Paradox within the twin paradox

[teachmemore]

I also cannot understand what you mean by the two pulses of light "no longer moving apart". Are you thinking that the medium slows them down until they get trapped and eventually stop?

Please explain.

It is not that important, since this definition is incomplete, but ya, what I meant was that two two pulses of light are trapped within the same frame of reference. As to how the light is trapped there, it is unimportant. It could be by particle absorption, or by being reflected between theoretically perfect mirrors - doesn't matter.

 

[teachmemore]

I also cannot understand what you mean by the two pulses of light "no longer moving apart". Are you thinking that the medium slows them down until they get trapped and eventually stop?

Please explain.

Eventually stop? Sorry? No that is impossible. I just meant that they become trapped at a fixed distance apart from one another, which would imply that they are in the same frame of reference.

 

[ghwellsjr]

Wait a second here. c can be reached. It just can't be breached.

here is my definition of the absolute speed of a reference frame.

First I define the absolute stationary reference frame:
Lets say you have light traveling in two opposite directions, c and -c. Now when both these pulses of light are trapped in medium and no longer moving apart, they are both in the absolute stationary reference frame.

Now the absolute speed of any reference frame is their speed as measure from the absolute stationary reference frame.

Is that a sufficient definition?

It is not that important, since this definition is incomplete, but ya, what I meant was that two two pulses of light are trapped within the same frame of reference. As to how the light is trapped there, it is unimportant. It could be by particle absorption, or by being reflected between theoretically perfect mirrors - doesn't matter.

Well it does matter if you have some incorrect or incomplete concepts of matter, time, space and light, and their relationship to a frame of reference.

I'm wondering why you would think in any sense that "two pulses of light are trapped within the same frame of reference" and not think that about everything else, all matter is equally trapped within the same frame of reference. But then, the same two pulses of light are also trapped in any other frame of reference along with all matter. I just don't know why you are thinking about things being trapped. You need to explain.

 

[ghwellsjr]

Eventually stop? Sorry? No that is impossible. I just meant that they become trapped at a fixed distance apart from one another, which would imply that they are in the same frame of reference.

You think that two pulses of light traveling in opposite directions "become trapped at a fixed distance apart from one another"? Why do you think this?

 

[teachmemore]

You think that two pulses of light traveling in opposite directions "become trapped at a fixed distance apart from one another"? Why do you think this?

Firstly, the definition was using the scenario of two pulses of light becoming trapped at a fixed distance apart; no statement was being made about what would happen if two arbitrary light pulses were sent in opposite directions.

Secondly, the definition is incomplete, because the scenario is insufficient to define an absolutely stationary reference frame, so there is no need to dwell on it.

Do you not believe that it is possible for two beam of light to become fixed at a distance between one another? If so, please explain why it is not theoretically possible.

 

[matheinste]

There is a big difference between light being at rest and light being trapped in a frame of reference. One is not possible and one is. What I claimed is completely possible under the laws of physics.

My physics is a bit rusty but I thought that light in a medium still traveled at c and that absorption and re-emission processes caused the overall delay. What you mean by trapped in a medium, or at a certain distance apart in a medium I cannot even guess. However, I am no expert on such matters, but I do have a query: if light is at rest or trapped in a medium, how would we see it.

Matheinste.

 

[teachmemore]

Well it does matter if you have some incorrect or incomplete concepts of matter, time, space and light, and their relationship to a frame of reference.

I'm wondering why you would think in any sense that "two pulses of light are trapped within the same frame of reference" and not think that about everything else, all matter is equally trapped within the same frame of reference. But then, the same two pulses of light are also trapped in any other frame of reference along with all matter. I just don't know why you are thinking about things being trapped. You need to explain.

I don't know why you are having such a hard time with the word trapped. It just means confined to a fixed coordinate or set of coordinates within the frame of reference.

