On Thu, Mar 6, 2014 at 11:32 AM, Edgar L. Owen <[email protected]> wrote:
> Jesse, > > Yes, from the point any two observers in the same inertial frame > synchronize clocks, their clocks will be synchronized in p-time BUT ONLY > FROM THEN ON (we can't know if they were previously synchronized unless we > know their acceleration histories). And only SO LONG AS they continue in > the same inertial frame OR undergo symmetric accelerations. > > Same ages is just a way to ensure synchronized clocks at the birth event > and make examples simpler. It has nothing to do with p-time synchrony per > se. > > So in your next paragraph your and Jimbo's proper clocks ARE synchronized > in p-time from then on under the conditions stated. > > But I don't understand the rest of your example since you just stated that > we are to ignore their PREVIOUS and SUBSEQUENT acceleration histories to > preserve the synchronies but then you start giving an example with > accelerations, which will obviously change their synchrony UNLESS they are > symmetric. > I clearly stated that the reason I was "giving an example" of accelerations was in case you DIDN'T accept the clocks were synchronized in p-time in my example with Jimbo, which ignored my and Jimbo's past acceleration histories and ages. My words were: "OK, I don't think it should be necessary to specify acceleration histories or ages if you agree with my statement about me and Jimbo above, but if you disagree with that statement I can give details about each pair's past history, though it makes the example a bit more complicated." Since you do accept my statement about p-time simultaneity in the Jimbo example, then there's really no NEED to assume anything about A/B and C/D's past accelerations being symmetric, we can just assume that at some point before the experiment happened, A and B came to rest in frame F and synchronized their clocks in frame F, and C and D came to rest in frame F' and synchronized their clocks in frame F', and subsequently their x(t) and T(t) functions in frame F were as I described. However, in the rest of your post you are responding to my example of a history where A and B had symmetrical accelerations before the experiment, and so did C and D, so I will discuss that example; maybe it makes the statements about p-time simultaneity conceptually clearer to think of their history that way, although if you think it'd be simpler I'd also be just as happy to make the assumption above that each pair synchronized clocks after they came to rest in the same frame. > You seem to claim that the accelerations are symmetric but you keep > describing them as stopping in different frames at different times which > indicates they are NOT symmetric. > In my example both accelerations were totally symmetric in the frames where the twins started out at rest next to each other with synchronized clocks. A and B's accelerations were totally symmetric in the unprimed frame F where they started out both at rest at position x=12.5, and C and D's accelerations were totally symmetric in the primed frame F' where they started out both at rest at position x'=7.5. Of course since C and D stopped accelerating simultaneously in the primed frame F' (at time t'=-12 in F'), they stopped accelerating at different times in the unprimed frame F which I had used to describe their x(t) and T(t) functions, but surely your criteria for "symmetrical accelerations" is just that there is ONE specific frame where all their proper accelerations are simultaneous, namely the frame where they started out at rest and next to each other with synchronized clocks? Assuming that's your criteria, then F' is that one specific frame for C and D (and note that according to relativity, C and D's proper times T also remain synchronized in frame F' at all coordinate times), and F is that one specific frame for A and B (and A and B's proper times T also remain synchronized in F at all coordinate times). > > The only way to ensure the accelerations are symmetric is for both A and B > to have the same proper accelerations at the same proper times AFTER they > synchronize clocks. Are you doing that? If not you are not using MY method. > Yes, I was doing that. In my example I said that in the unprimed frame F, "A and B were originally at rest at position x=12.5, with both having the same ages, and let's say that their proper time clocks have been set to read T = -18 years at the moment they were born". Since they were right next to each other with the same ages and their proper time clocks both showing a time that's just their age minus 18, naturally their clocks were originally synchronized. Then they accelerated in a completely symmetrical way in frame F, with all changes in acceleration being simultaneous in F, including the event of their both ceasing their acceleration and coming to rest again in F, which happened at t=-12 in F. > > Also you seem to be switching from synchronized proper clocks which I > assumed did NOT reflect actual ages to ACTUAL AGES which doesn't work. > I assumed that A and B were both born at the same time and place, and that the custom in their society is to set their clocks to T=-18 at birth, so their clocks show the amount of time until (or since) they reach voting age. And I assumed exactly the same was true for C and D. So as long as their clocks travel with them, there is no ambiguity; the time T on their clock at a given point on their worldline is ALWAYS just their age minus 18. Does this satisfy you that identical T values for A and B will be simultaneous in p-time, and likewise identical T values for C and D will be simultaneous in p-time? 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 [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/groups/opt_out.
