Understand Special Relativity and Time paradox

[zonde]

If you say that Einstein's clock synchronization convention is arbitrary then I can change it and try to implement it in particular inertial frame. As a result I won't get classical physical laws in that inertial frame.

You will get the same physical laws that you would get with Einstein's convention as long as you do it in a consistent way.

This goes against the things that we learn from SR. So I say it's wrong.

 

[zonde]

Note that he was not asking a question about the Theory of Special Relativity. He was asking a question about the Principle of Relativity, Einstein's first postulate. They're not the same thing. The PoR is based on observable raw data that among other things concludes that things will be reciprocal between two inertial observers and so the OP was wondering how from the PoR you could determine which of the two observers would be older when they both conclude that the other one is aging more slowly. Note that he specified his brother would travel at a constant speed.

So I introduced him to Bondi's brilliant analysis which only requires one additional piece of "raw data", that the propagation of light is independent of the speed of the source--a fact that has been observed experimentally. This fact is also specifically stated as part of Einstein's second postulate, but it is not enough to establish Einstein's Theory of Special Relativity. It is also a fact that is in agreement with Lorentz's Ether Theory, by the way.

And so from these experimentally based observations, Bondi concludes that the rates at which the traveling brother sees the Stay-At-Home brother's clock ticking between coming and going at the same speed are reciprocals of each other and from this it is easy to conclude that the traveling brother can predict ahead of time that he will see his brother's clock accumulate more time than his own during the trip. See post #7.

About that part in bold - where did you get it?

Besides it doesn't make sense to say that PoR is based on observable raw data because it doesn't speak about raw data but about laws of physics instead. Laws of physics is certainly different thing than raw data.

 

[ghwellsjr]

About that part in bold - where did you get it?

Besides it doesn't make sense to say that PoR is based on observable raw data because it doesn't speak about raw data but about laws of physics instead. Laws of physics is certainly different thing than raw data.

The laws of physics are derived from observable raw data. As the wikipedia article on the Principle of Relativity says:

Any principle of relativity prescribes a symmetry in natural law: that is, the laws must look the same to one observer as they do to another.

And that means there cannot be any raw data that violates those laws.

Or to put it another way--if there were any data that was not symmetrical between two inertial observers with a relative motion between them, then it would be possible to write another law that would violate the PoR.

But in this case, we are talking about the observed Doppler shifts between two inertial observers with relative motion. Do you doubt that they will see the same shift in each other?

 

[ghwellsjr]

If you say that Einstein's clock synchronization convention is arbitrary then I can change it and try to implement it in particular inertial frame. As a result I won't get classical physical laws in that inertial frame.

You will get the same physical laws that you would get with Einstein's convention as long as you do it in a consistent way.

This goes against the things that we learn from SR. So I say it's wrong.

What things? Can you be specific?

I invite you to read the wikipedia article on the One-Way Speed of Light concerning Lorentz ether theory and Edwards' theory. Both of these use a clock synchronization convention that is different from Einstein's and yet they get the same physical laws. These examples should be enough to show you that clock synchronization conventions are arbitrary, meaning that we are not compelled by any raw data to select one over the other. We have a different kind of good reason to select Einstein's; as he stated, it's simple.

 

[ghwellsjr]

hmm. I think the idea was that EM phenomena was dependent on velocity relative to the ether. These dependencies were Lorentzian transforms, but it was assumed that these transforms had nothing to do with transforms of true time and space, they were only thought of as part of the theory of EM. So in this way, time and space were assumed Galilean, while EM phenomena had this Lorentzian transform property. So the explanation of light signals being sent between the twins could be explained by Galilean relativity, using this weird form of EM equations. But what does this mean for the ageing of the twins? It depends on what you assume is the mechanism for the ageing process, and if it also is affected by travel through the ether.

Yes, in LET the EM phenomena was dependent on velocity relative to the ether. But if you want to follow Bondi's argument to conclude that the inertial twin will age more than the traveler, it works just as well with the assumptions of LET, namely that the propagation of light is independent of its source and the PoR which means that it is impossible to identify the rest state of the ether, in other words, no ether wind will ever be detected.

