Time paradox


by jaumzaum
Tags: paradox, time
BruceW
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Jan31-13, 03:15 PM
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explaining the twin problem by the light signals that are sent between the twins is an interesting way to do it. Once we define electromagnetism as a 'law' of physics, then say that the laws of physics are the same in all reference frames, then we have effectively only used the principle of relativity. (after all, this is how Einstein first came up with his relativity). I don't really understand what ghwellsjr meant by saying that the principle of relativity and the theory of special relativity are different things... I had always thought of them as synonymous.

Edit: well, maybe special relativity is a subset of the principle of relativity, because I would think that the theory general relativity is also a part of the principle of relativity.

Another edit: "principle of relativity" could be used in a different context, too. For example, there is also Galileo's relativity, so you could also use Galileo's relativity to explain the twin problem. You could get the correct answers, but the laws of electromagnetism would be horribly complicated, compared to the laws of electromagnetism in Einstein's relativity.
Austin0
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Feb1-13, 01:19 AM
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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
Given an extended coordinate frame (v -->+x) of conventionally synched clocks with a range from x= -100 to x=100 with the Traveler at x=0 and the center of resynchronization.
...
In this case if vx' is less than dT =20 the -x clocks continue to increment forward. At x=-200 they would remain at the same value and beyond that would actually be decrementing back from previous time.
...
Hopefully you will agree that such a chart would be without gap or overlap throughout the defined domain?
Quote Quote by DaleSpam View Post
I do agree if by "defined domain" you specifically mean x=-100 to x=100. It appears that you are applying the usual MCIRF synchronization convention that bobc2 is using, but over a limited spatial domain. That is the correct way to do it. Once you try to extend it into a region with an overlap then you have problems. You are avoiding those problems by limiting the domain, which is a perfectly legitimate thing to do, assuming I understood you correctly.
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
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Feb1-13, 03:17 AM
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Quote Quote by PeterDonis View Post
But he also implicitly specified that his brother turns around--otherwise he wouldn't come back to Earth. What piece of observable data corresponds to the turnaround? The shift from Doppler redshift to Doppler blueshift.

Bondi's analysis, as you present it, also includes the observation I stated above. Perhaps he didn't use the word "Doppler", but if we want to talk about each twin "seeing" the other's clock "run slower", the only piece of raw data that that can correspond to is the observed Doppler shift--or equivalently the observed "tick rate" of light signals emitted by each twin, as received by the other twin. Each twin does not see, as raw data, the other twin's "adjusted" clock rate; he only sees the Doppler-shifted raw data itself. See further comments below.
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.
Quote Quote by PeterDonis View Post
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.
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).
Quote Quote by PeterDonis View Post
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.
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.
Quote Quote by PeterDonis View Post
...
I don't know if Bondi included the additional observable I described above (when during the trip each twin observes the turnaround). If he didn't, then what I said above does go further than his analysis.
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
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Feb1-13, 03:33 AM
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Quote Quote by BruceW View Post
explaining the twin problem by the light signals that are sent between the twins is an interesting way to do it. Once we define electromagnetism as a 'law' of physics, then say that the laws of physics are the same in all reference frames, then we have effectively only used the principle of relativity. (after all, this is how Einstein first came up with his relativity). I don't really understand what ghwellsjr meant by saying that the principle of relativity and the theory of special relativity are different things... I had always thought of them as synonymous.
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.
Quote Quote by BruceW View Post
Edit: well, maybe special relativity is a subset of the principle of relativity, because I would think that the theory general relativity is also a part of the principle of relativity.
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.
Quote Quote by BruceW View Post
Another edit: "principle of relativity" could be used in a different context, too. For example, there is also Galileo's relativity, so you could also use Galileo's relativity to explain the twin problem. You could get the correct answers, but the laws of electromagnetism would be horribly complicated, compared to the laws of electromagnetism in Einstein's relativity.
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
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Feb1-13, 05:51 AM
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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
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Feb1-13, 09:53 AM
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Quote Quote by ghwellsjr View Post
I did provide these other details in post #23
Yes, I see you did. Another thread that has gone too long...
PAllen
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Quote Quote by ghwellsjr View Post
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.
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
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Feb1-13, 10:47 AM
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Quote Quote by Mentz114 View Post
The twins paradox happens because clocks show a time that is dependent on their worldlines, not universal Newtonian time.
.....
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 ?
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
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Feb1-13, 12:06 PM
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Quote Quote by ghwellsjr View Post
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.
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.

