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Paul B. Andersen wrote:So you can claim what the Lorentz transform predicts for
the twin paradox, but can you apply the Lorentz transform to prove
that you are right?
Consider the following thought experiment:
Given an inertial frame K with coordinates [t, x]. (y = z = 0)
Twin A stays stationary at x = 0 in K, while twin B starts from
x = 0 when A’s clock shows 0 and travels at the constant speed v
to x = L, where she turns abruptly around with a brief, very high acceleration for a very short time, and thereafter travels back
to x = 0 at the constant speed v.
She is back at the time T as measured in K.
Since twin A is stationary in K, her proper time when twin B is
back will be τA = T.
If K'[t',x'] is moving along the positive x axis of K[]
The Lorentz transform is:
t' = γ(t - (v/c²)x)
x' = γ(x - vt)
inverse:
t = γ(t' + (v/c²)x')
x = γ(x' + vt')
γ = √(1 − v²/c²)
The challenge is:
Show what the LT predicts the proper time of B
is perceived to be τB = T.
You are free to use as many frames of reference you might wish.
SIMPLY PUT:Quite. Time dilation between two inertial human biological entities.
You have TWO reference frames (E and E'), which have a DIFFERENTIAL
SPEED OF v. For SR, as it was installed since 1906, the COMMON SPEED of
both frames IS IRRELEVANT (it could be 1,500 times v).
You have TWO imaginary observers at E and E' origins, pretending that
they are 100% human biological entities.
Relativism SAYS that there is TIME DILATION WITH INERTIAL MOTION, and
the choice of any reference frames is IRRELEVANT.
CHOICE ONE: You select E as the frame AT RELATIVE REST compared with E',A bit awkward put, but OK. (REMOTE TIME?)
which is moving far away at speed v. THEN, the humanoid at E PERCEIVES
that the REMOTE TIME for the other humanoid at E' is RUNNING SLOWER THAN
HIS. So, the humanoid at E BELIEVES that the bastard at E' IS AGING MORE
SLOWLY THAN HIM.
CHOICE TWO: Adopt E' as being at RELATIVE REST. Then it's E the frameOK. E' is stationary in an inertial frame.
that is moving away at !v! speed. Relativists claim that TIME DILATION
is going ON over the frame E, and now is the humanoid at E' who says: I
PERCEIVE that time at E is running slower than mine, so the bastard at E
is AGING SLOWER THAN ME!
The PARADOX, explained without using ANY STUPID FORMULA, is that bothQuite.
humanoids PERCEIVE THAT THE OTHER IS AGING SLOWER.
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