Paradox within the twin paradox

[ghwellsjr]

How is this symmetrical if there is an unequal number of pulses exchanged between these counters? At any time near the end of the voyage, the traveling counter can determine that he is moving faster than the stationary one by comparing the total pulses received with the total counts made.

This here is what I need to think about.

I was under the impression that the traveling counter counts more slowly simply because it is travelling, and so, knowledge about which one is traveling is crucial to determining which counter counts the fewest times.

Maybe you could benefit from my explanation of relativistic doppler in this post (#4) on another thread:
https://www.physicsforums.com/showpost.php?p=2970458&postcount=4

There are two important things to recognize here. First, it is the relativistic doppler that is the means by which each observer recognizes that the other one's clocks are running slower than their own. But it is not just the rate that each receives the signals that is necessary for them to make this determination, they also need to know (by prior agreement) that each one is emitting the signals at what they each consider to be the same rate, and they need to know the relative speed, either by prior agreement or knowledge (as is the case when twins start out together and one "tells" the other one what speed he will be traveling at) or by measuring the speed of the other one and this they can do by sending a series of signal to the other one which is reflected back to them. Of course all this takes time and is somewhat complicated to explain. All we are doing here is illustrating for us (because we have more knowledge than the observers/counters/clocks in the scenario) how the relativistic doppler works.

And the second thing to recognize is that if it weren't for the reason that we need SR, the doppler would not be symmetric and it would be dependent on the relative speed of the other body and the speed of each body in the medium, in this case the absolute at-rest aether.

 

[teachmemore]

By "counts more slowly" do you just mean how fast its own clock is ticking, or are you talking about the rate it receives signals from the other counter? If you're just talking about clock rates (the rate it counts seconds), then relative to the "stationary" frame its clock does tick more slowly, but not in any absolute sense. In the traveling counter's own rest frame, its clock is ticking normally while the stationary counter's clock is ticking slowly.

I understand that in relativity all inertial frames are equally valid as far as the basic laws of physics are concerned. You are neglecting the fact that not all factors required to solve this problem lay within the confines of special relativity.

Specifically, special relativity does not say anything about deriving information about the present based on data preserved from the past; which is a crucial factor in understanding the thought experiment I have presented.

By insisting on understanding what happens for only the factors in this experiment for which special relativity applies, you have come to incorrect reasoning - specifically, about what is real or absolute, as defined by the experiment.

When I laid out this thought experiment, I explicitly stated that one counter is travelling, while the other is not. For you to think that special relativity tells you that you can not know which frame is moving faster is clearly false. Special relativity only tells you that you can not know which frame is moving faster by the factors of the scenario for which special relativity applies. It is easy to determine from one frame, that another frame is moving faster than it simply by looking at historically preserved information within that one frame.

Furthermore, although due to the laws of special relativity, we can never truly know which frame in the universe is the true stationary frame (at least I can't comprehend a way in which we would determine this). We can conceive a stationary frame, and it does not go against any known laws of physics for such a frame to exist - an absolute stationary frame. Again, special relativity does not say that such a frame does not exists, only that without prior knowledge, you can not determine whether you are in it.

But, for this thought experiment, I have clearly stated that one frame is stationary and the other frame is travelling. You cannot change these factors in the problem any more than you could do such a thing in reality. This does not defy special relativity. Such information is outside the confines of special relativity, because it is derived from properties of the universe for which special relativity says nothing about.

Again, special relativity only says something about what you can know through relativistic transformations. It does not tell you anything about what you can know through other means! It does not tell you about any absolute aspects of reality. It only tells you about relative qualities of reality.

I have clearly defined in my thought experiment that one counter is stationary and the other counter is travelling. It is perfectly reasonable to make such absolute statements, and these statements are made outside the confines of special relativity. These factors of the thought experiment cannot be changed.

