The Physical Meaning of the Relatvity of Simultaneity

[yuiop]

Time dilation is a comparison between two different inertial frames at the same event, not a comparison from a single inertial frame before and after acceleration.

That is a narrow formal definition. I am talking about time dilation in the widest sense. In other words I take the question "Is time dilation physical?" to mean "Does the rate of an ideal clock change in any physically meaningful way, due to motion or acceleration?" and I would say the answer to that can be yes.

For example, if a train is going away from an observer that is at rest with respect to the track and the frequency of a sound signal from the train appears to be lower to the observer, is time running slower in any physical sense for clocks onboard the train. Most people would agree the answer to that question is no and that the observed drop in frequency is an artifact of the measurement method, due to classical Doppler shift and the finite speed of sound waves. (The analysis being done in purely classical Newtonian terms here). This would be classed as an audio illusion of time slowing. Similarly we could create an optical illusion of frequency changes due to classical Doppler shift of light signals, but above and beyond that illusion due to the measurement method, is time dilation predicted by relativity that can manifest itself in a physically meaningful way (such as differential ageing in the twins paradox).

Another example. I will call this the gravitational twin's paradox. The twins are initially together at the top of some great tower on a massive body. One twin descends to the bottom of the tower and remains there for some time. Each twin has a clock that emits signals at one second intervals. The twin at the top of the tower sees the clock at the bottom of the tower emit signals at a slower rate than his own clock or in other words he sees the signals from the lower clcok as red shifted. I have seen it argued on this forum that the this is an optical illusion brought about by the "stretching" of the light wavelength of the signal from the lower twin with the implication that the clcok of the lower twin is not "really" running slower that the clock of the twin at the top of the tower. However, I guarantee that if the twin at the top of the tower were to descend down to the twin at bottom of the tower at the same rate as the first twin descended, that the twin that had been at the bottom of the tower the longest will have aged the least in a real physical sense. At the extreme, if one twin was a young baby and the other a wrinkled old man when they get together at the bottom of the tower, it is difficult to argue that the difference between real time dilation and apparent time dilation is "just a case of semantics" as some people have also argued here.

 

[Al68]

OK we have reached agreement about synchronization.
But this still, really, begs the original meaning of my question with its assumption of a normal concept of synchronization with its, as you put it, previous knowledge of zero interval of synchronization.

Some disagree, but I consider SR's simultaneity convention completely normal. Long before SR, people used a similar convention for determining if events were simultaneous. Einstein specifically refers to this in his 1905 paper, and shows the consequences of combining the historical definition of simultaneous with the postulates of SR.

In fact, many believe were it not for the many patent applications at the turn of the century regarding different methods to synchronize clocks between distant cities using signals sent back and forth, and the fact that Einstein's job was to review those patents, he would have never has his insight about the consequences of the speed of light being constant and isotropic in any inertial frame.

But I'm getting off topic here, and I'm not sure what question you're referring to in "this still, really, begs the original meaning of my question...".

 

[Hans de Vries]

Addressing the original question:

An inertial reference frame S' moves with respect to another inertial reference frame S in the positive x direction of S. The clocks in S and S' are synchronized at the instant t = t '= 0 when the coordinate origins O and O' of the two frames coincide. At this instant a light wave is emitted from the point O = O'. After time t it is observed in S that the light wave is spherical with a radius r = ct and is described by the equation r^2 = x^2 + y^2 + z^2 which means that the center of the light sphere as determined in S is at O. Consider now the shape of the light wavefront in S' at time t'. Is it also a sphere whose center is at O'? If so, does this lead to a paradox? If not, does this lead to a contradiction with the principle of relativity?

Yes, it is a sphere also. How it becomes a sphere again is shown in the attached picture.

How can we really understand this world we live in?