All matter IS at a fixed coordinate within a frame of reference. It does not need to be "trapped" to remain there because it is part of the frame of reference. Light on the other hand always travels at c relative to any frame of reference; hence, it must be trapped to remain at a fixed coordinate within the frame of reference. In a sense, absorption of light into matter accomplishes this feat. Or, creation of matter from light, as has been done in high speed particle accelerators.

 

[teachmemore]

My physics is a bit rusty but I thought that light in a medium still traveled at c and that absorption and re-emission processes caused the overall delay. What you mean by trapped in a medium, or at a certain distance apart in a medium I cannot even guess. However, I am no expert on such matters, but I do have a query: if light is at rest or trapped in a medium, how would we see it.

Matheinste.

We would not be able to see the trapped light pulse.

An example of a trapped light pulse is the "light clock" regularly used in special relativity thought experiments.

Edit: Another example would be an absorption process where the light is permanently absorbed as part of the particle; and is not re-emitted. Usually, photons will be re-emitted, but we have no way to tell that those photons are the same photons that were absorbed - I mean, at least not by standards of modern physics - maybe one day someone will come up with a theory that will allow us to find out such detailed information about the process of photon absorption and emission.

 

[teachmemore]

Does anyone have any thoughts on the issue of information being exchanged between reference frames that are in contact in space? ei. like my example of a device which is switched by a passing rocket?

 

[ghwellsjr]

Firstly, the definition was using the scenario of two pulses of light becoming trapped at a fixed distance apart; no statement was being made about what would happen if two arbitrary light pulses were sent in opposite directions.

Secondly, the definition is incomplete, because the scenario is insufficient to define an absolutely stationary reference frame, so there is no need to dwell on it.

Do you not believe that it is possible for two beam of light to become fixed at a distance between one another? If so, please explain why it is not theoretically possible.

You started off by saying two pulses of light were traveling in opposite directions. I guess from other posts you are simply saying that while they are light, they are traveling and have no fixed coordinates but when they hit something, then they have a fixed distance between them. Is this correct?

Now you are asking about two beams of light "to become" a fixed distance between one another and the confusion starts all over again. To me (and I think everyone else) a pulse of light is what you get when you turn a laser (or some other light source) on and off and a beam of light is what you get when you turn a laser (or some other light source) on and leave it on. The only way in which your question would make sense to me is if you were thinking of two lasers a fixed distance apart but otherwise aimed in the same direction and you turn them both on. Then the two beams would be parallel a fixed distance apart. But, somehow, I don't think this is what you had in mind because you used the expression "to become" and I suspect you are still thinking in terms of the beams being pointed in opposite directions. It is really important when discussing SR that we have a clear understanding of what light does so please explain what your concepts are.

 

[matheinste]

We would not be able to see the trapped light pulse.

An example of a trapped light pulse is the "light clock" regularly used in special relativity thought experiments.

.

Hardly light at rest though.

As regards absorption, if a photon is absorbed I think it does not remain a photon, but its energy is absorbed raising the energy level or levels of bits within the atom by which it is absorbed.

But most of this is irrelevant to a definition pseudo absolute motion.

Matheinste.

 

[teachmemore]

You started off by saying two pulses of light were traveling in opposite directions. I guess from other posts you are simply saying that while they are light, they are traveling and have no fixed coordinates but when they hit something, then they have a fixed distance between them. Is this correct?

Now you are asking about two beams of light "to become" a fixed distance between one another and the confusion starts all over again. To me (and I think everyone else) a pulse of light is what you get when you turn a laser (or some other light source) on and off and a beam of light is what you get when you turn a laser (or some other light source) on and leave it on. The only way in which your question would make sense to me is if you were thinking of two lasers a fixed distance apart but otherwise aimed in the same direction and you turn them both on. Then the two beams would be parallel a fixed distance apart. But, somehow, I don't think this is what you had in mind because you used the expression "to become" and I suspect you are still thinking in terms of the beams being pointed in opposite directions. It is really important when discussing SR that we have a clear understanding of what light does so please explain what your concepts are.