Yes, again, I understand that this distinction does not make any difference to the physical laws experienced in each reference frame. Those laws are preserved by special relativity. But it does certainly make a difference to the absolute statements we can make about this hypothetical scenario. The moving counter does count fewer times than the stationary counter. That is an absolute which can not be changed. It is made absolute, because the fact that the stationary counter is stationary is also absolute, as well as the fact that the traveling counter is travelling, is not stationary, and is going at an absolute speed relative to c.

hmmm. All this makes me consider, the only absolute speeds in the universe have to be defined as a factor of c. Otherwise, the speed is relative. Anyway, does any of this make sense to you?

 

[teachmemore]

By "counts more slowly" do you just mean how fast its own clock is ticking, or are you talking about the rate it receives signals from the other counter? If you're just talking about clock rates (the rate it counts seconds), then relative to the "stationary" frame its clock does tick more slowly, but not in any absolute sense. In the traveling counter's own rest frame, its clock is ticking normally while the stationary counter's clock is ticking slowly.

Ok. Before you can help me to come to an understanding on this, we need to be on the same page.

I want to know if you agree with the following statement:

I have an "absolutely" stationary counter and I have an "absolutely" traveling counter. According to special relativity, the traveling counter "sees" only a moving counter and the stationary counter "sees" only a moving counter. Neither one can determine which counter is really the counter that is moving, except through past preserved information (ie. One of the counters accelerated away from the other at sometime in the past). In this case, both counters are moving slower relative to the other counter, but only one is "actually" moving slower - and that is the traveling counter.

Do you agree?

 

[JesseM]

I understand that in relativity all inertial frames are equally valid as far as the basic laws of physics are concerned. You are neglecting the fact that not all factors required to solve this problem lay within the confines of special relativity.

I don't see why they wouldn't...

Specifically, special relativity does not say anything about deriving information about the present based on data preserved from the past;

Not sure what you mean. Certainly in SR if you know the positions of various parts of a system at some point in the past you can use the dynamical equations of the laws of physics to predict how they will move around at later times, that's what all dynamical equations are designed to do. What specific "data preserved from the past" are you talking about in your example, and what "information about the present" is that data being used to derive?

By insisting on understanding what happens for only the factors in this experiment for which special relativity applies, you have come to incorrect reasoning - specifically, about what is real or absolute, as defined by the experiment.

Again more specifics would be helpful, what precisely do you think is "real or absolute", and not frame-dependent, in your experiment?

When I laid out this thought experiment, I explicitly stated that one counter is travelling, while the other is not.

I understood this to mean that one is traveling relative to the inertial frame we are using, not in any absolute sense. If you are saying that one counter is traveling in an absolute, frame-independent sense, then your scenario involves metaphysical claims that can't be verified experimentally, because there's no actual experimental way to test whether something is "travelling" in any frame-independent sense (no matter what experiment you think up, all frames will make the same predictions about the readings of your instruments, in spite of the fact that they have different opinions on whether any given instrument is 'travelling' or 'at rest')

For you to think that special relativity tells you that you can not know which frame is moving faster is clearly false.

The only notion of "motion" in relativity is relative motion, you can't talk about whether something is moving or at rest (or which of two objects is moving faster) in any absolute sense.

It is easy to determine from one frame, that another frame is moving faster than it simply by looking at historically preserved information within that one frame.

What do you mean "from one frame"? Of course I agree that relative to a specific choice of frame you can define the speed of any other frame or object, but I thought you were talking about deciding which is stationary and which is moving in a "real or absolute" sense. When you said it is "clearly false" that "you can not know which frame is moving faster", did you just mean "moving faster" in a relative, non-absolute sense? If so I don't know why you think I would deny that you can determine which of two objects or frames is moving faster relative to some specific frame, of course I would agree with that!

Furthermore, although due to the laws of special relativity, we can never truly know which frame in the universe is the true stationary frame (at least I can't comprehend a way in which we would determine this). We can conceive a stationary frame, and it does not go against any known laws of physics for such a frame to exist - an absolute stationary frame. Again, special relativity does not say that such a frame does not exists, only that without prior knowledge, you can not determine whether you are in it.

