Relativity, time and the speed of light

[shchr]

Can special relativity describe a proper time of non-inertial frame?
PS. I seem to have made a mistake in the last post. Jane's time advanse seems to depend on how long she takes to change two frames seeing from Joe as well as what value the acceleration takes.

 

[Hurkyl]

By using an inertial frame of reference, one can use the differential formula:

(c dτ)² = (c dt)² - dx² - dy² - dz²

to compute proper times along an accelerating worldline.

Similarly, one uses basic differential geometry to construct, in the inertial frame the proper coordinate axes for the accelerating worldline at each point.

Then, we can align the coordinate axes to form a rectilinear system. (Though we typically have the problem that distant events appear multiple times in the new system)

That is how we can use special relativity to construct the physics of an accelerating frame. The work involved in doing such is, of course, very similar to what one would do in General Relativity (but in GR reference frames would be limited to be local things)

 

[shchr]

For everyone who are interested in uniform acceleration in relativity.
aether.lbl.gov/www/classes/p139/homework/eight.pdf

 

[Albrecht]

Hurkyl and shchr
thank you for the answers.

Regarding the twin paradox

By my understanding the acceleration of Jane has generally to be taken into account. If we believe in the equivalence of acceleration and gravitation then acceleration will make it's own contribution. - However the time difference between the frames depends stationary on the frames and should be independent from the specifics of the acceleration. If Jane changes into the new frame this new frame will not "know" what the history of Jane was.

On the other hand we should in the gedanken experiment be able to eliminate this contribution. If we assume the Jane does not make a normal turn-around but jumps into another spaceship which comes with the same speed from the opposite direction then we can reduce the acceleration time to almost 0. (Jane's body will not be able to withstand this but for the understanding of the relativity process this does not matter.)

This is for my understanding in agreement to the website linked by shchr:
aether.lbl.gov/www/classes/p139/homework/eight.pdf

It is right that the normal Lorentz transformation yields the correct result for the final state, when Jane meets Joe again. But in the meantime we have a situation which looks physically not very logical.

The intermediate problem comes from the requirement of symmetry between all inertial frames (Einstein). We can first look to it in the naive way. When, as in the given example, Jane flies away 3 years (Jane's time) she has to regard her own frame as the frame at rest, so she has, knowing relativity, to assume that Joe's ageing is dilated. Also when she flies back she again will regard her own frame as the frame at rest and assume that Joe's ageing is again dilated. So when she comes back and meets Joe she will expect that Joe is now 2 years younger than she is (taking also into account the contraction of the travel distance). But she would now see that he is in fact 2 years older than she is.

This logical problem is (formally) resolved in the relativity of Einstein by the fact/statement that Jane changes her reference frame at her turn around and that at this moment she has to adapt to the new time.

The physical conflict with this formal way is clearly visible if during the whole travel Joe transmits time-coded signals towards Jane, say one per second like the GPS satellites do it. At her first leg she will receive these signals at a reduced rate due to the Doppler effect on one hand and at an increased rate due to her own dilated time measurement. Both effects compensate to a certain degree. When she turns around she will now receive an increased rate of the signals from the Doppler effect as well as from her dilated time measurement. But all the time she will receive these signals in the correct sequence! No signal will be lost or has an inverted time sequence.

If Jane knows the Lorentz transformation (Einstein), she knows that she is in a different reference frame after her turn around and she has to adapt her time to the time of the new frame in a big step. - But when she looks to the time signals coming from Joe she will not find it logical to do so.

Whatever Jane does with her clock setting, the increased signal rate which she receives during her return will give her a continuous information of an increased ageing process at the location of Joe relative to her. And when she now meets him again, there is not at all a surprise that he has aged more than she did.

The whole process is on the other hand very simple and free of sudden time adaptations, i.e. Jane's clock time behaves continuous to her signal reception, if Lorentz rather than Einstein is used. I shall explain it in 2 steps:

1. Assume that Joe is in the absolute frame at rest. Then Jane has nothing to do than to use the differential Lorentz version
dt' = dt * SQRT(1-v^2/c^2)
to correct permanently her own time indications in relation to Joe's time. She has to do it on both legs and on return she will have the correct time relation between herself and Joe
2. Assume that Joe is not in the absolute frame at rest. Then Joe as well as Jane have to make the time corrections as given above according to their individual speeds in relation to the absolute frame at rest. - This works for every assumed absolute frame at rest.

The result of case 2 will be the same as in case 1, and both results will be correct. And you may see that this is a simple logic without any logical conflicts and without any sudden time changes.

The basic difference between the way of Lorentz in relation to the way of Einstein is that, following Lorentz, Jane cannot assume that both legs of her travel are equivalent frames at rest.

