Re: Incorrect mathematical integration

On Thu, 25 Jul 2024 20:30:09 +0000, Richard Hachel wrote:

>
In the case you are proposing, there is no contraction of the distances,
because the particle is heading TOWARDS its receptor.
>
The equation is no longer D'=D.sqrt(1-Vo²/c²) and to believe this is to
fall into the trap of ease, but D'=D.sqrt[(1+Vo/c)/ (1-Vo/c)] since
cosµ=-1.

You are conflating Doppler effect with length contraction.  LC is ALWAYS
D'=D.sqrt(1-Vo²/c²).

For the particle the distance to travel (or rather that the receiver
travels towards it) is extraordinarily greater than in the laboratory
reference frame.
>
R.H.

Your assertion is in violent disagreement with the LTE:
dx' = gamma(dx - vdt)
dt' = gamma(dt - vdx)
For an object stationary in the unprimed frame, dx = 0:
dx' = gamma(-vdt)
dt' = gamma(dt)
v' = dx'/dt' = -v
For an object moving at v in the unprimed frame, dx' = 0
v = dx/dt = v.
There is no "extraordinarily greater" speed in either frame.  This
is true in Galilean motion also.  Galileo described it perfectly
with his ship and dock example and blows your assertion out of the
water, so to speak.