Well, belief in such an absolute stationary frame is a metaphysical hypothesis, like believing in God or the soul. Not only does relativity say that there is no empirical way to determine which frame is the absolute frame, it also says there is no physical reason why you need the hypothesis of an "absolute frame". Of course it also does not rule this hypothesis out, I actually made this point myself recently on [post=2980648]another thread[/post]:

Also note that you are free to believe that one inertial frame's definition of simultaneity is "correct" in some absolute metaphysical sense, as long as there is no physical experiment that will actually distinguish the "correct" inertial frame from any other inertial frame this does not conflict with SR, which is just meant to be a physical theory and not a metaphysical one.

But, for this thought experiment, I have clearly stated that one frame is stationary and the other frame is travelling.

You didn't state that one was "stationary" in an absolute metaphysical sense, I thought you just meant that we could adopt the terminology of calling one the "stationary" frame and one the "travelling" frame.

You cannot change these factors in the problem any more than you could do such a thing in reality.

Well, I didn't change that factor, I didn't say anything about any frame being stationary or at rest in an absolute sense. I just pointed out that, without changing the motion of the two counters, you could change when they were programmed to start transmitting signals (so they no longer started sending signals simultaneously in the stationary frame), and this would change the final number of signals each had received when they met.

Again, special relativity only says something about what you can know through relativistic transformations. It does not tell you anything about what you can know through other means! It does not tell you about any absolute aspects of reality. It only tells you about relative qualities of reality.

Relativity certainly tells you about frame-independent facts, it wouldn't be much use as a physical theory if it didn't! For example, it can tell you how much proper time will elapse between two events on an object's worldline (like the event of a person leaving his twin and the event of his reuniting with him), the answer to questions about proper time doesn't depend on what frame you use to do your calculations.

I have clearly defined in my thought experiment that one counter is stationary and the other counter is travelling. It is perfectly reasonable to make such absolute statements, and these statements are made outside the confines of special relativity. These factors of the thought experiment cannot be changed.

OK, as I said you never made clear that you were talking about absolute metaphysical truths outside the domain of physics. But even with that understanding, I don't see why you would disagree with anything I've said so far, I don't think I said anything about changing the definition of which counter is "stationary" for example. What specific previous statement of mine do you disagree with?

Yes, again, I understand that this distinction does not make any difference to the physical laws experienced in each reference frame. Those laws are preserved by special relativity. But it does certainly make a difference to the absolute statements we can make about this hypothetical scenario. The moving counter does count fewer times than the stationary counter. That is an absolute which can not be changed. It is made absolute, because the fact that the stationary counter is stationary is also absolute, as well as the fact that the traveling counter is travelling, is not stationary, and is going at an absolute speed relative to c.

Yes, if you believe in absolute time and space this is true, although this is a metaphysical faith I don't share (by http://en.wikipedia.org/wiki/Occam's_razor]Occam's[/PLAIN] razor it seems simpler to dispense with the idea of absolute motion and absolute simultaneity, since these things provide no useful explanatory role and we can have a perfectly good ontology of spacetime without them)

hmmm. All this makes me consider, the only absolute speeds in the universe have to be defined as a factor of c. Otherwise, the speed is relative. Anyway, does any of this make sense to you?

Yes, I think the distinction between absolute (but unverifiable) truths and physically-verifiable truths helps clarify what you're saying. Of course, about that last part, if there is an absolute time and space then the speeds of slower-than-light objects are absolute too, although in physics terms they are relative.

 

[JesseM]

want to know if you agree with the following statement:

I have an "absolutely" stationary counter and I have an "absolutely" traveling counter. According to special relativity, the traveling counter "sees" only a moving counter and the stationary counter "sees" only a moving counter. Neither one can determine which counter is really the counter that is moving, except through past preserved information (ie. One of the counters accelerated away from the other at sometime in the past). In this case, both counters are moving slower relative to the other counter, but only one is "actually" moving slower - and that is the traveling counter.

Do you agree?

