flow downstream. Clocks, however, are man made objects that do what we tell them to do. For everyday use we regulate clocks to match the noon-to-noon interval,we use stop watches to compare race contestants, and for rocket launches the clocks count backwards.
Asserting the relation for synchronizing clocks ( Einstein, 1905) ta1+ta2 =2 tb represents the use of the isotropic nature of light to tell the clocks a and b how to relate to each other. Taking t(X,Y,Z,T) as the time of the moving frame, and entering the coordinates of the stationaryframe X,Y,Z,T for the light emission at ta1,the reflection at tb, and the return at ta2 (taking account of the Postulate of Constant Light Speed ) leads to the transform relation t = (T-vX/c2)/√(1-v2/c2). When entering values of X and T as independent variablesthe dimensions of t are the same as those of T. The analysis as a whole suggests that t is a time assigned to the clocks of the moving frame by the properties of light, and is not related to any everyday time the clocks might have. SR time is more like a stopwatdh, measuring t and T as each frame has its own view of the light wave.
For me, these ideas greatly clarify SR clocks, any one else?

2. Mar 18, 2012

### lugita15

You're right that Einstein synchronization convention, like all conventions, is an arbitrary choice we make, not a property of time itself. And the fact that the one-way speed of light is constant according to it is just a logical consequence of our arbitrary definition, not something fundamental to nature. But as this long thread will attest, the story arguably doesn't end there. There are other synchronization conventions like slow clock transport, just as arbitrary as Einstein's, but having the property that the value of the one-way speed of light according to them is an empirical property of the universe, not just a trivial consequence of our definition.

3. Mar 18, 2012

### pervect

Staff Emeritus
As far as science goes, we aactually need something to measure time, before we can do much with it.

Abstract discussions of what time is, in a philosophical sense, really belong in the philosophy forum.

And on a philosophical level, I'd personally disagree - time IS what we measure with clocks, at least this works better than some of your other suggestions. For instance, the seasons - which change in length, as the Earth's rotation gradually slows. Modern clocks actually measure something more fundamental than the cycle of the seasons.

But this is ultimately philosophy, and one can debate it endlessly -because it has no experimentally testable consequences.

Meanwhile, science can tell us a lot of usefull things about how clocks behave - and about how the seasons behave as well - because it's about things we can actually measure, and questions can actually be settled by pointing to experiment, rather than debated without end and without any resolution.

4. Mar 19, 2012

### Staff: Mentor

Note the subtle difference in these two statements that actually makes them compatible. JM's statement that clocks and time are not the same thing is a strawman caricature of pervect's statement. You can do the same thing with other measurable quantities.

"Mass is a scale" vs. "mass is what we measure with a scale"
"Temperature is a thermometer" vs. "temperature is what we measure with a thermometer"

People who like to agonize and philosophize over time like to attack the first statement while scientists like to make the second statement. It explains partly why scientists have so little patience for the discussion.

5. Mar 20, 2012

### JM

The key to Einsteins theory is his Light Postulate. As I understand it, he based it on emperical evidence, Michaelson et al. OK?

6. Mar 20, 2012

### JM

I hadnt intended a philosopical discussion. But rather an attempt to understand Einsteins relativity. He places clocks in his two frames without stating basis or calibration ( re day, no.of seconds per day). There has resulted endless debate about the relation of the two sets of clocks. My conclusion that the time of the moving frame is assigned, and that the everyday time of the moving frame has no bearing ( when viewing from the stationary frame ) seems to me to resolve these discussions.
If clocks are man made, what does science say about their behavior?

7. Mar 20, 2012

### ghwellsjr

And his Principle of Relativity Postulate. It's no wonder you have issues with your next post if you leave that out.
If you want to understand Einstein's Special Relativity, you need to accept the answers that you are given by people who already understand it instead of putting up resistance to them.

Do you know what Einstein means by a Frame of Reference? Do you know how he defines it? Do you understand that it is based on, not just man-made clocks, but man-made rulers and man-made protractors and man-made structures? A Frame of Reference is entirely man-made and so is all of science. Why this fixation on just the clocks?

And most importantly, how can you tell which is the moving frame that has no bearing with regard to time because it is assigned and which is the stationary frame for which time has bearing and for which time is not assigned?

