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On the nature of the infinite fall toward the EH 
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#235
Dec1012, 10:04 AM

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#236
Dec1012, 10:14 AM

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PF Gold
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So, I still claim, no exceptions in SR or GR:  time dilation is a coordinate feature, not an observable.  Doppler between a chosen emitter and a chosen receiver is an invariant observation.  Differential aging between different space time paths between given events is an invariant observation. 


#237
Dec1012, 10:21 AM

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PF Gold
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#238
Dec1012, 10:25 AM

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PF Gold
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http://www.physicsforums.com/showpos...9&postcount=23 


#239
Dec1012, 10:35 AM

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PF Gold
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#240
Dec1012, 11:08 AM

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PF Gold
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Think of the Kruskal chart, and singularity region in the right half (that matches the GP singularity ordering). Specifically, to make it easy, think of a two singularity arrival events that are nearly horizontal in the chart, and close together, and connect them out with light paths to some static, radial, external world line. Now, within this sliver, we just change all simultaneity surfaces by one degree from horizontal, counterclockwise. [Edit: Actually, KS shows a stronger result. It is global, and reverses GP singluarity arrival ordering for 'half' the singularity arrival events. It seems to me, that distortions of KS can reverse GP ordering in a consistent global chart for all singularity arrival events before (in GP sense) any chosen one. What you can't do is accomplish this for the whole singularity arrival sequence.] 


#241
Dec1012, 11:54 AM

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PF Gold
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#242
Dec1012, 02:55 PM

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PF Gold
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V' = V  k U U' = U using the conventions where V is the KS time coordinate, 1 < k < 1. Lines of constant V' are spacelike everywhere; lines of constant U' are the same as lines of constant U. While the metric gets ugly, it is not hard to see that increasing k towards 1 shifts the inflection in singularity ordering as far to the right as desired; decreasing k towards 1 shifts the inlection to the left. So, for any two events on the singularity, you can get an ordering where the left is first for some k close to 1, and where the right is first for some k close to 1. Each of these charts is global, with the same time ordering for causal curves as the original KS chart. This fully justifies (better late than never) my original statement that for any two light signals reaching the singularity from Lucky, Lucky can consider the arrival events to be the reverse of the emission events. The only thing Lucky can't do is achieve such an inversion over the whole history of a static world line. It can be achieved for any segment of interest, but not for the whole past/future eternal history. Also, note that none of this contradicts Dalespam's improved wording: If light from e1 reaches Unlucky as Unlucky reaches the singularity, light from any event e2, later on Lucky's world line, will not reach Unlucky at all. This wording is coordinate independent. Wording on the order of the two singularity arrival events is coordinate dependent (as expected by the spacelike relation between them). A final observation is that Lucky can achieve total time order on the singularity consistent with their world line time order using a variety of coordinates (Lemaitre, GP, EF, etc.). A mirror Lucky in region III would use a mirror version of each these coordinate systems to achieve a total singularity ordering consistent with their world line. 


#243
Dec1012, 07:23 PM

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#244
Dec1012, 07:43 PM

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PF Gold
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#245
Dec1012, 07:44 PM

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#246
Dec1012, 08:08 PM

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#247
Dec1012, 11:41 PM

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PAllen, I obviously need to read up on close orbiting neutron stars, but what does SOL mean? 


#248
Dec1012, 11:49 PM

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#249
Dec1112, 06:51 AM

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Please clarify what the claimed error is according to you  I'm sure that you understand it much better than I do. 


#250
Dec1112, 08:45 AM

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PF Gold
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You are entitled to your interpretation, but it is important to note that it is considered incorrect by every expert here. 


#251
Dec1112, 08:48 AM

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PF Gold
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#252
Dec1112, 08:57 AM

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http://www.academia.edu/2120610/The_..._Physics_1988_ 


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