Memorandum For The Record
On Star Ship Navigation
J: I was wrong when I said there was nothing new to learn about the
"Twin Paradox", but the new insight has nothing to do with Zielinski's
original thesis here. I correct my original error of 2^-1/2 that should
not have been in the frame-invariant formula, and show that it is
possible, from L2's accumulated proper time at the end of the mission,
to calculate the precise point in L2's world line when he fires his
rocket engine to do the turn-about.
Minkowski Diagram is L1|>L2 i.e. fig 3 p.73 W. Pauli "The Theory of
Relativity" Dover Paper
On Feb 22, 2005, at 8:58 PM, wrote:
Jack Sarfatti wrote:
Z: "I am saying this is due to inconsistent synchronization of clock A
events in the non-geodesic frame of clock B."
J: Meaningless. OK, show how your alternative method works for the GPS
system?
Z: "By this I simply mean that the synchronization of clock A events in
the rest frame of clock B changes when you change matching GIFs at the
turnaround."
J: This is meaningless. Show exactly what you mean. Give precise
operational procedures. I have no idea of what you are talking about.
Also you failed to catch my low-level algebra error. The correct formula
in Pauli's fig 3 has no 2^-1/2 it's simply
s(L2) = [1 - (v/c)^2]^1/2s(L1)
Now what happens if L2 turns around at time t/n, n = 3, 4, .... rather
than at t/2?
Also the "kink" in L2's world line means infinite acceleration for zero
time, an impulse approximation that allows us to use SR and neglect GR
time dilation correction from the inertial force in L2's non-inertial
frame in the turn-around.
Z: "Obviously it must, since in SR event synchronization depends on the
observer's GIF."
J: Problem for general n. In inertial rest frame of L1 that stays same
in entire history, unlike rest frame of L2 that fires rockets in outer
space to turn about
vt/n = ut(1 - 1/n)
u is slower speed on return lap of L2 in order to reach L1 in same time
t for any choice of n.
Therefore outward bound
s(L2 out)^2 = (ct/n)^2 - (vt/n)^2
Inward bound
s(L2 in)^2 = (ct/n)^2(n - 1)^2 - (vt/n)^2
s(L2) = (ct/n){[(n - 1)^2 - (v/c)^2]^1/2 + [1 - (v/c)^2]^1/2}
= s(L1){[(n - 1)^2 - (v/c)^2]^1/2 + [1 - (v/c)^2]^1/2}/n
Note that when n = 2
{[(n - 1)^2 - (v/c)^2]^1/2 + [1 - (v/c)^2]^1/2}/n = [1 - (v/c)^2]
.
|
