Re: Paper Series: Shift-symmetry in Einstein’s Universe

On Sat, 13 Jul 2024 20:17:32 +0000, Ross Finlayson wrote:

>
Hmm... so now some scientists, physicists, and mathematicians
(I hesitate to call them, "researchers") say they've written
a formalism where the superluminal or tachyonic isn't
imcompatible with Special Relativity, after all.
>
https://journals.aps.org/prd/abstract/10.1103/PhysRevD.110.015006

Just published last month, but the Figure 1 recalls the
"reinterpretation" "principle" (RIP) of Bilaniuk, Deshpanda
and Sudarshan -- which I call Rest In Peace.  Backward in
time was a BIG problem with RIP, which they endorsed to
solve the negative energy problem arising from the four-
momentum formalism: P' = eta P = gamma[E/c - pv/c, p - vE/c].
Unfortunately, p > E/c for tachyons, so for some values of
v/c, E' is negative.  BDS hypothesized that negative energy
meant the tachyon was traveling backward in time for certain
certain values of v and appeared to go in the opposite direction.
They didn't bother to look at the 3-momentum term which didn't
reverse under those conditions: p NEVER reverses sign in the 4MF.
The only credible conclusion is that the 4MF is not valid
when E' reverses sign.  This is confirmed by the fact
that if the basic equations
E = mc^2/sqrt(u^2/c^2 - 1)
p = mu/sqrt(u^2/c^2 - 1)
are valid then, by the first postulate,
E' = mc^2/sqrt(u'^2/c^2 - 1)
p' = mu'/sqrt(u'^2/c^2 - 1)
are also valid, and E' NEVER reverses sign over the full
range -infinity < u' < infinity!  This has been explained in
DOI: 10.13189/ujpa.2023.170101.
If you remember, DON'tknOw contended that the 4MF was a
"definition" and therefore inviolate, which, of course,
is the purest baloney since E' can be derived by applying
u = (u' + v)/(1 + uv/c^2) to E = mc^2/sqrt(u^2/c^2 - 1).
The problem with the 4MF when applied to tachyons is that
a quaint little mathematical rule gets violated when the
1 + uv/c^2 term goes negative.  BDS forgot about this and
thus RIP was born -- and died when it pointed out.
"Civilization advances by extending the number of important
operations which we can perform without thinking of them."
― Alfred North Whitehead
This adage has its limitations, particularly in physics.
One must make sure the tools still work when moving into
a new domain.