Synchronization vs. Simultaneity

[Mowgli]

At the core of SR is a definition of what is meant by two clocks being synchronous. Two clocks A and B are assumed to synchronize if a ray of light takes the same time to go from A to B as it will take to go from B to A.

 

Simultaneity, on the other hand, can be defined as follows: two events X and Y are simultaneous to an observer O if light rays from X and Y reach O at the same time (as seen by O's clock.)

 

Are these two definitions compatible?

 

Cheers,

Mowgli

[swansont]

Two clocks A and B are assumed to synchronize if a ray of light takes the same time to go from A to B as it will take to go from B to A.

 

Under what conditions would this not be true?

[Mowgli]

swansont:

Under what conditions would this not be true?

If A is in motion...

 

Actually, this is something that I find weird. If B is in motion, A and B are still considered synchronized, but not if A is in motion.

[swansont]

If A is in motion...

 

Actually' date=' this is something that I find weird. If B is in motion, A and B are still considered synchronized, but not if A is in motion.[/quote']

 

I don't think that's true. Whether A or B is in motion is not something that can be absolutely determined.

 

Just because the light ray takes the same amount of time to go A->B as B->A does not mean clocks are synchronized. Clocks are synchronized if they are set to the same reading. If the clocks are at rest, you have to account for the speed of light in sending the signal. If the clocks are moving, you have to account for relativity effects.

[Mowgli]

swansont:

Just because the light ray takes the same amount of time to go A->B as B->A does not mean clocks are synchronized. Clocks are synchronized if they are set to the same reading. If the clocks are at rest, you have to account for the speed of light in sending the signal. If the clocks are moving, you have to account for relativity effects.

But this is exactly what Einstein said in his 1905 paper. I quote from the paper below.

Einstein:

If at the point A of space there is a clock, an observer at A can determine the time values of events in the immediate proximity of A by finding the positions of the hands which are simultaneous with these events. If there is at the point B of space another clock in all respects resembling the one at A, it is possible for an observer at B to determine the time values of events in the immediate neighbourhood of B. But it is not possible without further assumption to compare, in respect of time, an event at A with an event at B. We have so far defined only an “A time” and a “B time.” We have not defined a common “time” for A and B, for the latter cannot be defined at all unless we establish by definition that the “time” required by light to travel from A to B equals the “time” it requires to travel from B to A. Let a ray of light start at the “A time” tA from A towards B, let it at the “B time” tB be reflected at B in the direction of A, and arrive again at A at the “A time” t'A.

In accordance with definition the two clocks synchronize if

tB − tA = t'A − tB.

We assume that this definition of synchronism is free from contradictions, and possible for any number of points; and that the following relations are universally valid:—

1. If the clock at B synchronizes with the clock at A, the clock at A synchronizes with the clock at B.

2. If the clock at A synchronizes with the clock at B and also with the clock at C, the clocks at B and C also synchronize with each other.

Sorry to sound as though I was trying to “trap” you. Believe me, I agree completely with your statement quoted above. I just don't know how to reconcile it with the synchronization assumption (and the subsequent generalizations) above.

[swansont]

Einstein is saying that you have to account for the light travel time when doing the synchronization.

 

So yes, it is what Einstein said in his paper. But it's not the only thing he said - you have to be setting the clocks to the same reading, too, which is what you left out of your first post.

[Mowgli]

Einstein is saying that you have to account for the light travel time when doing the synchronization.

Is that what Einstein is saying here in this statement? I just don't see it. Here is the statement again.

Einstein: "Let a ray of light start at the “A time” tA from A towards B, let it at the “B time” tB be reflected at B in the direction of A, and arrive again at A at the “A time” t'A. In accordance with definition the two clocks synchronize if

tB − tA = t'A − tB."

Suppose I have the clock A with me. Then any other clock B will be synchronized with my clock A, because the definition of sycnrhonism is always true.

Now consider a clock B in motion with respect to me. It can synchronize with a clock A only if A is moving in tandem with B (in the same inertial frame, ie.) Otherwise the condition tA - tB = t'B - tA cannot be true. Thus B cannot be synchronized to A, in contradiction with the first generalization.

Einstein: "If the clock at B synchronizes with the clock at A, the clock at A synchronizes with the clock at B."

Again, consider a clock B in motion with respect to me. Exactly as above, it can synchronize with a clock C only if C is moving in tandem with B (in the same inertial frame, ie.) Otherwise the condition tC - tB = t'B - tC cannot be true. But A is in synch with both B and C.

But this is in contradiction with the second generalization.

Einstein: "If the clock at A synchronizes with the clock at B and also with the clock at C, the clocks at B and C also synchronize with each other."

I must be missing something obvious here, can you help me spot it?

 

 

So yes' date=' it is what Einstein said in his paper. But it's not the only thing he said - you have to be setting the clocks to the same reading, too, which is what you left out of your first post.[/quote']

Sure, Einstein didn't actually state in his paper, may be he thought it was obvious

[swansont]

Where Einstein says "We have not defined a common “time” for A and B, for the latter cannot be defined at all unless we establish by definition that the “time” required by light to travel from A to B equals the “time” it requires to travel from B to A." I thought it was fairly obvious that he meant to synchronize clocks. I also thought it was obvious he is saying you have to account for the light travel time.

 

He's dealing with a single inertial frame. The last line from that section: "It is essential to have time defined by means of stationary clocks in the stationary system, and the time now defined being appropriate to the stationary system we call it ``the time of the stationary system.''"

[Mowgli]

He's dealing with a single inertial frame.

Aha! That makes a lot more sense. Thanks for clearing it up!

 

Where Einstein says "We have not defined a common “time” for A and B' date=' for the latter cannot be defined at all unless we establish by definition that the “time” required by light to travel from A to B equals the “time” it requires to travel from B to A.[/i']" I thought it was fairly obvious that he meant to synchronize clocks. I also thought it was obvious he is saying you have to account for the light travel time.

Well, I think he's saying that the speed of light is a constant in an inertial frame. Later on, he will impose the assumption that it is the same constant for all inertial frames.

 

Coming back to my original question, is this definition of synchronism compatible with (or the same as) the notion of simultaneity?

At the core of SR is a definition of what is meant by two clocks being synchronous. Two clocks A and B are assumed to synchronize if a ray of light takes the same time to go from A to B as it will take to go from B to A.

 

Simultaneity' date=' on the other hand, can be defined as follows: two events X and Y are simultaneous to an observer O if light rays from X and Y reach O at the same time (as seen by O's clock.)[/quote']