Time paradox

BruceW

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

zonde

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

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

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

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

DaleSpam

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".

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.

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

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

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.
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.
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.
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

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

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

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

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.
Are you sure you disagree with what I actually said?
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.
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

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:

zonde

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

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.

ghwellsjr

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

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

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.