Which Clock Shows Less Time When They Collide?

[Doc Al]

Edit: Just for clarification, Though O & A are in same rest frame, O will agree that the light signal reached to both A & B simultaneously. I don't see any reason for A to think so.

All observers in the same frame will agree when things are simultaneous.

How will B decide that the signal reached A long before it reached B? I hope not from the space-time diagram.

I'm not sure how best to answer that, since I must assume you know something about relativity. Do you understand that two clocks separated along their direction of motion (with respect to a second frame) can be synchronized within their own frame yet be out of synch according to that second frame? (This is the relativity of simultaneity.)

Forget space-time diagrams for the moment. Imagine that the frame A-O extends all the way along the x-axis. Further imagine that frame A-O has clocks everywhere--every meter, if you like. Of course, all of these clocks are synchronized. Further imagine that when the signal sent out by O reaches clocks A and B, by prearrangement all the clocks in frame A-O are set to read 0. (Nothing wrong with doing that, since you can always synchronize clocks in the same frame.) In particular, at the instant he receives the signal, B is just passing a frame A clock. Of course it reads 0.

At that instant, does B think that clock A also reads 0? No! According to frame B, the clocks in frame A-O are all out of synch by varying degrees. When the clock he passes reads 0, the clock at A reads some time > 0, since according to B clocks at the rear of a moving frame are ahead of clocks at the front.

In order to understand relativity, you need to be comfortable with three facts about clocks and measuring rods:
(1) Moving clocks run slow (time dilation)
(2) Moving rods are contracted (length contraction)
(3) Moving clocks, synchronized in their own frame, are out of synch (if separated along the direction of motion)

The third one--the relativity of simultaneity--is the tricky one.

 

[AntigenX]

All observers in the same frame will agree when things are simultaneous.

That may not be true. Consider two stationary (wrt each other) observers separated by some distance along x axis. Now if there is a light flash at origin, they won't agree about the time of the flash, even though their clocks were synchronized. They can agree only after considering the time the light might have taken to travel the distance between them. I think that would also be considered the relativity of simultaneity.

I'm not sure how best to answer that, since I must assume you know something about relativity.

That would be some (undeserved for me) generosity from your side.

Do you understand that two clocks separated along their direction of motion (with respect to a second frame) can be synchronized within their own frame yet be out of synch according to that second frame? (This is the relativity of simultaneity.)

Yes, I get that.

Forget space-time diagrams for the moment.

Thanks a Lot (seriously)!

Imagine that the frame A-O extends all the way along the x-axis. Further imagine that frame A-O has clocks everywhere--every meter, if you like. Of course, all of these clocks are synchronized. Further imagine that when the signal sent out by O reaches clocks A and B, by prearrangement all the clocks in frame A-O are set to read 0. (Nothing wrong with doing that, since you can always synchronize clocks in the same frame.)

Well, there is a problem now with the prearrangement. All clocks in any frame, which are spatially separated, can not all be set to read zero by any mechanism instantaneously. At the least they will require a light flash, which will reach each clock at different time. If at all this is possible, please explain how to prearrange the things.

In particular, at the instant he receives the signal, B is just passing a frame A clock. Of course it reads 0.

At that instant, does B think that clock A also reads 0? No! According to frame B, the clocks in frame A-O are all out of synch by varying degrees. When the clock he passes reads 0, the clock at A reads some time > 0, since according to B clocks at the rear of a moving frame are ahead of clocks at the front.

Yes, but that is only possible if there is any mechanism to synchronize all clocks to 0 simultaneously (or instantaneously in other words). Synchronization also takes time, I suppose!

In order to understand relativity, you need to be comfortable with three facts about clocks and measuring rods:
(1) Moving clocks run slow (time dilation)
(2) Moving rods are contracted (length contraction)
(3) Moving clocks, synchronized in their own frame, are out of synch (if separated along the direction of motion)

The third one--the relativity of simultaneity--is the tricky one.

I perfectly agree, and after some random attempts, I chose Time Dilation to be the first one. I also read here (which was probably your post), that most problems and so called paradoxes are related to relativity of simultaneity.

