Understand Special Relativity and Time paradox

[PeterDonis]

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.

Nobody is insisting on that. What others have been saying is that you can analyze the entire situation using a single *inertial* frame of reference. You, by contrast, insist on switching inertial frames from event to event. How is that supposed to help any? The only reason I can see for your insistence on doing this is to somehow justify your claims about simultaneous spaces; but you can't then turn around and use your claims about simultaneous spaces to justify switching inertial frames from event to event.

 

[BruceW]

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.

Hmm. For the moment, just considering an inertial frame (i.e. not the frame of the traveling twin), and if spacetime transforms in a Lorentzian way, then this gives us an invariant - the spacetime interval. So, using an integral along the worldline of the traveling twin, we can calculate the proper time along this worldline.

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.

I conceive the inconceivable :) The point is that we must state the things that we are going to define as 'clocks', if we want to be saying that we have 'proved' something.

 

[BruceW]

I didn't say anything about the Principle of Relativity explaining how light gets Doppler shifted, only that it does in a symmetrical manner.

In that case, your principle of relativity is just saying that light gets Doppler shifted in a symmetrical manner. Which is not enough to explain the twin paradox. Sure, you can go down a line of reasoning from this which does correctly explain the twin paradox, but such a line of reasoning is not obvious, only plausible.

 

[ghwellsjr]

In that case, your principle of relativity is just saying that light gets Doppler shifted in a symmetrical manner.

Good--we're making progress.

Which is not enough to explain the twin paradox.

Correct--I never said it was.

Sure, you can go down a line of reasoning from this which does correctly explain the twin paradox, but such a line of reasoning is not obvious, only plausible.

Can we forget about the Twin Paradox for awhile? Can we focus on what I am trying to do?

I want to add one more assumption which has experimental support and that is that the propagation of light is independent of the source of the light. So when observer C is moving away from observer A and toward observer B, and observer A sends a flash of light towards observer B, if observer C sends his own flash of light towards observer B at the instant that he sees observer A's flash of light arrive at his location, the two flashes of light will propagate at the same speed toward observer B and observer B will see them both arrive at his location at the same instant.

Try not to associate this with the Twin Paradox or any explanation of the Twin Paradox. This is something entirely different involving three inertial observers. Do you understand the situation I have described? Do you agree with everything I said? Are there any questions or doubts?

 

[PAllen]

Hmm. For the moment, just considering an inertial frame (i.e. not the frame of the traveling twin), and if spacetime transforms in a Lorentzian way, then this gives us an invariant - the spacetime interval. So, using an integral along the worldline of the traveling twin, we can calculate the proper time along this worldline.

I think this is backwards. We start with the fact that, say, a specific clock has advanced an hour. This is objective fact. Everyone sees that this specific clock has advanced an hour between two firings of a flash bulb right next to it (identifiable events). Then we invent mathematical models like coordinates, metrics, invariants that allow objective facts to be treated as invariants. Physical assumptions must relate to measurements, not mathematical abstractions. Thus, Einstein assumed things like 'every inertial observer will measure the two way speed of light the same'; 'if two sources next to each other but at different speeds flash a lights, any observer will get the light from them at the same time; and 'no experiment can distinguish inertial motion from rest from withing a closed lab'. Your proposal to me lacks any character of being a physical assumption.

I conceive the inconceivable :) The point is that we must state the things that we are going to define as 'clocks', if we want to be saying that we have 'proved' something.

Such an assumption as I described is rarely stated; in fact numerous times, arguments like that are, without further justifications, assumed to refute a theory that predicts something like that. For example, we say there is a paradox to resolve if one observer is predicted to see a bomb explode and another observer sees no explosion. If the paradox can't be resolved, we treat this as ipso facto disproof of a theory.

 

[Austin0]

The problem with this as it stands is that the stay-at-home twin also sees two reciprocal "clock rates": he sees the traveling twin's clock ticking slower than his outbound and faster than his inbound, and the two rates are reciprocals of each other. In fact they are exactly the *same* rates as the traveling twin sees. So just this observation alone isn't sufficient to account for the different elapsed times.

