Which Clock Shows Less Time When They Collide?

[Dale]

so that A and B's clocks agree momentarily

In A's rest frame.

 

[Phrak]

This problem is simply the one-clock vs. two-clock problem presented in a somewhat obscure manner.

 

[Mentz114]

DaleSpam,
yes, in A's rest frame. I didn't say it, but it's part of the (obscure) requirement.

The geometry in that diagram is unbelievably tricky. I had a go at working out the transmission times in M's frame but failed.

M

 

[robphy]

DaleSpam,
yes, in A's rest frame. I didn't say it, but it's part of the (obscure) requirement.

The geometry in that diagram is unbelievably tricky. I had a go at working out the transmission times in M's frame but failed.

M

It shouldn't be too difficult... trigonometrically.
What are the relationships among A,B, and M?

 

[Dale]

That does in fact, but I'm afraid not much. Can you suggest where should I start, to get 'real' understanding of space-time diagrams? from word go?

Hi AntigenX,

The wikipedia http://en.wikipedia.org/wiki/Minkowski_diagram" page is a decent intro, but IMO the real thing is to actually sit down and construct some on your own. Get some feel for how to build one that is numerically accurate. For a good start do a standard "twin paradox" diagram. Then have one twin send light flashes to the other at regular intervals and determine what the other twin receives. It may not teach you anything new about the physics, but it will help you get used to drawing the diagrams in a scenario that is fully understood. You might also try a light clock.

 

[Janus]

Thank you for the bold face wrong!

Though, I must say, you are still not getting my point. From post#1 of this thread, I have been asking "is it at all possible for any observer to make two clocks (in relative motion) read zero reading at some arbitrary instant?". I haven't got any plain answer yet, though plenty I got.
Janus's posts have some very close indications that it is possible for some observer who is in relative motion wrt both A and B.
Also you will notice that I have stressed several times throught the thread to suggest some method of starting the clocks simultaneously for at least one observer. The plea has gone unheard.
Through this thread I wish to understand "how time dilation is real and not apparent (physical and not mere mathamatical)?". This has not been attempted at all.

Yes, it is perfectly possible to arrange things such that both clocks start simultaneously for any given observer. For instance, by placing the origin of the flash closer to A than to B, (as shown in the attachment)you can have both clocks start simultaneously as far as A is concerned.

With such an arrangement, according to A: Both clocks start simultaneously. B runs slower during the period before collision and then after both clocks have stopped will have accumulated less time.

So according to A, B "really" runs slower.

However, according to B: Clock A starts significantly before clock B. B runs slower than A until the collision. After A and B stop, B will have accumulated less time than A even though A ran slower than B. This is because clock A had accumulated a great deal of time before clock B even starts.

So according to B, A "really" runs slower, but it also "really" started ticking sooner.

You can't just look at the accumulated time on both clocks at the end, and say which clock "really" ran slower.

I think the part of the problem you are having is that you are equating "real" with "absolute", that unless you can say which clock absolutely ran slower, can dilation isn't "real".

But time itself is relative and not absolute, and relative time measurement is as "real" as time gets.

 

[AntigenX]

Sorry people for very very late reply.

I was trying to learn some space time diagrams, but I think it will take some time to learn their proper representation and more importantly, their correct interpretation. Meanwhile, thank you all, especially, Janus, DaleSpam, Mentz114 and others for their concern.

Here are my replies to the responses...

Here's a plain answer to that question (if I understand it): Of course! (You might want to reread your post #1 if you think you asked that question.)

I didn't mean literally from post#1, instead, from the very beginning was what I meant. Thanks for reading post#1 though.

As to how to do it, that will take some prearrangement. One way is to send signals to each clock that will reach them simultaneously according to you. You may have to send the signals at different times. Arrange to have both clocks reset to zero at the instant they receive their signals. Is that what you want?

I think that is what I want, provided, the source of signals is stationary w.r.t. at least one clock A or B. It has been suggested that, in such a situation, there is no need to consider three frames but only two, but I would like to retain three frames (as a personal preference), if at all it is possible.

I am sorry about the communication difficulties here, but I did answer this when I said:In other words, yes, you can do it but you must specify the reference frame in which the clocks read 0 at the same "arbitrary instant" and are "equidistant". There is nothing inherently wrong with the idea of an instant (simultaneous) nor is there anything wrong with the idea of equidistant. But simultaneity and distance are relative (frame variant), so the reference frame must be specified.

Don't feel sorry, you have been very cooperative. I should have made it clear that I do not understand anything except plain things.

AntigenX,

This diagram illustrates a method for M to send 2 light pulses so that A and B's clocks agree momentarily at the orange line. Red lines are light beams.

So when A sees his clock reset, he knows that if he had instantaneous comms (horizontal line) he'd see B's clock reseting as his does.

I have not tried to work out the times involved.

M

This would work, but, As I mentioned earlier, the person matching the clocks is in relative motion with both the clocks, which is the case I wish to avoid.

This problem is simply the one-clock vs. two-clock problem presented in a somewhat obscure manner.

DaleSpam,
yes, in A's rest frame. I didn't say it, but it's part of the (obscure) requirement.