I agree that if there is such a thing as absolute time and space, then there will be some absolute truth about which is "really" moving at a smaller speed and which is "really" sending signals more quickly, but this truth would be impossible to determine by any empirical means, and personally I don't actually believe in absolute time and space, it seems like an unnecessarily cumbersome idea given that it would play no useful role in explaining anything (by analogy, do you believe in an 'absolute left and right'?) And I don't understand the statement "Neither one can determine which counter is really the counter that is moving, except through past preserved information (ie. One of the counters accelerated away from the other at sometime in the past)"--why would acceleration in the past tell you anything about which is moving in an absolute sense? You can always find an inertial frame where the two counters were initially traveling together at some nonzero speed, then the acceleration of one counter caused it to come to rest in that frame, and since the "absolute frame" is completely unknowable we have no reason to rule out the idea that this frame is in fact the absolute one.

 

[teachmemore]

Definitely not, there is no objective truth about which is "moving near c" and which is "stationary", that depends on your frame of reference. Whatever is happening with the counters in the "stationary" frame, you could construct an analogous pair where the choice of when each counter started sending signals was different, in such a way that the counter which was "travelling" relative to the stationary frame would be the one to receive 5265 signals over the course of a year of its own proper time (would actually be 100 years in the stationary frame), while the counter that was at rest in the stationary frame would receive 525600 over 3.65 days in the stationary frame, and yet each counter started sending signals simultaneously in the rest frame of the traveling counter (not simultaneously in the stationary frame).

You see. Your thinking is so focused on the relative aspects of this thought experiment that you fail to see the non-relative ones; which would allow you to come to an absolute answer about the pulses seen by each of these counters.

It appears to me that the added complexity you have introduced by neglecting the absolute states of this thought experiment is causing you to confuse what is possible in reality with what is possible when only special relativity is taken into account. ie. In your abstract example here what you have basically done is moved the stationary frame to the traveling frame - ie. symmetrically swapped frames - which is physically impossible. It could never be done in reality, because there is more to be taken into account than just special relativity. Other physical aspects of reality would be broken. You would basically be forced to brake the continuity of information through time.

There is definitely objective truth about which is moving and which is not. It is defined/ingrained in the very nature of the thought experiment just as a rocket, which had accelerated away from the Earth would be known by the people in the rocket and the people on Earth to be traveling faster than Earth relative to c and would be an absolute fact that is ingrained in the reality of the universe.

 

[teachmemore]

I agree that if there is such a thing as absolute time and space, then there will be some absolute truth about which is "really" moving at a smaller speed and which is "really" sending signals more quickly, but this truth would be impossible to determine by any empirical means, and personally I don't actually believe in absolute time and space, it seems like an unnecessarily cumbersome idea given that it would play no useful role in explaining anything (by analogy, do you believe in an 'absolute left and right'?) And I don't understand the statement "Neither one can determine which counter is really the counter that is moving, except through past preserved information (ie. One of the counters accelerated away from the other at sometime in the past)"--why would acceleration in the past tell you anything about which is moving in an absolute sense? You can always find an inertial frame where the two counters were initially traveling together at some nonzero speed, then the acceleration of one counter caused it to come to rest in that frame, and since the "absolute frame" is completely unknowable we have no reason to rule out the idea that this frame is in fact the absolute one.

Ah. Excellent! So this is where there is confusion between us.

To me, it sounds like your mind is totally stuck in the relative.

c is absolute. correct?

So if the Earth is moving at a factor of c, say X*c, if a rocket accelerates away from the Earth in any arbitrary direction, how could it possible be moving slower than X*c?

It sounds to me like you object to notating speed as a factor of c? Because if a speed of a factor of c were possible, it would imply that absolute speeds are in fact possible.

 

[teachmemore]

Let me pose this question to you then and see if you can answer it:

If I am moving slower than the speed of light, how is it possible that I am not moving at a fraction of the speed of light? And if I am moving at a fraction of the speed of light, then how is it possible that my speed is not absolute?

 

[teachmemore]

Yes, I think the distinction between absolute (but unverifiable) truths and physically-verifiable truths helps clarify what you're saying. Of course, about that last part, if there is an absolute time and space then the speeds of slower-than-light objects are absolute too, although in physics terms they are relative.

Not in "Physics" terms. In "Special Relativity" terms. Special Relativity only deals with the relative aspects of reality. Where as not all problems in physics deal with the purely relative; as I am trying to point out.