The difference, as the Usenet Physics FAQ page on the Doppler Shift Analysis makes clear, is *when* each twin sees the change from slower to faster ticking of the other's clock. The traveling twin sees it when he turns around, halfway through the trip; the stay-at-home twin sees it only when the light signals emitted by the traveling twin at the turnaround reach him--i.e., much *later* than halfway through the trip.

*That* is the key asymmetry, the *observable* asymmetry, between the two twins. Your analysis in post #7 was fine as far as it went; it explains how the traveling twin can predict that the stay-at-home twin's clock reading will be greater than his. But it does *not* explain why the stay-at-home twin can't apply exactly the same reasoning. That requires including the observed asymmetry I just described in the analysis: this shows that the stay-at-home twin *does* apply the same reasoning, but he applies it to different observed data (observed change from redshift to blueshift is towards the end of the trip vs. halfway through). If you do the same calculation you described in post #7 for the stay-at-home twin, averaging the two reciprocal clock rates but with the correct weighting for the relative times (your formula assumed 50-50 weighting, but that's only valid for the traveling twin--for the stay-at-home twin the slower tick rate is weighted much more than the faster tick rate), you will get the stay-at-home twin's (correct) prediction that the traveling twin will have aged less when they meet.

I just want to point out that all the valid points you make here are well known to ghwellsjr
and have been completely covered by him in his analysis in previous threads.

 

[PeterDonis]

I just want to point out that all the valid points you make here are well known to ghwellsjr
and have been completely covered by him in his analysis in previous threads.

I know; see my post #294.

 

[Austin0]

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.

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--
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.
.

. I'm trying to put ourselves in the situation before Einstein's theory of Special Relativity or even before Lorentz's Ether Theory, in fact before any theory. ... without invoking SR .

Bondi ...his brilliant scheme to identify the Doppler ratios as being reciprocal and the idea of averaging them to determine that the inertial observer would be older than the traveler.

In other words, you don't have to incorporate any theory that involves spacetime or transformations. .

Some comments on your and Bondi's demonstrations as I understand them.

You propose that in a classical context (pre SR) with a single postulate of constant finite signal propagation independent of the source or any medium, that time dilation and differential aging can be derived as well as symmetry and reciprocity of signal reception ratios. WOuld you say this was an accurate appraisal?

Well I have no doubt that both symmetry and reciprocity are actualities in the real world. But that is only because I think that SR accurately describes that world.
In SR both these properties of the Doppler effect are not assumptions but can be directly derived and demonstrated through the application of fundamental kinematics.
In a classical context they are purely ad hoc assumptions . Assumptions which in themselves directly predetermine the end results.
As far as I can see Bondi does not derive them from first principles, he simply introduces them as assumptions.

He assumes that the ratio observed by Alfred of signals received from Brian (traveling away towards Charles) is the reciprocal of the ratio observed by Charles of the Brian signals received (as Brian is approaching).

Likewise he assumes that the ratio observed by Alfred of Brian signals is symmetrical (equivalent) to the ratio observed by Brian of Alfred signals.
I submit both these assumptions are unwarranted in a classical framework.

In SR both the symmetry and reciprocity of observed signal ratios is directly a consequence of time dilation.
Introduced through the gamma factor embedded in the Relativistic Doppler equation and the LT kinematics.

They are not inherent properties of signal exchange between inertial observers but can only occur with the necessary condition of time dilation taking effect.

it would seem then, that to adopt them as initial premises or assumptions is to implicitly introduce time dilation to derive time dilation. Also to invoke SR as these properties are only valid in that context.

So I would like to know if you see points that I am misunderstanding or am in error and if this makes any sense as I have outlined it.

I hope you will understand that none of this reflects on your Doppler analysis of the Twins differential aging . I have a sincere appreciation of your presentation and think it is a great illustration (for those who question) that direct observation would correspond to abstract calculation.(surprise,surprise) I think it is a valuable contribution on it's owm merits without additional claims.

