The Physical Meaning of the Relatvity of Simultaneity

[matheinste]

With regards the two spheres question, purely by chance, while looking at ether theories I cam across the following from Whittaker-a History of Theories of the Ether and Electricity Volume 2. 1953. Page 36.

-------Some of the consequences of the new theory seemed to contemporary physicists very strange. Suppose, for example, that two inertial sets of axes A and B are in motion relative to each other, and that at a certain instant their origins coincide: and suppose that at this instant a flash of light is generated at the common origin. Then, by what has been said in the subsequent propagation, the wave-fronts of the light, as observed in A and in B, are spheres whose centres are the origins of A and B respectively, and therefore DIFFERENT spheres. How can this be?

The paradox is explained when it is remembered that a wave-front is defined to be the locus of points which are SIMULTANEOUSLY in the same phase of disturbance. Now events taking place at different points, which are simultaneous according to A’s way of measuring time, are not in general simultaneous according to B’s way of measuring: and therefore what A calls a wave-front is not the same thing as what B calls a wave-front. Moreover, since the system of measuring space is different in the two inertial systems, what A calls a sphere is not the same thing as what B calls a sphere. Thus there is no contradiction in the statement that the wave-fronts for A are spheres with A’s origin as centre, while the wave-fronts for B are spheres with B’s origin as centre.

In common language we speak of events which happen at different points of space as happening ‘at the same instant of time,’ and we also speak of events which happen at different instants of time as happening ‘at the same point of space.’ We now see that such expressions can have a meaning only by virtue of artificial conventions; they do not correspond to any essential physical realities.-------


Matheinste.

 

[Austin0]

It is perhaps worth pointing out that, in relativity, the concept of simultaneity is a convention rather than an experimentally meaningful idea. As nothing can be transmitted instantaneously from A to B, nature doesn't care about "simultaneity" at all. It's a man-made concept which eases our mathematical analysis within a frame of reference, but has no real "physical" significance.

In pre-relativistic physics, all observers agreed on what was simultaneous, which is why we intuitively feel simultaneity is important. In relativity, nobody agrees on simultaneity, but they all agree on the speed of light; it's the notion of being able to send light from event A to event B which is the important relation in connecting events (rather than simultaneity).

Hi DrGreg While agreeing completely with all you have stated here I would like to clarify a point.

simultaneity is a convention rather than an experimentally meaningful idea

WOuld you agree with the idea that this is a result of our lack of technilogical ability to accelerate systems of clocks and rulers to significant velocities rather than a limitation of meaningful conceptions?
That if we were able to do so, we would expect to experimentally confirm the relative desynchronization of clocks between systems. Which, lacking any ,even hypothetical means of determining instantaneous simultaneity, would demonstrate and confirm SR concepts regarding the matter.??
To my mind this still leaves open an even more intriguing question : Is the desynchronization purely the result of the conventional procedure for synchronization or is it the result of and represents an actual temporal displacement of some incomprehensible kind??
Specifically ; in this case if we assume two systems with clocks synched with the convention, even if this method is actually arbitrary the simple mechanical desynchronization produced by the convention would seem to explain all the observed phenomena with regard to the centered light spheres in both systems. AS well as the contraction resulting from the difference of ideas of distance derived from measurements taken at the "same" time in different systems.
On the other hand the desynchronization or shift of simultaneity may not be a result of a synch method but may be an intrinsic resuly of relative velocity , an actual temporal/spatial shift which the convention also conveniently ensures.
AN experimental test of these alternatives might be ; If a system in inertial motion has its clocks synched by converntion and is then accelerated to a new significant velocity before resuming inertial motion there would seem to be two possibilities:
The clocks need to be resynched through convention. Light measurement would not automatically be correct.
Or
The acceleration and new relative velocity has in itself shifted the clocks into a new relative synchronization so the measured speed of light would remain isotropic and constant without requiring adjustment to the clocks.
It may be the answer must await empirical determination but I am drawn to number two in spite of the obvious logical reasons why it shouldn't apply.
ANy comments appreciated thanks

 

[Al68]

AN experimental test of these alternatives might be ; If a system in inertial motion has its clocks synched by converntion and is then accelerated to a new significant velocity before resuming inertial motion there would seem to be two possibilities:
The clocks need to be resynched through convention. Light measurement would not automatically be correct.
Or
The acceleration and new relative velocity has in itself shifted the clocks into a new relative synchronization so the measured speed of light would remain isotropic and constant without requiring adjustment to the clocks.