Ya sorry. I meant pulse, not beam.

 

[ghwellsjr]

Does anyone have any thoughts on the issue of information being exchanged between reference frames that are in contact in space? ei. like my example of a device which is switched by a passing rocket?

Your concept of a reference frame is all mixed up. It is not something physical. It is a co-ordinate system that we use to describe and analyze situations. All inertial reference frames extend in all directions throughout all of space and go from eternity past to eternity future. It doesn't make sense to ask about frames that are in contact because all frames cover all space.

You can take the situation involving all of your objects described in one frame and use the Lorentz Transformation to see what it would look like in another frame but there is no sense in which the frames come in contact.

Now if you want to talk about exchanging information between two observers that are traveling with respect to one another, there's no problem with that, as long as you limit the speed of information exchange to c. You don't have to actually build such a device, or be concerned about the practicality of such a device, all you have to do is say that observer A sends a coded light beam to observer B and it travels at the speed of light in the reference frame that you have defined the motions of the two observers. You don't have to get more complicated than that.

 

[teachmemore]

Hardly light at rest though.

As regards absorption, if a photon is absorbed I think it does not remain a photon, but its energy is absorbed raising the energy level or levels of bits within the atom by which it is absorbed.

But most of this is irrelevant to a definition pseudo absolute motion.

Matheinste.

Ya. The light is not every at rest. agreed.

And ya. as far as light absorption, who the hell knows what happens to it. It is all just speculation. We only know that it it can both be incorporated into the particle and that the particle can be converted into light and emit light by e=mc^2.

 

[cavalier3024]

As you describe B 'sees' them as starting at the same time. Everything is done from B's reference frame.

I altered it slighly though to make the end points effectively at the same point in space. ie. the reference frames are touching so that they exchange data instantly.

This was done through a hypothetical device which exists in the same reference frame as clock/counter B, but at the same position as the clock/counter A when it passes the device. Counter B knows the distance of this device relative to itself and can therefore calculate the elapsed time since B was 'switched' by A.

Do you see? Normally, B would receive the first pulse from A, telling B that A had started at a point in time when from A's reference frame, it had already started ticking. BUT, through this device, B's frame of reference is physically in contact with A at the moment it starts ticking, so that through B's frame of reference, information is sent to B about the earlier time in which A started, all through direct physical contact.

The difference between your thought experiment here and mine, is that both reference frames are touching one another at both end points, when the clock A starts, and when the clocks meet and touch one another in space. This allows information to be sent to clock B, that it would otherwise not have access to.

Edit: So I guess the question is - how does instant traversal of data between reference frames at the two end points affect the problem?

if i understand you correctly, the purpose of this hypothetical device is to help synchronize the two clocks A and B?
if so, it doesn't really provide a solution, and to explain why i need to first see if we agree about relative simultaneity. what i say is that if from A's point of view two events happen at the same time, then from B's point of view they will happen at different times (and vice-versa).
so if the two events are A's counter starting and B's counter starting, then it is impossible that both A and B will think that those events happened at the same time.
either from B's point of view it will happen at the same time and from A's view B's clock started sooner, or the other way around.
do you agree with that?

 

[ghwellsjr]

Ya sorry. I meant pulse, not beam.

OK, so I will change your question to be:

"Do you not believe that it is possible for two pulses of light to become fixed at a distance between one another? If so, please explain why it is not theoretically possible."

The only way I can understand this question is if we think of two light sources a fixed distance apart, emitting two pulses of light in the same direction, and they travel forever at that same fixed distance apart. But they don't "become fixed at a distance between one another" some time after they were emitted, they started off that way and they remain that way forever (unless they hit something which ends their existence and then I wouldn't say they were any distance apart).

And all of this has nothing to do with any frames of reference, it's just physics.

So please help me understand your concepts of light and being fixed and how that relates to reference frames. It's very important if we are going to make progress.

