Post 89 explains how to do the calculations from the perspective of the accelerated twin. Post 113 shows that your "symmetric" paradox isn't a paradox at all.
Martillo talks about the twin paradox
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Post 89 explains how to do the calculations from the perspective of the accelerated twin. Post 113 shows that your "symmetric" paradox isn't a paradox at all.
Janus58
Valued Senior Member
You will obtain the same final result as you do for when you apply SR from just the frame of the "at rest" Twin. When they meet up again, Both traveling twins will be the same age and younger than the "stay at home" brother.
What you keep neglecting is what happens to the other two brothers according each "traveling" brother when he is accelerating back towards the other two at the end of his outbound leg. If you invoke GR, you also invoke the equivalence principle. This means his acceleration back towards his brothers can be treated as being equivalent of his staying still and his brothers "falling" towards him due to a gravitational field. In effect, he is lower in the field than his brothers are. Thus, due to gravitational time dilation his brother's time rate will run faster than his during his own "turn around" period. And since the other traveling brother is the highest this field, his will run the fastest. The result is when he totals up the accumulated time he calculates for all three, taking all effects into account he finds that he will have aged the same as the other traveling brother and less than the stay at home brother upon their re-meeting. This holds true no matter which of the traveling Brothers you pick.
You have managed finally to mess up all SR.
Two inertial reference frames, which have a relative speed between them and should have time dilation and length contraction, now we have to wait the end.
Maybe they are these two traveling twins who going to meet the "stay at home" brother, and between them there is no time dilation and length contraction.
martillo
Registered Senior Member
tach's mistake in post 89:
The problem is you thought that doing this you would obtain the timings as observed by the moving frame. That's wrong. Always while applying Lorentz Transfom the frame of observation is K the frame "at rest". The observer is always that attached to frame K not K' as you assumed.
So you were wrong and never a moving twin will age more than a twin "at rest".
The problem is that to correctly apply Lorentz transform always the frame K means the frame "at rest" which is the frame of observation and K' the moving frame. This way the result $$\Delta t > \Delta \tau$$ means elapsed time in the moving frame K' smaller than the elapsed time in the frame K "at rest". This is the same to say a twin in the moving frame K' age less than a twin in the frame K "at rest". This is right and is the conclusion that was always obtained.
The problem is you thought that doing this you would obtain the timings as observed by the moving frame. That's wrong. Always while applying Lorentz Transfom the frame of observation is K the frame "at rest". The observer is always that attached to frame K not K' as you assumed.
So you were wrong and never a moving twin will age more than a twin "at rest".
No, that doesn't follow. Symmetry between the two travelling twins just means they must have the same descriptions of each other. For example, in the left twin (L)'s frame, suppose the right twin (R)'s clock reads some time $$t_{2}$$ when L's clock reads $$t_{1}$$. Then symmetry implies that when R's clock reads $$t_{1}$$, L's clock must read $$t_{2}$$ in R's frame. This is exactly what you have in your scenario and symmetry requires nothing stronger than this. In particular, symmetry does not require that L and R's clocks must always read the same in their respective frames.
I don't know where you get the impression I'm "stuck". I am not "worried" that, say, R's clock might read something different than $$t = 0$$ in L's frame right after L has accelerated. I know it will happen. I can mentally visualise this quite easily with the help of Minkowski diagrams, and if necessary I know at least a couple of different ways of working out the exact numbers. After they've both accelerated, R's clock will not read $$t = 0$$ in L's frame, and L's clock will not read $$t = 0$$ in R's frame.
No, that's what all the twins observe when they cross each other.
martillo
Registered Senior Member
Sorry, I'm not able to analyze your reasoning. I'm not qualified to discuss in terms of equivalence principle, gravitational time dilation, twins "falling" towards the others, etc applied to the twins' paradox.
martillo
Registered Senior Member
Looks confusing but seems right.
