On Tue, Mar 4, 2014 at 5:45 PM, Jesse Mazer <[email protected]> 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 [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.