 

[teachmemore]

Your concept of a reference frame is all mixed up. It is not something physical. It is a co-ordinate system that we use to describe and analyze situations. All inertial reference frames extend in all directions throughout all of space and go from eternity past to eternity future. It doesn't make sense to ask about frames that are in contact because all frames cover all space.

You can take the situation involving all of your objects described in one frame and use the Lorentz Transformation to see what it would look like in another frame but there is no sense in which the frames come in contact.

Now if you want to talk about exchanging information between two observers that are traveling with respect to one another, there's no problem with that, as long as you limit the speed of information exchange to c. You don't have to actually build such a device, or be concerned about the practicality of such a device, all you have to do is say that observer A sends a coded light beam to observer B and it travels at the speed of light in the reference frame that you have defined the motions of the two observers. You don't have to get more complicated than that.

ah. thank you, but the coded light pulse would not be able to relay all the information that my device would because the observer A does not know the distance between himself and observer B from observer B's frame of reference. Observer A only knows the distance as he observes it to be from his own reference frame and when the pulse reaches observer B, observer B has no way to find out at what distance observer A was from him in his own reference frame. The device gets around this.

 

[teachmemore]

OK, so I will change your question to be:

"Do you not believe that it is possible for two pulses of light to become fixed at a distance between one another? If so, please explain why it is not theoretically possible."

The only way I can understand this question is if we think of two light sources a fixed distance apart, emitting two pulses of light in the same direction, and they travel forever at that same fixed distance apart. But they don't "become fixed at a distance between one another" some time after they were emitted, they started off that way and they remain that way forever (unless they hit something which ends their existence and then I wouldn't say they were any distance apart).

And all of this has nothing to do with any frames of reference, it's just physics.

So please help me understand your concepts of light and being fixed and how that relates to reference frames. It's very important if we are going to make progress.

Now add to this the condition that the two light pulses do not begin at this fixed distance.

Edit: oh geeze, sorry. scratch that. The condition is that the two light pulses begin at a fixed distance, but then become an unfixed distance, and then return to a fixed distance. how is that? ;-)

Edit: although, I suppose it could be said that they do not begin at a fixed distance from one another, because they are moving away from one another from the instant they start. The distance between them is always changing from the beginning until they become "trapped" in the same frame of reference.

 

[teachmemore]

if i understand you correctly, the purpose of this hypothetical device is to help synchronize the two clocks A and B?
if so, it doesn't really provide a solution, and to explain why i need to first see if we agree about relative simultaneity. what i say is that if from A's point of view two events happen at the same time, then from B's point of view they will happen at different times (and vice-versa).
so if the two events are A's counter starting and B's counter starting, then it is impossible that both A and B will think that those events happened at the same time.
either from B's point of view it will happen at the same time and from A's view B's clock started sooner, or the other way around.
do you agree with that?

Ah, maybe here is where it will clear up the difference in our understanding.

If the two clocks are in contact with one another, even though they are in different frames of reference; when B perceives that they start at the same time, A will also perceive that the two clocks start at the same time. It is the only case when relativity can be simultaneous. If there is any distance between them, then relativity cannot be simultaneous and the mere fact that from one frame the events are simultaneous tells us that from the other reference frame, they are not.

If you can tell me why I'm wrong here, then maybe I will finally understand!

Edit: So to summarize what I have said here. I agree with you for all cases except the case where the two clocks are in contact with one another. If the two clocks are in contact with one another, then the exchange is instantaneous and they are both immediately aware of one another's event.

 

[JesseM]

Ah, maybe here is where it will clear up the difference in our understanding.

If the two clocks are in contact with one another, even though they are in different frames of reference; when B perceives that they start at the same time, A will also perceive that the two clocks start at the same time. It is the only case when relativity can be simultaneous. If there is any distance between them, then relativity cannot be simultaneous and the mere fact that from one frame the events are simultaneous tells us that from the other reference frame, they are not.