Let me see if I can summarize Bondi's argument. He says that if you have two inertial observers, A & B, in relative rest but separated by a great distance, and one of them, A, sends repetitive signals to the other, B, there will be no Doppler shifts. Then a third inertial observer, C, traveling from A to B will observe some Doppler shift ratio from A which will be less than one and which we can call DSR1. Then if that traveler creates his own repetitive signal(s) at the same rate he receives them from A and sends them to B, we know they will travel side by side on their way to B. When they get there, B will observe them both arriving at the same rate but the ones that were sent by C were sent with Doppler shift ratio that is the reciprocal of DSR1. We know that the speed that C is traveling away from A is the same as the speed that C is traveling toward B and so the Doppler shift ratios for the same speed coming and going are reciprocals of each other.

Therefore, in the twin scenario, since the traveling twin spends the same amount of time going and coming at the same speed, we can simply average the two Doppler shift ratios and we will get a number greater than one, meaning the traveler sees the other twin's clock running faster than his own.

If you want a better explanation, read Bondi's in the link in post #7.

 

[zonde]

The laws of physics are derived from observable raw data.

No, where did you get this idea? You just invent law of physics and then test it against raw data. You can't derive them.

Or to put it another way--if there were any data that was not symmetrical between two inertial observers with a relative motion between them, then it would be possible to write another law that would violate the PoR.

But in this case, we are talking about the observed Doppler shifts between two inertial observers with relative motion. Do you doubt that they will see the same shift in each other?

In this case we are talking about observed Doppler shifts between three inertial observers, namely stay at home twin, traveling twin on the forward trip and traveling twin on the backward trip.
We have two Doppler shifts and each Doppler involves two observers. One observer for each Doppler is the same. So it's three observers.

 

[Dale]

Both of these use a clock synchronization convention that is different from Einstein's and yet they get the same physical laws.

Hi ghwellsjr, I think the confusion is that when you say "same physical laws" you mean that the experimentally measurable predictions are the same (which I think is the usual meaning). I suspect that zonde means that the algebraic formula is the same.

Zonde, the way to distinguish whether two laws are the same is to examine the experimental predictions they make, not just the formulas. Often the formulas describe the same physics in terms of different things.

For instance, for conservative forces Lagrangian mechanics and Newtonian mechanics are the same physical laws despite the fact that the mathematical expressions look different. One describes the physics in terms of energy and an optimal path between two boundary points, the other describes the physics in terms of forces and a differential equation from an initial point. But they both describe the same physics.

Here, one simultaneity convention will describe physics in terms of a different time coordinate than another, but they both describe the same physics.

No, where did you get this idea? You just invent law of physics and then test it against raw data. You can't derive them.

I agree with this.

 

[BruceW]

... it works just as well with the assumptions of LET, namely that the propagation of light is independent of its source and the PoR which means that it is impossible to identify the rest state of the ether, in other words, no ether wind will ever be detected.

Well, you have to introduce some more assumptions, e.g. that the ageing of the twins is also affected by the ether. According to wikipedia, Lorentz never thought that true spacetime transformed in a Lorentzian way. So whether the ether could be detected depends on how you define the LET.

Therefore, in the twin scenario, since the traveling twin spends the same amount of time going and coming at the same speed, we can simply average the two Doppler shift ratios and we will get a number greater than one, meaning the traveler sees the other twin's clock running faster than his own.

Agreed. Although, really the traveler sees the other twin's clock ticking slower on the outbound journey and faster on the inbound journey, but you are right that the frequencies are in a proportion such that when the twins meet up, the stay-at-home twin's clock has ticked more times than the traveler's clock, over the total journey (by a factor of gamma). As I said, this is an interesting way to explain the twin paradox.

To me, the principle point of this explanation is that the wavefronts of light given out from the stay-at-home twin are emitted in a steady manner (according to an inertial frame) over the whole journey. This is not true of the wavefronts emitted by the traveling twin, because he does the turnaround. I think this is pretty much the same as what PeterDonis was saying in his post 288.

 

[PAllen]

Well, you have to introduce some more assumptions, e.g. that the ageing of the twins is also affected by the ether. According to wikipedia, Lorentz never thought that true spacetime transformed in a Lorentzian way. So whether the ether could be detected depends on how you define the LET.

But Lorentz did believe that physical length contraction occurred (by virtue of moving through the aether). He was forced to conclude this by his analysis of various experiments. I believe, that by 1905 or so, independent of Einstein, he had concluded that no method would be able to detect movement through the aether (physical length contraction couples EM effects to mechanical effects, and without logical contradictions, you - if you are as smart as Lorentz - are soon forced to see that all processes must be similarly affected). His model of why this was so was completely different from Einstein's, but the result was the same.

