On Thu, Feb 13, 2014 at 9:37 PM, Jesse Mazer <[email protected]> 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/xtjSyxxi4awJ if 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 [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.