Yes, that's exactly right. Disagreements between frames about simultaneity only occur for events that happen at different spatial locations, if two events happen at the same time and the same position in one frame, then all other frames agree those events happened at the same time and position.

 

[cavalier3024]

Ah, maybe here is where it will clear up the difference in our understanding.

If the two clocks are in contact with one another, even though they are in different frames of reference; when B perceives that they start at the same time, A will also perceive that the two clocks start at the same time. It is the only case when relativity can be simultaneous. If there is any distance between them, then relativity cannot be simultaneous and the mere fact that from one frame the events are simultaneous tells us that from the other reference frame, they are not.

If you can tell me why I'm wrong here, then maybe I will finally understand!

Edit: So to summarize what I have said here. I agree with you for all cases except the case where the two clocks are in contact with one another. If the two clocks are in contact with one another, then the exchange is instantaneous and they are both immediately aware of one another's event.

yep. that's true, but still, only one can happen - either the two clocks are at the same location when they start, or they are at the same location some time after they start, when they measure each other. in either case there is a point in time where the two clocks are at different locations, and at that point my argument is valid.

so if what you say is that the two clocks start at the same location then yes, they will start simultaneously. but let's say that after some time they measure each other. each will see that the other is 'younger' (it's counter ticked less times) but that's not a paradox.. its a basic relativity consequence - when a moving object looks towards the direction opposite to its speed, the further away he looks the more backwards in time he will see.
so in this case they will both see each other's clocks tick slower and they will both see each other as younger..

 

[JesseM]

so if what you say is that the two clocks start at the same location then yes, they will start simultaneously. but let's say that after some time they measure each other. each will see that the other is 'younger' (it's counter ticked less times) but that's not a paradox.. its a basic relativity consequence - when a moving object looks towards the direction opposite to its speed, the further away he looks the more backwards in time he will see.

You seem to be saying that the fact that each measures the other to be younger is just a consequence of the fact that light takes some time to travel between them so they are seeing the other as they were in the past, but that's not correct! Time dilation is what remains after you correct for light delays. For example, suppose you and I are moving apart at 0.6c, and we both started from the same location when we were both aged 30. Also suppose I have a ruler at rest relative to me, and I am at the x=0 light years on my ruler. Then when I am 46 years old, if I look through my telescope I see an image of you next to the the x=6 light-year mark on my ruler, at age 38. Since you emitted this light when you were 6 light-years away from my position, I can calculate that you "really" emitted that light 6 years earlier, when I was only 40. Still, that means that even when I account for the light delay, I'm still left with the conclusion that you were age 38 when I was 40, so that's the "real" time dilation in my frame. And this effect is also completely symmetrical as long as we are both moving inertially: if you had your own ruler at rest relative to yourself and you were at the x=0 mark on your ruler, then when you were 46 you'd be seeing the light from the event of me turning 38 and passing the x=6 mark on your ruler, so you'd conclude that in your frame I was turning 38 when you were turning 40.

 

[cavalier3024]

You seem to be saying that the fact that each measures the other to be younger is just a consequence of the fact that light takes some time to travel between them so they are seeing the other as they were in the past, but that's not correct! Time dilation is what remains after you correct for light delays. For example, suppose you and I are moving apart at 0.6c, and we both started from the same location when we were both aged 30. Also suppose I have a ruler at rest relative to me, and I am at the x=0 light years on my ruler. Then when I am 46 years old, if I look through my telescope I see an image of you next to the the x=6 light-year mark on my ruler, at age 38. Since you emitted this light when you were 6 light-years away from my position, I can calculate that you "really" emitted that light 6 years earlier, when I was only 40. Still, that means that even when I account for the light delay, I'm still left with the conclusion that you were age 38 when I was 40, so that's the "real" time dilation in my frame. And this effect is also completely symmetrical as long as we are both moving inertially: if you had your own ruler at rest relative to yourself and you were at the x=0 mark on your ruler, then when you were 46 you'd be seeing the light from the event of me turning 38 and passing the x=6 mark on your ruler, so you'd conclude that in your frame I was turning 38 when you were turning 40.

exactly! what i tried to say is that: the fact that each measures the other to be younger is NOT just a consequence of the fact that light takes some time to travel between them. i don't know why you thought that i thought the opposite.. but anyway thanks for clarifying my case..