 

[JesseM]

You see. Your thinking is so focused on the relative aspects of this thought experiment that you fail to see the non-relative ones; which would allow you to come to an absolute answer about the pulses seen by each of these counters.

Huh? What am I failing to see? I already acknowledged you are free to introduce the idea of absolute time and space, I just pointed out that you hadn't explained clearly that this was what you were doing, and also that I don't personally believe in such an entity.

It appears to me that the added complexity you have introduced by neglecting the absolute states of this thought experiment is causing you to confuse what is possible in reality with what is possible when only special relativity is taken into account.

Can you be more specific about what you think I have said that is wrong or confused?

ie. In your abstract example here what you have basically done is moved the stationary frame to the traveling frame - ie. symmetrically swapped frames - which is physically impossible.

No I didn't, you are obviously misunderstanding something. All I suggested was that we can change the timing of when each counter starts sending signals, and this will change the fact about which counter has received more signals when they meet. This needn't change the fact about which counter is in a state of absolute rest and which is in a state of absolute motion, it just means that in absolute terms they sent their first signals non-simultaneously rather than simultaneously (though in relative terms, they did send their first signals simultaneously in the rest frame of the traveling counter, it's just that this frame's definition of simultaneity does not match with absolute simultaneity). Since human experiments will have no way of knowing which counter is "stationary" in absolute terms (even if we, in our godlike role as the ones who define the thought-experiment, do know that), they will have no way of knowing it is more "accurate" to program the counters to start sending signals simultaneously in the first counter's frame rather than in the second counter's frame.

There is definitely objective truth about which is moving and which is not.

That's a statement of metaphysical faith on your part, akin to saying "there is definitely a God" or "there is definitely an absolute truth about which counter is 'further to the left' in an absolute sense, not just relative to some observer". I am agnostic about God but very skeptical about the idea of "absolute left" or "absolute time", they seem like totally superfluous metaphysical ideas to me, much easier to just adopt an eternalist ontology where all points in spacetime are equally real and there is no need for any absolute truth about simultaneity.

It is defined/ingrained in the very nature of the thought experiment

If you want to do a thought experiment which assumes there is such a thing as absolute space and time I'm happy to go along with that for the purposes of discussion, even though I don't really believe in such notions. Again, nothing I said required changing the definition of which counter was "really" moving or which clock was "really" ticking slower.

just as a rocket, which had accelerated away from the Earth would be known by the people in the rocket and the people on Earth to be traveling faster than Earth relative to c

Huh? No it wouldn't, not even if absolute time and space existed. How can you rule out the idea that the Earth was already moving at some large speed, say 0.8c, relative to absolute space? You're not a geocentrist are you? If you agree there's no way any human could rule out such a possibility, then obviously if the rocket accelerated away from the Earth in the opposite direction from the direction the Earth is moving in an absolute sense, then as the rocket accelerates its absolute speed will decrease, not increase. (Perhaps the word 'acceleration' is confusing you, in physics the term simply refers to any change in speed whether an increase or a decrease, and even if there was such a thing as absolute speed, if relativity is correct acceleration at 1G should feel exactly the same regardless whether your absolute speed is increasing or decreasing. Didn't you agree earlier that even if absolute motion exists, there would be no experimental way to determine which frame is the absolute frame?)

 

[JesseM]

Let me pose this question to you then and see if you can answer it:

If I am moving slower than the speed of light

In absolute terms, or relative to some frame? If you are moving at 0.8c in absolute terms, this is a fact that could only be known by God or other supernatural beings, there'd be no empirical experiment you could do that would demonstrate you were moving at an absolute speed of 0.8c rather than an absolute speed of 0.5c or even 0. On the other hand, if you are only claiming that you are moving at 0.8c in the inertial rest frame of some other object like a planet, then this is a well-defined physical claim that can be tested empirically, but it doesn't imply there is such a thing as absolute motion.

And if I am moving at a fraction of the speed of light, then how is it possible that my speed is not absolute?

