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Re: Simplified Twin Paradox Resolution.
Posted:
Jan 5, 2013 8:57 PM
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On 5/01/2013 5:59 AM, Koobee Wublee wrote:
> On Jan 3, 11:10 pm, PD as Sylvia Else wrote:
>> On 4/01/2013 5:03 PM, Koobee Wublee wrote:
>
>>> 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.
>
> Prove what, PD? The equation describing spacetime? If you have to
> ask, you are indeed a moron. It is a good thing that you are an ex-
> college-professor of physics. May God have mercy on your ex-
> students. <shrug>
>
It was I who wrote "Prove it".
You assert that there are a paradox. I take it you mean in the sense
that the theory gives two results for one situation, such that they are
impossible to reconcile.
I challenge you to show that mathematically, rather than just asserting
it. Do not just point at the maths above and claim that it's obvious.
Sylvia.
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