8. Mar 20, 2012

### lugita15

Well before Einstein, theory of relativity came out, Lorentz explained the results of the Michelson-Morley experiment in terms of aether. He said that objects moving with respect to the aether are contracted by the aether, and clocks moving with respect to the aether slow down. Thus Lorentz could explain why the speed of light seemed to be the same in all frames: it was because the rulers and clocks used to measure the speed of light were inaccurate because of length contraction and time dilation. But then it was found (not by Einstein, I might add) that the Lorentz transformation related not only the aether to other frames, but also other frames to each other. Thus Einstein's theory of relativity distinguishes itself from Lorentz's theory by treating all frames as equal, and thus saying that the speed of light really is the same in all frames.

9. Mar 20, 2012

### JM

The two frames are equivalent. One could choose either one and the properties would be the same. I chose to 'view from the stationary frame' as Einstein named it. The moving frame is the one with velocity v in the X direction of the staationary frame.

10. Mar 20, 2012

### JM

So, do you think that he based his light postulate on empirical results?

My apologies for not knowing how to work the 'quotes'.
JM

11. Mar 20, 2012

### 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)​

12. Mar 20, 2012

### lugita15

Maybe I wasn't clear enough. Lorentz had a theory which said that things moving with respect to the aether experience length contraction and time dilation. 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.

13. Mar 24, 2012

### JM

George, Here is a more considered response to your post #7.

I have read a lot of books and papers on SR and have not found the answers to my questions. The authors are not available to me so I am trying on my own to understand what it is that they are saying. I hope this forum can help. The question under discussion in this thread is 'what is the relation between the clocks of the stationary and moving frames?' My understanding is given in post #1 with the following addition.
A light ray starts at the origin of the stationary frame K and reaches the location X at time T. During this time the origin of the moving frame advances a distance vT, leaving the distance X-vT for the light to travel to reach X. The light postulate says that the light travels at speed c in both frames, so X=cT, and X-vT=ct. Combining these equations leads to t=T-vX/c2. This is exactly the approximation of the Lorentz transform for v/c<<1. This analysis did not make any use of the clocks of the moving frame.
My conclusion is that the time of the moving frame is determined (assigned ) by the light postulate, and is independent of any'everyday' time the moving clocks might have.

Do you agree?

14. Mar 24, 2012

### GeorgeDishman

What science tells us is that, if you draw a spacetime diagram of say the twin paradox, clocks measure time in the same way that an odometer would measure distance if the diagram showed two cars driving across a salt lake. Newton assumed they would work like altimeters in a balloon and a plane taking different paths to reach the same altitude. If you think of Einstein's statement that "time is what a clock measures" and then understand what that says about the nature of time itself, SR will start to make sense.

15. Mar 25, 2012

### Staff: Mentor

I don't know why you would claim that. Isn't t the time according to clocks in the moving frame?

16. Mar 25, 2012

### Mentz114

I think Einstein tried to imagine what would happen if one caught up with and passed a light pulse. This could happen if the speed of light was not the same for all observers. He found the idea had absurd consequences and did not fit in with Maxwell's equations. However, if SoL is the same in all frames, order is restored and Maxwell's equations are not violated. See "The Electrodynamics of Moving Bodies".

17. Mar 25, 2012

### harrylin

Do you claim that the rotation of the Earth and the seasons do not function as natural clocks?
Another natural clock is set up with C14; the oldest clock is the rotating Earth (providing days), then refinements came in the form of sun dials and mechanical clocks.

No, that would lead to self contradiction; light is simply defined to be isotropic wrt to the chosen reference system.
I think that that is quite right.

18. Mar 25, 2012

### harrylin

Nearly so: the light postulate commonly includes the synchronisation convention, however a convention is itself not a postulate and the light postulate doesn't prescribe what people should do*.
By the way, this convention was already in use before special relativity. For practical reasons astronomers had to assign times to distant events, and this was done by assuming the same speed of light in all directions. And note that the times of both frames (also the stationary frame) are assigned by the synchronisation convention.

* 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

Last edited: Mar 25, 2012
19. Mar 27, 2012

### 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

20. Mar 27, 2012

### JM

DaleSpam:
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