If you are moving at a fraction of the speed of light in absolute terms, then of course this presupposes that you do have an absolute speed. But of course there is no reason for a skeptic about absolute time and space to believe "you are moving at a fraction of the speed of light in absolute terms" is true in the first place! They don't believe you have an absolute speed at all!

 

[JesseM]

Not in "Physics" terms. In "Special Relativity" terms. Special Relativity only deals with the relative aspects of reality.

Wrong, wrong, wrong. Relativity uses relative quantities like velocity and time dilation in its calculations, but the whole point of using them is to make predictions about absolute frame-independent facts, like the proper time a given clock will elapse between two events on its worldline, or a fact about whether two objects will collide, or what G-force some object will measure on an accelerometer, etc. In fact Einstein once tried to get people to use the term "invariance theory" in place of "relativity theory" because the physical "meat" of the theory is in its calculations of invariant quantities like proper time, and the term "relativity" often confuses people in exactly this way.

 

[teachmemore]

Huh? What am I failing to see? I already acknowledged you are free to introduce the idea of absolute time and space, I just pointed out that you hadn't explained clearly that this was what you were doing, and also that I don't personally believe in such an entity.

Can you be more specific about what you think I have said that is wrong or confused?

No I didn't, you are obviously misunderstanding something. All I suggested was that we can change the timing of when each counter starts sending signals, and this will change the fact about which counter has received more signals when they meet. This needn't change the fact about which counter is in a state of absolute rest and which is in a state of absolute motion, it just means that in absolute terms they sent their first signals non-simultaneously rather than simultaneously (though in relative terms, they did send their first signals simultaneously in the rest frame of the traveling counter, it's just that this frame's definition of simultaneity does not match with absolute simultaneity). Since human experiments will have no way of knowing which counter is "stationary" in absolute terms (even if we, in our godlike role as the ones who define the thought-experiment, do know that), they will have no way of knowing it is more "accurate" to program the counters to start sending signals simultaneously in the first counter's frame rather than in the second counter's frame.

That's a statement of metaphysical faith on your part, akin to saying "there is definitely a God" or "there is definitely an absolute truth about which counter is 'further to the left' in an absolute sense, not just relative to some observer". I am agnostic about God but very skeptical about the idea of "absolute left" or "absolute time", they seem like totally superfluous metaphysical ideas to me, much easier to just adopt an eternalist ontology where all points in spacetime are equally real and there is no need for any absolute truth about simultaneity.

If you want to do a thought experiment which assumes there is such a thing as absolute space and time I'm happy to go along with that for the purposes of discussion, even though I don't really believe in such notions. Again, nothing I said required changing the definition of which counter was "really" moving or which clock was "really" ticking slower.

Huh? No it wouldn't, not even if absolute time and space existed. How can you rule out the idea that the Earth was already moving at some large speed, say 0.8c, relative to absolute space? You're not a geocentrist are you? If you agree there's no way any human could rule out such a possibility, then obviously if the rocket accelerated away from the Earth in the opposite direction from the direction the Earth is moving in an absolute sense, then as the rocket accelerates its absolute speed will decrease, not increase. (Perhaps the word 'acceleration' is confusing you, in physics the term simply refers to any change in speed whether an increase or a decrease, and even if there was such a thing as absolute speed, if relativity is correct acceleration at 1G should feel exactly the same regardless whether your absolute speed is increasing or decreasing. Didn't you agree earlier that even if absolute motion exists, there would be no experimental way to determine which frame is the absolute frame?)

OK. Ya. I totally screwed up there in claiming the direction could be arbitrary.

 

[teachmemore]

In absolute terms, or relative to some frame? If you are moving at 0.8c in absolute terms, this is a fact that could only be known by God or other supernatural beings, there'd be no empirical experiment you could do that would demonstrate you were moving at an absolute speed of 0.8c rather than an absolute speed of 0.5c or even 0. On the other hand, if you are only claiming that you are moving at 0.8c in the inertial rest frame of some other object like a planet, then this is a well-defined physical claim that can be tested empirically, but it doesn't imply there is such a thing as absolute motion.

