Which Clock Shows Less Time When They Collide?

[Mentz114]

DaleSpam,
you should keep a copy of your last post and use it as a standard answer. Carve it in stone.

M

 

[AntigenX]

Hello all,

Thanks for your co-operation and support and replies and (at the least) your patience!

From re-reading all the posts, I gather that "the clock in a reference frame would accumulate more time, from which the clock matching light flash was emitted". I think, for matching the clocks, only two light signals are required (from a single flash), the motion of the source is obviously not important.

I mean, what difference it makes if the source was motionless or in motion w.r.t. any frame? or, It goes away from its original position (spacetime coordinates) after emitting the flash?

The outcome of the discussion is however, If after emitting the flash, the source remains stationary w.r.t. A, A will accumulate more time, but if the source remains stationary w.r.t. B, B will accumulate more time.

This is something I can not digest, provided, the speed of light does not depend upon relative velocity of source or observer. In fact light does not have any frame of reference.

Anyways, these questions have been asked and re-asked by me and responded and re-responded by many of you, and I still remain unconvinced. I think I need extensive reading of the subject. I have gathered some books on SR (and GR too) some suggested in this thread and others by google searching. I will take some time to go through it. Meanwhile, I would stop bothering you all.. precisely, I would not be posting on this thread. Consider it solved!

Thanks again...

AX

 

[Doc Al]

I mean, what difference it makes if the source was motionless or in motion w.r.t. any frame? or, It goes away from its original position (spacetime coordinates) after emitting the flash?

The motion of the source after emitting the flash certainly makes no difference at all. All that matters is: Does the flash arrive at both clocks simultaneously? According to what frame? Note that if the flash arrives simultaneously in one frame, it cannot arrive simultaneously in the other.

The outcome of the discussion is however, If after emitting the flash, the source remains stationary w.r.t. A, A will accumulate more time, but if the source remains stationary w.r.t. B, B will accumulate more time.

Not exactly. If the flash is arranged to arrive simultaneously according to frame A, then A accumulates more time. But if the flash arrives simultaneously according to frame B, then B accumulates more time. Note the complete symmetry.

This is something I can not digest, provided, the speed of light does not depend upon relative velocity of source or observer. In fact light does not have any frame of reference.

The speed of the light does not depend on the relative velocity of source or observer, but the speed of everything else does!

Best of luck in your study of SR!

 

[yuiop]

...
To answer the question of how A and B decide which clock started first, draw a vertical line that is midway between the clock start events in each of the reference frames. Imagine the clocks are programmed to flash back an echo signal when they start. Now all they have to do is notice if the echoed signals return to the midpoint at the same time. If the echoed start signal from one of the clocks arrives at the center line first, they will decide that is the clock that started first. In this particular case A decides the clocks start at the same time while B decides the left hand clock (belonging to A) started first.

...
Now there is a problem (for me, of course) here. Where to draw the line? In the space time diagram? If yes, Which one? When A is stationary or B is stationary? I don't think that's possible for any of them. As I proposed above, Let's simplify this with two "two way" signals from both clocks to the other clock and back. That will surely give both the time interval. Let them both match their own measured time intervals with the other (may be by another information rich signal) to decide which clock started first. Anything wrong?

I decided to upload a more accurate detailed spacetime diagram to illustrate what is happening. Frame S is the frame that observers A1,A2, and A3 are all at rest in while frame S' is the frame that observers B1, B2 and B3 are all at rest in. A1 and B1 are the primary observers that we have been discussing so far. A2 and B2 are the "mid point observers that I introduced. The start flash is shown as F or F'. The echoed signal from the clock to comfirm they have started is shown by the green arrows. The midpoint observer A2 sees both echoed signals arrive simultaneously and confirms the clocks both started simultaneously if the A frame. The midpoint observer B2 see the echoed signals arrive separately and confirms that the A clock started before the B clock as far as the B observers are concerned, by an interval of t2-t1 shown in the diagram. Hope that helps.

 

[Dale]

DaleSpam,
you should keep a copy of your last post and use it as a standard answer. Carve it in stone.

M

Thank you Mentz, that is very kind!

 

[Dale]

I decided to upload a more accurate detailed spacetime diagram to illustrate what is happening.

Very nice! What is the relative velocity you used? I "eyeball" it around 2/3 c.

 

[yuiop]

Very nice! What is the relative velocity you used? I "eyeball" it around 2/3 c.

Thanks ..and you are spot on. 0.66c

Just in case anyone is interested, the proper times measured by the clocks at that relative velocity is 4.173 seconds for the A clock and 3.135 seconds for the B clock and those times are of course by definition observer independent.