Pete B

Simply read the chapter of my book which was written with the intention to
let people thoroughly understand the mechanisms behind non-simultaneity.
http://physics-quest.org/Book_Chapter_Non_Simultaneity.pdf


Regards, Hans

 

[Austin0]

Another example. I will call this the gravitational twin's paradox. The twins are initially together at the top of some great tower on a massive body. One twin descends to the bottom of the tower and remains there for some time. Each twin has a clock that emits signals at one second intervals. The twin at the top of the tower sees the clock at the bottom of the tower emit signals at a slower rate than his own clock or in other words he sees the signals from the lower clcok as red shifted. I have seen it argued on this forum that the this is an optical illusion brought about by the "stretching" of the light wavelength of the signal from the lower twin with the implication that the clcok of the lower twin is not "really" running slower that the clock of the twin at the top of the tower. However, I guarantee that if the twin at the top of the tower were to descend down to the twin at bottom of the tower at the same rate as the first twin descended, that the twin that had been at the bottom of the tower the longest will have aged the least in a real physical sense. At the extreme, if one twin was a young baby and the other a wrinkled old man when they get together at the bottom of the tower, it is difficult to argue that the difference between real time dilation and apparent time dilation is "just a case of semantics" as some people have also argued here.

I am happy to see that someone else has a problem with this common explanation of wavelength stretching due to transit up the gradient.
It is not just an idea presented in this forum but I have found it in accepted explanations of, for instance ; the red shift of light coming up the gravity well to reach earth.
Where it is proposed to be an in transit effect , happening after emmission and no mention of the shift due to dilation of the frequency of the emitting electron due to position in the field. {which you seem to be talking about here]
I have brought this up in several threads but the responce has been they were just two different descriptions of the same phenomena. It seems to me that if the gravitational effect due to locale is valid , and it seems to be verified to a great degree, the a shift due to transit is not merely superfluous but simply invalid. That if it also occurred then there should be an additive quantitative red shift at the receiver beyond what is calculated and explained by the expected shift at emission. Does this make any sense ? SO far nobody has seemed to know what I was talking about.

 

[Austin0]

In an old thread (that I am too lazy to track down right now) I demonstrated that using the "relativistic rocket equations" http://math.ucr.edu/home/baez/physics/Relativity/SR/rocket.html and the equations of Born rigid motion http://www.mathpages.com/home/kmath422/kmath422.htm, that the clocks would be be out of sync after the acceleration phase. These equations are based on SR and the Lorentz transformations and as far as I know, are not controvertial

OK I forget that the Born hypothesis is considered by many to be established SR.
I think it is somewhat speculative as apposed to the fundamental postulates but that is just my opinion and I wouldn't attempt to prove it wrong although I have found many questions regarding it which I would enjoy discussing with you, but this is probably not the appropriate thread.

That is another way of looking at it, but the end result is the same.

Actually , given the Born premise of differential dilation due to the greater rear acceleration your original way of looking at it is correct and I understand it completely.

Consider the following experiment. Say we start with two identical rockets facing in opposite directions and at rest with respect to each other. At the nose and tail of each rocket are synchronised ideal clocks that have been sealed to make them tamper proof. At a later time, one of the rockets accelerates away and then settles down to a constant non zero velocity relative to the other rocket. An observer onboard the rocket that accelerated, would be able to determine that that it was his rocket that underwent acceleration, simply by comparing the clocks fore and aft on his own ship even if he slept through the acceleration phase and even if there were no accelerometers onboard the rocket. At the end of the experiment the observer onboard the accelerated rocket could consider himself at rest and that it was the other rocket that is moving away, but he would be aware that "something physical had happened to his own rocket". On the other hand, if each rocket only had a single clock each, then the situation would have the appearance of being symmetrical, if they missed the acceleration phase

Once again , given the premise, your example is interesting and defintiely valid.

 

[heldervelez]

Addressing the original question:


Yes, it is a sphere also. How it becomes a sphere again is shown in the attached picture.

Simply read the chapter of my book which was written with the intention to
let people thoroughly understand the mechanisms behind non-simultaneity.
http://physics-quest.org/Book_Chapter_Non_Simultaneity.pdf

Regards, Hans

Congratulation Hans, your answer is on target.

A lot of misconceptions and complications that I see in this forum (SR) simply go away if we read your explanations.

Your book is very good in every aspect.
Thank you for sharing. I will devote more attention to it.