It seems that each choice is half right.

The clocks would be out of synch, but light measurement would still automatically be correct, since it does not rely on clocks being in synch, only that they run at the same rate.

The second choice is also right that light would remain isotropic and constant without requiring adjustment to the clocks, although the clocks are out of synch.

Clocks in an inertial frame that are out of synch will still show equal elapsed time for equal distances traveled by light.

For example, if light is emitted equidistant between two clocks, one reading zero and the other reading t1 when the light is emitted, the first will read t and the second will read t + t1 when the light is received, both showing an elapsed time of t.

 

[YellowTaxi]

@ heldervelez. You are certainly free to prefer Lorentz's Aether Theory over Einstein's Special Relativity, but since Lorentz's aether is, by design, completely undetectable experimentally you are simply not going to get a lot of enthusiastic support for the extra and unnecessary complication. Go ahead and use it, and we will go ahead and not use it, and we will still all agree on everything measurable.

- including the constancy of any observer's value of c

But the difference between the 2 versions IMHO is just an argument of semantics. Neither is superior or more logical than the other. Until somebody can give a logical reason for the constancy of c. Or show that an ether does exist.

but since Lorentz's aether is, by design, completely undetectable experimentally

Are you certain of this Dale? Most our experiments to detect the aether have been carried out on Earth. (not much use really). Like trying to show that everybody in the world speaks English because we talked to everyone in england and they all spoke English.

And secondly can't it be argued that einstien's GR is just an aether theory ? The Aether just distorts in a region of large mass density.

 

[matheinste]

Don't advocates of both theories agree that it is, even in theory, impossible to decide beteween the two formulations. That is, no experiment can be designed to decide between the two. Both formulations predict exactly the same observable outcomes.

Matheinste.

 

[Dale]

But the difference between the 2 versions IMHO is just an argument of semantics.

I tend to agree.

Are you certain of this Dale? Most our experiments to detect the aether have been carried out on Earth.

Yes, I am certain of it. Both theories are simply interpretations of the Lorentz transforms. So they make the same predictions in all circumstances. An extra-terrestrial experiment which detected aether would disprove both SR and Lorentz's Aether Theory.

 

[yuiop]

...
“To account for these experiments on the basis of a fixed ether it would be necessary to introduce ingenious assumptions as to a change in length or Lorentz-Fitzgerald contraction just sufficient to give a null effect in the Michelson experiment, and as to a change in period or time dilation just sufficient to give a null effect in the Kennedy experiment-all to the end of retaining a fixed ether so devilishly constructed that its existence could never be detected.”
...

The above attack on the Lorentz Ether theory suggests that Special Relativity does not treat time dilation or length contraction as a physical manifestation, but just a difference of opinion between observers where all such measurements are simply "relative".

But...

AN experimental test of these alternatives might be ; If a system in inertial motion has its clocks synched by convention and is then accelerated to a new significant velocity before resuming inertial motion there would seem to be two possibilities:
The clocks need to be re-synched through convention. Light measurement would not automatically be correct.
Or
The acceleration and new relative velocity has in itself shifted the clocks into a new relative synchronization so the measured speed of light would remain isotropic and constant without requiring adjustment to the clocks.