 

[JesseM]

exactly! what i tried to say is that: the fact that each measures the other to be younger is NOT just a consequence of the fact that light takes some time to travel between them. i don't know why you thought that i thought the opposite.. but anyway thanks for clarifying my case..

OK, I thought you were saying it was just an optical effect because of the statement "when a moving object looks towards the direction opposite to its speed, the further away he looks the more backwards in time he will see." That's true in terms of what's seen visually (for example, if I look at two stars 10 and 20 light-years away and at rest in my frame, then the image of the one 20 light-years away is what the star looked like 20 years 'backwards in time' in my frame, further back than the image of the one 10 light-years away), but after you correct for light delays I don't think it makes sense to say "the further away he looks the more backward in time he will see", but time dilation still exists when you correct for light delays with an object in motion relative to you. As long as you agree with that, no problem!

 

[cavalier3024]

after you correct for light delays I don't think it makes sense to say "the further away he looks the more backward in time he will see"

why not? let's ignore the delay caused by light. even now, two observers moving relative to each other will 'see' the same event happen at different times (lets assume that both observers are currently at the same position and that the event occurs at a different position). and the difference between this times will be bigger the farther away the event is from the observers. therefore, the moving observer will 'see' farther into the past the farther away he looks, relative to the other observer (if he looks at a direction opposite to his movement. if he will look forward he will see into the future, relative to the other observer)
thats why relativity of simultaneity is possible..

its kinda hard to explain it in words but from lorentz transform u get http://upload.wikimedia.org/math/c/0/f/c0ff5f091774a86621f711d11e7c0068.png" . so what i was saying is that the bigger x is (the farther away you look) the bigger the time difference (the more you will see into the past, relatively)

 

[JesseM]

why not? let's ignore the delay caused by light. even now, two observers moving relative to each other will 'see' the same event happen at different times (lets assume that both observers are currently at the same position and that the event occurs at a different position). and the difference between this times will be bigger the farther away the event is from the observers.

The difference is greater, yes, but it's not the case that this always means the event is further in the past the greater the distance of the observers, it might be further in the future for at least one of the observers.

 

[teachmemore]

People keep trying to explain this with a 'delay', claiming 'relativity of simultaneity', which shows that they are missing it.

It is easy to setup a thought experiment where simultaneity can be ensured. In this case I used a device which is in the frame of reference of counter B, when it comes in contact with counter A.

This device could potentially record a variety of information from A, and at the time within its own reference frame that corresponds to the simultaneous instant that counter A resets itself. This information can then be transmitted to counter B. Counter B can then do the calculation in order to set itself to the time it 'would' have counted to had it simultaneously reset itself with counter A. Counter B could also find out other details about Counter A, using information such as A's relative speed to B (of course, an agreement could have been made between the two counters at some point in history that this whole experiment would be done at a specific relative speed to one another, and this could have been arranged.)

If you are following me so far, then maybe you will be able to help me understand.

I'm going to simplify my thought experiment slightly.

Firstly, counter A and B are relative, so we make no assumptions about who is stationary and who is traveling from a "god's" view.

When counter B receives its signal, it will be able to do a relativistic calculation to find out the precise count that counter A has reached at the instant in its own reference frame that is simultaneous to the instant in B's reference frame for which it received the signal.

Counter B can now be assured that it has set itself to the same count in its own reference frame that A has reached in its own reference frame at that simultaneous instant. Counter A is not aware of this information, but it is still a fact for counter A of course.