 

[ghwellsjr]

Well, you have to introduce some more assumptions, e.g. that the ageing of the twins is also affected by the ether. According to wikipedia, Lorentz never thought that true spacetime transformed in a Lorentzian way. So whether the ether could be detected depends on how you define the LET.

In order to prove, without actually doing the experiment, that an observer traveling at one speed (0.5c in the OP's case) by going away from an inertial observer and then returning at the same speed, will age less than the inertial observer, it is only necessary to assume that nothing in the experiment will look any different to any of the observers if conducted at any other state of inertial motion for all observers (that's the Principle of Relativity as demonstrated in the case of LET that the ether wind could not be detected) and that the propagation of light, although it can be different in every state of inertial motion, is the same for different sources of light (which is certainly true under LET). This is important in Bondi's argument so that the light from C takes the same time to reach B as the light that from A takes to reach B after it passes C.

In other words, you don't have to incorporate any mechanism such as the aging is affected by the ether or any theory that involves spacetime or transformations. Of course, you do have to assume that the aging is not going to change for no good reason such as would happen in a situation caused by gravity, for example.

Agreed. Although, really the traveler sees the other twin's clock ticking slower on the outbound journey and faster on the inbound journey, but you are right that the frequencies are in a proportion such that when the twins meet up, the stay-at-home twin's clock has ticked more times than the traveler's clock, over the total journey (by a factor of gamma). As I said, this is an interesting way to explain the twin paradox.

Now you are going beyond what I presented in post #7. In that post, I wasn't explaining the twin paradox, only answering the OP's question: which observer will be older? In order to establish that the final ratio of accumulated times is gamma, you do have to make more assumptions which is what I did in post #23.

To me, the principle point of this explanation is that the wavefronts of light given out from the stay-at-home twin are emitted in a steady manner (according to an inertial frame) over the whole journey. This is not true of the wavefronts emitted by the traveling twin, because he does the turnaround. I think this is pretty much the same as what PeterDonis was saying in his post 288.

And which I also pointed out in response to PeterDonis in my post #291 saying that I already covered that in post #23 and which he agreed in post #294 that there is a lot of repetition going on in this thread.

 

[ghwellsjr]

No, where did you get this idea? You just invent law of physics and then test it against raw data. You can't derive them.

I don't think anybody invented any law of physics without first having raw data on which to invent that law. I agree that the law should be further testable and new experiments invented to test the theory in areas that the original raw data didn't cover but that's a side issue and not related to the point or the argument that Bondi or I are making.

In this case we are talking about observed Doppler shifts between three inertial observers, namely stay at home twin, traveling twin on the forward trip and traveling twin on the backward trip.
We have two Doppler shifts and each Doppler involves two observers. One observer for each Doppler is the same. So it's three observers.

I'm not asking you about the twin situation because we don't have two inertial observers in that situation. I'm asking you for any two inertial observers with relative motion. Do you doubt that they will see the same Doppler shift in each other, even if the experiment is repeated under different states of inertial motion for both of them? And if they ever saw a different Doppler shift, do you doubt that that would violate the Principle of Relativity?

 

[BruceW]

But Lorentz did believe that physical length contraction occurred (by virtue of moving through the aether). He was forced to conclude this by his analysis of various experiments. I believe, that by 1905 or so, independent of Einstein, he had concluded that no method would be able to detect movement through the aether (physical length contraction couples EM effects to mechanical effects, and without logical contradictions, you - if you are as smart as Lorentz - are soon forced to see that all processes must be similarly affected). His model of why this was so was completely different from Einstein's, but the result was the same.

Ah, my bad. I am not very familiar with the history. I think they should teach more history of science in schools :) maybe the non-scientists don't find it so interesting.

The thing I was really trying to say was about the explanation of the twin paradox, that if we assume there is some kind of principle of relativity, and that EM phenomena transform in a Lorentzian way, then it is not a priori obvious that any general phenomena must transform in a Lorentzian way. We would have to make this another assumption.

As it happens, experimental evidence suggests that all phenomena observed by an inertial frame agree with the Lorentz transform rule. But we still need to remember that we are making this assumption when we explain things like the twin paradox.

Edit: except maybe quantum stuff that does not conserve parity. But we don't care about that, because we are talking about large-scale phenomena.

Edit again: Ignore my last edit. Lorentz transforms are a passive transform, while the non-conservation of parity happens under an active transform, so they are not related.

 

[Austin0]

I don't think anybody invented any law of physics without first having raw data on which to invent that law. I agree that the law should be further testable and new experiments invented to test the theory in areas that the original raw data didn't cover but that's a side issue and not related to the point or the argument that Bondi or I are making.