If you are moving at a fraction of the speed of light in absolute terms, then of course this presupposes that you do have an absolute speed. But of course there is no reason for a skeptic about absolute time and space to believe "you are moving at a fraction of the speed of light in absolute terms" is true in the first place! They don't believe you have an absolute speed at all!

OK. So your claim is that any statement made about the possibility of absolute speed is a belief. One way or the other.

 

[teachmemore]

In absolute terms, or relative to some frame? If you are moving at 0.8c in absolute terms, this is a fact that could only be known by God or other supernatural beings, there'd be no empirical experiment you could do that would demonstrate you were moving at an absolute speed of 0.8c rather than an absolute speed of 0.5c or even 0. On the other hand, if you are only claiming that you are moving at 0.8c in the inertial rest frame of some other object like a planet, then this is a well-defined physical claim that can be tested empirically, but it doesn't imply there is such a thing as absolute motion.

If you are moving at a fraction of the speed of light in absolute terms, then of course this presupposes that you do have an absolute speed. But of course there is no reason for a skeptic about absolute time and space to believe "you are moving at a fraction of the speed of light in absolute terms" is true in the first place! They don't believe you have an absolute speed at all!

Wait a second here. I am making a general statement about all relative frames. I did not say anywhere that these relative frames could have knowledge about their precise speed. I'm only stating that by the very principles of special relativity, they have to be moving at a speed slower than light speed. Since light speed is an absolute, then by saying that anything can move slower than light speed implies that it is moving at an absolute speed.

 

[teachmemore]

1. Let's start by saying that all we know is that the speed of light is absolute and c.

2. Now, all relative frames in the universe have to be moving at an absolute velocity between -c and c; by the very principles of special relativity ( no frame can reach c, which is an absolute speed)

3. It then follows that all relative frames in the universe are moving at a speed between (exclusive) c and -c relative to c.

My point is that the theory of special relativity cannot be logically conceptualized without first conceptualizing speeds relative to c, which is an absolute speed.

 

[HallsofIvy]

1. Let's start by saying that all we know is that the speed of light is absolute and c.

2. Now, all relative frames in the universe have to be moving at an absolute velocity between -c and c; by the very principles of special relativity ( no frame can reach c, which is an absolute speed)

3. It then follows that all relative frames in the universe are moving at a speed between (exclusive) c and -c relative to c.

My point is that the theory of special relativity cannot be logically conceptualized without first conceptualizing speeds relative to c, which is an absolute speed.

No, it is not. That seems to be your basic problem. You have referred to "absolute speed" repeatedly but have not defined that phrase. What do you mean by "absolute speed"?

 

[teachmemore]

No, it is not. That seems to be your basic problem. You have referred to "absolute speed" repeatedly but have not defined that phrase. What do you mean by "absolute speed"?

Thank you. Thinking about this made me realize that in order to define an absolute speed relative to c, c would have to be reachable. Since it is not, I can't seem to be able to define it.

 

[teachmemore]

I can't thank you all enough for bearing with me.

I need to take some time, like maybe a few weeks, to contemplate all this stuff to determine whether everything here is clear to me.

 

[teachmemore]

Thank you. Thinking about this made me realize that in order to define an absolute speed relative to c, c would have to be reachable. Since it is not, I can't seem to be able to define it.

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?

 

[matheinste]

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?

Apart from any other misunderstanding of physics, such as light being at rest in a medium, how do you know what the motion of the medium is with respect to which the light is at rest?

You can conjure up any definition you like as an aid to calculation or understanding, but that does not make that definition a description of reality.

Matheinste.

 

[teachmemore]

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?

Hmmm. This just shows that the two light pulses are in the same reference frame.

 

[jtbell]

Now when both these pulses of light are trapped in medium and no longer moving apart,

What are you referring to, here? If you're thinking of those experiments which slowed down and stopped (or nearly stopped) light pulses traveling through a material object or medium, then the medium itself becomes a preferred frame as far as the motion of light is concerned. But this is not an absolute frame because you can have two different chunks of material moving with respect to each other.