In Lorentz fundamental paper the contraction also happens in the transverse direction (with a factor distinct from the longitudinal). With this the Ehrenfest’s paradox solution is easier.
I mean a circular disk is always a circular disk, otherwise there are no 'real' circular disks because we are always moving in respect to something and the elipse form is the norm.


(by the way on your book: ch 4.12 page 26 easer must be easier )

 

[Dale]

There is no acceleration involved in the comparison which is assumed to take place after attaining a new inertial velocity.
...
You could easily make a comparison between a frame initially at rest with a second frame , which then accelerates to a new velocity . COuldnt you then quatitatively derive a dilation factor through comparison to this refernce frame that would be equivalent to a comparison of a single frame before and after acceleration? ... Frame B is then accelerated through whatever profile to effect a return pass by Frame A in an inertial state. ...
In what way do you think this would not be logically and quantitatively equivalent to a comparison of B [accelearated] with B when it was comoving with A ?

You are not being very self-consistent here. Frame B is cearly non-inertial, so the the Lorentz transform does not apply.

 

[Austin0]

Originally Posted by Austin0
There is no acceleration involved in the comparison which is assumed to take place after attaining a new inertial velocity....
You could easily make a comparison between a frame initially at rest with a second frame , which then accelerates to a new velocity . COuldnt you then quatitatively derive a dilation factor through comparison to this refernce frame that would be equivalent to a comparison of a single frame before and after acceleration? ... Frame B is then accelerated through whatever profile to effect a return pass by Frame A in an inertial state. ...
In what way do you think this would not be logically and quantitatively equivalent to a comparison of B [accelearated] with B when it was comoving with A ?

You are not being very self-consistent here. Frame B is cearly non-inertial, so the the Lorentz transform does not apply.

Frame B passes through a non-inertial phase but no comparison takes place during that interval. WHen it is again inertial after having gone through acceleration , decceleration and reversal of direction and cessation of thrust to pass the original reference frame it is once again inertial

 

[Dale]

Frame B passes through a non-inertial phase but no comparison takes place during that interval.

The fact that you make no comparisons during some period does not make frame B inertial. In fact, due to the relativity of simultaneity you can always find some inertial coordinate system where you are making the comparisons during the non-inertial phase.

In any case, these mental gymnastics that you are trying to go through do not change what length contraction is. It is a single comparison between two different reference frames, not a before-and-after comparison in a single reference frame.

 

[Austin0]

=DaleSpam;2512024]The fact that you make no comparisons during some period does not make frame B inertial.

As has been pointed out in other threads there is a possible assumption that any frame in significant relative motion, at some point underwent a period of acceleration.
That does not prevent them being considered inertial if they are traveling at constant velocity during the interval of evaluation. Agreed?

In fact, due to the relativity of simultaneity you can always find some inertial coordinate system where you are making the comparisons during the non-inertial phase.

In any case, these mental gymnastics that you are trying to go through do not change what length contraction is. It is a single comparison between two different reference frames, not a before-and-after comparison in a single reference frame .

What you call mental gymanastics appears to me to be simple transitive logic.
If : Frame B is equivalent to frame A when compared while inertial and comoving.

And frame B is inertial but with a relative velocity when a second comparison is conducted with frame A.

Then the relationship of frame B [at the relative velocity] to frame A is equivalent to the relationship of frame B [at the relative velocity] to frame B when it was comoving with frame A.
You keep reiterating a specific definition of what length contraction or time dilation is, but do not address any reason for why this relationship would not be equivalent or further
why any other reference frame would not agree to this equivalence.
I also do not see how any other frame could possibly observe the periods of comparison as occurring during the acceleration phase as the comparisons could only take place while the relevant clocks and observers in A and B were cojacent. Perhaps you could elaborate on your proposition?
Maybe there is some basic semantic or other miscommunication going on here. :-)

 

[Dale]

As has been pointed out in other threads there is a possible assumption that any frame in significant relative motion, at some point underwent a period of acceleration.
That does not prevent them being considered inertial if they are traveling at constant velocity during the interval of evaluation. Agreed?