Quote Quote by ghwellsjr
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.
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.
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Quote Quote by BruceW View Post
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.
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".
Quote Quote by BruceW View Post
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.
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.
Quote Quote by BruceW View Post
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.
That is also a good point.
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Quote Quote by Austin0 View Post
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.
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
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Quote Quote by ghwellsjr View Post
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".
Yeah, that was my bad, really.

Quote Quote by ghwellsjr
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.
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.
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Feb1-13, 11:59 PM
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Quote Quote by ghwellsjr View Post
Quote Quote by zonde View Post
If you say that Einstein's clock synchronization convention is arbitrary then I can change it and try to implement it in particular inertial frame. As a result I won't get classical physical laws in that inertial frame.
You will get the same physical laws that you would get with Einstein's convention as long as you do it in a consistent way.
This goes against the things that we learn from SR. So I say it's wrong.
zonde
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Quote Quote by ghwellsjr View Post
Note that he was not asking a question about the Theory of Special Relativity. He was asking a question about the Principle of Relativity, Einstein's first postulate. They're not the same thing. The PoR is based on observable raw data that among other things concludes that things will be reciprocal between two inertial observers and so the OP was wondering how from the PoR you could determine which of the two observers would be older when they both conclude that the other one is aging more slowly. Note that he specified his brother would travel at a constant speed.

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

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

Besides it doesn't make sense to say that PoR is based on observable raw data because it doesn't speak about raw data but about laws of physics instead. Laws of physics is certainly different thing than raw data.
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Quote Quote by zonde View Post
About that part in bold - where did you get it?

Besides it doesn't make sense to say that PoR is based on observable raw data because it doesn't speak about raw data but about laws of physics instead. Laws of physics is certainly different thing than raw data.
The laws of physics are derived from observable raw data. As the wikipedia article on the Principle of Relativity says:
Any principle of relativity prescribes a symmetry in natural law: that is, the laws must look the same to one observer as they do to another.
And that means there cannot be any raw data that violates those laws.

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

But in this case, we are talking about the observed Doppler shifts between two inertial observers with relative motion. Do you doubt that they will see the same shift in each other?
ghwellsjr
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Feb2-13, 02:21 AM
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Quote Quote by zonde View Post
Quote Quote by ghwellsjr View Post
Quote Quote by zonde View Post
If you say that Einstein's clock synchronization convention is arbitrary then I can change it and try to implement it in particular inertial frame. As a result I won't get classical physical laws in that inertial frame.
You will get the same physical laws that you would get with Einstein's convention as long as you do it in a consistent way.
This goes against the things that we learn from SR. So I say it's wrong.
What things? Can you be specific?

I invite you to read the wikipedia article on the One-Way Speed of Light concerning Lorentz ether theory and Edwards' theory. Both of these use a clock synchronization convention that is different from Einstein's and yet they get the same physical laws. These examples should be enough to show you that clock synchronization conventions are arbitrary, meaning that we are not compelled by any raw data to select one over the other. We have a different kind of good reason to select Einstein's; as he stated, it's simple.
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Feb2-13, 03:31 AM
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Quote Quote by BruceW View Post
hmm. I think the idea was that EM phenomena was dependent on velocity relative to the ether. These dependencies were Lorentzian transforms, but it was assumed that these transforms had nothing to do with transforms of true time and space, they were only thought of as part of the theory of EM. So in this way, time and space were assumed Galilean, while EM phenomena had this Lorentzian transform property. So the explanation of light signals being sent between the twins could be explained by Galilean relativity, using this weird form of EM equations. But what does this mean for the ageing of the twins? It depends on what you assume is the mechanism for the ageing process, and if it also is affected by travel through the ether.
Yes, in LET the EM phenomena was dependent on velocity relative to the ether. But if you want to follow Bondi's argument to conclude that the inertial twin will age more than the traveler, it works just as well with the assumptions of LET, namely that the propagation of light is independent of its source and the PoR which means that it is impossible to identify the rest state of the ether, in other words, no ether wind will ever be detected.

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

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

If you want a better explanation, read Bondi's in the link in post #7.
zonde
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Feb2-13, 04:22 AM
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Quote Quote by ghwellsjr View Post
The laws of physics are derived from observable raw data.
No, where did you get this idea? You just invent law of physics and then test it against raw data. You can't derive them.

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

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


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