 

[shchr]

Albrecht:
It is very difficult for me to analyze your assertion. Let it simple. In the case 2 above, i.e., Joe is not at rest, what happens when Jane observes Joe? Conversely, what happens when Joe observes Jane?

 

[Albrecht]

shchr wrote:

It is very difficult for me to analyze your assertion. Let it simple. In the case 2 above, i.e., Joe is not at rest, what happens when
Jane observes Joe? Conversely, what happens when Joe observes Jane?

My preceding posting regarding the twin paradox had 2 parts:
1. I have tried to explain why Einstein yields the correct result but is physically difficult
2. I have tried to explain that also Lorentz yields the correct result and is physically easy.

I understand you refer to part 2.

If Joe is at rest and he observes Jane he will see that her clock proceeds with a reduced speed in relation to his clock. Her motion is in no respect special, she moves at her specific speed outbound and then at the same speed back to him.

If now Joe is not at rest but moves with speed v0 in relation to the frame at rest towards Jane, then Jane does in fact not move with v as Joe believes but with v0+v (later v0-v). Now the clock of Jane proceeds even slower than assumed above. But also the clock of Joe proceeds slower than if he would be at rest. Also the distance from Joe to Jane is reduced due to contraction which is however only noticeable by an observer at rest. These effects altogether compensate each other and cause that Joe will make exactly the same observations as in the case when he is at rest.

If Joe is at rest and Jane observes Joe she will observe, if she receives time coded signals from him, that these signals arrive at a reduced rate. If she is aware of her motion she will understand why the rate is reduced in the way I described in my preceding posting. On her way back she receives the signals at an increased rate (and will in the summary come to the conclusion that Joe ages faster than she does).

If she is not aware of her motion when she moves away, i.e. she believes that she is at rest now, she will have the impression that Joe ages more slowly than she does. But when she turns around then she has in this case to be aware of the fact that she is now at a very high speed (twice of the speed assumed above) and now when observing the time coded signals, she will come to the conclusion that Joe ages very rapidly. This rapid ageing will overcompensate the reduced ageing of Joe which she observed on her first leg of motion.

If now again Joe is not at rest and Jane moves correspondingly at a different speed (in relation to the frame at rest) on her travel away from Joe and later towards him, the effects of her different speed and of the speed of Joe and also of the contraction will again compensate each other for every phase of her travel and cause that she will not notice the change. So Jane's observations are exactly the same as if Joe would be at rest.

This is the observation. I this understandable?

 

[shchr]

If now Joe is not at rest but moves with speed v0 in relation to the frame at rest towards Jane, then Jane does in fact not move with v as Joe believes but with v0+v (later v0-v). Now the clock of Jane proceeds even slower than assumed above. But also the clock of Joe proceeds slower than if he would be at rest. Also the distance from Joe to Jane is reduced due to contraction which is however only noticeable by an observer at rest. These effects altogether compensate each other and cause that Joe will make exactly the same observations as in the case when he is at rest.

If now again Joe is not at rest and Jane moves correspondingly at a different speed (in relation to the frame at rest) on her travel away from Joe and later towards him, the effects of her different speed and of the speed of Joe and also of the contraction will again compensate each other for every phase of her travel and cause that she will not notice the change. So Jane's observations are exactly the same as if Joe would be at rest.

Why is Joe specific? Both Joe and Jane are moving with respect to the rest frame.

 

[wimms]

Acceleration is manipulation of timeflow rate. Inertial frame has unchanging timeflow rate, dependant on v relative to point of departure.

 

[Albrecht]

shchr wrote:

Why is Joe specific? Both Joe and Jane are moving with respect to the rest frame.

Joe is specific because he is all the time in the same inertial frame. This frame may be assumed to be the absolute frame at rest .

Jane on the other hand can only be in the absolute frame at rest in one of both legs of motion as she undergoes an acceleration.

Whether the situation of Joe is in fact the absolute frame at rest or not does not change the result. The effects of his motion to the clock speed of Joe and to the clock speed of Jane together with the effect of contraction compensate each other to an extent that it does not matter for the result whether he moves or not. Jane is different because she cannot be in the frame at rest all the time and the compensation does not work.

You find this process of compensation described and mathematically proven in all textbooks about the relativity of Einstein. The authors show and prove how it works in detail that, if you observe a physical situation from a different frame, you will have the same relation between the physical quantities time, length and velocity as in the original one. Please look to the chapters about addition of velocities and about synchronisation of clocks.

wimms wrote:

Acceleration is manipulation of timeflow rate. Inertial frame has unchanging timeflow rate, dependant on v relative to point of departure.

I believe that the timeflow rate is in fact the clock rate, i.e. the circulation frequency of all periodic processes. It is right that there is no change of the rate if there is no acceleration. But the rate also depends on the velocity of the frame (according to the Lorentzian version).

