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What is or is not a paradox?
On Dec 30, 4:17 pm, Sylvia Else wrote:
I started writing a post about this yesterday, then scrubbed it  too What is a paradox in special relativity (hereinafter SR)? I've expressed the view that to contain a paradox, SR has to predict, from different frames, outcomes that are mutually incompatible. An example that comes to mind (though not directly arising) from a recent discussion is that in one frame, there is massive destruction on a citywide scale, and in another other frame, nothing much happens. Clearly, if SR were to make such predictions for two frames, it would have to be regarded as seriously wanting. Of course, it does no such thing. But people seem to want to regard measurements in two frames as mutually incompatible if they give different results. I am at a loss to understand why people would seek to regard those different results as constituting a paradox that invalidates SR (well, leaving intellectual dishonesty aside). From the Lorentz transformations, you can write down the following equation per Minkowski spacetime. Points #1, #2, and #3 are observers. They are observing the same target. ** c^2 dt1^2 ds1^2 = c^2 dt2^2 ds2^2 = c^2 dt3^2 ds3^2 Where ** dt1 = Time flow at Point #1 ** dt2 = Time flow at Point #2 ** dt3 = Time flow at Point #3 ** ds1 = Observed target displacement segment by #1 ** ds2 = Observed target displacement segment by #2 ** ds3 = Observed target displacement segment by #3 The above spacetime equation can also be written as follows. ** dt1^2 (1 B1^2) = dt2^2 (1 B2^2) = dt3^2 (1 B3^2) Where ** B^2 = (ds/dt)^2 / c^2 When #1 is observing #2, the following equation can be deduced from the equation above. ** dt1^2 (1 B1^2) = dt2^2 . . . (1) Where ** B2^2 = 0, #2 is observing itself Similarly, when #2 is observing #1, the following equation can be deduced. ** dt1^2 = dt2^2 (1 B2^2) . . . (2) Where ** B1^2 = 0, #1 is observing itself According to relativity, the following must be true. ** B1^2 = B2^2 Thus, equations (1) and (2) become the following equations. ** dt1^2 (1 B^2) = dt2^2 . . . (3) ** dt2^2 = dt2^2 (1 B^2) . . . (4) Where ** B^2 = B1^2 = B2^2 The only time the equations (3) and (4) can coexist is when B^2 = 0. Thus, the twins paradox is very real under the Lorentz transform. shrug Within the Lorentz transform, the little professor from Norway, paul andersen, was able to play a mathemagic trick, and he is not alone. In doing so, the Minkowski spacetime was not recognized in his little applet. He is out in the very left field chasing chickens again. shrug Tom and other selfstyled physicists have recognized that fault and moved on to claim a mythical proper time flow where all local time flow is a projection of this absolute time flow. Oh, excuse Koobee Wublee. Not absolute time but proper time whatever $hit it is. However, these guys cannot explain why the projection did not cancel out on the traveling twins return trip. So, equations (3) and (4) are still indicating the paradox regardless if projection or not. shrug Well, sooner or later, these bozos are going to wake up someday and ask themselves what the fvck was I thinking?. Guess what? The time projection crap is the last piece of float the selfstyled physicists are clinging on to. Take that away. They will sink. That is why the selfstyled physicists are very reluctant to give the time projection crap a serious thought. shrug 
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