Which clock is slower?

AntigenX

Simple question (derived from some unanswered posts from various posters, mostly mitesh9)...

Two identical clocks A (stationary) and B (moving towards A) with a relative velocity v, so that it will collide with A after some time. (the notion of stationary/moving is for the sake of simplicity, otherwise, its impossible to judge it as per SR)

The clocks are set to read "zero" by a flesh of light equidistant from both. That means, they are set to the origin of their time axis. their spetial co-ordinates are different but their time co-ordinates at the start (flash of light) are same, which can be used as a reference to calculate their respective accumulated time, to which both the clocks will agree.

The clocks are of special kind, and have some mechanism that is infinitely sensitive to touch. so the clocks will stop the moment they are touched by the other clock. Note that, acceleration has no part to play, because, the clocks stop before the acceleration starts.

Now the questions.

1. When they collide, the clocks will stop. Which clock has accumulated less time? Presumably B, but how, because, we can not tell which clock is moving/stationary.

2. For clocks to collide, they should have same spacetime co-ordinates. Though their space co-ordinates are same at the time of collision, their time co-ordinates will be different (due to time dilation sufferred by B), in which case, they should not collide at all? How can they collide then? And if they do, then where has gone the time dilation?

3. More questions If the discussion proceeds ...

DaleSpam

Please draw the spacetime diagrams for your scenario. That will answer all your questions.

AntigenX

Thank you for your suggestion, but If I draw spacetime diagram considering A stationary, it will say B is slow and vice versa. Further, the solutions must be possible even without spacetime diagrams, No?

DaleSpam

Draw them and see. Don't to forget to include the spacetime diagrams for the flash of light that you are using to start the clocks.

DocZaius

The method of starting both clocks at the same time is problematic to me. Be very careful about the beam of light "equidistant" from each clock sending out the signal to start clocks.

AntigenX

Well, space time diagrams for A and B are two right angle triangles, mirror images of each other, having three vertices...

1. The origin
2. Clock Start Event (flash of light)
3. Collision Event

I don't see any point in drawing spacetime diagram for flash of light's point of view (or for that matter any point of view). The thing is, two clocks started at the same time, stopped an can be analyzed by anybody now. They are no longer dynamic things but static.

The method can be any arbitrary method. This is not the question at all, except, if it is not possible to make both clocks to read zero at same instant by any means. If at all it is possible by any way, we may include that as the standard way of doing this.

As to your point, the isotropy of light speed makes it possible to set both clocks zero at any arbitrary instant by an equidistant light flash.

DaleSpam

OK, here is your first problem. The spacetime diagrams are not triangles, they are quadrilaterals. There are four events of interest.

1. the flash of light
2. clock A receives the flash (and is set to 0)
3. clock B receives the flash (and is set to 0)
4. clock A and B collide (and read out their times)

In SR light doesn't have a "point of view", so just draw the diagrams for the rest frames of A and B, but include the light on each diagram.

You may not see the point, but that is just because you haven't done it. Try it and see. Honestly, if you are unwilling to even attempt it then there is really no point in the rest of us even bothering to respond to your posts. You cannot expect to overcome your confusion without some minimal effort on your part.

PS You will undoubtedly make some mistakes at first, but I can help you correct your diagram and the process will teach you more than anything else I can think of. I really consider it the most valuable exercise someone can do to learn SR.

AntigenX

This is equivalent to my system of two spacetime diagrams drawn using flash of the light to be the start point, and putting the stationary observer at origin.

My sentence meant the spacetime diagram you just proposed. I do not imply any point of view of light, but the point of view of the observer stationed at the spacetime co-ordinates of light flash.

As I have recently said earlier in some other post, I have never disregarded spacetime diagrams, but It seems that the current trend in SR is "Draw spacetime diagrams else you won't learn SR". My efforts are no less than anyone else trying to learn SR. It's just that I have chosen the other way. I do not want to let spacetime diagrams dictate my thinking at this stage.