 

[PAllen]

Well I have no doubt that both symmetry and reciprocity are actualities in the real world. But that is only because I think that SR accurately describes that world.
In SR both these properties of the Doppler effect are not assumptions but can be directly derived and demonstrated through the application of fundamental kinematics.
In a classical context they are purely ad hoc assumptions . Assumptions which in themselves directly predetermine the end results.
As far as I can see Bondi does not derive them from first principles, he simply introduces them as assumptions.

I think the value of the exercise is the show there are multiple sets of physical assumptions that can lead the the same prediction (differential aging, in this case). As to which is adhoc in the pre-relativity sense, this is subjective. Neither Bondi's assumptions nor Einstein's were expected in the 1800s. Aether theories did predict that light speed should be source independent, but they also predicted that Doppler would not be symmetrical, and that motion through the aether could also be detected by measurements of the two way speed of light. Either of these is measurable. Both get at the issue of the aether becoming undetectable. Either, combined with other assumptions, can lead to SR. Since Doppler is part of what is seen in the twin scenario (extra signals not needed - they just have to be able to see each others clocks), it is instructive work from this. The twins are not making measurements light speed unless this is added. The one that turns around will have some difficulties measuring two way light speed as well.

I assume you realize that Einsteins arrived at SR by making 3 main assumptions (undetectability of inertial motion; constancy of two way speed of light; light speed independent of emitter velocity). He also added a convention that put the theory in a particular [arguably, the simplest] form. He could have chosen a different convention, and gotten a theory with slightly different equations, that made the same predictions. So it really boils down to which sets of unexpected assumptions to make. My view is it is useful to understand that there are multiple choices.

 

[bobc2]

Nobody is insisting on that.

DaleSpam Post #50:
Quote by bobc2: "I have not presented the turn-around in the context of non-intertial frames."
DaleSpam: "Yes, you did…"

DaleSpam Post #46:

I agree that the naive approach at defining a non-inertial frame is not nonsense in general, but only to the left of the crossover. At that point it violates one of the fundamental requirements of a coordinate system, and therefore it does become illogical. You can use this approach to make statements about the stay at home twin, but not the red guy. Your claims about the red guy's clock running backwards are therefore indeed nonsense.

Also, the Lorentz transform transforms between inertial frames, so it is reasonable to disregard it here where we are dealing with non inertial frames. And after you cobble together the various pieces the resulting transform is decidedly not the Lorentz transform anymore anyway.

PAllen Post #35:

…They relate points on the two world lines in a smooth, non-repeating way. Thus, there is no reason a rational traveler should ever believe the home clock is running backwards.

PAllen Post #75: Please note further that the derivation of simultaneity convention for inertial observers relies on:

- being inertial long enough to apply a clock synchronization method (establishing simultaneity), for clocks a given distance apart. It is also preferred only in the sense that all reasonable methods agree.

- A non-inertial observer has a different past than co-moving inertial observer. This means that physical synchronization methods they might use will come out different from the comoving inertial frame. They also won't agree with each other.

Post #190: …even as a mathematical convention, talking about blue's simultaneous spaces does imply an overall simultaneity convention for the blue world line. For this, there are mathematical requirements - any region where a proposed simultaneity convention for blue has intersecting surfaces is outside the domain of that convention. If you want to talk about a blue simultaneity for such a region, you must adopt a different convention that does not have intersecting surfaces…

What others have been saying is that you can analyze the entire situation using a single *inertial* frame of reference.

No. That was not my impression.

You, by contrast, insist on switching inertial frames from event to event. How is that supposed to help any?

That's what I just finished explaining in my last couple or so posts.

The only reason I can see for your insistence on doing this is to somehow justify your claims about simultaneous spaces; but you can't then turn around and use your claims about simultaneous spaces to justify switching inertial frames from event to event.

I just looked at the turnaround in the context of the sequence of Rocket rest frames, then looked at the implications. The sequence of Rocket rest frames (as explained in my last two posts, similar to Rindler and other sources) was a natural way to analyze the turnaround, then the other observations naturally followed.

 

[BruceW]

Correct--I never said it was.