Though I've started getting the "feel" of SR and (honestly) the excitement is immense, but before I can get to the real taste, I must overcome my limitations.

 

[Doc Al]

That may not be true. Consider two stationary (wrt each other) observers separated by some distance along x axis. Now if there is a light flash at origin, they won't agree about the time of the flash, even though their clocks were synchronized. They can agree only after considering the time the light might have taken to travel the distance between them.

Of course, to interpret their raw observations they must correct for light travel time. That's what it means to measure when the flash occurred as opposed to when the light happened to reach a particular observer.

I think that would also be considered the relativity of simultaneity.

Nope. The relativity of simultaneity is what you find after you take into account light travel time. (Otherwise it would be rather silly!)

Well, there is a problem now with the prearrangement. All clocks in any frame, which are spatially separated, can not all be set to read zero by any mechanism instantaneously. At the least they will require a light flash, which will reach each clock at different time. If at all this is possible, please explain how to prearrange the things.

Trivial, at least as a thought experiment. Assume all clocks in frame A-O have been synchronized. (Start those signals years in advance, if you like.) Arrange for the signal to reach B when all clocks read 0 (or whatever).

Yes, but that is only possible if there is any mechanism to synchronize all clocks to 0 simultaneously (or instantaneously in other words). Synchronization also takes time, I suppose!

This is a thought experiment. If you understand how to synchronize two clocks, that's all you need. (The "clocks everywhere" was just a visual to help you understand what a "frame" means. It doesn't matter.)

I perfectly agree, and after some random attempts, I chose Time Dilation to be the first one. I also read here (which was probably your post), that most problems and so called paradoxes are related to relativity of simultaneity.

Though I've started getting the "feel" of SR and (honestly) the excitement is immense, but before I can get to the real taste, I must overcome my limitations.

One difficulty is that for most situations you cannot treat time dilation apart from the relativity of simultaneity and length contraction. They all work together.

 

[AntigenX]

Of course, to interpret their raw observations they must correct for light travel time. That's what it means to measure when the flash occurred as opposed to when the light happened to reach a particular observer.

Nope. The relativity of simultaneity is what you find after you take into account light travel time. (Otherwise it would be rather silly!)

I still can't digest how will A and B decide whose clock started first (according to themselves, of course). Any better way?

Trivial, at least as a thought experiment. Assume all clocks in frame A-O have been synchronized. (Start those signals years in advance, if you like.) Arrange for the signal to reach B when all clocks read 0 (or whatever).

This is a thought experiment. If you understand how to synchronize two clocks, that's all you need. (The "clocks everywhere" was just a visual to help you understand what a "frame" means. It doesn't matter.)

I understood the purpose of clocks everywhere, but don't think it's appropriate, because it tells A and B instantaneously about when other's clocks started. How is this acceptable? At most, they can communicate with light signal, nothing less than that.

One difficulty is that for most situations you cannot treat time dilation apart from the relativity of simultaneity and length contraction. They all work together.

One of them is the one I am facing now .

 

[Doc Al]

I still can't digest how will A and B decide whose clock started first (according to themselves, of course). Any better way?

You do realize that they disagree, right? And that "which is first" depends on what frame is talking?

I understood the purpose of clocks everywhere, but don't think it's appropriate, because it tells A and B instantaneously about when other's clocks started. How is this acceptable? At most, they can communicate with light signal, nothing less than that.

Sorry, don't understand what you're trying to say here. Once clocks are synchronized, I "know" what the other clocks read (in my own frame, of course). No further "communication" required.

I strongly suggest getting a decent relativity book and starting at step one.

 

[Dale]

How will B decide that the signal reached A long before it reached B? I hope not from the space-time diagram.

Hi AntigenX,

Yes, it is very easy to see from the space-time diagram. See attached.

Forget space-time diagrams for the moment.

Nooooooo! Et tu Doc Al?

One difficulty is that for most situations you cannot treat time dilation apart from the relativity of simultaneity and length contraction. They all work together.

Yes, that is why I am such a fan of the diagrams. That one I posted earlier shows geometrically how all three work together at the same time. As I said before, drawing it myself from the Lorentz transforms was really crucial to my learning SR.

 

[Doc Al]

Nooooooo! Et tu Doc Al?