As to your PS, I don't have any doubt that spacetime diagrams are helpful, but it's not the only way, No? I have many reasons for not drawing spacetime diagrams, the chief being, it's perception and interpretations are highly personal and can create more conflicts, driving us far from the original question (as is the case now). Further, I do not doubt the intentions of others who may wish to help me, and as you asked me, I figured out the spacetime diagram from my point of view (I hope you are not telling me to really draw it! though it wont make any difference).

Apart from these, Is the question so non-trivial that can not be solved without spacetime diagram? We are deviating from the original questions.

DaleSpam

Of course they are not the only way. However, you obviously are not learning using your way, so why not try my way?

When I was learning SR I was very much in your situation. I had also failed to grasp it using the other ways, and I struggled with the basics for years. It wasn't until I sat down and went through the personal effort to draw a few spacetime diagrams that SR finally clicked. I really wish that someone had done for me what I am trying to do for you.

No, it is so trivial that the fact that you even asked it indicates that you need to spend some effort learning the basics. I am deliberately not answering your question, instead I am trying to help you learn how to answer it yourself.

AntigenX

Well, then see the attached gif.

Attached Thumbnails

 

Janus

You haven't shown the light in these diagrams, as asked.

AntigenX

May be I am too bad at drawing diagrams, however, the midway point between A and B, which is labeled "Flash" is light flash.
The time for light signals to travel to the clocks is ignored (which does not make any difference to the situation I suppose), because the clocks starts after the signal reaching them, so anything before that is irrelevant.

yuiop

It does make a difference. If the flash occurs at a point a point that is truely midway between A and B (in A's frame) then A and B will not be equidistant from the flash when the signal arrives at A and B. If you would like to draw a more accurate version of your initial diagram that includes the light signals just draw the light signals as lines that are 45 degrees from the vertical t axis while all physicals objects travel on lines that are less than 45 degrees from the t axis. This is true in any frame.

For every event with coordinates (x,t) in A's frame there should be a corresponding event (x',t') in B's frame where x' and t' are defined by the Lorentz Transformation


What happens before is relevant. You are seem to be assuming your flah will reach A and B simultaneously in A's frame but B is moving away from the flash so B's clock is "zeroed" later than A's clock in A's frame.

AntigenX

Two questions,

1. Is my diagram wrong?
2. If yes, can you please correct it (though I shouldn't be asking this)?

Again, I think we are deviating from the original questions. The method of starting the clocks is not important, but what happens after the clocks are matched (not synchronized)!

Janus

And herein is your mistake. Because the time it takes for the light signals to travel cannot be ignored because It doesn't take an equal amount of time for the light to travel from emission point to A and B, according to A or B. Each determines that the flash reached the other before them.

Heres an modified attachment of your diagram showing the travel of the light flash(in blue). Light paths in space time diagrams follow 45° angles. Maybe it will clear things up for you.

Attached Thumbnails

 

Mentz114

Here is my attempt to draw the space time diagram for the observer midway between A and B. Where did I go wrong ?

Attached Thumbnails

 

AntigenX

Thank you kev for your suggestion and Janus for pointing out my mistake and revising my diagram...

All said and done, the original question is still unanswered. Which will be the slower clock? We are stressing upon the method of setting both clocks at zero, which may be any arbitrary method. But what after that? As is now clear from revised diagrams, the equidistant light flash can't work. Lets say then that there was some other non-equidistant flash that set them zero. Which clock will be slower then? Let the flesh be from such a distance so that the light travels same distance to reach clocks A and B. It's settled now I suppose.

Or is it impossible to set both clocks read zero? It doesn't seem impossible!

And even in the revised diagrams, from both point of views, the other clock is slower. How to decide which clock is slower? Or should we say the clock which is "really" moving is slower? But we have no way to decide which clock is moving!

Further, If at all any clock is slower, the collision should not happen, because, due to different time co-ordinates, clocks A and B will reach the collision point at different instants.