The first option is the prediction of SR and the Lorentz transformations. After a synchronised system has been accelerated, its clocks will no longer be in sync when it acquires a new constant velocity. The one-way measured speed of light will no longer be correct or directionally symmetric until the clocks are resynchronised. This also poses the question as to how the clocks got out of sync, if we hold to the interpretation of Special Relativity that time dilation is not actually a physical occurrence. If we interpret the time dilation and length contraction of Special Relativity as physical, then it is quite ingenious how they are just sufficient to ensure that the speed of light is constant for all inertial observers. Maybe nature is devilishly constructed whichever way you look at it.

 

[matheinste]

The above attack on the Lorentz Ether theory suggests that Special Relativity does not treat time dilation or length contraction as a physical manifestation, but just a difference of opinion between observers where all such measurements are simply "relative".

Because there is no differnce in predictions between the two formulations I am OK with either of them. But Einstein's seems simpler and, to me, more aesthetically pleasing. I have no personal desire to attack followers of LET or their beliefs as the differences of viewpoint are irrelevant to physics if not to philosophy.

As regards how SR treats the reality of length contraction I personally take the view of Rindler and most other textbook writers when they say "Length contraction is 'real' in every sense of the word", and is, in theory, experimentally demonstrable.

Matheinste

 

[Austin0]

It seems that each choice is half right.

The clocks would be out of synch, but light measurement would still automatically be correct, since it does not rely on clocks being in synch, only that they run at the same rate.

The second choice is also right that light would remain isotropic and constant without requiring adjustment to the clocks, although the clocks are out of synch.

Clocks in an inertial frame that are out of synch will still show equal elapsed time for equal distances traveled by light.

For example, if light is emitted equidistant between two clocks, one reading zero and the other reading t1 when the light is emitted, the first will read t and the second will read t + t1 when the light is received, both showing an elapsed time of t.

Hi Al68
There may be some miscommunication here as to the meaning of out of synch.
It seems to me fairly sure that unsynched clocks cannot measure the elapsed transit time of anything at all. They must be synched by some rational method and operate on the assumption of simultaneity/synchronicity even if in the case of SR this is an operational assumption with no implcation of actuality outside the frame.

For example, if light is emitted equidistant between two clocks, one reading zero and the other reading t1 when the light is emitted, the first will read t and the second will read t + t1 when the light is received, both showing an elapsed time of t

In your example here you omitted the time of emission at the midpoint. Consequently the observed proper times at the two receivers have no basis for evaluating the elapsed time.
For them to have a time for the emission requires, both that they know the observed time at the midpoint and that that clock is not only operating at the same rate but is synchronized with their clocks.

In my example the assumption was that after attaining a new velocity that simple , normal one way light tests or measurements would be conducted, on the naive assumption that the clocks were still in synch. And would then either be correct or not.
If the clocks are no longer in synch they will not directly return isotropic measuremnts at c. I agree that asynchronous clocks can be used to correctly make those measurements but only if the degree or interval of desynchronization is known beforehand. This effectively synchronizes them through calculation.
If the distance is known, this discrepancy can of course be determined as the tests become one way synchronization procedures; as the proper time at the midpoint is transmitted and the recipient clocks can determine the correct time of reception from this [Emission T + D/c = Reception T ] and then correct their clocks.
It is a given that the measured speed of light will be isotropic and constant if correctly measured in any frame but in my setup the question was really an either or ,,,,with a clearcut A or B outcome regarding purely the clocks. Thanks

 

[Dale]

After a synchronised system has been accelerated, its clocks will no longer be in sync when it acquires a new constant velocity. ... This also poses the question as to how the clocks got out of sync, if we hold to the interpretation of Special Relativity that time dilation is not actually a physical occurrence.

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.

 

[Dale]

Because there is no differnce in predictions between the two formulations I am OK with either of them. But Einstein's seems simpler and, to me, more aesthetically pleasing. I have no personal desire to attack followers of LET or their beliefs as the differences of viewpoint are irrelevant to physics if not to philosophy.

I agree completely.

As regards how SR treats the reality of length contraction I personally take the view of Rindler and most other textbook writers when they say "Length contraction is 'real' in every sense of the word", and is, in theory, experimentally demonstrable.

