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The case for True Length = Rest Length 
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#109
Mar311, 06:41 PM

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#110
Mar311, 09:08 PM

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Have you ever seen a "lines of simultaneity" analysis of the twin paradox? It looks something like this: See that "gap" in the stationary twin's world from the traveling twin's perspective? If you study this for a bit you'll realize that ALL of their relative age differential exists because of this gap. (Note: the only reason the stationary twin appears to age "instantly" is because the graph shows, as most do, that the traveler turns around "instantly". A more reasonable rate of acceleration while turning around would produce a period of extremely fast aging for the stationary twin, yet one devoid of an unnatural gap.) 


#111
Mar311, 10:07 PM

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It is clear that shortcut taken by the twin doing the round trip accounts for the difference in age, not the turnaround acceleration. All the turnaround does is to give the round trip twin interesting variations in his view of the other twin's clock (as has already been pointed out in ealier posts). We can show the respective views each has of the other's clocks on the return trip if necessary (someone else could probably do that since I'm running out of steam). 


#112
Mar311, 10:28 PM

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Anyway, you are correct in a sense; it isn't the acceleration per se, it's the frame change. Have you ever played the game Portal? Super fun. Anyway, you have a gun that can open "portals" on any flat surface. You create two of them, and then you can travel between them instantly. Jump through one, and your momentum is carried through the other. The physics really plays with your head, especially when jump through the floor and enter through a vertical wall (and your momentum continues), or you place one directly on the floor below the other in the ceiling (so you fall "for eternity"). Anyway, my point is that if we could get our hands on one of these guns then producing an asymmetrical time dilation between two observers without either one of them accelerating would be possible. Until then, frame changing is synonymous with accelerating! 


#113
Mar311, 10:44 PM

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I certainly agree with you that the round trip twin did accelerate during the turnaround. However, the spacetime diagram implies a relatively insignificant increase in proper time during the turnaround. We could have shown a magnification of the turnaround to indicate that the glevels for the blue guy would not be as high as might be inferred from my diagram. But, again, the length of the world line (curve) during turnaround for the blue guy would be relatively insignificant. Besides, it is obvious that it is the high speed at the end of the acceleration that provides the short cut through spacetime. We're not doing anything like sending the blue guy off to the neighborhood of a black hole. In any case we keep the acceleration under control so as to keep the problem in the realm of Special Relativity. 


#114
Mar411, 01:42 AM

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You asked me:
And then I also explained what the stationary twin's keen eye sees of the traveling twin's clock. I said that for way more than half of the trip, he sees the traveling twin's clock ticking at some rate slower than his own (the same slow rate that the traveling twin sees during the first half of the trip). Then I said that near the end of the trip, he sees the traveling twin's clock ticking at some rate higher than his own (the same high rate that the traveling twin sees during the last half of the trip). The sum total of all the ticks is the amount of aging the traveling twin experience. The fact that the stationary twin counted low rate ticks for much more than half of the trip illustrates how he sees the traveling twin as aging less than himself. But then you responded by saying that all of the differential aging occurs during the acceleration at turn around which has nothing at all to do with what the twin's keen eye sees. Why do you ask me to explain what he sees and then complain about something that has nothing to do with what he sees? You also asked me if I can see something in a graphic but the graphic is broken. All I can see is a framed box with an X in it. So I cannot respond to your questions but it really doesn't matter because as I already explained, you haven't shown what either twin sees which is what you asked me to explain. And keep in mind, I explained what each twin sees without bringing Special Relativity into the picture. You can also explain the Twin Paradox, as I said before, by using any frame of reference. But you have to be careful to illustrate in that frame what each twin actually sees and it will be exactly the same as I described without using SR. It doesn't matter which frame you use to analyze a scenario, they all agree on what each observer sees. So my simple question to you is: do you deny my description of what the twin's see? 