Believe it or not, I'm a huge fan of the space-time diagram. To me, only when you've mastered such can you say you understand basic relativity. Nonetheless, I also think one must be able to explain things by understanding the relativistic behavior of clocks and rods.

In this case, AntigenX seemed intimidated by the diagrams and was complaining how no one would give him a plain answer to his question. So I gave him one.

But please carry on the good fight!

 

[robphy]

DaleSpam,
In your attachment, there may be some misinterpretation of the role of the open circles and the labels A and B at the base of the triangles. I fear that someone might misinterpret that there are events "A" and "B" that are simultaneous with the flash-event in A's frame... and that those same events are mutually simultaneous in B's frame. (I suggest losing the open circles [suggestive of point-events] at the base of the triangles... or else giving them appropriate labels... since it appears that A and B really refer to worldlines and not events.)

 

[Dale]

You are correct, sorry I was too lazy to edit it correctly. There are four events of interest:

1) the flash (labeled with a circle)
2) the collision (labeled with a circle)
3) clock A starts (no circle, the intersection of the flash and worldline A)
4) clock B starts (no circle, the intersection of the flash and worldline B)

The other circles are indeed not representative of any event, and the horizontal line connecting A Flash and B is also not representative of anything. Also, I think it is usually useful to show both frames coordinate axes on each drawing.

 

[yuiop]

I still can't digest how will A and B decide whose clock started first (according to themselves, of course). Any better way?
..

Hi AntigenX,

I am going to make a shot at making an analogy that might help with your understanding of simultaneity (or confuse the heck out of you) but here goes.

For the analogy I am going to use sound instead of light. Imagine you stretch your arms out and click the fingers of your left and right hands at the same time. Your arms are the same length and you hear the left and right clicks reach your ears at the same time. For this anology we will pretend that your nervous system operates much faster than the speed of sound and is effectively instantaneous in comparison. Now you get on a superfast powered scateboard with your left arm stretched out in front of you and your right arm behind. When you click your fingers again, the sound from your left hand reaches your left ear before the the sound from your trailing right hand. You decide to synchronise your hands and click your right hand slightly before your left hand so that the left and right clicks arrive at your ears at the same time when cruising superfast on your scateboard. Now you pass some observers standing next to the road who just happen to be standing next to each of your hands when you clicked them and they say you did not click them at the same time. Now of course you also know that you are not clicking your the fingers of your left and right hands at the same time, but in relativity using light signals there is nothing faster than light to compare the light signals with, so you can only rely on the simultaneous arrivel of two signals from two events that are the same distance away from you to tell you that the two events happened at the same time. Observers that are not moving at the same speed as you will not agree that those two events occurred at the same time.

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.

 

[granpa]

simultaneity:

suppose we arbitrarily decide to redefine time so that everytime you move 1 meter north you move one year into the future. what's wrong with this scenario? well for one thing the laws of physics as we know them won't work with this definition of time. all physics equations will have to be completely rewritten. so time is not arbitrary. physical processes work in a certain way and that requires us to define time and simultaneity in a certain very definite way.

when a rocket moves near the speed of light the physical processes that occur on board that ship change and that requires the people on board the rocket to change their clocks to match.

 

[Doc Al]

when a rocket moves near the speed of light the physical processes that occur on board that ship change and that requires the people on board the rocket to change their clocks to match.

That would violate the principle of relativity.

 

[granpa]

that is the principle of relativity.

the processes change from the point of view of an observer that stationary. the people on the rocket will not notice anything.

 

[matheinste]

Hello granpa.

Quote:-

----when a rocket moves near the speed of light the physical processes that occur on board that ship change and that requires the people on board the rocket to change their clocks to match.------

Quote:-

----the processes change from the point of view of an observer that stationary. the people on the rocket will not notice anything.-----

Question. Why would they want to change their clocks.


Matheinste.

 

[Doc Al]

the processes change from the point of view of an observer that stationary. the people on the rocket will not notice anything.

Correct.

when a rocket moves near the speed of light the physical processes that occur on board that ship change and that requires the people on board the rocket to change their clocks to match.

Incorrect. (And it contradicts your statement above.)

