
Re: Simplified Twin Paradox Resolution.
Posted:
Jan 4, 2013 2:10 AM


On 4/01/2013 5:03 PM, Koobee Wublee wrote: > 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>
Prove it. Show that you can properly derive an equation that is manifestly false.
Sylvia.