But you are saying it is enough if you also assume speed of light to be the same, as measured by any inertial observer? I still disagree with this, for the same reason:

Sure, you can go down a line of reasoning from this which does correctly explain the twin paradox, but such a line of reasoning is not obvious, only plausible.

Try not to associate this with the Twin Paradox or any explanation of the Twin Paradox. This is something entirely different involving three inertial observers. Do you understand the situation I have described? Do you agree with everything I said? Are there any questions or doubts?

Yeah, it all seems fine. You were saying the speed of light is independent of the speed of the source.

 

[zonde]

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.

I have looked at the link you provided and I don't see that there is any confusion about the word "reciprocal" as there it is written explicitly as 3/2 vs 2/3.

So let me say my objection differently. Find in the link you provided page 77/78. There is a sentence:
"Accordingly, by Brian's watch the flashes will not arrive every 6 minutes, but at longer intervals, simply because each flash has greater distance to cover than the preceding flash."
We don't know how Brian's watch is working. That's the very thing we are trying to find out. So let's suppose that flashes will arrive at shorter intervals and next sentence will read:
"For a suitable speed, which we need not work out now, we may suppose that the flashes are received every 4 minutes by Brian's watch."
instead of 9 minutes. Do we run into any contradictions further along the line?

 

[zonde]

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.

As you vary q you have to vary Newtonian equations as well. You have to vary both together and only then you get the same experimental predictions.

 

[BruceW]

I think this is backwards. We start with the fact that, say, a specific clock has advanced an hour. This is objective fact. Everyone sees that this specific clock has advanced an hour between two firings of a flash bulb right next to it (identifiable events). Then we invent mathematical models like coordinates, metrics, invariants that allow objective facts to be treated as invariants. Physical assumptions must relate to measurements, not mathematical abstractions.

hmm. Yes, ok, I would also need to say how the idea of 'coordinates' relates to physical measurements, if I wanted to show that the theory is consistent. On a slightly related topic, after going on google, I found this paper: http://synset.com/pdf/100_en.pdf Which essentially says that you can define SR by using the same axioms of classical mechanics, minus the axiom of simultaneity, and plus the axiom of speed of light being the same in all inertial frames. (They also go on to say about what happens if we relax the axiom of c being same in all inertial frames, but this is not really relevant to our discussion, I think).

 

[Dale]

As you vary q you have to vary Newtonian equations as well. You have to vary both together and only then you get the same experimental predictions.

Yes. But what you are doing is not changing the laws of physics, but rather expressing them in terms of new quantities.

 

[Dale]

DaleSpam Post #50:
Quote by bobc2: "I have not presented the turn-around in the context of non-intertial frames."
DaleSpam: "Yes, you did…"

Here I am insisting that YOU are unwittingly introducing a non-inertial frame; I am not insisting "that we can only analyze the situation using a single accelerated frame of reference".

DaleSpam Post #46:

I agree that the naive approach at defining a non-inertial frame is not nonsense in general, but only to the left of the crossover.

And here, are you seriously taking my statement that the "non-inertial frame is not nonsense in general" as me insisting "that we can only analyze the situation using a single accelerated frame of reference"?

Let me be clear. I am not insisting "that we can only analyze the situation using a single accelerated frame of reference". I am insisting that you have to use some frame of reference and that you have to follow the mathematical requirements in order to have a valid one. YOU are the one who brings in the non-inertial frame using the MCIRF simultaneity convention, and I am simply pointing out that in part of the spacetime it fails to meet the mathematical requirements.

I just looked at the turnaround in the context of the sequence of Rocket rest frames, then looked at the implications. The sequence of Rocket rest frames (as explained in my last two posts, similar to Rindler and other sources) was a natural way to analyze the turnaround, then the other observations naturally followed.

No, the other observations only follow when you transition from the 4D inertial frames to a sequence of 3D simultaneous spaces, which you have done repeatedly throughout this thread. In none of the 4D inertial frames does the red guy's clock go backwards at any point. You cannot have it both ways. Either you are looking at 4D inertial frames, in which case the clock never goes backwards, or you are looking at your 3D simultaneous spaces, in which case you are defining a simultaneity convention in a non-inertial frame which cannot cover the red guy.

