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Re: Simplified Twin Paradox Resolution.
Posted:
Jan 7, 2013 1:28 AM
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On Jan 6, 5:47 am, "Paul B. Andersen" <some...@somewhere.no> wrote:
> On 6/01/2013 3:59 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>
>
> > - - -
>
> > 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 co-exist is when B^2 = 0.
> > Thus, the twins? paradox is very real under the Lorentz transform.
> > <shrug>
> It's a variant of the old Dingle argument,
> @t1/@t2 = @t2/@t1 is a contradiction.
> (@ = partial derivative)
>
> See: http://tinyurl.com/ah3ctmm
>
> Koobee's response: http://tinyurl.com/a9jkwxp
> <<
> What Koobee Wublee wrote that you have quoted was an application of
> the Lorentz transform in a specific scenario. You don?t understand
> all that, and apparently, you don?t know what you are talking about as
> usual. It is laughable that a college professor from the University
> of Trondheim would attempt to swindle his way out using irrelevant,
> bullshit claims. <shrug>
>
> You are cornered. Why don?t you stay in the topic of discussion?
> <shrug>
> >>
Excellent documentations, paul. When you are plagued with these
embarrassing blunders, at least, you have a skill in good
documentations. Koobee Wublee is indeed very grateful that you are
able to document His great posts. Seriously, paul. All that good
documentations still did not save you from that job in the private
industry, did it? When someone charging in claiming a Doppler shift
in 10^-8 should be seriously considered in adjusting the carrier
frequencies for compensations, the management just have to do the best
for either parties. :-)
By the way, Koobee Wublee never uses the partial derivative like what
you have done. dt still basically the rate of time flow when
comparing two observers. Thus, total derivative has to be
considered. <shrug>
Or better yet, if you are still confused with the Lorentz transform,
why don?t you look into the equations describing Minkowski spacetime
which Koobee Wublee has included in this post? That should leave no
confusion about what Dingle had to say was actually visionary. Well,
not quite. The stuff is so simple that it is a big surprise when all
the so-called bright minds in the scientific communities have so much
trouble understanding. What a shame, no? <shrug>
> His arguments were as lethal and to the point as always. :-)
You bet, paul. Glad you are finding amusement amid these gross
blunders of yours. In doing so, you started personal attacks. Not
until Koobee Wublee pointed out to you, you have now calmed down. By
the way, have you finished the JAVA applet yet with the twins
traveling using the exact same acceleration profile? Please also
leave an adjustable coasting time with no acceleration in the
program. <please and thanks in advance>
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