When the two counters meet, Counter B reads A's counter.

Now here is the paradox: The counters were matched in there own respective frames of reference at a simultaneous instant in time, so they should still match counts when they meet on another, due to the symmetry between them. But, if this is the case, counter B will get a surprise, because from the time it set itself to match counter A in A's own reference frame, counter A has been moving slow for counter B.

This thought experiment is meant to rule out the relativity of simultaneity and to be independent of any "godly" knowledge of exact velocities of the two counters. It has also been designed to rule out any acceleration.

I should mention, the device was probably not required at all, just an ability for counter B to do special relativity calculations. The exact distance from A to B in A's reference frame and the relative velocity between A and B could be agreed upon ahead of time before A goes off into space to start the experiment. A could easily determine these factors by monitoring acceleration and time as it got itself into position to start the experiment. In this way counter B could be previously endowed with such knowledge.

Edit: This paradox would imply that absolute knowledge of frames of reference does exist, due to an impossibility of symmetry between to frames of reference in the universe, we can just not attain such absolute knowledge through special relativity calculations alone. For instance, if this experiment was carried out in space, we could then compare clocks and determine the actual absolute values for Earth's frame of reference relative to the rest of space.

Edit: Also, it follows that IF absolute frames of reference exist in space, symmetry between two frames of reference would be impossible; meaning, you can't just pick and choose, if someone is going faster than you, he will age slower and you would need to know if he is going faster before you could know whether he is aging slower.

Edit: Of course it also follows that if all reference frames are symmetrical, then there are no absolute frames of reference in the universe and that it is impossible to be in an absolutely stationary frame.

 

[JesseM]

People keep trying to explain this with a 'delay', claiming 'relativity of simultaneity', which shows that they are missing it.

It is easy to setup a thought experiment where simultaneity can be ensured. In this case I used a device which is in the frame of reference of counter B, when it comes in contact with counter A.

This device could potentially record a variety of information from A, and at the time within its own reference frame that corresponds to the simultaneous instant that counter A resets itself. This information can then be transmitted to counter B. Counter B can then do the calculation in order to set itself to the time it 'would' have counted to had it simultaneously reset itself with counter A.

"Simultaneously" in whose frame? Of course you could design things so that B will reset itself to read some time T "simultaneously" with A reading T as simultaneity is defined in B's rest frame, but in that case A and B will not read T simultaneously in A's rest frame. Likewise you could design things so they both read T simultaneously in A's rest frame, but then they wouldn't read T simultaneously in B's rest frame. So simultaneity hasn't been "ensured" in any absolute sense, only relative to some particular choice of reference frame. And since A and B are moving relative to one another, even if they both read T simultaneously in one of these frames, after that they will start to get progressively more out-of-sync because one is ticking slower than the other.

I'm going to simplify my thought experiment slightly.

Firstly, counter A and B are relative, so we make no assumptions about who is stationary and who is traveling from a "god's" view.

When counter B receives its signal, it will be able to do a relativistic calculation to find out the precise count that counter A has reached at the instant in its own reference frame that is simultaneous to the instant in B's reference frame for which it received the signal.

This is confusing, does "in its own reference frame" refer to A's frame or B's? Certainly when B receives the signal, it could figure out what count A has reached simultaneously with B receiving the signal using the definition of simultaneity in B's frame, or it could figure out what count A has reached simultaneously with B receiving the signal using the definition of simultaneity in A's frame. Which one are you talking about here, if either?

Counter B can now be assured that it has set itself to the same count in its own reference frame that A has reached in its own reference frame at that simultaneous instant. Counter A is not aware of this information, but it is still a fact for counter A of course.

I don't get what you mean here. If B set sets itself to time T such that the event of B reading T is simultaneous with the event of A reading T in A's frame, then they do not read T simultaneously in B's frame. Likewise if B sets itself so that they both read T simultaneously in B's frame, they do not read T simultaneously in A's frame. You seem to be suggesting it could be a "fact" in both frames that they are both at the same count T the moment after B receives the first signal and resets itself, but that's impossible.

