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Synchronized Clocks in Frames boosted by Acceleration 
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#1
Dec512, 04:32 AM

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I have often thought about how the oneway speed of light can be measured without having to use synchronized clocks, which tends to be controversial because the clocks are normally synchronized by using oneway light in the first place. Recently, Don Lincoln of FermiLab suggested a method to me. To convince myself, I tested it in a thought experiment, using two clocks and two cables in a frame that is boosted by accelerating it to a new inertial frame. I thought it useful to share it and get other opinions.
First, Don Lincoln's test. Consider two spaceships connected by a taut cable of 600 units long. Add Don’s second identical cable, folded back and strapped at the halfdistance point (for ease of presentation) so that the setup becomes equivalent to his scenario, with the cables calibrated for identical transmission times. Accelerate the whole ‘lab’ lengthwise to 0.6c in such a way that the cables do not stretch (Bornrigidity) and let it coast again. I used the Rindler coordinates equation [itex]t = \sqrt{x^2\sigma^2}[/itex], where [itex]\sigma[/itex] is the distance of the start of the curve from the origin (1 and 1.6 units respectively). The origin coincides with the common light cone of Rindler observers with constant proper acceleration ([itex]a[/itex]), where [itex]a =1 / \sigma[/itex]. The other relevant equations are: [itex]\tau = \sigma[/itex]asinh(a t) and v/c = tanh(a [itex]\tau[/itex]). The spacetime diagram is a tad busy, but gives an overview of all the values calculated for the acceleration phase and the later cruise phase. Click on the thumbnail below if you do not see the diagram. For simplicity, use a cable with a signal speed of exactly 0.6c, so that a signal takes exactly one time unit to travel the length of the cable. After the acceleration, the speed of the pulse relative to the original reference frame is [itex](0.6\pm0.6)/(1+0.36)[/itex]c, i.e. 0.882c in the forward direction and zero in the return direction. In the reference frame the acceleration lasts for t=0.75 units for the blue ship and t=1.2 units for the front ship. The corresponding ship proper times are [itex]\tau_{blue}[/itex]=0.69 and [itex]\tau_{red}[/itex]=1.11 units. The latter clock must be set back by 0.42 units to [itex]\tau'_{green}[/itex]=0.69 units in order to be synchronized with blue again. The pulse in cable 1 is transmitted simultaneously with the laser pulse and arrives back at the oscilloscope at [itex]\tau_{blue}[/itex]=1.69, while the cable 2 pulse arrives at [itex]\tau_{blue}[/itex]=2.29. This gives a time delay of 0.6 units, which is the travel time of the laser pulse. Since we expect the proper length of the cable to remain the same before and after acceleration, this seems to indicate that it is a true clocksyncindependent measurement of the oneway speed of light in an inertial frame. If correct, this also means that calibrated cables can be used to synchronize distant clocks without slow transport involved. 


#2
Dec512, 09:07 AM

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You should read the wikipedia article on the oneway speed of light. You will see that you have misunderstood what Don was telling you or else he has fooled himself and you. You cannot measure the oneway speed of light, period. All attempts, no matter how complicated or subtle, either are measuring the twoway speed of light or are in fact using the equivalent of synchronized clocks.
You and/or Don have made the faulty assumption that the propagation of an electrical signal down a cable is a constant no matter the orientation of the cable. Suppose that in his setup, you start with the two 1000foot cables stretched out 500 feet away and back. You are assuming that the time it takes for the signals to get 500 feet away is identical to the time it takes for the signals to get back so that when you stretch out one of the cables the full length it will take the same time to go oneway as it did to go both ways for half the distance. Can you see that this is flawed? 


#3
Dec512, 09:43 AM

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#4
Dec512, 09:54 AM

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Synchronized Clocks in Frames boosted by Acceleration
You need the signal speed in the cable to be the same both ways. This is similar to moving objects (or sending light) between the spaceships.



#5
Dec512, 10:51 AM

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#6
Dec512, 11:00 AM

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In the original form, everything is being done in the lab frame, and the calibration process IS a clock synchronization process  the cables are clocks (easily synchronized clocks, but impractical for general use because they only tick twice so can only make a single measurement). The only possibly questionable assumption is the assumption that the signal propagation time won't depend on whether the cable is laid straight or coiled; that assumption can be verified experimentally. This synchronization process falls apart completely as soon as the cable is set in motion, as in OP's spaceship version. So, although I see nothing wrong with Don Lincoln's oneway measurement, it's still a synchronizedclock measurement; and OP's spaceship variant does not provide a counterexample to teh need for twoway measurements. 


#7
Dec512, 11:09 AM

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#8
Dec512, 11:44 AM

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#9
Dec512, 01:01 PM

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#10
Dec512, 01:10 PM

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So I decide that a reasonable simultaneity convention is that the transmission time of a signal (the signal speed need not be, and probably isn't, the speed of light) in the cable is constant provided the cable remains at rest relative to me. Hence my claim that the cable, after appropriate testing, IS a synchronized clock; and in the future I can use my calibrated cable as a pair of synchronized clocks without repeating the calibration process. But of course all this does is prove that the detectors at the ends of my cables can be used as synchronized clocks. There's no challenge here to the fact that a oneway measurement requires a synchronized clock; instead I claim that a synchronized clock is hidden in Lincoln's formulation of the thought experiment, and OP has inadvertently lost it. 


#11
Dec512, 01:55 PM

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Why did we bother with the electrical cables? We already know that when we do this experiment with light and a mirror that we cannot say that the time it takes for the light to propagate in both directions is the same unless we arbitrarily define them to be the same. If we cannot say that they are the same for light in free space, then we cannot say that they are the same for the electrical signals in cables. 


#12
Dec512, 02:49 PM

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The problem is that you earlier said in post #6 that you saw nothing wrong with Don Lincoln's oneway measurement but his claim was that the oneway speed of light can be measured without having to use synchronized clocks. It would have made more sense if you had pointed out that there was something wrong with Don's claim because he was in fact not measuring the oneway speed of light but rather defining it by using the virtual synchronized clocks of his cables. 


#13
Dec512, 03:02 PM

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Secondly, propagation speed in a real cable has different dynamics than a pulse of light in vacuum, e.g. a real observer can comove with a pulse in a cable. Is it correct to sweep this difference under the carpet when replacing the cables with light pulses? I'm happy either way, but I'm simply not convinced by your argument up to this point. 


#14
Dec512, 03:29 PM

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#15
Dec512, 09:45 PM

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To further illustrate, if we bring the two clocks slowly together after the acceleration, we expect them to be out of sync. If we bring the two ends of the straightened cable together again, I expect the cables to still have the same simultaneity as before the acceleration, i.e. I do not expect to have to adjust their lengths to show local simultaneity, ala Lincoln's test. I may be wrong on the latter, but then I want to understand why. 


#16
Dec512, 11:10 PM

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#17
Dec512, 11:50 PM

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#18
Dec612, 12:23 AM

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If you understand that claiming to be able to measure the oneway speed of light is equivalent to the claim of being able to identify the absolute rest state of ether, then you will not be enticed by any such claim. It may take a lot of detailed analysis to identify the flaw in these claims, which is what Zhang has done, but for me, it's like a claim to have invented a perpetual motion machinethe US patent office has no interest in any such claimand I have no interest in analyzing the details of these complicated schemes that claim to measure the oneway speed of light. The simple ones, like slow transport of clocks or Don's scheme I'll take on but not much beyond those. 


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