Yes it does. I f the travels of both twins are perfectly symmetric they and their clocks experience exactly the same physical effects and so the the twins must look the same and the clocks must read the same time at any instant.
Right but where is the problem with that? Do you think because of that there would be no way to get the clocks synchronized in the problem? Always there's a way,, for example they can wait for a signal emitted symmetrically from the twin "at rest".
Not at all.
Janus58
Valued Senior Member
Maybe you should try and learn what SR actually say will happen in the scenario before spouting off about what "messes it up". During their outbound and inbound legs, Each of the traveling brothers would measure time dilation for both the stay at home brother and the other traveling brother. However, when they "turnaround" their brother's time will advance ahead of their own. For the stay at home brother this advance forward in time is enough to overcome the slowing due to time dilation on the out bound and inbound legs, leaving him to have advanced more net time when they meet again. For the other traveling twin it ends up exactly canceling out the effect of the time dilation for both legs leaving no net time difference between the two traveling brothers. In other words, for one traveling brother, his counterpart's clock runs like this; Very slow(outbound), very fast (during turnaround), very slow (inbound), with them showing the exact same total elapsed time when they meet up again.
Then you should stop spewing idiocies.
Like I said, you need to stop spewing idiocies. If you do not understand the derivation, I could explain it to you. Not that this would help.
There is no "applying Lorentz Transform" in the solution I posted.
Crackpottery is not a curable mental disease.
martillo
Registered Senior Member
Lot of the more notable physicists were considered crackpots at the time they presented their ideas. Only after they were recognized they became wisdom scientists and lot of time passed to that some times. So that kind of comments means nothing.
No, you're still neglecting that the twins don't define simultaneity the same way as each other after they've accelerated. That matters.
Your reasoning works in the "rest" frame, because the "rest" twin describes both travelling twins in a symmetrical way. But it doesn't work in the travelling twins' frames because they don't describe themselves the same way they describe their other twins. For example, in the left twin's (L) description, L is sitting at the origin of his own reference frame, feeling pseudo-gravitational forces if he happens to be accelerating, while R is following some complicated trajectory in L's frame. If L is accelerating, then L also expects R's clock to experience gravitational time dilation and gain time, possibly very rapidly depending on distance and the magnitude of the acceleration.
I really don't see how to make this more clear to you. We are not just looking at what happens in the "rest" frame. Relativity has something definite to say about your scenario, even when looking at the travelling twins' perspectives, and it specifically contradicts what you are saying.
There is no way to force that all the twins consider all three clocks to be synchronised once they are moving with different velocities.
That gets the twins' clocks synchronised in the "rest" frame, but not in their own frames once they're moving.
And you should notice that none of these notable physicists were trying to revive older, already refuted theories. That is a crucial difference that hacks never see.
"They laughed at Columbus, they laughed at Fulton, they laughed at the Wright brothers. But they also laughed at Bozo the Clown." --Carl Sagan
Try showing a bit of tach, Tach. OnlyMe isn't a crank.
martillo
Registered Senior Member
May be you don't know but I think in a totally new Physics' theory which I begun to develop and needs further development. You can find the link to its website in my profile if you want.
martillo
Registered Senior Member
I don't understand how could be a difference in the synchronization of the clocks. I said:
If you synchronize the clocks at the start of the travels and they make perfectly symmetric travels then both clocks reads exactly the same time at any instant after. How can you think they could get de-synchronized? There's no way...
And how many more people in history have believed they have a correct explanation for something only to be wrong?
There are more laypersons online making claims about science than there are actual scientists! They cannot all be right, many of them, sorry, many of you are inconsistent with one another. If you're right then Farsight is wrong. If Farsight is right then QWC is wrong. If QWC is right then Sylwester is wrong. On and on, each excluding the others.
Besides, I think it's a poor example because the majority of the scientists you're referring to presented detailed working, considered experiments, made predictions. They could, when asked, provide proper coherent explanations and derivations. When I ask the hacks here for details, for derivations of their results, there's usually just silence or an attempt to change the subject.