 

[ghwellsjr]

I just looked at the turnaround in the context of the sequence of Rocket rest frames, then looked at the implications. The sequence of Rocket rest frames (as explained in my last two posts, similar to Rindler and other sources) was a natural way to analyze the turnaround, then the other observations naturally followed.

Your fundamental problem is that you continue to promote the idea that Einstein's simultaneity convention for establishing a rest frame is natural. It doesn't come from nature nor is it obvious. Simultaneity only seems natural and obvious to you because you ignore Einstein's argument that since it is not natural, he is free to establish any convention he wants (that is consistent with the data). His argument against Lorentz's concept (and practically everybody else's) of an absolute ether rest state is not because there is evidence against it, but simply that his theory will also work even if you believe there is an absolute ether rest state. We choose to adopt Einstein's theory only because it is simpler than Lorentz's. You have stated that you do not believe this, you believe that there is some fundamental flaw in Lorentz's Ether Theory and that it cannot be true because it violates some aspect of nature. As long as you continue to hold these false ideas, you will never be able to understand why your conclusions about simultaneity for accelerating observers are also mere conventions, just like they are for inertial observers.

 

[ghwellsjr]

Some comments on your and Bondi's demonstrations as I understand them.
...
You propose that in a classical context (pre SR) with a single postulate of constant finite signal propagation independent of the source or any medium, that time dilation and differential aging can be derived as well as symmetry and reciprocity of signal reception ratios. WOuld you say this was an accurate appraisal?

No.

I never proposed a single postulate of constant finite signal propagation... That is Einstein's second postulate. I said in post #7 that I was proposing only a portion of Einstein's second postulate, the part that says that the propagation of light is independent of the source but I was not identifying that speed as Einstein did and which is necessary to establish SR.

This is probably a confusing issue. I would recommend that you look up the wikipedia article on the One-Way Speed of Light and look down to the section called "Experiments that can be done on the one-way speed of light". There you will see that it is possible to determine experimentally that light from two different sources with relative velocity propagate at the same speed but we cannot measure what that speed is. This is also assumed to be true both in a classical context (pre SR) where ether is affirmed and in a relativistic context (SR) where ether is denied. Bondi did not specifically state that he was adopting this assumption but it is obvious that he is.

Well I have no doubt that both symmetry and reciprocity are actualities in the real world. But that is only because I think that SR accurately describes that world.
In SR both these properties of the Doppler effect are not assumptions but can be directly derived and demonstrated through the application of fundamental kinematics.
In a classical context they are purely ad hoc assumptions . Assumptions which in themselves directly predetermine the end results.
As far as I can see Bondi does not derive them from first principles, he simply introduces them as assumptions.

Yes, the Doppler effects of symmetry and reciprocity are actualities in the real world and SR accurately describes that world but SR is not what makes those effects real. As long as we adopt the Principle of Relativity (apart from SR), then even in a classical context the correct conclusion can be drawn that the traveling twin's clock will accumulate less time than the inertial clock. The Principle of Relativity predates SR and is part of the classical context. Based purely on that principle plus the assumption that light from different sources propagates at the same speed but without identifying that speed (as explained previously) and even with a belief in an absolute ether, it can be proven that a non-inertial clock will accumulate less time than an inertial clock.

He assumes that the ratio observed by Alfred of signals received from Brian (traveling away towards Charles) is the reciprocal of the ratio observed by Charles of the Brian signals received (as Brian is approaching).

Likewise he assumes that the ratio observed by Alfred of Brian signals is symmetrical (equivalent) to the ratio observed by Brian of Alfred signals.
I submit both these assumptions are unwarranted in a classical framework.

Yes, Bondi does make more assumptions as he continues his discussion that includes Charles because he wants to eventually give a full explanation of the Twin Paradox which includes the Doppler that both twins see. But I didn't do that because that was not my goal. I was only using his proof that the Doppler ratios are inverses for coming and going at the same speed. And then I only expressed the Doppler that one twin sees. That is sufficient to prove which twin is older when they reunite. But the limited assumptions that I made are warranted in a classical framework.

