Time paradox

Austin0

First to clarify:
I am not interested in determining simultaneity only in coordinate synchronization. Nor am I advocating the MCIF implmentation as a preferrable convention.
As stated, my sole ain is to gain a picrure of a chart generated with that convention to compare with the anomalous behavior in the area under discussion.

Quote by Austin0 View Post
Well at least we seem to have some agreement ;-)
But I suspect you are viewing what I am describing through an a priori assumption that the limited domain i am describing must fall inside the problematic area where intersection and divergence occurs in the standard diagram. not really analyzing the implications of what I am outlining. in the case under discussion per bobc2's diagrams the bad patch occurs in the positive x sector.

In the chart i am outlining the limit to valid coordinate assignment , the point where coordinates overlap and have redundant assignments occurs in the negative x sector.

In the positive x direction they can be extended indefinitely until reaching the actual limit of the Rindler Horizon , which I think we agree lies outside the range of the intersection and divergence we are talking about.

So ,yes i am proposing that such a chart would cover the problem sector without internal problem whatsoever.
With no anomalous events or temporal ambiguities. It appears to me that a complete chart constructed in the manner I outlined before

T₀
x=-100,t₀ and x=100, t₀

T₁=T₀+20..
x=-100,t₁=t₀+10,,,x=100,t₁=t₀+30

T₂=T₀+40
x=-100,t₂=t₀+20 ,,,x=100,t₂=t₀+60

could not possibly contain any such artifacts. From this I infer that such artifacts could only come from the Minkowski graphing of such a frame and is not inherent in the use of the convention as the basis of an accelerated chart..

So if you see flaws in my thinking please let me know.

ghwellsjr

Whether the OP was referring to Doppler or Time Dilation, his question was targeting the issue of how can the Principle of Relativity which implies symmetry result in an asymmetry between the observers. Of course, since the OP is inertial and his brother is not, the scenario is not symmetrical and that was what DaleSpam pointed out in post #2 where he also gave the answer to the OP's question (who will be older?) but he didn't explain why or how that could be determined. So that's what I did in post #7.
You are providing a good explanation for much more than the OP asked. He just wanted to know which one would be older and for that, you only have to examine one of the observers and that's what I did (for his brother).
All very true, but, like you said, in post #7, I only went as far as I had to in order to answer the OP's question. But I did provide these other details in post #23 where I presented the spacetime diagrams to illustrate the different Inertial Reference Frames and to explain in great detail how the identical Doppler shifts apply differently to the two observers.
Bondi does go further but he doesn't do it immediately for a twin scenario. He does it for three inertial observers and he states the formula that I mentioned at the end of post #7. I find his book very difficult to read because he is goes into a lot of detail and he repeats himself. In any case, my only interest in his book was 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.

ghwellsjr

Einstein based his Theory of Special Relativity on two principles, the first being the Principle of Relativity and the second being that all light propagates at c. Look at section 2 of his 1905 paper introducing SR.
No, it's the other way around, the PoR is a subset of SR. SR encompasses more than the PoR, namely that second principle. And SR is a subset of GR.
As Einstein mentions in the second paragraph of his introduction, he is extending Galileo's PoR for mechanics to include electromagnetism. But I don't know how you could explain the twin problem with just the PoR applied to mechanics.

Mentz114

Something I absolutely cannot understand is this fascination with the twins paradox. It's been analysed in such detail so often, one would think there was some magic new physics in there just waiting to be discovered. There is no gold mine. The twins paradox happens because clocks show a time that is dependent on their worldlines, not universal Newtonian time. And SR gives us the means to calculate this for a given worldline.

Can anyone tell me what this detailed burrowing is hoping to achieve.

I don't mean to be critical, but I don't remember going through this phase when I first encountered relativity ( not for long, in any case) so what am I missing ?

PeterDonis

Yes, I see you did. Another thread that has gone too long...

PAllen

I'm almost done with a blog entry on a topic related to this. What I come up with is that the one minimal approach is that you need to assume there is some form of signal (e.g sound) whose speed is independent of emitter's speed; and also that Doppler for this type of signal is symmetric: if A and B moving inertially relative to each other, each sees the same Doppler factor (this is not true for sound). Given the existence of a signal type with these properties, differential aging can be deduced. Nothing else is needed. (To get an explicit formula for differential aging, you do need more; but what I stated is all you need to show there must be differential aging).

BruceW

I think it is because integrating the proper time along a worldline is left until later on in a course on SR. Therefore, we will get students that are partway through their course asking about the twin paradox.

BruceW

I would say the principle of relativity is a more general concept that could potentially be used in other theories than just in SR and GR. But I guess it doesn't matter, because I can't think of any other examples right now.

I wouldn't use the PoR applied to mechanics. I would not use mechanics at all. I meant that you could use Galilean relativity (i.e. simultaneity being absolute, and additive velocities), with a slightly weird kind of electromagnetism, which incorporates the movement of a 'luminiferous ether'. (And in fact, this is what they did before Einstein's theory). Of course, this gives the same predictions as Einstein's relativity, and since physics is simpler in Einstein's relativity, we use Einstein's relativity instead of Galilean relativity.

By 'same predictions', I mean for electromagnetic phenomena. Using Galilean relativity will give incorrect results for mechanics when velocities are near the speed of light. They never noticed this before Einstein came up with his relativity, because such velocities are rare on human scale.

ghwellsjr

Just because PoR is a subset of SR doesn't mean it can't be used in other theories. I can think of one, Lorentz Ether Theory, which denies Einstein's second principle and instead assumes that light propagates at c only in the ether rest frame.

But I can see how saying that PoR is a subset of SR might be confusing, but I was just bouncing off your terminology. The important thing is that they are different and it's Einstein's arbitrary second principle that is added to PoR to make SR. That sounds to me like PoR is a subset of SR, but if it's still confusing, don't use the term "subset".
I wouldn't use mechanics at all either, in fact, I don't even know how you would. But I think the real distinction is between Galilean Transforms and Lorentzian Transforms, the former being an incorrect basis for relativity while the later is correct as a basis for relativity but not exclusive to Einsteinian relativity. Otherwise, I agree with your statements.
That is also a good point.

DaleSpam

I will have to look in detail at your mapping. It would have been helpful if you could actually write down the equation for transforming coordinates.

However, if you do not get overlap in the region where the graphing shows the overlap then I guarantee that you are not using the momentarily co-moving reference frame notion of simultaneity. There is nothing wrong with that, but it is a different simultaneity convention and doesn't have any bearing on the Minkowski diagrams that bobc2 has presented.

In other words, bobc2's drawings are correct and accurately reflect the inherent problem in the "MCIRF convention". His problem is that he refuses to recognize that as a problem and exclude that region from coverage (as you seem correctly willing to do).

BruceW

Yeah, that was my bad, really.

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.

zonde

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

zonde

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

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

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

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

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.

In this case we are talking about observed Doppler shifts between three inertial observers, namely stay at home twin, travelling twin on the forward trip and travelling 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.