 

[shchr]

Joe is specific because he is all the time in the same inertial frame. This frame may be assumed to be the absolute frame at rest .

So, all inertial frames are assumed to be the absolutely-at-rest frame, aren't they? This means that there is no absolutely-at-rest frame, doesn't it? It is contrary to your previous assertion, i.e., there is a frame which is absolutely at rest.
Does anyone have an opinion?

 

[Albrecht]

This means that there is no absolutely-at-rest frame, doesn't it?It is contrary to your previous assertion, i.e., there is a frame which is absolutely at rest.

This is definitely wrong. Please read again my previous posting.

There is exactly one absolute frame at rest. However, if somebody is in another inertial frame and performes experiments, then the measurement results, which deviate from the ones made in the absolute system at rest, cause compensations to each other so that the experimenter will not see any difference.

Example (simplest possible): If Mike and Mary are in a frame which is not the frame at rest. They have both dilated times indicated on their respective clocks. If they now compare their clocks they will not see any deviation to each other.

 

[wimms]

Originally posted by Albrecht
I believe that the timeflow rate is in fact the clock rate, i.e. the circulation frequency of all periodic processes. It is right that there is no change of the rate if there is no acceleration. But the rate also depends on the velocity of the frame (according to the Lorentzian version).

Why is 'clock rate' more correct?
How I understand it is that time/clock rate is really independant of anything external. When Jane starts off from earth, she initially has same rate as earth. During acceleration, rate changes relative to earth. When acceleration stops, rate that was achieved is sustained until deceleration starts, and is convertible to Earth's rate via lorentz.

What puzzles me, is there really any chance to determine time rate of approaching relativistic body, if it has never been in same rate frame as us. We can transform rate by knowing its v, but is the result we'd get credible? What if the departure frame of this body had different rate than we have? Do we have to assume that there exists universal time rate depending on v relative to universal absolute rest frame?

 

[shchr]

However, if somebody is in another inertial frame and performes experiments, then the measurement results, which deviate from the ones made in the absolute system at rest, cause compensations to each other so that the experimenter will not see any difference.

So, an experimenter cannot determine which is the absolutely-at-rest frame. This means there is no way to know what inertial frame is absolutely-at-rest physically. From physical point of view, it is equal to the fact that there is no absolutely-at-rest frame. For me, your absolutely-at-rest frame is arbitrarily selected from among inertial frames. Which inertial frame is absolutely at rest seems to be the problem of belief, because there is no way of knowing the absolute rest.

 

[Albrecht]

shchr wrote:

Which inertial frame is absolutely at rest seems to be the problem of belief, because there is no way of knowing the absolute rest.

This is correct. Up to now we were not able to find the absolute frame at rest. I wrote it already several times in my preceding postings. So it is a belief. (Unless we have true superluminal signals; then we know it.)

On the other hand, the assumption of Einstein that time and space change at motion is also a belief as it is not necessary.

So we have the choice:

Either we believe that there is a frame at absolute rest. Then we can maintain our traditional understanding of space and time.

Or we believe that every inertial frame is truly equivalent to each other. But then we have to accept the complicated assumptions of Einstein about time and space.

The historical reason why Einstein liked his version and why many years(!) later the physical community accepted it, was the cultural background of this decision. It was understood as intellectually clean and "beautiful" (Einstein) that the assumption of a frame at absolute rest (called ether) could be omitted. This had to do with the intellectual tradition in Germany: Everything was taken as valuable that could be related to Greek philosophy. It does not fit very well to the world-structure ideas of Plato that there exits an ether.

But is this really a physical argument?

wimms:
Sorry, I shall answer your comment by tomorrow.

 

[shchr]

This is correct. Up to now we were not able to find the absolute frame at rest. I wrote it already several times in my preceding postings. So it is a belief. (Unless we have true superluminal signals; then we know it.)

Thank you, Albrecht, for talking with me.
If we discuss further, it would go to a place no one can decide which is correct. So I suggest to stop talking about the existence of absolutely-at-rest frame.
Anyway, Nimtz's experiment was interesting one. Thank you for your information. But I want to remind you the existence of Galilean relativity in which infinite speed is allowed, at last.

 

[Albrecht]

wimms wrote

Why is 'clock rate' more correct?

What we physically observe is a clock rate which includes of course all periodic motions. To call this indication "time" is already a decision towards a specific physical model. So "clock rate" is more open for physical causes.

What puzzles me, is there really any chance to determine time rate of approaching relativistic body, if it has never been in same rate frame as us.

For my understanding it is in fact worse. Even if an approaching relativistic body has earlier been in the same frame as us, we do not know what it's rate at motion now is. It always depends on the physical model used.

