Which Clock Slows Down with Time Dilation?

[Hivoyer]

If you send an ultra precise clock circling at a huge speed on a train and leave a clock stationary near the rails and then compare them,there would be a small difference in the time they display,right?But if everything is relative,doesn't that mean that from the point of view of the people in the train and the clock in the train,it's the stationary clock that's moving?How do we know which clock gets slowed down?

 

[cragar]

they will both accuse the other person of their clock ticking differently.

 

[ghwellsjr]

The clock that is accelerating, changing its velocity by changing its direction, is the one that is slowed down relative to the one on the track which is not changing its speed.

Einstein explained this at the end of section 4 of his 1905 paper.

In order for the time dilation effect to be reciprocal, the two clocks must both be inertial, that is traveling in a straight line at a constant speed.

 

[bcrowell]

You may be interested in this actual implementation of the experiment you imagined: C.O. Alley, in NASA Goddard Space Flight Center Proc. of the 13th Ann. Precise Time and Time Interval (PTTI) Appl. and Planning Meeting, p. 687-724, 1981 (SEE N82-20494 11-36), http://www.pttimeeting.org/archivemeetings/index9.html

The only difference is that they used a plane instead of a train. Because the plane is up in the air, there is also a gravitational time dilation effect, which is comparable in size to the kinematic one.

 

[Naty1]

The clock that is accelerating, changing its velocity by changing its direction, is the one that is slowed down relative to the one on the track which is not changing its speed.

Close: EACH is ticking slower according to the other as they observe from an intertial... fixed velocity...perspective. But at the conclusion of the trip, when the clocks are compared side by side back at the original location, then

The clock that is accelerating, changing its velocity by changing its direction, is the one that is slowed down relative to the one on the track...

Who sees what depends on their frame of reference...

 

[ghwellsjr]

Close: EACH is ticking slower according to the other as they observe from an intertial... fixed velocity...perspective. But at the conclusion of the trip, when the clocks are compared side by side back at the original location, then

Who sees what depends on their frame of reference...

When does the clock on the circling train ever get to "observe from an intertial... fixed velocity...perspective"?

 

[GrayGhost]

The clock that is accelerating, changing its velocity by changing its direction, is the one that is slowed down relative to the one on the track which is not changing its speed. Einstein explained this at the end of section 4 of his 1905 paper.

Yes, I always found that interesting. The theory did not model acceleration. The 2 clocks are in motion wrt one another, and thus the moving clock must run slow over the defined interval. Both record the other in motion though. However, when Einstein proved the value and meaning of phi(of v), it became clear that the direction of motion was of no issue wrt the LT solns, then add that the theory was built upon the inertial POV. Thus, without even modeling the accelerating clock's own POV, we know what the end result must be. The accelerated clock experiences less duration over the defined interval. I'd imagine that this gave Einstein a good feeling in relation to his subsequent development of his equivalency principle, when defining his hypotheses on gravitation. I mean, I'd be surprised if it didn't.

GrayGhost