I just don't like using the word "real" as it always leads to semantic arguments about the definition of "real". So instead I describe length contraction as "coordinate dependent and measurable". That way people who think that "real" -> "coordinate independent" can draw the conclusion that length contraction is "unreal" and people who think that "measurable" -> "real" can draw the conclusion that length contraction is "real", both without drawing me into the semantic argument.

 

[Austin0]

The above attack on the Lorentz Ether theory suggests that Special Relativity does not treat time dilation or length contraction as a physical manifestation, but just a difference of opinion between observers where all such measurements are simply "relative".

But...



The first option is the prediction of SR and the Lorentz transformations. After a synchronised system has been accelerated, its clocks will no longer be in sync when it acquires a new constant velocity. The one-way measured speed of light will no longer be correct or directionally symmetric until the clocks are resynchronised. This also poses the question as to how the clocks got out of sync, if we hold to the interpretation of Special Relativity that time dilation is not actually a physical occurrence. If we interpret the time dilation and length contraction of Special Relativity as physical, then it is quite ingenious how they are just sufficient to ensure that the speed of light is constant for all inertial observers. Maybe nature is devilishly constructed whichever way you look at it.

Does either SR or the Lorentz math really make any predictions in this regard?
For all the factors: time dilation, contraction and desynchronization the math provides a quantitative prediction for observed relationships but as far as I can see does not go into any mechanism behind these effects and therefore neither provides nor leads to any real expectations outside of inertial conditions.
As you question here,,, how would the clocks get out of synch?
Although in this example it seems to me more a case of them retaining the original synchronization which is no longer appropriate to the new velocity rather than positing a change in the clocks.
The second alternative, where the clocks directly return correct readings at a new velocity would seem to suggest a change in the clocks themselves through acceleration or relative velocity. Which is not so different from a change in length is it? In which case as is discussed right here, it is somewhat unclear as to the meaning or physicallity of these "changes" and certainly no rational physics to explain a mechanism effectuating this in any of the cases.
To my mind SR does provide a rational explanation for the logically challenging isotropic constancy of c but time dialtion and length contraction by themselves are insufficient. It seems to demand clock desynchronization as an essential element as well.
In any case it appears to be a fiendishly clever arrangment of physical factors , no argument there.

 

[Austin0]

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.

Why do you make the distinction if we are talking about the concept??
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?

 

[matheinste]

I agree completely.

I just don't like using the word "real" as it always leads to semantic arguments about the definition of "real". So instead I describe length contraction as "coordinate dependent and measurable". That way people who think that "real" -> "coordinate independent" can draw the conclusion that length contraction is "unreal" and people who think that "measurable" -> "real" can draw the conclusion that length contraction is "real", both without drawing me into the semantic argument.

The inverted commas around 'real' are my addition as I am aware that the word can cause all sorts of problems. I quoted from memory but I have copied from source below. I don't know if the addition of the words "relative to a given frame" make it any more acceptable.

---It must be stressed that the phenomenon is not to be regarded as illusory, due perhaps to some peculiarity in our methods of measurement: relative to a given frame it is real in every possible sense.----

Rindler--Special Relativity. Published by Oliver and Boyd second ediition 1966 page 26.

Matheinste.

 

[Austin0]

Suppose, for example, that two inertial sets of axes A and B are in motion relative to each other, and that at a certain instant their origins coincide: and suppose that at this instant a flash of light is generated at the common origin. Then, by what has been said in the subsequent propagation, the wave-fronts of the light, as observed in A and in B, are spheres whose centres are the origins of A and B respectively, and therefore DIFFERENT spheres. How can this be?
Matheinste.

I have nothing to add to the general explanation which is well covered by this post and others in this thread.
What seems to be central to the logical confusion of the OP and others is the term observation. The actual colocated observers in both frames simultaneously observe the same singular spherical wavefront. Just at different proper times. These are the actual "observations"
There are no observers in either frame that have the perspective we enjoy looking at the situation. Within the systems it is impossible to "observe" the spheres or relation to the origin. This has to be calculated from the disparate measurements after the fact and then reconstructed. These constructions are the two spheres, which as you point out have no objective reality outside of the individual frames.