Hell, its usually worse than that. Almost every hack here peddling a pet idea is demonstrably ignorant of science. None of them, none of you, have access to real experimental data. You don't go get raw data, you just arm wave. For example, you talk about neutrinos and atoms etc. You've never worked with scattering cross section data from accelerators. You've never worked with neutrino telescope data. You've never worked with spectral data from supernovas. You've never worked with the raw data from tests of relativity. So that means you can only rely on what other people have distilled from said data. This is a real problem if you're trying to do away with the models used to distil the data. For example Sylwester says the Standard Model is fundamentally wrong. He then goes on to claim he can accurately predict the value of the strong coupling constant. But he doesn't do it by working with raw data from accelerators, he does it by looking up what physicists have interpreted from accelerator data using the Standard Model!! He denounces the model and then claims he can match something defined by the model!
But it gets even worse. If you don't have experimental data then you need to work with models others have constructed. By that I mean that if someone has confirmed that, for instance, general relativity is able to accurately model GPS network behaviour up to some level of precision and you don't have the raw network data then you can check your own model by comparing to the GR predictions we know to be very accurate. But this requires you understand the GR models. Farsight, Sylwester, you and many others (I'd say all of the pet theory peddling hacks here actually) don't know the mainstream models! Sure, I imagine you can give me a qualitative overview of what GR says about the GPS network (faster clocks go slower, gravitational time dilation etc) but none of you can calculate the precise predictions of the model.
For example, Farsight likes to claim he's a world leading expert in electromagnetism. He cannot model any electromagnetic system and he cannot solve in the most rudimentary of homework problems pertaining to electromagnetism. He, like pretty much all of you, is for all intents and purposes innumerate. And since the language of physics is mathematics you're all essentially illiterate in the language you need to talk in. People like Heaviside might have been considered a fringe guy in physics but he did a hell of a lot to advance the understanding of Maxwell's equations, he formulated them into the way it's currently taught to undergraduates. He put in time and effort, learnt what he needed to in order to present his work properly. You, Farsight, Sylwester, et al, are incapable of doing that even if your ideas weren't nonsense.
So you can tell yourself "I'm going through what some great physicists had to go through" but it's confirmation bias. We hear about such people because they accomplished something, they produced work which stood up to scrutiny. We don't hear of the tens, hundreds, even thousands of times as many people who were also in the same position but whose ideas were ignorant nonsense. You think you're in that tiny tiny group of people who claim they've done great things and actually have. Thus far you and everyone else on this forum with a pet theory have shown that is simply not the case.
That's only true in the "rest" frame. In the "rest" frame, both travelling twins are stopped to begin with, then at the same time they start accelerating at the same rate until they reach the same speed, only in opposite directions. So in the "rest" frame they start synchronised and they remain synchronised all the time and they're the same age when they cross over.
Your argument does not work in the travelling twins' frames because there is no such symmetry there: the way the left twin describes himself is not the same as the way he describes the right twin in his frame. There is no symmetry in that sense.
There is only symmetry in the sense that the way the left twin describes the right twin is the same as the way the right twin describes the left twin. For example, just after the left twin accelerates, he might say that his clock still reads $$t_{\mathrm{L}} = 0$$ while the right twin's clock reads $$t_{\mathrm{R}} = T$$. The right twin would say the same thing in reverse: after he has just accelerated, he would say his clock still reads $$t_{\mathrm{R}} = 0$$ while the left twin's clock reads $$t_{\mathrm{L}} = T$$. That is the only way in which the left and right twin's descriptions of things are symmetric.
I just told you: simultaneity is frame dependent in relativity. When e.g. the left twin compares his clock with the right twin, he's considering what time the right twin's clock reads "at the same time" as his own clock reads something. The de-synchronisation comes from the fact that, after they've accelerated, the left and right twins don't agree on what "at the same time" means any more.