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Implications of the statement Acceleration is not relative 
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#145
Feb1813, 04:34 AM

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Earth is shown as the wide blue line and the rocket as a wide red line. Dots along each path indicate one unit of elapsed Proper Time and I have marked most of them. I have also marked the four events that you indicated. Here is a diagram to show the rocket at rest: Both Earth and the rocket send a signal to the other one every unit of Proper Time. These signals provide the information that accounts for the visualization that you mentioned at the end of your post. The diagrams make it obvious that the situation is not symmetrical between the Earth and the rocket. They also make it clear that either diagram will provide all the information to determine the visualization of either observer. You should track a few of the signals, noting the Proper Time (according to the dots) they were sent and received and then go to the other diagram and confirm the same information. I didn't necessarily use the same coordinates that you used but, again, this will have no bearing on any outcome. The Coordinate Times are not significant when comparing between frames, only the Proper Times matter. 


#146
Feb1813, 09:39 AM

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It may be useful to elaborate a little on Langevin's discussion about the fact that acceleration has an absolute sense, as he meant it in a slightly different way than those people in this forum to which your first post relates; however Langevin gave the "twin" example for exactly this purpose, to illustrate the "absolute" effects of acceleration. The way he meant it is made clear by his description (as well as by the text that precedes it, but that's too long to cite here):
Only a uniform velocity relative to it cannot be detected, but any change of velocity, or any acceleration has an absolute sense. [..] the laws of electromagnetism are not the same in respect to axes attached to this [accelerated] material system as in respect to axes in collective uniform motion of translation. We will see the appearance of this absolute character of acceleration in another form. [..] For [..] observers in uniform motion [..]l the proper time [..] will be shorter than for any other group of observers associated with a reference system in arbitrary uniform motion. [..] We can [..] say that it is sufficient to be agitated or to undergo accelerations, to age more slowly, [..] Giving concrete examples: [..] This remark provides the means for any among us who wants to devote two years of his life, to find out what the Earth will be in two hundred years, and to explore the future of the Earth, by making in his life a jump ahead that will last two centuries for Earth and for him it will last two years, but without hope of return, without possibility of coming to inform us of the result of his voyage, since any attempt of the same kind could only transport him increasingly further [in time]. For this it is sufficient that our traveler consents to be locked in a projectile that would be launched from Earth with a velocity sufficiently close to that of light but lower, which is physically possible, while arranging an encounter with, for example, a star that happens after one year of the traveler's life, and which sends him back to Earth with the same velocity. Returned to Earth he has aged two years, then he leaves his ark and finds our world two hundred years older, if his velocity remained in the range of only one twentythousandth less than the velocity of light. The most established experimental facts of physics allow us to assert that this would actually be so. [etc.]  starting p.47 of http://en.wikisource.org/wiki/The_Ev...Space_and_Time 


#147
Feb1813, 06:35 PM

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#148
Feb1813, 06:53 PM

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#149
Feb1813, 07:11 PM

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Another factor on my side was that I thought you did not understand exactly what I was troubled by. Working through the twin paradox, looking for an answer to what troubled me, also led me to understand why SR is valid for solving the problem, at least with respect to kinematics. (I don't say SR isn't valid with respect to dynamics, only that I don't know enough to say it is.) I know that what I did wrt the twin paradox is at the most elementary level. But for me, it was like the transition from saying "ga ga, goo goo" to standing up on two feet and taking a step or two (before stumbling). Hopefully I will be less annoying in future. 


#150
Feb1813, 07:57 PM

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I don't say that I fully understand the concept of "absolute proper acceleration" being compatible with "no absolute space". However, it seems to me that this is something that needs to be considered with the dynamics of SR. Kinematically, the spacetime diagram shows that the rocket is at rest in its noninertial frame. That, by the way, is the objection that I felt was being dismissedthe call for consideration of the case in which the rocket is at rest. If I (now, or finally) understand George correctly, that objection is intentionally dismissed by Taylor and Wheeler. Indeed, when the objection is raised, it could be shown, using the spacetime diagram that is already under consideration, that the rocket is at rest throughout the episode. What the objector wants (or at least, what I wanted) was for the symmetrical diagram to be drawn, because he thinks that this is the only spacetime diagram in which the rocket is at rest. That thought is based on a misconception of the spacetime diagrama misconception which I began to perceive as I thought more about the spacetime diagrams I drew for the poleinbarn paradox. 


