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#181
Jan2313, 12:22 PM

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#182
Jan2313, 07:36 PM

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Given a single extended accelerated physical system of clocks and rulers do you think that right after turnaround this system would be congruent with x_{1} intersecting event A? Would there, or not, be a traveler at A with a clock reading of t'=5+(a hair)?? 


#183
Jan2313, 09:40 PM

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If you don't get this sketch, I could easily select simultaneous spaces much farther away from the start of the trip and from the turnaround. I didn't think this would be such a problem. I'm not showing an accelerated frame at all, so that's not relevant here. 


#184
Jan2313, 09:44 PM

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#185
Jan2313, 09:53 PM

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A "sequence of simultaneous spaces" is a simultaneity convention, in this case a noninertial one. You may try to disguise it all you like, but that is what you are doing. Inventing new terms like "3D worlds" and "simultaneous spaces" doesn't change what it is. 


#186
Jan2313, 09:59 PM

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#187
Jan2313, 10:27 PM

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However, as the blue guy moves along his worldline, the event B is presented to his outgoing simlultaneous space first (right at the start of the outgoing trip). Then. event A is presented to blue's simultaneous space just after blue completes his turnaround. Also, just before blue enters his turnaround path, event C is presented to blue's simlultaneous space. Then, event A is not presented to the blue simultaneous space until after the turnaround is complete. 


#188
Jan2313, 10:54 PM

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A sequence of simultaneous spaces is a simultaneity convention. And I have already told you that the naive simultaneity convention used here cannot cover the red worldline because it violates the few mathematical requirements of a coordinate system. Your statement is mathematically invalid, as I pointed out well over 100 posts ago. I don't know why you persist in it. 


#189
Jan2313, 11:02 PM

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I would like to bring up this earlier comment. I am trying to understand bobc2's position.
So I would ask in what model Andromeda Paradox is supposed to appear. 


#190
Jan2313, 11:02 PM

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#191
Jan2313, 11:12 PM

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Quote by Austin0
it was understood that this depicted inertial phases before and after turnaround. When you attribute the x _{1} axis to the traveler you are implicitly applying it to an accelerated frame. I.e. there is no turnaround without acceleration. So whether the traveler frame is accelerating at that time is not relevant , In the context of the overall trip it is noninertial. Quote by Austin0 Whether or not you are talking about a single accelerated system I am asking your thought regarding the x_{1} axis as it would apply to such a system (with the edit above). If there was such a comoving system at that time after turnaround (inertial) would it correspond (be congruent) to the x_{1} axis in your chart? Would there, or not, be a traveler at A with a clock reading of t'=5+(a hair)?? 


#192
Jan2313, 11:17 PM

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When we speak about reality, do we mean only single moment of space or do we include all past and all future?
I believe that with reality we mean single slice of spacetime i.e. we do not include all past and all future. 


#193
Jan2413, 12:20 AM

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#194
Jan2413, 10:16 AM

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You folks still seem to be troubled by the approximaty of the simultaneous spaces to the accelerated turnaround point in my sketches. So, here is a sketch where we consider the simultaneous spaces far far removed (years and millions of miles) from the turnaround neighborhood. We still have the same interesting feature about the order of events. Event A occurs before event B in the 2nd Black's rest frame. However, for the travelling twin moving along his worldline, event B is presented to his return trip simultaneous space before it is presented to his outgoing simultaneous space.
To emphasize the distinction between the outgoing frame and the return trip frame (not a single acceleration frame), I've colored the outgoing frame blue and the return frame red. The stayathome twin has the worldline along the black X4 axis. 


#195
Jan2413, 11:11 AM

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You seem to think that I am having difficulty understanding your point. I understand your point quite clearly. Your point is not unclear, it is wrong. EDIT: oops, it is PAllen's post 190 


#196
Jan2413, 11:30 AM

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#197
Jan2413, 12:09 PM

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Of course, I remain convinced that, even where applicable, making such statements as 'this is where the distant clock really runs faster than mine' are physically meaningless and conceptually grossly misleading. 


#198
Jan2413, 04:47 PM

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