 

[granpa]

i guess i phrased that badly. they wouldn't be aware of anything changing. rather it is the stationary observer that must take it into account to understand what is happening on the ship

the point being that what is considered simultaneous isn't arbitrary. the laws of physics governing a certain object require that from the point of view of the object certain things must be considered simultaneous.

 

[AntigenX]

You do realize that they disagree, right? And that "which is first" depends on what frame is talking?

Sure, they are bound to disagree, but I am not getting how will A decide when did B start and vice versa. As I said earlier, some communication between A and B is required for them to comunicate, so that they come to know when the other clock started wrt himself.

Sorry, don't understand what you're trying to say here. Once clocks are synchronized, I "know" what the other clocks read (in my own frame, of course). No further "communication" required.

Exactly, Once all the clocks are "in sync" in my frame, I know what the other read, but somebody moving relative to me can't know it without any communication with some clock of my frame.

I strongly suggest getting a decent relativity book and starting at step one.

Sure, Any suggestions, considering my current state of mind ?

 

[AntigenX]

Hi AntigenX,

Hello DaleSpam, nice to see you back!

Yes, it is very easy to see from the space-time diagram. See attached.

Yes, It is clear from spacetime diagram, but just as we required light flash to match clocks A and B, we should require light flash for telling clocks A and B, about when the other's clock started. And if we do that, suppose by (two, for bot A and B, as soon as their clocks start) two way light signals, both will get same results.

Also, even after considering the spacetime diagrams, both A and B will not be able to decide which one should they consider, because, though they are aware of their relative motion, they don't really know which one is actually moving!

Nooooooo! Et tu Doc Al?

!

Yes, that is why I am such a fan of the diagrams. That one I posted earlier shows geometrically how all three work together at the same time. As I said before, drawing it myself from the Lorentz transforms was really crucial to my learning SR.

 

[AntigenX]

Believe it or not, I'm a huge fan of the space-time diagram. To me, only when you've mastered such can you say you understand basic relativity. Nonetheless, I also think one must be able to explain things by understanding the relativistic behavior of clocks and rods.

Exactly!

In this case, AntigenX seemed intimidated by the diagrams and was complaining how no one would give him a plain answer to his question. So I gave him one.

But please carry on the good fight!

I never thought you would be so sporty. Though, I should have understood this from number of your posts !

 

[AntigenX]

Hello kev!

Hi AntigenX,

I am going to make a shot at making an analogy that might help with your understanding of simultaneity (or confuse the heck out of you) but here goes.

For the analogy I am going to use sound instead of light. Imagine you stretch your arms out and click the fingers of your left and right hands at the same time. Your arms are the same length and you hear the left and right clicks reach your ears at the same time. For this anology we will pretend that your nervous system operates much faster than the speed of sound and is effectively instantaneous in comparison. Now you get on a superfast powered scateboard with your left arm stretched out in front of you and your right arm behind. When you click your fingers again, the sound from your left hand reaches your left ear before the the sound from your trailing right hand. You decide to synchronise your hands and click your right hand slightly before your left hand so that the left and right clicks arrive at your ears at the same time when cruising superfast on your scateboard. Now you pass some observers standing next to the road who just happen to be standing next to each of your hands when you clicked them and they say you did not click them at the same time. Now of course you also know that you are not clicking your the fingers of your left and right hands at the same time, but in relativity using light signals there is nothing faster than light to compare the light signals with, so you can only rely on the simultaneous arrivel of two signals from two events that are the same distance away from you to tell you that the two events happened at the same time. Observers that are not moving at the same speed as you will not agree that those two events occurred at the same time.

Got it.

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?

 

[Dale]

Yes, It is clear from spacetime diagram, but just as we required light flash to match clocks A and B, we should require light flash for telling clocks A and B, about when the other's clock started.

Sure, you can consider whatever mechanism you want for B to get the information that A started his clock. For example:
1) A sends a flash indicating that he started his clock
2) B uses radar echoes to determine when he started his clock
3) Another observer, B junior, is at rest wrt B and with a synchronized clock and right next to A when A starts his clock. B junior writes down the time and sends it to B via FedEx.

