
Re: Simplified Twin Paradox Resolution.
Posted:
Jan 4, 2013 1:03 AM


On Jan 3, 5:52 pm, Sylvia Else <syl...@not.at.this.address> wrote:
> Instead, on Earth there is a clock and a camcorder with a very powerful > telescopic lens and a tranceiver There is also a spacecraft travelling > at velocity v towards Earth, similarly equipped. For simplicity, we > treat Earth + clock + camcorder + transceivers as a single point. > Similarly for the spacecraft. > > After some time T in its own frame, the spacecraft encounters a most > similar spacecraft headed towards Earth at velocity v relative to Earth. > As they pass, the first spacecraft transmits its entire camcorder > recording to the second spacecraft, and the second spacecraft's clock is > set to the value shown by the first spacecraft's clock. The camcorder on > the second spacecraft then starts recording, continuing the recording it > just received.
Instead of v, let?s say (B = v / c) for simplicity. The earth is Point #0, outbound spacecraft is Point #1, and inbound spacecraft is Point #2.
According to the Lorentz transform, relative speeds are:
** B_00^2 = 0, speed of #0 as observed by #0 ** B_01^2 = B^2, speed of #1 as observed by #0 ** B_02^2 = B^2, speed of #2 as observed by #0
** B_10^2 = B^2, speed of #0 as observed by #1 ** B_11^2 = 0, speed of #1 as observed by #1 ** B_12^2 = 4 B^2 / (1 ? B^2), speed of #2 as observed by #1
** B_20^2 = B^2, speed of #0 as observed by #2 ** B_21^2 = 4 B^2 / (1 ? B^2), speed of #1 as observed by #2 ** B_22^2 = 0, speed of #2 as observed by #2
When Point #0 is observed by all, the Minkowski spacetime (divided by c^2) is:
** dt_00^2 (1 ? B_00^2) = dt_10^2 (1 ? B_10^2) = dt_20^2 (1 ? B_20^2)
When Point #1 is observed by all, the Minkowski spacetime (divided by c^2) is:
** dt_01^2 (1 ? B_01^2) = dt_11^2 (1 ? B_11^2) = dt_21^2 (1 ? B_21^2)
When Point #2 is observed by all, the Minkowski spacetime (divided by c^2) is:
** dt_02^2 (1 ? B_02^2) = dt_12^2 (1 ? B_12^2) = dt_22^2 (1 ? B_22^2)
Where
** dt_00 = Local rate of time flow at Point #0 ** dt_01 = Rate of time flow at #1 as observed by #0 ** dt_02 = Rate of time flow at #2 as observed by #0
** dt_10 = Rate of time flow at #0 as observed by #1 ** dt_11 = Local rate of time flow at Point #1 ** dt_12 = Rate of time flow at #2 as observed by #1
** dt_20 = Rate of time flow at #0 as observed by #2 ** dt_21 = Rate of time flow at #1 as observed by #2 ** dt_22 = Local rate of time flow at Point #2
So, with all the pertinent variables identified, the contradiction of the twins? paradox is glaring right at anyone with a thinking brain. <shrug>
Did PD get it right?
> [snipped garbage]
Of course not, what do you expect from an Einstein Dingleberry? <shrug>
After abandoning the projection crap, is Tom very busy trying to find an excuse to resolve this through projection again? Koobee Wublee is not surprised since Tom has already decided SR as a valid hypothesis despite lack of any professional validations. <shrug>
POINT BLANK IN YOUR FACES, PD, PAUL (ANDERSEN), AND TOM (ROBERTS)! <shrug>

