SRT Clocks Again Einstein, 1905: Q&A

[exmarine]

Einstein, 1905:
From this there ensues the following peculiar consequence. If at the points A and B of K there are stationary clocks which, viewed in the stationary system, are synchronous; and if the clock at A is moved with the velocity v along the line AB to B, then on its arrival at B the two clocks no longer synchronize, but the clock moved from A to B lags behind the other which has remained at B by 1/2 tv2/c2 (up to magnitudes of fourth and higher order), t being the time occupied in the journey from A to B.

My question: Does the A clock have to be stopped (brought to rest, “stationary”) when it reaches location B? Does it make any difference? If it is stopped, does it resume running at the proper rate?

 

[Bill_K]

Does the A clock have to be stopped (brought to rest, “stationary”) when it reaches location B?

No

Does it make any difference?

No

If it is stopped, does it resume running at the proper rate?

Yes

 

[exmarine]

So if A is accelerated it slows down, and if decelerated it speeds up? How does it “know” the difference? That may be a clumsy way to ask the question, but I can’t figure out a better way.

 

[1977ub]

If you are traveling with the clock, you don't see any difference. When A is measured to be traveling relative to those in the rest frame, A's clock is measured to run more slowly by them. The faster A is measured to be traveling relative to them, the slower A's clock is measured to be running.

 

[pervect]

So if A is accelerated it slows down, and if decelerated it speeds up? How does it “know” the difference? That may be a clumsy way to ask the question, but I can’t figure out a better way.

There isn't any absolute time, or master universal clock, so statements likes "clocks slowing" or "clocks speeding up" have to involve a pair of clocks, not just one.

In Special Relativity, the clock that reads the longest time between two events in space-time will be the one undergoing inertial, unaccelerated motion.

An accelerating clock that passes t hrough the same two events will (in SR) always read a shorter time than the inertial clock.

Furthermore, if you wish to compare clocks that aren't at the same exact point in space-time, the answer depends on the particular observer - in particular their notion of what events are simultaneous. Just as there is no universal "master clock", there is no universal notion of what "now" means. Different observers have different (and just as correct) notions about the topic.

 

[exmarine]

So are you saying that Einstein’s clock A only *appears* to run slower to a “stationary” observer (with clock B in that frame)?

 

[tiny-tim]

hi exmarine!

So if A is accelerated it slows down, and if decelerated it speeds up? How does it “know” the difference? That may be a clumsy way to ask the question, but I can’t figure out a better way.

the simplest way of "knowing" is to use a clock consisting simply of a ray of light bouncing between two mirrors on the side walls of the spaceship (ie perpendicular to the direction of travel)

then each "tick" of the clock is the ray hitting one or the other mirror

(the spaceship observer of course regards the rate of this clock as constant)

the stationary observer, also, can tell the time on the spaceship clock by observing the ticks …

he does notice that it's slowing down (because it's zigzagging, and so has to travel further)!

 

[1977ub]

So are you saying that Einstein’s clock A only *appears* to run slower to a “stationary” observer (with clock B in that frame)?

If A is initially confident that his clock is synchronized with B - by sending light signals back and forth - then A travels to B's location, experiencing acceleration and deceleration, then they both A & B confirm that A's clock as ticked fewer times than B's.