In SR both the symmetry and reciprocity of observed signal ratios is directly a consequence of time dilation.
Introduced through the gamma factor embedded in the Relativistic Doppler equation and the LT kinematics.

They are not inherent properties of signal exchange between inertial observers but can only occur with the necessary condition of time dilation taking effect.

it would seem then, that to adopt them as initial premises or assumptions is to implicitly introduce time dilation to derive time dilation. Also to invoke SR as these properties are only valid in that context.

So I would like to know if you see points that I am misunderstanding or am in error and if this makes any sense as I have outlined it.

I hope you will understand that none of this reflects on your Doppler analysis of the Twins differential aging . I have a sincere appreciation of your presentation and think it is a great illustration (for those who question) that direct observation would correspond to abstract calculation.(surprise,surprise) I think it is a valuable contribution on it's owm merits without additional claims.

SR works because it accurately reflects the Doppler effects--not the other way around. The horse is the Doppler effects, the cart is SR. Don't get the cart before the horse. The Doppler effects occur no matter what theory we invent to explain them.

And thanks for your continued affirmations of my efforts to explain SR.

 

[Alain2.7183]

I agree that the naive approach at defining a non-inertial frame is not nonsense in general, but only to the left of the crossover.

That seems to say that the rapid aging of the home twin, when the traveling twin reverses from outbound to inbound, is OK, but that if the traveling twin then reverses from inbound back to outbound, then the rapid decrease in the age of the home twin isn't OK. But if the second reversal immediately follows the first reversal, shouldn't the net effect be that the home twin ends up with the same age as before the first reversal?

 

[Dale]

That seems to say that the rapid aging of the home twin, when the traveling twin reverses from outbound to inbound, is OK, but that if the traveling twin then reverses from inbound back to outbound, then the rapid decrease in the age of the home twin isn't OK

That is correct, a decrease in age is never OK.

But if the second reversal immediately follows the first reversal, shouldn't the net effect be that the home twin ends up with the same age as before the first reversal?

Even so. The problem is having any situation where the same event is mapped to multiple coordinates. This happens any time that the age decreases.

See Ch 2, especially p. 33-38
http://arxiv.org/abs/gr-qc/9712019

 

[ghwellsjr]

Correct--I never said it was.

But you are saying it is enough if you also assume speed of light to be the same, as measured by any inertial observer?

I was very careful to say in post #7 and every other time since then when commenting on this topic that no one is measuring the speed of light. All the observer can do is measure that the flashes of light coming from two different co-moving sources travel together at the same speed but he cannot tell what that speed is.

I still disagree with this,

Are you sure you disagree with what I actually said?

...for the same reason:

Sure, you can go down a line of reasoning from this which does correctly explain the twin paradox, but such a line of reasoning is not obvious, only plausible.

Again, for right now, I'm not talking about the Twin Paradox. Do you still disagree? And if so, you need something more than that the line of reasoning is not obvious. And if you understand the argument, it is not just plausible, it is incontrovertible proof.

Try not to associate this with the Twin Paradox or any explanation of the Twin Paradox. This is something entirely different involving three inertial observers. Do you understand the situation I have described? Do you agree with everything I said? Are there any questions or doubts?

Yeah, it all seems fine. You were saying the speed of light is independent of the speed of the source.

In the limited scenario which I borrowed from Bondi, I'm assuming the Principle of Relativity and I'm adding the observable assumption that the speed of light is independent of the speed of the source and proving that the outbound Doppler is the inverse of the inbound Doppler when the speeds are the same. That's what we are focusing on right now. Do you have any problem with that conclusion? Even if it is not obvious, do you see it as incontrovertible proof?

 

[ghwellsjr]

I have looked at the link you provided and I don't see that there is any confusion about the word "reciprocal" as there it is written explicitly as 3/2 vs 2/3.