I agree with you completely. The history of science is a co-evolution of inductive reasoning , derived from empirical data, and deductive inferences applied to those derived structures.
Case in point. A certain classical cosmological model:
The cosmos as a crystal sphere rotating the Earth was directly derived (inducted) from
observation. The turtles (we can assume) were pure deductive invention.

Most of the history is similar. The fundamental electrodynamic Laws ,Ohm's etc.
were directly derived from experimental observation. Were, in essence, mathematical descriptions of that raw data.
Later Maxwell, Lorentz et al deductively inferred other aspects of the theory from this basic structure.
it is actually rarer for the opposite to occur.
A couple of examples:
Copernican Heliocentricity and Einstein's Gravity, where significant evolutions of the model were not the result of , or derived from , new or improved observations but resulted directly from internal deduction applied within the established data and interpretations of that data.

While these type of cases do support the concept of a theory as an invention that is then confirmed or falsified by further experimental observation , I think this is somewhat one sided , in that they are not the general case nor , as you pointed out , do these arrive out of thin air. ( A data-less vacuum).

 

[bobc2]

So, I take it that we are on the same page with the sketch below representing our traveling twin in his rocket during the turnaround.

And in the same sense that we considered the sequence of instantaneous rockets as presented in the stay-at-home twin's frame, we can also recognize the sequence of hyperplanes of simultaneity indicated by the Lorentz-Poincare' transformations to the traveling coordinates.

The sequence of instantaneous 3-D rocket volumes that the traveling twins is living in are clearly not the same physical 3-D rocket volumes that are depicted in the sketch above. The physical 3-D rocket that the traveling twin lives in is unique to him and represented uniquely in his coordinates.

 

[Dale]

And in the same sense that we considered the sequence of instantaneous rockets as presented in the stay-at-home twin's frame, we can also recognize the sequence of hyperplanes of simultaneity indicated by the Lorentz-Poincare' transformations to the traveling coordinates.

So what? I don't get your point. You showed an inertial simultaneity convention and now want to use that to infer what exactly about a non inertial simultaneity convention? And what is the chain of logic that leads you from one to the other?

The sequence of instantaneous 3-D rocket volumes that the traveling twins is living in are clearly not the same physical 3-D rocket volumes that are depicted in the sketch above. The physical 3-D rocket that the traveling twin lives in is unique to him and represented uniquely in his coordinates.

This is a lot of nonsense. The traveling twin is not dead under some simultaneity conventions and alive in others, so talking about the physical 3D rocket volumes they are living in is nonsense. And there is nothing particularly unique about the coordinates where the traveller is at rest.

 

[zonde]

I don't think anybody invented any law of physics without first having raw data on which to invent that law. I agree that the law should be further testable and new experiments invented to test the theory in areas that the original raw data didn't cover but that's a side issue and not related to the point or the argument that Bondi or I are making.

The problem with raw data is that there is a lot of it. And generally different observers don't share too much of it (usually none). But physical laws work for all observers (they share them so to say).

And what is the argument that Bondi is making?

I'm not asking you about the twin situation because we don't have two inertial observers in that situation. I'm asking you for any two inertial observers with relative motion. Do you doubt that they will see the same Doppler shift in each other, even if the experiment is repeated under different states of inertial motion for both of them? And if they ever saw a different Doppler shift, do you doubt that that would violate the Principle of Relativity?

Of course they will see the same Doppler shift.

But I do not see how it explains this statement of yours:

The PoR is based on observable raw data that among other things concludes that things will be reciprocal between two inertial observers

unless you admit that it is plain wrong.

 

[zonde]

Seems like I left this post without answer.

What things? Can you be specific?

Form Einstein's 1905 paper:
Chapter 1. Definition of Simultaneity starts with:

Let us take a system of co-ordinates in which the equations of Newtonian
mechanics hold good. In order to render our presentation more precise and
to distinguish this system of co-ordinates verbally from others which will be
introduced hereafter, we call it the “stationary system.”

and it ends with:

It is essential to have time defined by means of stationary clocks in the
stationary system, and the time now defined being appropriate to the stationary
system we call it “the time of the stationary system.”

So we can write out such statements:
- in "stationary system" equations of Newtonian mechanics hold good;
- time of "stationary system" is defined using Einstein's simultaneity convention.

This suggests that Einstein's simultaneity convention is essential for equations of Newtonian mechanics to hold good.

