Help Synchronize Clocks: A & B's Perspective

[Bos]

Please Help...Synchronized Clocks

I've posted this before and I just want to clear things up. If A and B are on a train moving at a constant velocity (A in the front and B in the back) and they are asked to set their clocks to 12:00 when the light from a lightbulb in the center reaches them. From their perspective, it hits them simultaneously and they indeed set their clocks to 12:00 at the same time. However, person C on the platform outside claims that the light hit person B first because the light had less distanc to travel. If person A and B both decided to jump out of the train at 12:05 (according to them), then from C's perspective, it would be person B who jumps out first, since to him, B set his clock a little before A. But now my question is how A and B's clock synch up again after jumping out of the train to meet up with C. Someone has previously said that because person C sees person B jump out first, person A enjoys time dilation a bit longer which is exactly enough for their clocks to synch up again. But if A enjoyed time dilation longer, wouldn't that mean that A's clock is still ticking slower relative to C's while B's clock is speeding up relative to A's. This would only further separate the two clocks. Since B's clock was initially ahead of A's (according to C), it must be B's clock that has to slow down while A's speeds up in order for them to synch up again, right? What am I missing cause its driving me nuts! Please help..thanks.

 

[JesseM]

I've posted this before and I just want to clear things up. If A and B are on a train moving at a constant velocity (A in the front and B in the back) and they are asked to set their clocks to 12:00 when the light from a lightbulb in the center reaches them. From their perspective, it hits them simultaneously and they indeed set their clocks to 12:00 at the same time. However, person C on the platform outside claims that the light hit person B first because the light had less distanc to travel. If person A and B both decided to jump out of the train at 12:05 (according to them), then from C's perspective, it would be person B who jumps out first, since to him, B set his clock a little before A. But now my question is how A and B's clock synch up again after jumping out of the train to meet up with C.

They don't...in C's frame, B's clock was ahead of A's clock at the moment B jumped out, and after that B's clock gets even further ahead of A's because B's clock is now ticking at the "normal" rate while A's continues to tick at a slowed-down rate until A jumps out (after that point, both clocks tick at the normal rate, so the amount that B's is ahead of A's will stay constant).

Someone has previously said that because person C sees person B jump out first, person A enjoys time dilation a bit longer which is exactly enough for their clocks to synch up again.

What post was that? Either that person is wrong or you misunderstood/misremembered.

 

[Bos]

Thanks for responding. You're logic is what I had expected. Here's what I don't get though. How could B's clock continue to be ahead of A's (from C's perspective) if now, since they've jumped out and are standing right next to C, they're all seeing from the same perspective. In other words, A and B would agree that they're clocks were synched (even when they jumped out). So now that they're all on the platform together, who prevails. Are the clocks synched up (as they should be from A and B's perspective) or is B's clock still ahead of A's (as from C's perspective). They all have to agree on the clocks and they have to be able to agree from BOTH perspectives. It can't be that the clocks are not synchronized because from A and B's perspectives, there was never a difference between the two (or between the time they jumped out). So back to the original question. How do both clocks become synchronized from C's perspective? Thanks again, especially JesseM.

 

[JesseM]

Thanks for responding. You're logic is what I had expected. Here's what I don't get though. How could B's clock continue to be ahead of A's (from C's perspective) if now, since they've jumped out and are standing right next to C, they're all seeing from the same perspective.

Both clocks are running at the same rate, but whether two clocks are in synch or not depends on how they were set...you could set two clocks to be out of synch in your own home, for example.

In other words, A and B would agree that they're clocks were synched (even when they jumped out).

No they wouldn't. You have to be clear on what frame you're using, you get yourself in trouble if you try to imagine the "point of view" of an observer who doesn't stick to a single inertial frame. At the moment before B jumps it's true that A's clock reads the same time as his in his own rest frame, but at the moment after B jumps he has a new rest frame with a different definition of simultaneity, and in this frame A's clock was behind B's at the moment B made the jump.

I think your confusion here is coming from trying to think in terms of a non-inertial coordinate system where B remains at rest both before and after the jump, and which at each moment looks like B's instantaneous inertial rest frame at that moment, but it's a well-known problem that non-inertial coordinate systems constructed in this way can give rise to to bad behaviors like distant clocks running backwards (in this case, in B's instantaneous inertial rest frame immediately before his jump at 12:05, A's clock would be synchronized with B's and would therefore also read just before 12:05, but in B's instantaneous inertial rest frame immediately after the jump, A's clock would read some earlier time like 12:03). And in general, the standard rules of relativity like the equations for time dilation and length contraction as a function of speed, or even the rule that says light beams always travel at a coordinate speed of c, don't hold in non-inertial coordinate systems.

 

[Bos]

Ahh. I see what you mean. Yea my confusion was definitely that I was assuming B's position to be static throughout the whole thing, and the answer lies in his motion while jumping. So to clear it up, when A and B hit the ground and meet up with C, all clocks WILL be ticking at the same rate but will NOT read the same, correct? Your explanation makes sense and I thank you cause you're the first one to actually answer that without some nonsense reply. I do have one last question though...

When you say in "B's instantaneous inertial rest frame immediately after the jump", isn't that implying that B in fact did jump before A. But this fact is only from C's perspective. From A and B's perspective, shouldn' they literally both jump simultaneously. So if that's the case then shouldn't A and B's clock still remained synchronized when they land? (By synchronized I do mean reading the same as well as ticking at the same rate).

Thanks a million

 

[Bos]

ok that makes sense... thanks

 

[Bos]

sorry bout all the questions but i can finally sleep now...haha

 

[JesseM]

Ahh. I see what you mean. Yea my confusion was definitely that I was assuming B's position to be static throughout the whole thing, and the answer lies in his motion while jumping. So to clear it up, when A and B hit the ground and meet up with C, all clocks WILL be ticking at the same rate but will NOT read the same, correct?

Right.

When you say in "B's instantaneous inertial rest frame immediately after the jump", isn't that implying that B in fact did jump before A.

Why do you think it implies that? It's just a statement about what's happening in that particular inertial frame, but there would be other inertial frames where A jumped before B.

From A and B's perspective, shouldn' they literally both jump simultaneously.

What is B's "perspective"? Again, are you assuming a non-inertial frame which at every moment looks just like B's inertial rest frame at that moment? If so, then note that if you assume the acceleration is instantaneous, B will not have a well-defined rest frame at the exact moment of the jump, although he'll have one immediately before and after. And if you assume the acceleration is brief but non-instantaneous, then B's definition of simultaneity will be swinging around wildly during that brief acceleration, going from thinking A's clock reads the same time at the beginning of the acceleration to thinking A's clock reads a significantly earlier time at the end. Meanwhile, if A accelerates in the same way, A's own definition of simultaneity also swings around during the acceleration, but he's accelerating towards B rather than away from him, he'll go from thinking B's clock reads the same time at the beginning of the acceleration to thinking B's clock reads a significantly later time at the end. Again, this is assuming that each one uses a non-inertial coordinate system whose definition of simultaneity at each moment matches the definition of simultaneity in their instantaneous inertial rest frame at that moment.

 

[Bos]

Wow you really cleared things up. I appreciate your detail because its really hard to grasp relativity from ALL frames of reference, especially non-inertial ones. Pretty sure I got it now, thanks.