On Tue, Mar 4, 2014 at 5:45 PM, Jesse Mazer <laserma...@gmail.com> wrote:
> > > I promise you the example has nothing to do with any frames other than the > ones in which each pair is at rest. Again, the only assumptions about > p-time that I make in deriving the contradiction are: > > ASSUMPTION 1. If two observers are at rest in the same inertial frame, > then events on their worldlines that are simultaneous in their rest frame > are also simultaneous in p-time > > ASSUMPTION 2. If two observers cross paths at a single point in spacetime > P, and observer #1's proper time at P is T1 while observer #2's proper time > at P is T2, then the event of observer #1's clock showing T1 is > simultaneous in p-time with the event of observer #2's clock showing T2. > > ASSUMPTION 3. p-time simultaneity is transitive > > That's it! I make no other assumptions about p-time simultaneity. But if > you want to actually see how the contradiction is derived, there's really > no shortcut besides looking at the math. If you are willing to do that, can > we just start with the last 2 questions I asked about the scenario? Here's > what I asked again, with a few cosmetic modifications: > > Please have another look at the specific numbers I gave for x(t), > coordinate position as a function of coordinate time, and T(t), proper time > as a function of coordinate time, for each observer (expressed using the > inertial frame where A and B are at rest, and C and D are moving at 0.8c), > and then tell me if you agree or disagree with the following two statements: > > For A: x(t) = 25, T(t) = t > For B: x(t) = 0, T(t) = t > For C: x(t) = 0.8c * t, T(t) = 0.6*t > For D: x(t) = [0.8c * t] + 9, T(t) = 0.6*t - 12 > > --given the x(t) functions for B and C, we can see that they both pass > through the point in spacetime with coordinates x=0, t=0. Given their T(t) > functions, we can see that B has a proper time T=0 at those coordinates, > and C also has a proper time T=0 at those coordinates. Therefore, by > ASSUMPTION 1 above, the event of B's proper time clock reading T=0 is > simultaneous in p-time with the event of C's proper time clock reading T=0. > Agree or disagree? > > --given the x(t) functions for A and D, we can see that they both pass > through the point in spacetime with coordinates x=25, t=20. Given their > T(t) functions, we can see that A has a proper time T=20 at those > coordinates, and D has a proper time T=0 at those coordinates. Therefore, > by ASSUMPTION 1 above, the event of A's proper time clock reading T=20 is > simultaneous in p-time with the event of D's proper time clock reading T=0. > Agree or disagree? > Another little correction--in the last two paragraphs there, where I said "Therefore, by ASSUMPTION 1 above", I should have written "ASSUMPTION 2", since in both cases I was deriving p-time simultaneity from the fact that two clock readings happened at the same point in spacetime. 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 email@example.com. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/groups/opt_out.