I invite you to read the wikipedia article on the One-Way Speed of Light concerning Lorentz ether theory and Edwards' theory. Both of these use a clock synchronization convention that is different from Einstein's and yet they get the same physical laws. These examples should be enough to show you that clock synchronization conventions are arbitrary, meaning that we are not compelled by any raw data to select one over the other. We have a different kind of good reason to select Einstein's; as he stated, it's simple.

Lorentz ether theory does not propose it's own clock synchronization convention. At least I didn't found it.

Edwards' theory introduces parameter q. But it does not claim that physical laws are the same as you vary q. It claims however that experimental predictions won't change as you vary q.

For reference, this discussion started with this claim:

You will get the same physical laws that you would get with Einstein's convention as long as you do it in a consistent way.

 

[ghwellsjr]

The problem with raw data is that there is a lot of it. And generally different observers don't share too much of it (usually none). But physical laws work for all observers (they share them so to say).

And what is the argument that Bondi is making?

I summarized it in post #305 at the top of this page:

Let me see if I can summarize Bondi's argument. He says that if you have two inertial observers, A & B, in relative rest but separated by a great distance, and one of them, A, sends repetitive signals to the other, B, there will be no Doppler shifts. Then a third inertial observer, C, traveling from A to B will observe some Doppler shift ratio from A which will be less than one and which we can call DSR1. Then if that traveler creates his own repetitive signal(s) at the same rate he receives them from A and sends them to B, we know they will travel side by side on their way to B. When they get there, B will observe them both arriving at the same rate but the ones that were sent by C were sent with Doppler shift ratio that is the reciprocal of DSR1. We know that the speed that C is traveling away from A is the same as the speed that C is traveling toward B and so the Doppler shift ratios for the same speed coming and going are reciprocals of each other.

And http://archive.org/stream/RelativityCommonSense/Bondi-RelativityCommonSense#page/n45/mode/1up is that link again.

Of course they will see the same Doppler shift.

But I do not see how it explains this statement of yours:

The PoR is based on observable raw data that among other things concludes that things will be reciprocal between two inertial observers

unless you admit that it is plain wrong.

I will admit that my choice of the word "reciprocal" could be confusing to someone whose native tongue is not English, especially since I used it again later with an almost opposite meaning. A better word would have been symmetrical.

 

[ghwellsjr]

Seems like I left this post without answer.


Form Einstein's 1905 paper:
Chapter 1. Definition of Simultaneity starts with:

Let us take a system of co-ordinates in which the equations of Newtonian
mechanics hold good. In order to render our presentation more precise and
to distinguish this system of co-ordinates verbally from others which will be
introduced hereafter, we call it the “stationary system.”

and it ends with:

It is essential to have time defined by means of stationary clocks in the
stationary system, and the time now defined being appropriate to the stationary
system we call it “the time of the stationary system.”

So we can write out such statements:
- in "stationary system" equations of Newtonian mechanics hold good;
- time of "stationary system" is defined using Einstein's simultaneity convention.

This suggests that Einstein's simultaneity convention is essential for equations of Newtonian mechanics to hold good.

Go back to the introduction:

...the phenomena of electrodynamics as well as of mechanics possesses no properties corresponding to the idea of absolute rest. They suggest rather that, as has already been shown to the first order of small quantities, the same laws of electrodynamics and optics will be valid for all frames of reference for which the equations of mechanics hold good.1 We will raise this conjecture (the purport of which will hereafter be called the “Principle of Relativity”) to the status of a postulate...

Lorentz ether theory does not propose it's own clock synchronization convention. At least I didn't found it.

Edwards' theory introduces parameter q. But it does not claim that physical laws are the same as you vary q. It claims however that experimental predictions won't change as you vary q.

For reference, this discussion started with this claim:

You will get the same physical laws that you would get with Einstein's convention as long as you do it in a consistent way.

It is not necessary to make a claim about the propagation of light in order to establish physical laws.

Isn't it significant to you that if you establish an Inertial Reference Frame according to Einstein's Special Relativity that for an inertial observer moving in that IRF light will not propagate at c relative to him and yet all the physical laws for him are still valid? This is because, the propagation of light is not measurable, it is not detectable, so how could it have any influence or bearing on any raw data or derived physical laws?