In all 3 cases, B doesn't get the information until later, but once he gets the information he can compensate for any transit time delays and correctly identify the instant (in B's frame) when A started his clock.

And if we do that, suppose by (two, for bot A and B, as soon as their clocks start) two way light signals, both will get same results.

You might think that intuitively, but if you work it out carefully you will determine that they will not both get the same results.

Also, even after considering the spacetime diagrams, both A and B will not be able to decide which one should they consider, because, though they are aware of their relative motion, they don't really know which one is actually moving!

The point is that "actually moving" has no physical meaning. Only their relative motion has any physical significance. It doesn't matter which one is "actually moving".

 

[AntigenX]

Sure, you can consider whatever mechanism you want for B to get the information that A started his clock. For example:
1) A sends a flash indicating that he started his clock
2) B uses radar echoes to determine when he started his clock
3) Another observer, B junior, is at rest wrt B and with a synchronized clock and right next to A when A starts his clock. B junior writes down the time and sends it to B via FedEx.

Whatever way (1,2 or 3) we may choose, we will consider that it will propagate at the speed of light.

In all 3 cases, B doesn't get the information until later, but once he gets the information he can compensate for any transit time delays and correctly identify the instant (in B's frame) when A started his clock.

Now, what reason we have to say that B doesn't get the information until later?

You might think that intuitively, but if you work it out carefully you will determine that they will not both get the same results.

No intuition required. Both A and B receive their start signal, immediately send two way echo, and further send their own time interval between echo send-receive to each other for comparison. Do you want to say that in doing so, they will send different times?

The point is that "actually moving" has no physical meaning. Only their relative motion has any physical significance. It doesn't matter which one is "actually moving".

Exactly, what I wish to point out. therefore, B must not think that clock A started earlier.

 

[Dale]

Exactly, what I wish to point out. therefore, B must not think that clock A started earlier.

A started earlier in B's reference frame. They started simultaneously in A's reference frame. Both statements are correct and neither contradicts the other.

 

[Doc Al]

Sure, they are bound to disagree, but I am not getting how will A decide when did B start and vice versa. As I said earlier, some communication between A and B is required for them to comunicate, so that they come to know when the other clock started wrt himself.

No communication is needed. B just receives the signal and resets his clock to zero. Then he compares his clock reading to the reading on Clock A when they meet. That's it!

Of course, in order to predict how the readings will compare, B must know that he received his signal at the same time as did clock A (according to the A-O frame, of course!).

Exactly, Once all the clocks are "in sync" in my frame, I know what the other read, but somebody moving relative to me can't know it without any communication with some clock of my frame.

The array of synchronized clocks is just to help you imagine what's going on. All that we need to agree on is what I say above: The two clocks receive the signal at the same time according to frame A-O. (That is equivalent to having those synchronized clocks.)

Sure, Any suggestions, considering my current state of mind ?

I recommend either (or both!) of these:
(1) N. David Mermin's https://www.amazon.com/dp/0691122016/?tag=pfamazon01-20;
(2) Taylor and Wheeler's https://www.amazon.com/dp/0716723271/?tag=pfamazon01-20.

Yes, It is clear from spacetime diagram, but just as we required light flash to match clocks A and B, we should require light flash for telling clocks A and B, about when the other's clock started. And if we do that, suppose by (two, for bot A and B, as soon as their clocks start) two way light signals, both will get same results.

Also, even after considering the spacetime diagrams, both A and B will not be able to decide which one should they consider, because, though they are aware of their relative motion, they don't really know which one is actually moving!

There's no such thing as "actually moving"--it's a meaningless concept! All motion is relative. Each observer, of course, views himself as at rest in his own frame. According to A, B is the one moving--and vice versa.

 

[calis]

Unbelievable... I red it all through.

apart from understanding how exactly the clock get synchronized and other unimportant questions, I clearly peel out, that after 6 pages of coments the original question still stands.

If the viewer is stationary relative to clock A ... it seems clock B is slower. and the colision happens right in the A clocks starting place... and vice versa (the A clock is slower in B frame, and the collision happens in B clock starting place)


If the viewer is right in the middle and both clock are getting close at same velocity both clocks time at any given time reads the same. and the collision occures right between the clocks starting positions.

