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