So let me say my objection differently. Find in the link you provided page 77/78. There is a sentence:
"Accordingly, by Brian's watch the flashes will not arrive every 6 minutes, but at longer intervals, simply because each flash has greater distance to cover than the preceding flash."
We don't know how Brian's watch is working. That's the very thing we are trying to find out. So let's suppose that flashes will arrive at shorter intervals and next sentence will read:
"For a suitable speed, which we need not work out now, we may suppose that the flashes are received every 4 minutes by Brian's watch."
instead of 9 minutes. Do we run into any contradictions further along the line?

We don't have to go further along the line--you just presented a contradiction right there. That suitable speed which would produce flashes at 4 minute intervals at Brian's watch would have to be negative which would only work if he started out some distance from Alfred but since he starts out colocated you have presented a contradiction.

You can't argue that we don't know how Brian's watch is working. We have to assume that all watches are working identically in order for them to be observing symmetrical Doppler shifts and you already agreed in post #316 that they will see the same Doppler shift:

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.

 

[zonde]

We don't have to go further along the line--you just presented a contradiction right there. That suitable speed which would produce flashes at 4 minute intervals at Brian's watch would have to be negative which would only work if he started out some distance from Alfred but since he starts out colocated you have presented a contradiction.

You can't argue that we don't know how Brian's watch is working. We have to assume that all watches are working identically in order for them to be observing symmetrical Doppler shifts and you already agreed in post #316 that they will see the same Doppler shift:

I have identified my problem with Bondi argument. He implicitly relies on Doppler shift. And if we pretend that we don't know about SR then it's classical Doppler shift not relativistic. But classical Doppler does not respect PoR.

And you are arguing exactly from the same position. You are using some Doppler-like phenomena even so you have not demonstrated how it is consistent with PoR.
And that is the very thing that SR does, like it or not.

 

[zonde]

The Principle of Relativity predates SR and is part of the classical context.

It is no argument.
In classical context PoR might have been slightly different PoR than the one you mean. In particular it was not applied to wave phenomena.
You see, the words stay the same but their meaning changes. And as a result your argument fails.

I was only using his proof that the Doppler ratios are inverses for coming and going at the same speed. And then I only expressed the Doppler that one twin sees. That is sufficient to prove which twin is older when they reunite. But the limited assumptions that I made are warranted in a classical framework.

SR works because it accurately reflects the Doppler effects--not the other way around. The horse is the Doppler effects, the cart is SR. Don't get the cart before the horse. The Doppler effects occur no matter what theory we invent to explain them.

You are using the same name for classical Doppler and relativistic Doppler. If you would identify in your argument these two equally valid effects by different names it would be easy to see that your argument is faulty.

 

[ghwellsjr]

I have identified my problem with Bondi argument. He implicitly relies on Doppler shift. And if we pretend that we don't know about SR then it's classical Doppler shift not relativistic. But classical Doppler does not respect PoR.

And you are arguing exactly from the same position. You are using some Doppler-like phenomena even so you have not demonstrated how it is consistent with PoR.
And that is the very thing that SR does, like it or not.

It is no argument.
In classical context PoR might have been slightly different PoR than the one you mean. In particular it was not applied to wave phenomena.
You see, the words stay the same but their meaning changes. And as a result your argument fails.


You are using the same name for classical Doppler and relativistic Doppler. If you would identify in your argument these two equally valid effects by different names it would be easy to see that your argument is faulty.

Like virtually all other classical principles and laws, the formulation for the Principle of Relativity had to change as a result of new experiments performed on wave phenomena, for example, the Michelson Morley Experiment. The words and meanings of all these principles and laws remained the same, they just required more complicated formulas to correctly express them. The classical formulation for the Principle of Relativity is the Galilean Transformation and it works well at low speeds. But at high speeds the correct formulation is the Lorentzian Transformation which works at any speed (less than the speed of light, of course).

The classical Doppler formulation is no exception. It had a simplified formula, which is still used today, just like F=ma is still used today, but we realize it is only a very good approximation and useful because the more complicated formula won't make any difference in our computation, as long as the speeds are small compared to the speed of light. However, there is a more complicated formulation that works at all speeds which you can read about here.

But I don't want to get sidetracked on this issue as it has no relevance to Bondi's argument concerning the inverse relationship of the Doppler shifts for coming and going at the same speed.

