
Re: Simplified Twin Paradox Resolution.
Posted:
Jan 6, 2013 6:43 PM


On 7/01/2013 1:25 AM, Vilas Tamhane wrote: > On Jan 6, 11:23 am, Sylvia Else <syl...@not.at.this.address> wrote: >> On 6/01/2013 3:59 PM, Koobee Wublee wrote: >> >> >> >> >> >> >> >> >> >>> On Jan 5, 5:57 pm, Sylvia Else wrote: >>>> On 5/01/2013 5:59 AM, 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> >> >>>> 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. >> >>> PD, are you turning into a troll now? For the n?th time, the >>> following is one such presentation of mathematics that show the >>> contradiction in the twins? paradox. >> >>>    >> >>> From the Lorentz transformations, you can write down the following >>> equation per Minkowski spacetime. Points #1, #2, and #3 are >>> observers. They are observing the same target. >> >>> ** c^2 dt1^2 ? ds1^2 = c^2 dt2^2 ? ds2^2 = c^2 dt3^2 ? ds3^2 >> >>> Where >> >>> ** dt1 = Time flow at Point #1 >>> ** dt2 = Time flow at Point #2 >>> ** dt3 = Time flow at Point #3 >> >>> ** ds1 = Observed target displacement segment by #1 >>> ** ds2 = Observed target displacement segment by #2 >>> ** ds3 = Observed target displacement segment by #3 >> >>> The above spacetime equation can also be written as follows. >> >>> ** dt1^2 (1 ? B1^2) = dt2^2 (1 ? B2^2) = dt3^2 (1 ? B3^2) >> >>> Where >> >>> ** B^2 = (ds/dt)^2 / c^2 >> >>> When #1 is observing #2, the following equation can be deduced from >>> the equation above. >> >>> ** dt1^2 (1 ? B1^2) = dt2^2 . . . (1) >> >>> Where >> >>> ** B2^2 = 0, #2 is observing itself >> >>> Similarly, when #2 is observing #1, the following equation can be >>> deduced. >> >>> ** dt1^2 = dt2^2 (1 ? B2^2) . . . (2) >> >>> Where >> >>> ** B1^2 = 0, #1 is observing itself >> >>> According to relativity, the following must be true. >> >>> ** B1^2 = B2^2 >> >>> Thus, equations (1) and (2) become the following equations >>> respectively. >> >>> ** dt1^2 (1 ? B^2) = dt2^2 . . . (3) >>> ** dt2^2 = dt1^2 (1 ? B^2) . . . (4) >> >>> Where >> >>> ** B^2 = B1^2 = B2^2 >> >>> The only time the equations (3) and (4) can coexist is... >> >> ... never >> >> In deriving [1] and [2] you prefaced them with caveats about who is >> observing whom. So they relate to different measurement situations. You >> cannot combine them in any meaningful way. >> >> Sylvia. > > Nobody is observing anybody. Everybody has right to write down > equations. >
And then? Koobee is trying to show that the equations contain an inconsistency, which is to say, that they cannot be a description of any reality.
Sylvia.

