Jesse, Your example does NOT establish any inconsistency. I NEVER said "I'm pretty sure you've said before that you agree that if SR predicts two clocks meet at a single point in spacetime, their two readings at that point must be simultaneous in p-time)." That is NOT true. Only if there is no relative motion or acceleration is it true. I really wish you could just get the basics of the theory straight.
Let me just give you the general method for all cases and see if you can understand it: If you are just trying to figure out the method of determining p-time simultaneity between any two observers in any combination of relativistic circumstances here it is. The general case of determining p-time simultaneity between any two relativistic observers. Assume observers A and B, both accelerating relative to each other, with different rates of relative motion and in different gravitational fields. Assume all possible relativistic effects between A and B. The method is trivially simple. I'll give two approaches: 1. Instantaneously pause all relativistic effects at any time t on A's clock and read the time t' on B's clock. These clock times are a point when A and B were/are in the same p-time current moment. 2. Do the same thing for any t you wish. The t' that corresponds will be the clock time in the same present moment of p-time as the t you paused at. 3. In general if you want to know what clock time t' of B occurred in the same p-time as any time t on A's clock, all you have to do is pause the experiment at t so that all relative motion ceases and just read t' on B's clock. Because this can be done at any point t on A's clock we can always determine what t' on B's clock occurred in the same p-time as that t simply by reading B's clock. Note this is exactly what happens when the twins meet up in the same p-time present moment and read each other's clocks to determine what clock times occurred at the same p-time, in that same common present moment. You can also do this with a calculation as well as by pausing the experiment. 1. Note there are two classes of relativistic effects in the general case: a. Reciprocal temporary effects of relative motion in which A and B each see the other's clock slow by the same amount. These effects vanish when relative motion ceases and A and B do NOT agree on these effects because they are equal and opposite. No permanent actual age differences are produced by this type of effect. b. Persistent and agreed effects of acceleration and gravitation in which one clock slows permanently relative to the other and both A and B agree on the amount of slowing. These effects persist after the relativistic differences vanish. They are permanent. And both A and B agree on these effects. These effects manifest as real permanent age differences. 2. At any desired time t on A's clock, identify, calculate and discard the effects of relative motion of type a. so that the only effects between A and B left are of type b., the actual real actual age differences up to point t on A's clock. We keep only the effects that would be/are permanent (type b. above) and disregard those that are not (type a. above). This is effectively the same as pausing the experiment at any t, because that is just a simpler method of eliminating effects of type a. Again all we have to do now is compare t and t' to see what t' of B occurred at the same p-time as t on A's clock. This will be the real age B is when A is t years old, which is the test of the same p-time. Both A and B agree on this age difference because it is real and persistent after all relativistic effects cease. 3. This can be done either in A's frame for any t, or in B's frame for any t'. 4. This process is transitive between any number of arbitrary observers in any relativistic situation. We can always find the clock time t-values of each that occurred in the same p-time, the same present moment of p-time. Edgar On Tuesday, February 11, 2014 2:00:23 PM UTC-5, jessem wrote: > > > > On Tue, Feb 11, 2014 at 1:13 PM, Edgar L. Owen <edga...@att.net<javascript:> > > wrote: > >> Jesse, >> >> Your condition C. was not example dependent. You just need to rephrase >> your condition C. as two observers with no relative motion AND in identical >> gravitational fields. Then it does hold and is consistent with conditions A >> and B. I already gave several examples. >> > > But I gave a different example where it leads to inconsistent conclusions, > are you going to address that? In my example, Alice and Bob have no > relative motion and are both in identical gravitational fields (zero > gravitational fields, since this is an SR flat spacetime example). > Likewise, Arlene and Bart have no relative motion and are both in identical > gravitational fields (again, zero). The only comparisons I made between > members of different pairs were ones that involved their passing next to > each other and comparing clock readings at the same point in spacetime, so > their relative motion shouldn't be an issue (I'm pretty sure you've said > before that you agree that if SR predicts two clocks meet at a single point > in spacetime, their two readings at that point must be simultaneous in > p-time). > > Please just look over the Alice/Bob/Arlene/Bart example I gave at > https://groups.google.com/d/msg/everything-list/jFX-wTm_E_Q/pxg0VAAHJRQJand > tell me if you disagree with any of the numbered conclusions about > p-time simultaneity 1-4. > > Jesse > > -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. 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