#115
Mar411, 03:00 AM

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#116
Mar411, 04:18 AM

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The overall experience per twin B is twin A's wildly spinning distant clock during periods of twin B's own proper acceleration. However, this "overall experience" is the superposition of 2 relativistic effects ... (1) the reciprocity of slower ticking clocks, andSo, the reciprocity of moving clocks always holds mathematically (as ghwellsjr stated), however the change in relative simultaneity counters that effect (from B's POV), twice over ... and so the reciprocity of moving slowertickingclocks cannot be observed, and can only be deduced as the superposition of 2 relativitic effects that concurrently concur. That said, I see you and ghwellsjr both as correct. However, if you think that relative clock rates are illusionary effect, in this you are mistaken. Whether inertial or undergoing proper acceleration, what a clock presently reads dictates its real time and thus the proper time experienced by the clock since the 1st of 2 spacetime events. GrayGhost 


#117
Mar411, 07:36 AM

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#118
Mar411, 07:46 AM

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#119
Mar411, 08:50 AM

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But, rjbeery does not agree with you or with me. I'm trying to figure out exactly what he disagrees with me about. That's why I asked him at the end of my post you referenced if he denies my description of what each twin sees. But to answer your question about where he said that all the differential aging occurs during the acceleration at turn around: 


#120
Mar411, 09:41 AM

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This all shows the even in one frame, you better clearly define how you measure something and how you interpret those measurements. Different, perfectly reasonable choices can lead to different results. 


#121
Mar411, 09:48 AM

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The overall experience per twin B is twin A's wildly spinning distant clock during periods of twin B's own proper acceleration.is not correct. Twin B (the traveling twin) never experiences twin A's clock wildly spinning and by that I mean twin B never observes twin A's clock wildly spinning. During the acceleration period twin B will see twin A's clock transition from a tick rate lower than his own to a tick rate higher than his own. If the acceleration is instant, the transition will be instant. If it is gradual, the transistion will be gradual. If the acceleration is in two parts where twin B decelerates to a stop and stays there for awhile and then accelerates in the backhome direction, the transition will be in two parts, first twin B will see twin A's clock transition from a tick rate lower than his own to a tick rate identical to his own and stay there for awhile and second twin B will see twin A's clock transition from the same rate as his own to a higher rate than his own. And twin A will see identical transitions in the tick rates of twin B's clock, except that instead of them occuring at the halfway point in the trip, they occur closer to the end of the trip. It's only this lack of symmetry in when the transitions occur that accounts for the twin's observations of the difference in aging when they finally reunite. Keep in mind that there are similar transitions that occur during twin B's initial acceleration and final deceleration but all these acceleration periods only complicate the issue which we are discussing which is the reciprocal time dilation that each twin observes of the other one's clock. If we make the accelerations be instant, then we can say that each one always observes the same time dilation of the other one's clock during the entire trip. If we insist on making the accelerations take time, then we have to put in a little caveat that the time dilation will not be reciprocal nor be constant during the entire trip but the effect is quite minor and really doesn't impact the point of the discussion. 


#122
Mar411, 09:58 AM

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#123
Mar411, 10:32 AM

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ghwellsjr, I'd like to apologize only for the reason that our discussion seems to have taken on a small bit of defensive posturing. Our mutual goal should be to further our understanding of Physics rather than to play a game of "speech and debate", parsing each others' words for errors.
That being said, since you're asking explicitly, I'll explain my position one last time. First of all, if you can't see my graphic of lines of simultaneity, let me try again, because it's important... http://chaos.swarthmore.edu/courses/PDG/AJP000384.pdf That's my perspective. All age differential is due in toto to the frame change caused directly by acceleration of one of the twins. Now, on to what you're saying... There are many ways to analyze the Twin Paradox, but trying to do so using only SR concepts devoid of acceleration will ultimately fail. The "cause" of the age differential is acceleration, period. That is and continues to be my point, and if you or anyone else has an interpretation of the Twin Paradox that does not involve a frame change based caused by acceleration I would be fascinated to learn of it. Thanks 


#124
Mar411, 10:54 AM

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#125
Mar411, 12:52 PM

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#126
Mar411, 01:04 PM

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