Ralph Rabbidge aka Henry Wilson has asked for the math of LET

First of all, it was Larmor who first came up with the Lorentz
transform. However, one of these two observers must be the absolute
frame of reference. That was 1897 or 1898 time frame. This version
should be called Larmor’s transform to avoid later confusions.
shrug

Writing down two Larmor’s transforms:

** #1 and #0 observe #2.
** #3 and #0 observe #2.

We get the following transform for #1 and #0 observing #2:

** dx12 = (dx02 - B01 c dt0) / sqrt(1 – B01^2)
** dy12 = dy02
** dz12 = dz02
** dt1 = (dt0 – B01 dx02 / c) / sqrt(1 – B01^2)

Where

** B01 c = speed of #1 as observed by #0

Or its reciprocal of the same transform:

** dx02 = (dx12 + B01 c dt1) / sqrt(1 – B01^2)
** dy02 = dy12
** dz02 = dz12
** dt0 = (dt1 + B01 dx12 / c) / sqrt(1 – B01^2)

And the following transform for #3 and #0 observing #2:

** dx32 = (dx02 - B03 c dt0) / sqrt(1 – B03^2)
** dy32 = dy02
** dz32 = dz02
** dt3 = (dt0 – B03 dx02 / c) / sqrt(1 – B03^2)

Or its reciprocal of the same transform:

** dx02 = (dx32 + B03 c dt3) / sqrt(1 – B03^2)
** dy02 = dy32
** dz02 = dz32
** dt0 = (dt3 + B03 dx32 / c) / sqrt(1 – B03^2)

In 1905 a few months before the monumental publications of Einstein
the nitwit, the plagiarist, and the liar, it was Poincare who first
combined the above transforms into a single one where any reference to
#0 can be eliminated by introducing B13 for example. The result is
what he would call the Lorentz transform. He’ll leave it as a
homework exercise for those interested to do so. shrug

So far so good, right? Larmor’s transform turns out to the Lorentz
transform all along. Relativity rules, and there is no way to detect
the absolute frame of reference, right? Wrong! shrug

Notice with the above analysis, both #1 and #3 are moving in
parallel. What if they are not? To answer this question, you need to
write Larmor’s transform where #1 is moving in any arbitrary
direction:


** d[s12] = d[s02] + [B01] ([B01] * [B02] / (1 + sqrt(1 – B01^2))
- c dt0) / sqrt(1 – B01^2)

** dt1 = (dt - [B01] * d[s02]) / sqrt(1 – B01^2)

Where

** d[s] = Displacement vector
** [b] c = Velocity
** [] * [] = Dot product of two vectors

Then, write down the transform of #3 and #0 observing #2, combine the
two transforms similar to what Poincare did, and see if any references
to the absolute frame vanish. If it does, the Lorentz transform is
valid. If not, the Lorentz transform is not mathematically
consistent. It is a fantasy that does not represent anything real
life. It is a manifestation of mathematical mistake, and 100 years of
physics have developed based on that mathematical mistake. shrug

You will be surprised as I was totally shocked a few years ago. The
demystification of special relativity must be done sooner or later.
shrug