No, I definitely do not agree. Remember a reference frame is a coordinate system. If you say, "let A be an inertial reference frame" then A never accelerated and A never will accelerate. There is no ambiguity whatsoever about its future or past state of motion.

Some specific object may be defined to be at rest only in some small region of that reference frame, and (provided the boundary conditions are completely specified) we do not need to make assumptions about the object outside of the specified region. But the reference frame itself is always and everywhere inertial by definition. Do you see the distinction?

What you call mental gymanastics appears to me to be simple transitive logic.
If : Frame B is equivalent to frame A when compared while inertial and comoving.

And frame B is inertial but with a relative velocity when a second comparison is conducted with frame A.

Then the relationship of frame B [at the relative velocity] to frame A is equivalent to the relationship of frame B [at the relative velocity] to frame B when it was comoving with frame A.
You keep reiterating a specific definition of what length contraction or time dilation is, but do not address any reason for why this relationship would not be equivalent or further
why any other reference frame would not agree to this equivalence.
I also do not see how any other frame could possibly observe the periods of comparison as occurring during the acceleration phase as the comparisons could only take place while the relevant clocks and observers in A and B were cojacent. Perhaps you could elaborate on your proposition?
Maybe there is some basic semantic or other miscommunication going on here. :-)

This is an exaggeration for effect, but to me, what you are trying to do is something like the following:
5+3=8
10-2=8
Therefore addition is subtraction.

It is just nonsense. Sure you for any given addition problem you can find an infinite number of subtraction problems with the same answer but that doesn't change the definition of what addition is.

Similarly for any given length contraction scenario you can find an infinite number of non-inertial coordinate systems that will give you the same factor as a before-and-after comparison of coordinate distances but that doesn't change the definition of what length contraction is. The misuse of defined terms only leads to confusion. If you want to define a before-and-after comparison of lengths then please coin a new term because length contraction is already defined.

 

[Austin0]

=DaleSpam;2512880]No, I definitely do not agree. Remember a reference frame is a coordinate system. If you say, "let A be an inertial reference frame" then A never accelerated and A never will accelerate. There is no ambiguity whatsoever about its future or past state of motion.

Some specific object may be defined to be at rest only in some small region of that reference frame, and (provided the boundary conditions are completely specified) we do not need to make assumptions about the object outside of the specified region. But the reference frame itself is always and everywhere inertial by definition. Do you see the distinction?

Yes I see the distinction you are pointing out.
I tend to forget and use the term frame when I should more correctly say inertial system.
YOu are saying that reference frames are abstractions that exist with or without clocks or observers and if a system changes relative velocity it is then actually changing reference frames rather than changing the RV of the frame.
SO semantically I agree, on the other hand situations [eg Twins etc] are discussed where there are systems with periods of acceleration and inertial periods and the significant part of what I said seems to pertain if you simply substitute the word system for frame.

This is an exaggeration for effect, but to me, what you are trying to do is something like the following:
5+3=8
10-2=8
Therefore addition is subtraction.

It is just nonsense. Sure you for any given addition problem you can find an infinite number of subtraction problems with the same answer but that doesn't change the definition of what addition is.

I would agree this is nonsense. I would also say it is not analogous at all.
A and B comoving.
A t = 4 and B t=4 [4 being the measured length of time in the systems]

A t = 4 and B(2) t=3 [B(2) being system B having moved to a relative inertial reference frame. Repeating the same interval in A t=4]

The relationship of B(2) to A = ( 3 to 4 )through direct measurement
Therefore the relationship of B(2) to B= (3 to 4) through the equivalence A= B
No other frames, inertial or otherwise are required.

That said; I am done. Though I am curious if, aside from the semantics and terminology, you seriously question the logic or think that B(2) to B = (3 to 4) would not be true.

Similarly for any given length contraction scenario you can find an infinite number of non-inertial coordinate systems that will give you the same factor as a before-and-after comparison of coordinate distances but that doesn't change the definition of what length contraction is. The misuse of defined terms only leads to confusion. If you want to define a before-and-after comparison of lengths then please coin a new term because length contraction is already defined[/QUOTE ]

 

[Al68]

Yes I see the distinction you are pointing out.
I tend to forget and use the term frame when I should more correctly say inertial system.
YOu are saying that reference frames are abstractions that exist with or without clocks or observers and if a system changes relative velocity it is then actually changing reference frames rather than changing the RV of the frame.

