On Jan 6, 5:47 am, "Paul B. Andersen" 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 a
** 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,
bull**** 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