Jesse, I guess I'm supposed to take that as a yes? You do agree that A's world line is actually shorter than C's (even though it is depicted as longer) because A's proper time along it is less than C's from parting to meeting? Correct? Strange how resistant you are to ever saying you agree when we actually do agree. Remember we are not counting points here, at least I'm not, we are trying to find the truth....
First, note you don't actually have to calculate anything. A and C just compare clocks when they meet and that gives the actual world line lengths. But, if you want to calculate to predict what that comparison will be, then you have to be careful to do it correctly. C can't just use the Pythagorean theorem on A's world line from his perspective on the x and y distances, he has to use it on the time dimension as well squareroot((y2-y1)^2 + (x2-x1)^2 - c(t2-t1)^2). It is the subtraction of this time term that will reduce the length of the slanting blue lines of A and B to THEIR PROJECTIONS ON C'S OWN WORLDLINE. I think that is what you are saying as well, but my point is that that NULLIFIES any effect on the length of the world lines by the SLANTING of the blue lines NO MATTER WHAT THEIR LENGTHS, and LEAVES ONLY the effects of the red curves. This must be the case because NON-accelerated relative motion DOES NOT affect proper time rates. This is because it is exactly the same from the perspective of A and C moving relative to each other, thus it cannot affect the lengths of their world lines. I'm trying to parse your last paragraph. Your diagram shows ONLY how A's and B's world lines appear in C's comoving frame. It does NOT show the proper LENGTHS of A's and B's world lines. I think we agree the lengths depicted are NOT the actual world line lengths. I claim the blue slanting lines of A and B, one set longer than the other, have NO EFFECT on the actual lengths of A's and B's world lines. Because when we calculate just their proper lengths subtracting the time term as I do above, their proper lengths reduce to their VERTICAL PROJECTIONS on C's vertical world line. In other words there is no difference in proper time rates of A, B or C during the intervals of the slanting blue lines. Thus, in my view, we are left with ONLY the effects of the curving red accelerations, and these are exactly the same for A and B. And when the lengths of those red acceleration segments are calculated we find that A's and B's world lines will both be SHORTER than C's world line AND by the SAME AMOUNT and that A's and B's world line lengths will be EQUAL due only to their equal accelerations. Perhaps to make this clearer consider just two blue lines of A and B slanted with respect to each other and crossing at P. From A's perspective B's line will be slanted, but from B's perspective A's line will be slanted in the other direction by an equal amount AND since this is NON-accelerated inertial motion only, both views are EQUALLY VALID. When we do the Pythagorean world line length calculation we get EXACTLY THE SAME RESULTS from both frame views. So both world line lengths are exactly equal. Thus slanted blue lines of ANY LENGTH have NO EFFECT AT ALL on world line lengths, and only curved red line accelerations do. If you disagree I can give you another example. Edgar On Friday, March 7, 2014 7:26:38 PM UTC-5, jessem wrote: > > > On Fri, Mar 7, 2014 at 7:20 PM, Edgar L. Owen <[email protected]<javascript:> > > wrote: > > Jesse, > > Do you understand why the world line that is depicted as LONGER in the > typical world line diagram is ACTUALLY SHORTER? > > E.g. in your diagram do you understand why even though A& > > ... -- 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 [email protected]. To post to this group, send email to [email protected]. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