 

[teachmemore]

Apart from any other misunderstanding of physics, such as light being at rest in a medium, how do you know what the motion of the medium is with respect to which the light is at rest?

You can conjure up any definition you like as an aid to calculation or understanding, but that does not make that definition a description of reality.

Matheinste.

Hey, I did not claim the light was at rest! Where did you get that idea?

 

[matheinste]

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.

There.

Matheinste.

 

[cavalier3024]

ok, so first, you can't define an absolute speed since there is no such thing as 'speed relative to C'. that is because no matter how fast you are moving, you will always see the light moving at the same speed, C.

about the paradox - its really simple. So you say that there are two clocks, A and B, that are moving toward each other.
form A's point of view A is stationary and B is moving towards him at a certain speed.
from B's point of view B is stationary and A is moving towards him at the same speed.
so far we have a symmetry, and it is true that each will see the other ticks slower. but the symmetry is broken when you say that the clocks start at the same time, because the term 'same time' is reference frame related. if you mean that A 'sees' them starting at the same time (i.e that in A's reference frame they start simultaneously). then B will not see it that way! B will 'see' his clock starting much later then A's clock!
so:
*from A's view, the clocks started at the same time, and B's clock ticks slower. when they meet B have less ticks.
*from B's view, A started before B. so even though and A's clock ticks slower, B will still show less ticks when they will meet. just like A is seeing it. no paradox.

 

[ghwellsjr]

Furthermore, although due to the laws of special relativity, we can never truly know which frame in the universe is the true stationary frame (at least I can't comprehend a way in which we would determine this). We can conceive a stationary frame, and it does not go against any known laws of physics for such a frame to exist - an absolute stationary frame. Again, special relativity does not say that such a frame does not exists, only that without prior knowledge, you can not determine whether you are in it.

You are absolutely correct in everything you said in this paragraph, except that I would not have made the restriction "due to the laws of special relativity", I would have said "due to the facts of nature".

Now here is what you need to understand about special relativity. Since we cannot know which is the absolute stationary frame, we can arbitrarily pick any inertial reference frame and assume that it is the one and only absolute stationary frame that only Mother Nature knows about and everything will be consistent and behave according to all the laws of nature and we will have no way of knowing if we picked the "wrong" absolute stationary frame. Mother Nature won't tell us if we are wrong and she appears not to care.

But note, you have to assume that this is the one and only reference frame. You cannot talk about any other reference frame. You have to specify everything in terms of this one frame that you selected.

Now, if you want, you can decide that you don't like that reference frame anymore and you want to pick another arbitrary one that is defined relative to your first one. Then you use the Lorentz Transform to rebuild eveything from your first frame so that it is now defined correctly in your second frame and you treat it as the one and only absolute stationary frame that only Mother Nature knows about and again, everything will be consistent, etc, etc, etc.

Don't make the mistake of thinking that multiple reference frames co-existent at the same time, such as the people on Earth are in a stationary frame and the people on the rocket ship are in a moving frame. If you do that, you will have to transform everything from one of those frames into the other frame before you can meaningfully discuss what is happening.

 

[teachmemore]

There.

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.

 

[teachmemore]

ok, so first, you can't define an absolute speed since there is no such thing as 'speed relative to C'. that is because no matter how fast you are moving, you will always see the light moving at the same speed, C.

about the paradox - its really simple. So you say that there are two clocks, A and B, that are moving toward each other.
form A's point of view A is stationary and B is moving towards him at a certain speed.
from B's point of view B is stationary and A is moving towards him at the same speed.
so far we have a symmetry, and it is true that each will see the other ticks slower. but the symmetry is broken when you say that the clocks start at the same time, because the term 'same time' is reference frame related. if you mean that A 'sees' them starting at the same time (i.e that in A's reference frame they start simultaneously). then B will not see it that way! B will 'see' his clock starting much later then A's clock!
so:
*from A's view, the clocks started at the same time, and B's clock ticks slower. when they meet B have less ticks.
*from B's view, A started before B. so even though and A's clock ticks slower, B will still show less ticks when they will meet. just like A is seeing it. no paradox.

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?

 

[ghwellsjr]

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.

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.