 

[BruceW]

In order to prove, without actually doing the experiment, that an observer traveling at one speed (0.5c in the OP's case) by going away from an inertial observer and then returning at the same speed, will age less than the inertial observer, it is only necessary to assume that nothing in the experiment will look any different to any of the observers if conducted at any other state of inertial motion for all observers (that's the Principle of Relativity as demonstrated in the case of LET that the ether wind could not be detected) and that the propagation of light, although it can be different in every state of inertial motion, is the same for different sources of light (which is certainly true under LET). This is important in Bondi's argument so that the light from C takes the same time to reach B as the light that from A takes to reach B after it passes C.

How about if we assumed Galilean relativity, and used ideas such as 'local time' and 'length contraction' as part of the theory of EM. So in this way, EM would transform in a Lorentzian way, but non-EM phenomena would not necessarily transform in a Lorentzian way. (Or to put it another way, EM is affected by the ether, and other phenomena may or may not be).

I know that this would disagree with experiment. But what I am trying to do is show that Bondi's explanation of the twin paradox using just relativity is also using other assumptions. And 'relativity principle' could mean more than one thing. A more rigorous definition of Einstein's relativity is needed for the twin paradox to be explained really.

p.s. I have not read Bondi's explanation, but I think I understand it from ghwellsjr's brief explanation.

 

[ghwellsjr]

How about if we assumed Galilean relativity, and used ideas such as 'local time' and 'length contraction' as part of the theory of EM. So in this way, EM would transform in a Lorentzian way, but non-EM phenomena would not necessarily transform in a Lorentzian way. (Or to put it another way, EM is affected by the ether, and other phenomena may or may not be).

I know that this would disagree with experiment. But what I am trying to do is show that Bondi's explanation of the twin paradox using just relativity is also using other assumptions. And 'relativity principle' could mean more than one thing. A more rigorous definition of Einstein's relativity is needed for the twin paradox to be explained really.

p.s. I have not read Bondi's explanation, but I think I understand it from ghwellsjr's brief explanation.

Bondi's explanation of the twin paradox did assume more things. But I was using only the very first part of Bondi's explanation which showed that the two Doppler shift factors for approaching and retreating at the same speed are reciprocals of each other. And from that we can prove that the Stay-At-Home twin is older than the traveling twin. I'm not saying by how much or even what the relationship is between speed and Doppler factor. Just which one is older. Just the question the OP asked.

So with that in mind, do you still think that we need more than:

1) the Principle of Relativity, which in this application simply means that two inertial observers moving with respect to each other will see the same Doppler shift in each other

2) the fact that light from A to B propagates at the same speed as the light from C to B

If you disagree, please state where the problem is in what I have just said. We don't need to get involved with transforms or simultaneity or synchronization or length contraction.

 

[Dale]

Edwards' theory introduces parameter q. But it does not claim that physical laws are the same as you vary q. It claims however that experimental predictions won't change as you vary q.

That is the same as claiming that the physical laws are the same. You seemed to have missed my previous post on this topic. Claiming that experimental predictions won't change as you vary q is in fact claiming that the physical laws are the same as you vary q.

 

[ghwellsjr]

So, I take it that we are on the same page with the sketch below representing our traveling twin in his rocket during the turnaround.

And in the same sense that we considered the sequence of instantaneous rockets as presented in the stay-at-home twin's frame, we can also recognize the sequence of hyperplanes of simultaneity indicated by the Lorentz-Poincare' transformations to the traveling coordinates.

The sequence of instantaneous 3-D rocket volumes that the traveling twins is living in are clearly not the same physical 3-D rocket volumes that are depicted in the sketch above. The physical 3-D rocket that the traveling twin lives in is unique to him and represented uniquely in his coordinates.

There is no point in compounding your argument to include a non-inertial observer when you haven't come to grips with your argument for an inertial observer:

If someone tells you that it takes 8 minutes and 20 seconds for light to get from the sun to the earth, you should realize that they are assuming (whether they know it or not) the common sun-earth inertial rest frame to be able to make that statement. Furthermore, that statement relies on the definition of a frame in Special Relativity such that it takes the same length of time for light to get from the Earth to the sun as it does for the light to get from the sun to the earth. Unless we make an assumption like this, we cannot and should not think that there is intrinsic in nature a meaning to the idea of simultaneous space that stretches between the Earth and the sun or between any other locations.