So not only we cannot agree what will each clock read at the moment of collision. we also cannot say where the collision will happen. And that's what the SR states. regarding the distance per time (it is speed) the time speed changes...but since we cannot agree on distance we therefore cannot agree on time it takes, we therefore cannot agree on speed...

chaos

 

[Doc Al]

Unbelievable... I red it all through.

apart from understanding how exactly the clock get synchronized and other unimportant questions, I clearly peel out, that after 6 pages of coments the original question still stands.

Clock synchronization, and how it is affected by relative motion, is key. The question has been answered clearly.

If the viewer is stationary relative to clock A ... it seems clock B is slower. and the colision happens right in the A clocks starting place... and vice versa (the A clock is slower in B frame, and the collision happens in B clock starting place)

True. So?

If the viewer is right in the middle and both clock are getting close at same velocity both clocks time at any given time reads the same. and the collision occures right between the clocks starting positions.

That's a different scenario than the one being discussed here. In that scenario neither frame A nor frame B will agree that both clocks receive the signal at the same time. (You have introduced a third frame.)

So not only we cannot agree what will each clock read at the moment of collision. we also cannot say where the collision will happen. And that's what the SR states. regarding the distance per time (it is speed) the time speed changes...but since we cannot agree on distance we therefore cannot agree on time it takes, we therefore cannot agree on speed...

Have you really read this thread? If we are given the starting position of each clock at the time that they are set to 0, and their relative speed, the calculation of what each clock will read when they meet is trivial.

 

[calis]

1st. clock synchronization is not the original question...
original question was... what time will each clock show.

2nd. this questions spells an uncertainty, because in each referance frame the readings after meeting is diferent. I can do the "trivial" calculations. but the problem starts when in each reference frame they are diferent.

3rd. I disagree that implementing a 3rd viewer or any viewer in any relative motion changes the experiment. By doing so I want to show that regardin the position of the viewer the mesurements change

4th I have red the thread. It would't make a point to make a post without saying or discussing any new ideas.

 

[Doc Al]

1st. clock synchronization is not the original question...
original question was... what time will each clock show.

The time that each clock will show is completely understood and unambiguous. (To fully understand the discussion requires understanding the relativity of simultaneity.)

2nd. this questions spells an uncertainty, because in each referance frame the readings after meeting is diferent. I can do the "trivial" calculations. but the problem starts when in each reference frame they are diferent.

Nonsense. Each reference frame agrees as to the time that each clock will show upon meeting.

3rd. I disagree that implementing a 3rd viewer or any viewer in any relative motion changes the experiment. By doing so I want to show that regardin the position of the viewer the mesurements change

You're wrong. If you just introduced a third frame as a "viewer", then nothing would change. That third frame would get the same answer for the clock readings as every other frame. I thought you wanted to change the scenario since you stated: If the viewer is right in the middle and both clock are getting close at same velocity both clocks time at any given time reads the same. That, of course, is not true if the viewer is just a passive viewer.

In order for them to "read the same at any given time" according to the third frame, they would have to have both read 0 at the same time according to the third frame. Unless you change the scenario, that's not true. (In the original scenario, the clocks are set to 0 at the same time according to frame A--not some third frame.) Once again, the relativity of simultaneity is key.

4th I have red the thread. It would't make a point to make a post without saying or discussing any new ideas.

You might want to rethink your post.

 

[Dale]

Just to be clear, distance, time, velocity, energy, simultaneity, etc. are all "relative" or frame-variant quantities. That does not mean that they are somehow uncertain or that they cannot be discussed exactly. It only means that when you describe one of these quantities you must also mention the reference frame where it is measured.

Once you specify a reference frame for all "relative" quantities then the physics are clearly defined and all observers will agree on the outcome of any physical experiment, e.g. both A and B agree that A's clock reads more at the collision. They may express the reason for the outcome differently, e.g. A will say it is because B's clock ran slow (in A's frame) while B will say it is because A started his clock earlier (in B's frame). But they will all agree on the outcome and will be able to calculate the viewpoint of the other frame.

 

[calis]

thank you dalespam you made it clear to me.