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Time paradox

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zonde
#343
Feb3-13, 11:24 PM
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Quote Quote by DaleSpam View Post
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
#344
Feb4-13, 12:19 AM
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Quote Quote by PAllen View Post
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).
DaleSpam
#345
Feb4-13, 06:30 AM
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Quote Quote by zonde View Post
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.
DaleSpam
#346
Feb4-13, 06:42 AM
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Quote Quote by bobc2 View Post
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".

Quote Quote by bobc2 View Post
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.

Quote Quote by bobc2 View Post
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
#347
Feb4-13, 08:58 AM
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Quote Quote by bobc2 View Post
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
#348
Feb4-13, 10:20 AM
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Quote Quote by Austin0 View Post
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.
Quote Quote by Austin0 View Post
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.
Quote Quote by Austin0 View Post
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.
Quote Quote by Austin0 View Post
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
#349
Feb4-13, 10:53 AM
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Quote Quote by DaleSpam View Post
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?
DaleSpam
#350
Feb4-13, 11:35 AM
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Quote Quote by Alain2.7183 View Post
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.

Quote Quote by Alain2.7183 View Post
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
#351
Feb4-13, 12:46 PM
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Quote Quote by BruceW View Post
Quote Quote by ghwellsjr View Post
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.
Quote Quote by BruceW View Post
I still disagree with this,
Are you sure you disagree with what I actually said?
Quote Quote by BruceW View Post
...for the same reason:
Quote Quote by BruceW View Post
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.
Quote Quote by BruceW View Post
Quote Quote by ghwellsjr View Post
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
#352
Feb4-13, 01:19 PM
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Quote Quote by zonde View Post
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:
Quote Quote by zonde View Post
Quote Quote by ghwellsjr View Post
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
#353
Feb4-13, 10:30 PM
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Quote Quote by ghwellsjr View Post
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
#354
Feb4-13, 10:58 PM
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Quote Quote by ghwellsjr View Post
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.

Quote Quote by ghwellsjr View Post
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
#355
Feb5-13, 12:41 AM
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Quote Quote by zonde View Post
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.
Quote Quote by zonde View Post
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
#356
Feb5-13, 01:54 AM
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Quote Quote by zonde View Post
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
#357
Feb5-13, 08:15 AM
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Quote Quote by PeterDonis View Post
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
#358
Feb5-13, 09:03 AM
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Quote Quote by PAllen View Post
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.
Quote Quote by PAllen View Post
The SR principle includes more phenomena.
No, you just said it was the same principle. There's only one Principle of Relativity.
Quote Quote by PAllen View Post
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.
Quote Quote by PAllen View Post
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
#359
Feb5-13, 09:39 AM
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Quote Quote by Alain2.7183 View Post
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
#360
Feb5-13, 10:01 AM
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Quote Quote by Alain2.7183 View Post
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?


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