Jesse, OK, I'm back...
Let me back up a minute and ask you a couple of general questions with respect to establishing which past clock times of different observers were simultaneous in p-time.... The only clocks in this example are the real actual ages of two twins.... 1. Do you agree that each twin always has a real actual age defined as how old he actually is (to himself)? Yes or no? 2. Do you agree that this real actual age corresponds by definition to the moment of his actually being alive, to his actual current point in time? (As a block universe believer you can just take this as perception or perspective rather than actuality if you wish - it won't affect the discussion). Yes or no? Now assume a relativistic trip that separates the twins.... 3. Do you agree that IF, for every point of the trip, we can always determine what ACTUAL age of one twin corresponds to the ACTUAL age of the other twin, and always in a way that both twins AGREE upon (that is frame independent), that those 1:1 correspondences in actual ages, whatever they are, must occur at the same actual times? That this would give us a method to determine what (possibly different) actual ages occur at the same actual p-time moment in which the twins are actually alive with those (possibly different) actual ages? Yes or no? Edgar On Friday, February 14, 2014 3:05:13 PM UTC-5, jessem wrote: > > > > On Thu, Feb 13, 2014 at 9:37 PM, Jesse Mazer <laser...@gmail.com<javascript:> > > wrote: > >> >> Do t and t' refer to proper times for A and B (defined only along each >> one's worldline), or coordinate times in the rest frame of A and B >> (coordinate times have a well-defined value for arbitrary events, and will >> agree with the proper time for the observer that's at rest in whichever >> coordinate system we're talking about)? If proper time, I don't know what >> you mean by "relationship between those variables", unless you're just >> talking about what pairs of readings are simultaneous in each frame. If >> coordinate time, then my answer is yes--the relationship between the >> coordinate time of an event in one system and the coordinate time of the >> same event in another system is just given by the Lorentz transformation >> equations for time: >> >> t' = gamma*(t - (vx/c^2)) >> t = gamma*(t' + (vx/c^2)) >> >> where gamma = 1/sqrt(1 - (v/c)^2), and v is the velocity of B's frame as >> measured in A's frame (with the assumption that we set up our coordinate >> axes so that B is moving along A's x-axis). >> > > > Small correction, the unprimed x in the second equations was meant to be > an x', i.e. the position coordinate of the event in the B's frame: > > t = gamma*(t' + (vx'/c^2)) > > And here's the corresponding Lorentz equations relating the position > coordinate assigned to a single event by the each of the two frames: > > x' = gamma*(x - vt) > x = gamma*(x' + vt') > > Incidentally, I'm going to be away this weekend but if you have time to > continue the discussion in the next couple days by responding to the post I > quoted above (and also to the post at > https://groups.google.com/d/msg/everything-list/jFX-wTm_E_Q/xtjSyxxi4awJif > possible, especially my questions at the end of that post about the > meaning of "same point in spacetime"), I can get back to you by early next > week. > > 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. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/groups/opt_out.
