SR/LET Thought Experiment Help - Three clocks problem

[Agrippa2]

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.

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 in bold so 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 because in 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!

 

[Dale]

Hi Agrippa2, welcome to PF!

Sorry I don't have time to respond to more, your problem set up is very detailed and introduces some things that I suspect you did not intend. However I just wanted to quickly comment on this:

the only observable difference between Special Relativity and Lorentz Ether Theory is the printouts of the Clocks.

There are NO observable differences between SR and LET. Both SR and LET are essentially different interpretations of the Lorentz transforms, which each uses to make all experimental predictions.

 

[ghwellsjr]

First off, I want to thank you for your detailed and thorough explanation of your questions--it's kind of rare here, usually it takes a lot of posts to figure out what the poster is asking. The only problem, I think, is that you intended for D to be directly under B in your diagrams but the font for entering the message is different than the font for displaying it and so D has moved to the left, at least on my screen. If you see this you can do what some other people do which is to use periods instead of spaces to position D.

There's no problem with your first two parts but part 3 has a problem. You have assumed that when a rigid platform is accelerated, all parts of it experience the same acceleration which cannot be true because the platform contracts which means the two clocks will no longer be in sync. This pretty much screws up the rest of your analysis.

In order to synchronize clocks in a Frame of Reference, you have to do it after the objects have achieved their final inertial state. So if in part 3, you brought the two clocks back together (the opposite of what happened in part 1) you would see that they are no longer in sync. This is kind of like the twin paradox where clocks are separated and brought back together but not symmetrically so they end up with different times on them, even though they start out and end up running at the same rate.

In part 4, if you properly synchronize the clocks, then they will indicate the same time on their printers (but realize this is only because you synchronized them so this would happen). This then will be a correct demonstration of the relativity of simultaneity.

If it were possible to do an experiment that would get different results under LET and SR, then it would be possible to identify an absolute ether rest state--not going to happen.

 

[Dale]

Hi Agrippa2, ghwellsjr essentially covered the point I was going to make. The exact details of the acceleration are important. Depending whose measurements of simultaneity and acceleration you use you can get the clocks desynchronized in different frames. What would probably be easier to analyze and closer to your intention would be to accelerate them all together and then do the synchronization/separation procedure you mentioned. That way all scenarios experience the same accelerations post-synchronization.