The geometry in that diagram is unbelievably tricky. I had a go at working out the transmission times in M's frame but failed.

M

I would like to know what is so obscure in this problem? And the extent of obscurity as well.

 

[AntigenX]

Yes, it is perfectly possible to arrange things such that both clocks start simultaneously for any given observer. For instance, by placing the origin of the flash closer to A than to B, (as shown in the attachment)you can have both clocks start simultaneously as far as A is concerned.

I want both the clocks started simultaneously by somebody stationary w.r.t. clock A or B, and suggested method can do that, If the light flesh is emitted from closer to A, such that the light beams have to cover same distance in both direction in the source's rest frame. In such a case, As is (obscure?) requirement of my problem, the source will be at rest wrt A. Now, the source is convinced that he started both clocks simultaneously according to himself. He also knows that A is at rest and B is moving wrt him. The question is, what will he find when, after collision, he will match the clocks? To the case, following discussion from you is also applicable...

With such an arrangement, according to A: Both clocks start simultaneously. B runs slower during the period before collision and then after both clocks have stopped will have accumulated less time.

So according to A, B "really" runs slower.

However, according to B: Clock A starts significantly before clock B. B runs slower than A until the collision. After A and B stop, B will have accumulated less time than A even though A ran slower than B. This is because clock A had accumulated a great deal of time before clock B even starts.

So according to B, A "really" runs slower, but it also "really" started ticking sooner.

It is explained that, According to A, B is slower, and According to B, A is slower. But the clocks have stopped now. Who will be wrong?

You can't just look at the accumulated time on both clocks at the end, and say which clock "really" ran slower.

Exactly why not?

I think the part of the problem you are having is that you are equating "real" with "absolute", that unless you can say which clock absolutely ran slower, can dilation isn't "real".

But time itself is relative and not absolute, and relative time measurement is as "real" as time gets.

Do I have any way to convince you guys that this is not the case? For me the strongest reason for not believing in absolute time is I haven't seen any clock showing any yet, else I would synchronize my own clock with it to be on time everywhere!

 

[Doc Al]

I think that is what I want, provided, the source of signals is stationary w.r.t. at least one clock A or B. It has been suggested that, in such a situation, there is no need to consider three frames but only two, but I would like to retain three frames (as a personal preference), if at all it is possible.

As far as I can see, there are only two reference frames: Clock A and the observer are in one; Clock B is in the other.

I want both the clocks started simultaneously by somebody stationary w.r.t. clock A or B, and suggested method can do that, If the light flesh is emitted from closer to A, such that the light beams have to cover same distance in both direction in the source's rest frame. In such a case, As is (obscure?) requirement of my problem, the source will be at rest wrt A. Now, the source is convinced that he started both clocks simultaneously according to himself. He also knows that A is at rest and B is moving wrt him. The question is, what will he find when, after collision, he will match the clocks? To the case, following discussion from you is also applicable...

Is the following an accurate summary of the set up?
(1) There's a clock A at some position along the x-axis.
(2) An observer (call him O) is at rest with respect to A and is at some position to the right of A along the x-axis.
(3) There's a clock B, which is moving towards A at some speed v, at some point to the right of O along the x-axis.

We all agree that it's perfectly possible to reset clock A and clock B to both read t = 0 at the same instant according to frame O (which is also frame A). Let's say we do that. Is your question: When clock B collides with Clock A, what will they both read?

Assuming that's your question, the answer is: Clock B will read less time than Clock A.

It's easy to understand from A's point of view: Clock B runs slow, so less time accumulates as it travels from its original location to point A.

It's a bit trickier to understand from B's point of view (it requires understanding of the relativity of simultaneity): According to B, Clock A runs slow. When observer O sent B the signal he thought it reached B at the same time it reached A (and it did--according to frame O-A). But according to B, the signal reached A long before it reached B. Even after accounting for time dilation of the moving clock A, more time accumulates on clock A than on on clock B.

Everyone agrees that clock A will read more time than clock B when they finally meet.

 

[AntigenX]

Is the following an accurate summary of the set up?
(1) There's a clock A at some position along the x-axis.
(2) An observer (call him O) is at rest with respect to A and is at some position to the right of A along the x-axis.
(3) There's a clock B, which is moving towards A at some speed v, at some point to the right of O along the x-axis.

Precisely! I should have done it this way, poor me...

We all agree that it's perfectly possible to reset clock A and clock B to both read t = 0 at the same instant according to frame O (which is also frame A). Let's say we do that. Is your question: When clock B collides with Clock A, what will they both read?

Yes.

Assuming that's your question, the answer is: Clock B will read less time than Clock A.

It's easy to understand from A's point of view: Clock B runs slow, so less time accumulates as it travels from its original location to point A.

got it.

It's a bit trickier to understand from B's point of view (it requires understanding of the relativity of simultaneity): According to B, Clock A runs slow.

got it.

When observer O sent B the signal he thought it reached B at the same time it reached A (and it did--according to frame O-A).

got it.
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.

But according to B, the signal reached A long before it reached B. Even after accounting for time dilation of the moving clock A, more time accumulates on clock A than on on clock B.

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

Everyone agrees that clock A will read more time than clock B when they finally meet.

Not clear yet.

 

[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.

 

[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.