When we see an event on the sun such as a solar flare and note the time on our clock, we know that any definition of a frame or any theory that attempts to explain how light propagates will affirm that we did see that flare at that time but any claim that the solar flare actually happened 8 minutes and 20 seconds earlier is nothing more than a concept of simultaneity that we put into nature, not one that we take out of nature.

ghwellsjr, I tend to feel that nature has put the relativity of simultaneity into our physics and into our reality. Nature gave us a speed of light that is the same for all inertial frames. That is something that we experience because nature put in the photon worldlines so as to bisect the angle between X4 and X1 (thus, the Lorentz-Poincare'-Minkowski-Einstein simultaneous spaces). Nature gave us the worldlines to follow through space-time along with the simultaneous space in which to experience nature. These simultaneous spaces, for each different observer, are unique. Further, nature manifests the laws of nature through the continuous sequence of simultaneous spaces we experience as we move along our worldines. If you were one of the ficticious hyperdimensional observers looking at the block universe (pedagogically speaking--refer to earlier post with the hyperdimensional observers), these Lorentz simultaneous spaces would not have the same significance as for one of us 3-dimensional creatures. However, even the hyperdimensional creature could make out patterns of 4-dimensional objects that can be identified as unique patterns, from which laws of physics could be derived. And those laws would be recognized as associated with the Poincare' group of transformations.

You are simply asserting that there are preferred (or unique) reference frames with complete disregard for one of the main tenets of Special Relativity that there is no preferred (or unique) reference frame. Can we deal with your claim in the simple inertial case because your more complicated non-inertial case clouds the issue?

You don't seem to realize or you are unwilling to accept that coordinates have no physical significance and that's because we invent the coordinates in order to make sense out of nature--nature does not compel us to use any particular definition of coordinates, not even the one that Einstein came up with that forms the basis of Special Relativity.

 

[zonde]

Let me see if I can summarize Bondi's argument. He says that if you have two inertial observers, A & B, in relative rest but separated by a great distance, and one of them, A, sends repetitive signals to the other, B, there will be no Doppler shifts. Then a third inertial observer, C, traveling from A to B will observe some Doppler shift ratio from A which will be less than one and which we can call DSR1. Then if that traveler creates his own repetitive signal(s) at the same rate he receives them from A and sends them to B, we know they will travel side by side on their way to B. When they get there, B will observe them both arriving at the same rate but the ones that were sent by C were sent with Doppler shift ratio that is the reciprocal of DSR1. We know that the speed that C is traveling away from A is the same as the speed that C is traveling toward B and so the Doppler shift ratios for the same speed coming and going are reciprocals of each other.

Therefore, in the twin scenario, since the traveling twin spends the same amount of time going and coming at the same speed, we can simply average the two Doppler shift ratios and we will get a number greater than one, meaning the traveler sees the other twin's clock running faster than his own.

And http://archive.org/stream/RelativityCommonSense/Bondi-RelativityCommonSense#page/n45/mode/1up is that link again.

There is something wrong with Bondi argument. Look, the frequency that observer C is receiving and retransmitting can be whatever and this Bondi argument about two ratios being reciprocal of each other will work just the same. So we just plug in such a frequency that we can easily see that result comes out wrong, say we take frequency higher than that transmitted by observer A so that traveling twin will be certainly older than stay at home twin after reunion, and we can check that Bondi argument still works.

 

[BruceW]

So with that in mind, do you still think that we need more than:

1) the Principle of Relativity, which in this application simply means that two inertial observers moving with respect to each other will see the same Doppler shift in each other

2) the fact that light from A to B propagates at the same speed as the light from C to B

If we define a principle of relativity that only says how light gets Doppler shifted, then no, this is not enough. From this, it is not clear how spacetime transforms between inertial frames, and so it is not clear that the twins would age differently.

If instead, you defined a principle of relativity that say that spacetime transforms in a Lorentzian way, and assume that age is a reliable 'clock', then I would say you have enough.

 

[PAllen]

If we define a principle of relativity that only says how light gets Doppler shifted, then no, this is not enough. From this, it is not clear how spacetime transforms between inertial frames, and so it is not clear that the twins would age differently.

If instead, you defined a principle of relativity that say that spacetime transforms in a Lorentzian way, and assume that age is a reliable 'clock', then I would say you have enough.

How is 'spacetime transforms in a Lorentzian way' relevant? That is a statement about transforming between a certain family of coordinates. What if nobody uses any coordinates? This fails to state a physical proposition at all, as worded.

My take on what else you have to assume is something that seems inconceivable to reject: that if, for a given observer not feeling any forces, a few co-located clocks operating by different principles remain in synch, then a different observer, seeing images of them, cannot see them differ. Make one of the clocks based on the frequency of a standard light emission.

