Time Dilation: Stationary vs. Moving Atomic Clocks

[robphy]

But it's also important to understand that even if you measure time using a different type of clock, like an atomic clock based on regular oscillations of cesium atoms, then if there's one frame where a light clock and a non-light-clock agree on the length of 1 second when they're at rest next to each other, then as long as the postulates of relativity are true, they must agree with one another in all frames.

Yes, that's very true.
But that argument might be best left to the end of the discussion...
to keep clean the logic of how far the lightclock can go in providing a standard of measurement in spacetime [probably analogous to specifying a unit circle for geometric constructions on the Euclidean plane].

In other words, from the lightclock construction alone, you have the tools to measure spacetime intervals [in units of ticks] and derive all of the kinematical "relativistic effects" [time-dilation, length-contraction, relativity-of-simultaneity, doppler, aberration, and even the Lorentz Transformations]. In fact, they can all be derived graphically on a spacetime diagram [as well as algebraically and trigonometrically].

Then, you can argue [as you do above, using the relativity principle] that you don't have to use a lightclock... but the lightclock is simpler to analyze than other timepieces. [You don't have to, say, model the mechanics of a rotating hand of a stopwatch in motion.]

 

[longshinewoole]

Why do you keep saying this? I've told you over and over again that I'm just saying that if you actually measure the time with clocks, you will find that this agrees with the time calculated by d/v. They are two separate methods of getting the time, which always end up giving the same result. To use the clock method, you'd have to actually check the times on the clocks, you couldn't just calculate d/v and assume that'd be the time interval.

I think this was where you people misunderstood things and still did not realize. It is true if we actually measure time with clocks, we will find that this agrees with the time calculated by d/v. I totally agree. But your interpretation is quite untrue. Let me repeat my simple example:

distance D__________ E.
distance F____________________G.

Let DE represent the height of the triangle in your thought experiment, and FG the hypotenuse. We let light move on them. We will get two time intervals DE/c and FG/c. If we use clocks to measure, we shall get two time intervals equal to DE/c and FG/c respectively. Ture as you said.

Your interpretation of these two different time intervals was: the clock that measured DE was running slower, time dilation. I believe such an interpretation was untrue.

The true interpretation should be: why the clock measured a shorter time interval was because the distance was shorter. Or, why DE/c is smaller than FG/c was because DE was shorter than FG.

I am sorry I do not wish to answer your other questions. Doing so would expand the discussion beyong my ability. I am just a leisure hobby reader. I believe language is used to identify objects we use in any experiment. If we did not use one, we should not mention it.

Please rewrite your thought experiment and try to leave out the words clocks and measure. Telling the truth you will use the height and hypotenuse to obtain times. And see what would happen.

 

[JesseM]

Your interpretation of these two different time intervals was: the clock that measured DE was running slower, time dilation. I believe such an interpretation was untrue.

The true interpretation should be: why the clock measured a shorter time interval was because the distance was shorter. Or, why DE/c is smaller than FG/c was because DE was shorter than FG.

And what if you use a clock whose measurement of time has nothing to do with dividing distance by velocity, like the rotating of the gears in an ordinary mechanical clock, or the oscillations of atoms in an atomic clock? How does it make sense to say that the moving clock measured a shorter time "because DE was shorter than FG"?