 

[ghwellsjr]

Teachmemore, when describing two light pulses, you finally settled on:

I suppose it could be said that they do not begin at a fixed distance from one another, because they are moving away from one another from the instant they start. The distance between them is always changing from the beginning until they become "trapped" in the same frame of reference.

Are you thinking that the faster something travels, the slower time goes for that thing and does this have anything to do with your statement that these two light pulses traveling in opposite directions from a common starting point eventually 'become "trapped" in the same frame of reference'?

 

[ghwellsjr]

Firstly, counter A and B are relative, so we make no assumptions about who is stationary and who is traveling from a "god's" view.

Teachmemore, I have been trying to get you to use just one frame of reference and now you want to use no frame of reference. When describing these thought experiments, you get to play "god". In fact you must play "god". You must define counter A's position and velocity starting from time zero and you must define counter B's position and velocity starting from time zero in a single frame of reference. You must define when the counters get reset as defined by the one frame of reference. You cannot talk about the reference frame for A and a different reference frame for B as if each reference frame applies only to one counter. All reference frames apply to all objects all the time.

I explained all this and gave you an example back in post #31. Please study and understand this, and follow its advice before you try to explain another thought experiment. If you don't understand it, please ask for clarification:

You have a misunderstanding of what a reference frame is. It is a co-ordinate system with time added. Think of the graphs you made in school. You drew a horizontal line and a vertical line. At the intersection you wrote the number zero to specify the origin. Then you put positive numbers off to the right and upwards and negative numbers off to the left and downwards. Even though the numbers stopped because of the limited size of your paper, you knew that they really extended all the way to infinity in all directions. Then if you wanted to describe two objects, you specified their locations in terms of the x,y co-ordinates and you could calculate their distance apart or whatever.

Now what if someone told you that they were going to make two graphs on two separate pieces of paper and put one object in one of the graphs and another object in the other graph and then they started moving the pieces of paper around trying to explain how the two objects in the two separate graphs moved in relation to one another. Wouldn't you say they were mixed up?

That's what you are doing in your thought experiment. Instead, you must start with one and only one reference frame. That's like your graph. You can say that one counter is stationary at the origin and the other one is one light year off to the left (for example) and traveling at 0.99995c toward the origin and at time zero both counters are set to zero and they send out a signal once per minute. Then we can analyze what will happen approximately one year later when the traveling counter reaches the stationary counter. They will have different counts, the traveling one will have a much lower count on it.

Just think about something. When this scenario starts, neither counter will have any knowledge of what the other counter is doing. It will take almost one year for the signals coming from the traveling counter to reach the stationary counter and then within less than half an hour, all the signals will arrive in a burst and then the counter will arrive. At a speed of 0.99995c, the traveling counter's time has slowed to 1% of normal. Since there are 525600 minutes in a year, this counter will have only sent out 5256 signals during his entire trip but they will arrive during the last 26.28 minutes (1-0.99995 or 0.00005 times the number of minutes in a year). That's a rate of 200 signals per minute as measured by the stationary clock.

On the other hand, the traveling counter will not see anything from the stationary counter until after about half a year. Then it will start seeing signals coming in two per minute (they are traveling towards him at the speed of light and he is traveling toward them at almost the speed of light, which approximately doubles the rate at which he receives the signals), except since his clock is running at 1% of normal, he will think they are coming in at 100 times that rate which is 200 per minute. And by the time he gets to the stationary clock, he will have received almost a year's worth of signals sent out at one per minute or very nearly 525600.

Now if you want to analyze the same scenario in another reference frame, the one in which the traveling counter is stationary, you have to correctly transform everything in the first frame to the second frame. You just can't say that the two counters will be zero at the start at the same time because that would be a different scenario.