#151
Feb1813, 08:39 PM

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my_wan said,
My understanding is that, even according to modern ideas, it is indeed a matter of free opinion as to whether the rocket acceleratesif one considers acceleration in the usual sense of "rate of change in velocity as measured with respect to a set of coordinates". The statement was, "Coordinate acceleration is relative". (Edit to clarify.) It is proper acceleration which is absolute; but one may be at rest in a coordinate system while experiencing proper acceleration. There is at least one person in the universe who will disagree with the claim that the rocket is accelerating: the observer in the rocket who is convinced that he is at rest. (This, I think, is along the lines of another comment on the claim, posted by someone else.) Still, I don't know anything about how the dynamics of the "resting while accelerating rocket" work, so I'm not making any statement of my own opinion on this issue. I'm only giving my understanding of what I have been told. 


#152
Feb1813, 10:00 PM

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#153
Feb1913, 02:19 AM

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In contrast, for me the definition of "proper acceleration" as given in Wikipedia is a misnomer for what I would call apparent gravitation.  http://en.wikipedia.org/wiki/Proper_acceleration It may be that such different definitions bugged you (they did bug me in earlier discussions). 


#154
Feb1913, 02:49 AM

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#155
Feb1913, 02:59 AM

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However, I'd like you to consider an issue related to the one you just raised here and that is, how does the rocket know when to turn around? The rocket cannot know from any direct measurement when the Earth has traveled 10 units away in the rocket frame. That distance is the difference between the spacial components of Event B and C which are simultaneous in the Earth frame but which have a distance between them of 16.67 in the rocket frame. Even if the rocket had instant access to the remote information, it would still have to do some calculation if it's based on distance to determine when to fire its rockets. To me, a much cleaner way to specify the Twin Paradox is to state the Proper Time on the traveler's clock when he should fire the rockets to turn around. This has the advantage that it doesn't require the specification of any reference frame. In fact, it doesn't even require fully specifying any events since we don't care about the spatial component. So if we know how long it takes for the traveler to get to the turnaround point and we know how fast he is traveling, those two parameters fully specify the complete Twin Paradox scenario (assuming of course that he is returning at the same speed he left at). I fully explained this in the thread you linked to in your opening post. 


#156
Feb1913, 03:07 AM

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#157
Feb1913, 03:30 AM

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#158
Feb1913, 06:18 PM

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I don't see how the claim is disproved by pointing out that the rocket changes inertial frames during the firing of the engine. The change of inertial frames only confirms what everyone knows: the rocket is noninertial. From the earth twin's point of view, the rocket is in an inertial frame, accelerates, and comes to rest in another inertial frame. The rocket twin disagrees with this assessment. He can point to the spacetime diagram (which the earth twin accepts as valid) and show that he remains at rest in his own frame, even while not at rest in any one inertial frame. To prove the rocket twin wrong, it must either be shown that his frame moved with respect to some absolute position marker, or that the laws of dynamics are violated if he does not move. There is no absolute position marker, and the laws of dynamics are not considered in my analysis. [If these statements are wrong, at least they are not bald statements; I've done my homework. ] 


#159
Feb1913, 06:44 PM

P: 221

What helped me was to realize that in the typical twoframe spacetime diagram, the world line of an inertial particle shows the particle both as moving and at rest. It is moving in one frame, and at rest in the other frame. Thus, the one spacetime diagram actually shows the case I wanted to seethe case in which the rocket twin considers himself at rest. The symmetrical diagram (which is invalid) is not needed. 


#160
Feb1913, 07:18 PM

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For perspective, I have read two or three explanations of the twin paradox to my 30+ son. He has some technical training, has a job that requires him to evaluate contractual language. He had exactly my reaction, without me making any comment. 


#161
Feb1913, 09:48 PM

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#162
Feb1913, 09:52 PM

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