Firstly, hello. This is my first post at Physics Forums, and I want to thank everyone in advance for contributing their thoughts and expertise here.(adsbygoogle = window.adsbygoogle || []).push({});

I'd like some help with the following thought experiment. My apologies if I'm posing too basic a problem, but I haven't been able to find sufficient information on my own. I've divided the problem into parts so that it's easier to reference. I've also highlighted my major questions inboldso it is clear what I am asking.

The Three Clock Problem

PART 1 - The Stationary Platform

We have a long stationary platform of arbitrary length and minimal width. There are three atomic clocks (Clocks A, B and C ) that sit together at the midpoint of the length. The clocks are synchronized while together, and then Clocks A and C are very slowly moved to either end of the platform leaving Clock B at the midpoint. Seen from the side it looks like this:

A__________B__________C

Importantly, even if relativistic effects are taken into account for the movement of Clocks A and C, Clocks A and C should at least still be in sync with one another, since they both underwent equal (though opposite) accelerations and velocities.

PART 2 - Flashing the Clocks

Clocks A and C have also been fitted with photodetectors, and the middle Clock B has been fitted with a flash unit of some kind. If light is detected by either Clock A and C, tiny printers contained within the clocks will print out the current time as read from the respective clock.

So, at a predetermined time (t_{B}=0), Clock B releases a flash of light. The light eventually reaches Clocks A and C, and they in turn print out their times, t_{A}and t_{C}.

Since Clocks A and C are in sync with one another and their distances from the source (Clock B) are equal, the times printed by Clocks A and C should also be equal (t_{A}= t_{C}). Importantly, it does not matter what the values of t_{A}or t_{C}are, only that are equal.

Part 3 - The Moving Platform

The stationary platform is placed on a straight track of arbitrary length. And an Observer D is added to the scene beside the track. It now looks like this:

A__________B__________C

D

The platform is slowly transported some distance away from Observer D, then accelerated on the track to a significant fraction of the speed of light. Arbitrarily, we can say the platform's velocity is raised to 0.5c relative to Observer D's frame of reference, which by the way, is also the inertial frame of reference.

We now have this situation:

A__________B__________C (v=0.5c that way ----->)

D (v=0, stationary)

The Clocks have gone through both acceleration and velocity changes relative to D, but they should all still be in sync with one another since they underwent the changes together.

Now, Clock B has been set up so that when it nears Observer D, it will release a flash of light, again at t_{B}=0. And that's just what it does:

A_________*B*_________C (v=0.5c that way ----->)

D (v=0, stationary)

* * represents the flash

PART 4 - Special Relativity - What's going on?

(Please let me know if my understanding in this section is correct.)

From Observer D's frame of reference, light propagates outward from B's instantaneous location traveling at velocity c in all directions. And since the platform is moving at v=0.5c, Clock A advances toward the traveling wavefront while Clock C retreats away from it at a significant rate, like this:

A*_________B___*______C (v=0.5c that way ----->)

D

* * represents the wavefront.

So, from D's frame of reference, Clock A will appear to have detected the light "first" and Clock C will appear to have detected it "second".

Now, according to Special Relativity,in the frame of reference of the moving platform, when Clock B flashes, the light propagates outwards from the Clock B necessarily at velocity c in all directions.

So, just as described in Part 2 of this problem, in the platform's reference frame, the light should reach Clocks A and C simultaneously. Thusly, Clocks A and C, still in sync with one another, will print out their internal times and confirm that t_{A}is indeed equal to t_{C}.

As I understand it, the apparent mismatch of simultaneity between what Observer D sees and what Clocks A and C print out is a result of the Relativity of Simultaneity, as described here (http://en.wikipedia.org/wiki/Relativity_of_simultaneity). So, while counterintuitive, I can understand how Observer D would see one thing and the Clock printouts would say another.

PART 5 (Last Part) - Lorentz Ether Theory and the One-Way Speed of Light

(If everything else in this problem seems valid, then this is my big question...)

As I understand it, when applied to this current problem, Lorentz Ether Theory (LET) is functionally equivalent to Special Relativity (SR), i.e. the math works out in both theories, though LET postulates an unproven "ether" and does not require the speed of light to be constant within a reference frame.

So for just a moment, looking at the problem from an LET perspective, first assume that the "ether" is at rest in relation to Observer D.

When the platform moves past Observer D and Clock B flashes, the light propagates outward (through the stationary "ether") at speed c. Because of the motion of the platform, Clock A reaches and detects the wavefront first and Clock C detects it second.

Now, still assuming LET and switching to the reference frame of the moving platform, Clock A still reaches and detects the wavefront first and Clock C detects it second. This is becausein the platform's frame of reference, the wave front is moving towards Clock A at speed 1.5c and toward Clock C and speed 0.5c.

Since these clocks are in sync, the resulting clock printouts should read that t_{A}is less than t_{C}.

Assuming that all the previous logic holds up, the only observable difference between Special Relativity and Lorentz Ether Theory is the printouts of the Clocks. If SR is correct, t_{A}and t_{C}should be equal. If LET is a more accurate model, then t_{A}should be less that t_{C}.

If we did this as a real experiment, what would the printouts read?

Note: I believe this question is related to the isotropy/anisotropy of light and the one-way measurement of the speed of light. As far as I'm aware, all practical experiments to date have involved a round-trip measurement of the speed of light, and that a one-way measurement of speed is not possible at this time. In this Three Clock problem, however, speed is not attempted to be measured, only the simultaneity of the wavefronts arriving at Clocks A and C.Does anyone know of any experiments that might answer what the results of the clock printouts would be in real life?

Well, that's it.

If you've made it this far, THANKS FOR READING!

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# SR/LET Thought Experiment Help - Three clocks problem

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