I Synchronizing clocks at different locations to measure speed of light

[pervect]

As I think about the issue more, I h ave to note that my calculations were NOT based on an experimental defintion for energy (or momentum), but rather on symmetry principles, i.e. Noether's theorem.

Most active posters in this thread are already familiar, but for any lurkers who may not be, I'll point to the wiki article, https://en.wikipedia.org/wiki/Noether's_theorem.

I do believe tying the theory to experiment is still a great goal - I just don't think my approach necessarily realizes that goal yet.

The theoretical approach I used is based on space-time symmetries, and it is open to questions of how we break space-time into space + time. Clock syncrhonization defines which set of points are considered to be "at the same time", so it's integral to the issue, but not something I've thought about enough yet.

Specifically, it seemed clear to me that my approach tied energy and momentum to a specific way of dividing space-time into space+time, and it's unclear how this affects the experiments.

 

[cianfa72]

As I understand things...

Definition: two clocks are said to be "synchronized" if their readings when located at simultaneous events are equal. Conversely, for synchronized clocks, their readings can only be identical if the clocks are located at a pair of simultaneous events.

Obviously, the state of being synchronized in this sense depends on the chosen simultaneity convention.

In the case at hand, the assumed simultaneity convention is such that pairs of clocks prepared and accelerated as described remain always synchronized.

I.e. they remain always synchronized w.r.t. the definition you gave (namely their readings are identical if they are located at a pair of simultaneous events -- in the case at hand simultaneous w.r.t. the simultaneity convention given by Einstein's synchronization procedure applied to a flock of inertial clocks at rest each other).

 

[PAllen]

Note, an invariant fact is that if you move the clocks away and then back together with identical acceleration profile, they will be in synch. The part subject to choice is whether or consider them synchronized while apart. There is no way to check this without some other convention. If you check them apart using light signals assuming light speed isotropy, you find them in synch. If you check them assuming anisotropy, you find them out of synch.

 

[cianfa72]

Note, an invariant fact is that if you move the clocks away and then back together with identical acceleration profile, they will be in synch. The part subject to choice is whether or consider them synchronized while apart. There is no way to check this without some other convention.

Ok yes, definitely.

If you check them apart using light signals assuming light speed isotropy, you find them in synch. If you check them assuming anisotropy, you find them out of synch.

Sorry, could you explain in detail how you plane to check those clocks when they are apart, by using light signals ? Thanks.

 

[PAllen]

Ok yes, definitely.


Sorry, could you explain in detail how you plane to check those clocks when they are apart, by using light signals ? Thanks.

At time t, clock 1 sends a signal to clock 2, triggering clock 2 to send its time reading to clock 1. We are assuming the clocks mutually stationary after having separated with identical acceleration profile. Also, that they started out in synch before separation. At some time on clock 1: t+k, the clock 2 reading arrives at clock 1. The clock 2 reading will be t+(k/2). All of this, so far, is invariant physics.

Now assumptions come in. If you assume one way light speed is isotropic, the clock 2 reading is what you expect for separated clocks that are synchronized. So the clocks are still synchronized under this model. If, instead you assume (for example) that the outbound light speed is 1.5c, inbound .75c (one of the allowed combinations), then, for properly synchronized clocks you expect the clock 2 reading to be t+(k/3). Since it is not, you conclude that the separation process has desynchronized the clocks ( because time dilation is anisotropic, in this model). So you are correctly observing the desynchronization predicted under this model.

 

[cianfa72]

At time t, clock 1 sends a signal to clock 2, triggering clock 2 to send its time reading to clock 1. We are assuming the clocks mutually stationary after having separated with identical acceleration profile. Also, that they started out in synch before separation. At some time on clock 1: t+k, the clock 2 reading arrives at clock 1. The clock 1 reading will be t+(k/2). All of this, so far, is invariant physics.

I believe you meant: when the light signal arrives back at clock 1 from clock 2 (at clock 1's own time t+k), the clock 2's sent encoded own time will be t +(k/2). This will be the reading/information that clock 1 "extracts" from the signal received back from clock 2.

 

[PAllen]

I believe you meant: when the light signal arrives back at clock 1 from clock 2 (at clock 1's own time t+k), the clock 2's sent encoded own time will be t +(k/2). This will be the reading/information that clock 1 "extracts" from the signal received back from clock 2.

Yes, fixed now.

 

[cianfa72]

At time t, clock 1 sends a signal to clock 2, triggering clock 2 to send its time reading to clock 1. We are assuming the clocks mutually stationary after having separated with identical acceleration profile. Also, that they started out in synch before separation. At some time on clock 1: t+k, the clock 2 reading arrives at clock 1. The clock 2 reading will be t+(k/2). All of this, so far, is invariant physics.

Yes, that is an invariant fact. We can check it taking the viewpoint of the inertial frame with coordinates $(x,t)$. The worldlines of the two clocks (proper) accelerating apart with the same acceleration profile are represented in those inertial coordinates by the same timelike curve symmetric about a straight line parallel to the $t$ axis. As you pointed out, the two clocks are assumed to be mutually stationary after receding apart with the same acceleration profile (as measured/assessed by constant round-trip travel time for the light signals exchanged between them). That's means, I believe, from that point on their worldlines became parallel straight lines when represented/drawn in inertial coordinates. By drawing in this chart the relevant light cones' boundaries representing the paths taken from light signals exchanged between those clocks, we can check your "invariant fact" claim.

 

[PAllen]

Yes, that is an invariant fact. We can check it taking the viewpoint of the inertial frame with coordinates $(x,t)$. The worldlines of the two clocks (proper) accelerating apart with the same acceleration profile are represented in those inertial coordinates by the same timelike curve symmetric about a straight line parallel to the $t$ axis. As you pointed out, the two clocks are assumed to be mutually stationary after receding apart with the same acceleration profile (as measured/assessed by constant round-trip travel time for the light signals exchanged between them)

No, as measured locally by an accelerometer, or by design with preprogrammed propulsion systems. The aim is to demonstrate:
1) There exist simultaneity conventions having nothing to do with light that are equivalent to the Einstein convention.
2) You only get to make one choice for isotropy (in cases where there is a choice not constrained by physics). If you assume it for one such case, then consistency forces the same choice for all other cases that have a choice. There is, in a sense, only one parameter controlling all such cases.

That's means, I believe, from that point on their worldlines became parallel straight lines when represented/drawn in inertial coordinates. By drawing in this chart the relevant light cones' boundaries representing the paths taken from light signals exchanged between those clocks, we can check your "invariant fact" claim.