 

[Dale]

Why do you make the distinction if we are talking about the concept??

I make the distinction because there appears to be some confusion in the community as a whole about what the terms "length contraction" and "time dilation" refer to.

If you are measuring "before" and "after" some process then it is simply not length contraction or time dilation. If you are involving acceleration then it is probably also not length contraction or time dilation (unless you are being really careful with the use of non-inertial frames). Length contraction and time dilation are comparisons between measurements in different reference frames for the same event, not comparisons between measurements in a single reference frame for different events.

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?

I certainly wouldn't use the word "easily" to describe it. This frame would be non-inertial so the usual SR formulas would not apply. You could do it if you were careful as I mentioned above, but you would have GR gravitational time dilation effects as well as SR velocity time dilation effects. And the results would be different depending critically on the specific details of how you arbitrarily chose to define your non-inertial coordinate system.

 

[Al68]

If the clocks are no longer in synch they will not directly return isotropic measuremnts at c. I agree that asynchronous clocks can be used to correctly make those measurements but only if the degree or interval of desynchronization is known beforehand. This effectively synchronizes them through calculation.

This is exactly what I meant. But knowing beforehand the "interval of desynchronization" is required even if that interval is zero, ie even if the clocks are in synch, that must be known beforehand.

Like you said, knowing the "interval of desynchronization" is what matters, making that interval equal to zero (synchronizing) just simplifies the math.

 

[Austin0]

Originally Posted by Austin0
Why do you make the distinction if we are talking about the concept??

I make the distinction because there appears to be some confusion in the community as a whole about what the terms "length contraction" and "time dilation" refer to.

If you are measuring "before" and "after" some process then it is simply not length contraction or time dilation. If you are involving acceleration then it is probably also not length contraction or time dilation (unless you are being really careful with the use of non-inertial frames). Length contraction and time dilation are comparisons between measurements in different reference frames for the same event, not comparisons between measurements in a single reference frame for different events.

Agreed there is confusion regarding terms.
I may have been unclear in my post. There is no acceleration involved in the comparison which is assumed to take place after attaining a new inertial velocity.
I am unsure of what you mean by referring to measuremnet of the same event. In the case of contraction are you referring to two simultaneous measurements within a frame as a single event?
In the case of dilation isn't it always a case of comparing the interval between two events as measured in different frames??

Originally Posted by Austin0
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?

I certainly wouldn't use the word "easily" to describe it. This frame would be non-inertial so the usual SR formulas would not apply. You could do it if you were careful as I mentioned above, but you would have GR gravitational time dilation effects as well as SR velocity time dilation effects. And the results would be different depending critically on the specific details of how you arbitrarily chose to define your non-inertial coordinate system

Simply put: Frame A and Frame B are comoving . A specific interval between events (dt) in A can be assumed to be the same as (dt') in B.
Frame B is then accelerated through whatever profile to effect a return pass by Frame A in an inertial state. The interval in A [dt ] is repeated and compared with the same interval measured in B [dt'] and the relative dilation observed and calculated .
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 ?
As you can see the period of acceleration does not enter into the comparison or measurements.

 

[Austin0]

This is exactly what I meant. But knowing beforehand the "interval of desynchronization" is required even if that interval is zero, ie even if the clocks are in synch, that must be known beforehand.

Like you said, knowing the "interval of desynchronization" is what matters, making that interval equal to zero (synchronizing) just simplifies the math.

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.

 

[yuiop]

Does either SR or the Lorentz math really make any predictions in this regard?

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.

As you question here,,, how would the clocks get out of synch?
Although in this example it seems to me more a case of them retaining the original synchronization which is no longer appropriate to the new velocity rather than positing a change in the clocks.

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

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.

 

[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.