If a system is accelerated, it's not an inertial system. The word system is commonly used to mean frame, so if I were referring to an object that accelerates relative to an inertial frame, I would say the object accelerated, not the frame or system. The acceleration is relative to the frame. If you're referring to the accelerated frame, or system, that co-moves with the accelerated object, then the object is stationary in such system, with no coordinate acceleration or velocity.

Of course, this is all just a convention, but not using it causes much confusion among those that do use it.

 

[Dale]

I agree with Al68's comments re: the use of the word system and object. But what you say is essentially correct.

SO semantically I agree, on the other hand situations [eg Twins etc] are discussed where there are systems with periods of acceleration and inertial periods and the significant part of what I said seems to pertain if you simply substitute the word system for frame.

I am glad that you mentioned this. Personally, I believe that a lot of the confusion regarding the twins paradox is a direct result of many people not clearly using appropriate terminology in distinguishing between reference frames and objects. In the twins paradox you have two twins, one is inertial and one is non-inertial. You can analyze the twins scenario in an infinite number of inertial reference frames and whenever you do so you obtain the correct result. It is only when people start confusing reference frames and objects that there is ever any suggestion that the twin's paths are equivalent.

I am curious if, aside from the semantics and terminology, you seriously question the logic or think that B(2) to B = (3 to 4) would not be true.

I am not sure what you are trying to say here. Are A and B and B(2) different reference frames or different objects, and what does an expression like B = (3 to 4) mean?

 

[vitruvianman]

See

http://www.bartleby.com/173/9.html

 

[yuiop]

I am happy to see that someone else has a problem with this common explanation of wavelength stretching due to transit up the gradient.
It is not just an idea presented in this forum but I have found it in accepted explanations of, for instance ; the red shift of light coming up the gravity well to reach earth.
Where it is proposed to be an in transit effect , happening after emmission and no mention of the shift due to dilation of the frequency of the emitting electron due to position in the field. {which you seem to be talking about here]
I have brought this up in several threads but the responce has been they were just two different descriptions of the same phenomena. It seems to me that if the gravitational effect due to locale is valid , and it seems to be verified to a great degree, the a shift due to transit is not merely superfluous but simply invalid. That if it also occurred then there should be an additive quantitative red shift at the receiver beyond what is calculated and explained by the expected shift at emission. Does this make any sense ? SO far nobody has seemed to know what I was talking about.

Hi Austin, sorry for the delay responding. I somehow missed your post. I have tried to answer your questions in a new thread https://www.physicsforums.com/showthread.php?t=366816" as we are probably going off topic in this thread.

 

[heldervelez]

Of course humans have minds which interpret observations.

I was enlarging on Schutz's definition of an observer.

"It is important to realize that an 'observer' is in fact a huge information gathering system, not simply one man with binoculars. In fact, we shall remove the human element entirely from our definition, and say that an inertial observer is simply a coordinate system for spacetime, which makes an observation simply by recording the location and time of any event"

The point I was trying to make is that reality is what is measured directly or indirectly as lengths or times, and we as humans of course interpret this to try and describe how the world works. If the "information gathering system" cannot measure or observe it, then it is of no relevance to non-philosophers.

Matheinste.

I posted https://www.physicsforums.com/showpost.php?p=2517037&postcount=14"as an answer 'a la Poincaré'

Indeed Schutz's definition of an observer is adequated to a child like mind, first answer, the obvious one.

 

[matheinste]

I posted https://www.physicsforums.com/showpost.php?p=2517037&postcount=14"as an answer 'a la Poincaré'

Indeed Schutz's definition of an observer is adequated to a child like mind, first answer, the obvious one.

I'm not sure what point your scenario is making but if it is saying that length is relative, then OK. But having defined a unit of measurement, length, time etc. then the question "has this unit changed" is a meaningless question.If one defines the length of ones arm as the unit of length, then by definition it remains the unit of length because you have no other unit to measure it against.

Matheinste.