John, A couple of points in response.
Yes, I agree that both A and B see each other's clocks running slower than their own DURING the trip. This is standard relativity theory mostly Lorentz transform if we just take non-accelerated relative motion. Also note that, contrary to your statement, in this case both A and B DO AGREE on "when the race starts and stops" because they both begin and end at the same present moment point in actual spacetime back on earth. I know that, and presumably we agree on it, but that was NOT the question I asked. The question is why when A gets to the center of the galaxy and stops relative to B that then his clock shows only 20 years passage, but B's clock shows 30,000+? Perhaps you didn't see my similar questions to Brent, to which he has either been unwilling or unable to reply, about this case. He says it's a matter of geometry, but neglects to point out that geometry must have its origin at B's earth bound frame. The question is why this geometry rather than the equal and opposite frame based in A's origin creates not only the transitory effect you reference above but also a real permanent effect. It seems we have to choose the correct geometry but what is the criterion for the correct geometry? It almost seems as if there must be some absolute real geometry centered at B's origin on the earth for this to work. Your analysis? Edgar On Sunday, February 2, 2014 11:51:21 AM UTC-5, John Clark wrote: > > On Sat, Feb 1, 2014 at 1:25 PM, Edgar L. Owen <edga...@att.net<javascript:> > > wrote: > > > I stated that A began his trip from earth ORBIT, not from blasting off >> from earth's surface, so A's acceleration is 1g for the ENTIRE trip. >> > > Then each would see the others clock as running slower than his own. You > might think this would lead to a paradox if they were, for example, timing > the same race with their stopwatch and writing the time in their notebook. > If each clock is going slower than the other shouldn't each number they > write be smaller than the other? The answer is no because the two can't > agree on when the race starts or stops, there is no universal "now" that > they can start and stop their stopwatch at so one of the two numbers > written down will always be larger than or equal to the other; one observer > will see the others stopwatch as running slower but he starts his watch so > much sooner that the number he writes down is the same or larger. > > > A's direction of acceleration doesn't JUST change if he decides to >> return. It reverses at the MIDPOINT of the trip so he can slow and stop at >> the galactic center. > > > Then the journey of the twins is NOT symmetrical, one experienced a change > in the direction of acceleration and one did not. > > > If he returns if would have to change it again at midpoint. >> > > So the 2 journeys are even more unsymmetrical, so when they got back > together and examined their clocks side by side it wouldn't be a surprise > that they don't match. > > > note also that the DIRECTION of B's acceleration is also continually >> changing relative to A's motion simply because the earth is rotating. >> > > In your thought experiment if you use the center of the Earth as the > origin then the direction of B's acceleration never changes, it's always > directly toward that center; and A's acceleration is always directly toward > that center or directly away from it. If you use some other point as the > origin the math would become considerably more complex but the answer would > be the same. > > John K Clark > > > > > -- 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. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/groups/opt_out.