Tell me something zonde, do you understand the argument, whether or not you agree with it?

 

[PeterDonis]

You are using the same name for classical Doppler and relativistic Doppler.

There is no "classical Doppler". What we call the "relativistic" formula for the Doppler effect does not actually require SR. It only requires Maxwell's Equations. Those equations are Lorentz invariant, so of course the Doppler formula derived from them is consistent with SR. But you don't need SR to derive it.

 

[PAllen]

There is no "classical Doppler". What we call the "relativistic" formula for the Doppler effect does not actually require SR. It only requires Maxwell's Equations. Those equations are Lorentz invariant, so of course the Doppler formula derived from them is consistent with SR. But you don't need SR to derive it.

I think there is a distinction worth making here. The principle of relativity as used to derive SR includes different phenomena than the same principle pre-SR. The SR principle includes more phenomena. Note that Doppler for sound in air does not follow the principle of relativity, and this is not a violation because air is material, and you can obviously detect your state of motion relative to some matter. In the same sense, circa 1850, a common belief was that POR did not apply to either light Doppler or speed of light, for the same reason. To the extent one believed aether was an exotic form of matter, this did not imply a violation of galilean POR.

 

[ghwellsjr]

I think there is a distinction worth making here. The principle of relativity as used to derive SR includes different phenomena than the same principle pre-SR.

Yes, it's the same principle. Just because Einstein applied it to all phenomena whereas other people didn't, doesn't change the principle. And by itself, there is no Special Relativity. SR requires another principle which includes the propagation of light which I was purposely excluding from my discussion of how to prove that the traveling twin ends up younger.

The SR principle includes more phenomena.

No, you just said it was the same principle. There's only one Principle of Relativity.

Note that Doppler for sound in air does not follow the principle of relativity, and this is not a violation because air is material, and you can obviously detect your state of motion relative to some matter.

That's like saying the addition of velocity doesn't follow the Principle of Relativity. Just because some people choose not to apply it to some particular phenomenon doesn't change the principle. In fact, the reason they don't apply it to particular phenomenon is because they don't believe that phenomenon adheres to the principle that never changes. But more importantly, Doppler for sound in air does follow the Principle of Relativity if you use the correct formulation as the link in my previous post shows. Same thing with the addition of velocity. You have to apply the correct formulation.

In the same sense, circa 1850, a common belief was that POR did not apply to either light Doppler or speed of light, for the same reason. To the extent one believed aether was an exotic form of matter, this did not imply a violation of galilean POR.

There is only one Principle of Relativity. It never changes. Just because some people in the past did not believe it applied to certain phenomenon, doesn't change the principle.

What you are calling galilean PoR just means his formulation of the transformation was incorrect, or more precisely, it only applied at low speeds which means it excluded light.

The issue that zonde is concerned about is whether the Principle of Relativity plus the principle that light from two sources with relative motion propagates at the same speed is enough to prove that the traveling twin will come back younger. Can I get some help on that score instead of this side track?

 

[Alain2.7183]

But if the second reversal immediately follows the first reversal, shouldn't the net effect be that the home twin ends up with the same age as before the first reversal?

And if the net effect of the two back-to-back reversals is that the home twin's age is the same after the second reversal as it was before the first reversal, then that means that the decrease in the home twin's age during the second reversal must be equal to the increase in the home twin's age during the first reversal, because they have to sum to zero. So that seems to imply that either both of the two results are valid, or else they are both invalid. Is my reasoning wrong somewhere here?

 

[ghwellsjr]

And if the net effect of the two back-to-back reversals is that the home twin's age is the same after the second reversal as it was before the first reversal, then that means that the decrease in the home twin's age during the second reversal must be equal to the increase in the home twin's age during the first reversal, because they have to sum to zero. So that seems to imply that either both of the two results are valid, or else they are both invalid. Is my reasoning wrong somewhere here?

If you stick with a single Inertial Reference Frame, then you never have to concern yourself with such brain bending issues. Why do you care about trying to figure out anything with a non-inertial accelerating frame?

Someone, please tell me. Why doesn't an analysis using an IRF satisfy?