I can imagine only one situation which makes real knowledge possible. If we can prove that we have superluminal signals and we have measurements of those signals which are precise enough, then we know that we have an inertial system at absolute rest and we are able to identify it. Related to this frame at absolute rest we can make absolute measurements of physical quantities; the clock rate of a reference clock (i.e. atomic references) could then be used as an absolute norm.

shchr wrote:

But I want to remind you the existence of
Galilean relativity in which infinite speed is allowed, at last.

So, what is your conclusion from this fact?
Galilei could live with a simple understanding of relativity in mind. He did not know about
- dilation of clocks
- contraction of physical objects.

In summary this was an interesting discussion and to some respect also shocking for me. I did not realize that there is so little knowledge about the history of relativity, it's different versions and interpretations, and the non-physical influences which caused Einstein to be the winner.

 

[Albrecht]

sdeliver645 wrote:

I am currently writing an e-mail to Prof. Selleri to clarify these issues. I will post the correspondence when I get a response.

So, what is the status of Prof. Selleri's response??

 

[pmb]

Originally posted by jby
It states that nothing can travel faster than light. But all the books that I've read on introduction to relativity use the train and light pulse to demonstrate length contraction and time dilation. And finally, they say that nothing can travel faster than light. How can this claim be made when they have just only consider light clock. What about mechanical clock, biological clock etc?

Think of it like this: The Principle of Relativity states that the laws of physics are the same in all inertial frames of referance.


Now take a look at the light clock. Just so that we're on the same page we'll use this derivation

http://www.geocities.com/physics_world/light_clock.htm

Let there be a man, a rabbit, and an atomic clock at rest in O close to the mechanical clock which are also at rest in O. The mechanical clock is designed to tick at the same rate at which the mans heart beats. Let's also assume that the rabbit's heart beats at twice the rate of the mans heart. It follows that the ratios of each of these frequencies is a constant. That ratio will not change if one measures these frequencies from anothere inertial frame. So it really doesn't matter what we use as a clock - so long as we know that the clock is reliable.

I hope that makes sense

Pete

 

[russ_watters]

Originally posted by Albrecht
On the other hand, the assumption of Einstein that time and space change at motion is also a belief as it is not necessary.

What else would explain observed time dilation? Whether Einstein assumed it or not (he had no way to verify it) it has since been verified through experimentation.

 

[Albrecht]

What else would explain observed time dilation? Whether Einstein assumed it or not (he had no way to verify it) it has since been verified through experimentation.

We have to distiguish between time and the measurement of time. Time is measured by periodic motions, some of them are used as clocks. The speed of clocks is slowed down, that is the only thing we can observe.

If we follow the relativity of Lorentz / Poincare then neither time nor space do change in any way. The "time dilation" we observe is in fact the change of clock indications, i.e. all periodic motions.

The dilation of clocks etc can be explained by today's understanding of elementary particle physics. The constituents of an elementary particle oscillate permanently with the speed of light c. (This was initially detected by Paul Dirac for the electron 1928.) If an elementary particle is moved, its rotation period has to slow down to maintain the speed limit of c. If Pythagoras is applied to this process, the result is exactly the "time dilation" given by Special Relativity.

 

[russ_watters]

Originally posted by Albrecht
We have to distiguish between time and the measurement of time. Time is measured by periodic motions, some of them are used as clocks. The speed of clocks is slowed down, that is the only thing we can observe.

If we follow the relativity of Lorentz / Poincare then neither time nor space do change in any way. The "time dilation" we observe is in fact the change of clock indications, i.e. all periodic motions.

So maybe this is just a question of semantics, but to clarify: Is there an absolute time independent of the measurement of time? If so, how can it be observed?

 

[Albrecht]

russ_watters wrote

So maybe this is just a question of semantics, but to clarify: Is there an absolute time independent of the measurement of time? If so, how can it be observed?

This question is strictly related to the existence of an absolute frame at rest. If there exists an absolute frame at rest, the time observed in this frame is the absolute time.

So, we know the absolute time as soon as we know the absolute frame. From the experiments which show superluminal signals we have to conclude, that there is an absolute frame at rest - if we trust that these experiments are true. The results are not very precise; they give the impression that our Earth conforms to the frame at rest within a margin of ca. one percent of the speed of light (i.e. 10 times the orbital speed of the Earth around the sun). That would mean that our time on Earth is quite close to the absolute time.

Anyway, we have to keep in mind that "time" is a human made entity. Nature provides us the fact that two events at the same location have a well defined sequence. We humans find it practical to put this sequencing onto a linear scale which we call "time". We use periodic motions for it, and all what we observe, when we believe to measure time, is the behaviour of periodic motion.