 

[ghwellsjr]

There is something wrong with Bondi argument. Look, the frequency that observer C is receiving and retransmitting can be whatever and this Bondi argument about two ratios being reciprocal of each other will work just the same. So we just plug in such a frequency that we can easily see that result comes out wrong, say we take frequency higher than that transmitted by observer A so that traveling twin will be certainly older than stay at home twin after reunion, and we can check that Bondi argument still works.

I'm afraid I have irreconcilably confused things by using the word "reciprocal" with two different meanings in two places in my original description. See if it makes sense using the word "symmetrical" in the first instance and "inverse" in the second instance. If that doesn't clear up the confusion, then just read Bondi's explanation in the provided link.

 

[ghwellsjr]

So with that in mind, do you still think that we need more than:

1) the Principle of Relativity, which in this application simply means that two inertial observers moving with respect to each other will see the same Doppler shift in each other

2) the fact that light from A to B propagates at the same speed as the light from C to B

If we define a principle of relativity that only says how light gets Doppler shifted, then no, this is not enough. From this, it is not clear how spacetime transforms between inertial frames, and so it is not clear that the twins would age differently.

If instead, you defined a principle of relativity that say that spacetime transforms in a Lorentzian way, and assume that age is a reliable 'clock', then I would say you have enough.

I didn't say anything about the Principle of Relativity explaining how light gets Doppler shifted, only that it does in a symmetrical manner. And I didn't say anything about any transformations. That is irrelevant. Just focus on the symmetrical aspects of Doppler.

 

[bobc2]

I don’t understand the reluctance to acknowledge implications of simultaneous spaces and relativity of simultaneity. I assumed that after everyone agreed on the rocket’s momentary at-rest state (in the stay-at-home rest frame) that it would then be easier to visualize the other momentary positions of the rocket (exhibiting length contractions). Then, once having accepted the momentary analysis concept, it would not be difficult to imagine doing Lorentz transforms to arrive at similar momentary at-rest states for the rocket in momentary rocket rest frames.

In other words, we observe that just as the entire rocket comes to rest at some instant in the stay-at-home rest frame, the rocket is always at rest in some inertial frame. Those are the rocket rest frames to which I’ve been referring.

It is a mistake to insist that we can only analyze the situation using a single accelerated frame of reference, because if you insist on that you are confronted with impossible misplaced implications of horizons and other artifact. Comments about overlapping charts are completely misplaced and irrelevant to the analysis. We use just one chart at a time.

 

[Dale]

it would not be difficult to imagine doing Lorentz transforms to arrive at similar momentary at-rest states for the rocket in momentary rocket rest frames.

In other words, we observe that just as the entire rocket comes to rest at some instant in the stay-at-home rest frame, the rocket is always at rest in some inertial frame. Those are the rocket rest frames to which I’ve been referring.

Sure, those are not difficult to imagine. They are called momentarily co-moving (MC) inertial reference frames (IRF). I don't think that anyone has an issue with that concept, and certainly I do not.

The thing that you seem to fail to understand is that there is nothing particularly unique or special about the MCIRF. By the first postulate, any IRF is as good as any other IRF. The fact that it is MC is perhaps convenient for some particular calculation, but otherwise of no physical importance.

It is a mistake to insist that we can only analyze the situation using a single accelerated frame of reference, because if you insist on that you are confronted with impossible misplaced implications of horizons and other artifact.

I have not insisted that, nor have I seen anyone else here do that. Do you believe someone has, if so, please quote the post that made you believe that their opinion was that the situation could only be analyzed using a single accelerated frame of reference.

Comments about overlapping charts are completely misplaced and irrelevant to the analysis. We use just one chart at a time.

If only that were the case. Every MCIRF is a 4D chart which covers all of spacetime with an inertial frame. Where YOU introduce a non inertial frame is when you go from talking about 4D charts to talking about a sequence of 3D simultaneous spaces. That is something that YOU insist on bringing into the analysis, not anyone else.

A sequence of 3D simultaneous spaces is a simultaneity convention, and with a simultaneity convention you have the a reference frame. So YOU are the one making a non-inertial frame, and YOU are the one insisting that it has some degree of physical significance, not anyone else. All we are doing is pointing out the fact that the non inertial frame that YOU have constructed violates some of the basic mathematical requirements for such things.

Go back and look at our discussions to this point. You will see that you consistently switch from talking about 4D frames to 3D simultaneous spaces, and you will see that the objections you have been getting all stem from the inappropriate use of the 3D simultaneous spaces, not the 4D frames.