From Osher Doctorow
Here E_2 or E2 is the tachyonic particle's energy, the subscript 2
(also indicated as in m2) referring to the tachyon, m to mass, and a
particle of (regular) mass M decays into a regular particle of mass m1
and a tachyon of mass parameter m2, with R2 being the phase space
factor (the threshold being for R2 if the threshold exists).
I should mention that the equation for E_2 or E2 of last time actually
involves PI (Probable Causation/Influence) with the addition of m2
beta gamma to all sides, so that we get:
1) E2 + m2 beta gamma = (M^2 - m1^2 - m2^2)/2M + m2 beta gamma > = 0
and dividing all sides by M or M/2 yields:
2) 2(E2 + m2 beta gamma)/M = (M^2 - m1^2 - m2^2)/M^2 + 2m2 beta gamma/
M > = 0
and now the "center" term is:
3) 1 - m1^2/M^2 - m2^2/M^2 + 2(m2/M)beta gamma
which has the required form 1 - x + y of PI with the obvious
definitions of x and y.
An inequality in the opposite direction for an upper bound is obtained
also, which I'll try to discuss later.
The author's (Radzikowsky's) Ph.D. thesis at Princeton University
(1992) was on Axiomatic Quantum Field Theory (AQFT) on curved
spacetime, and he thanks the algebraist A. S. Wightman of Princeton
and also K. Fredenhagen for in slightly different language stimulating
his research in tachyons.
This paper provides indirect support for Chodos, Hauser, and
Kostelecky's Phys. Lett. B 150: 431-435, 1985 paper with its
tachyonic neutrino hypothesis which Hughes and Stephenson were
"clearly" attempting to refute in their 1990 paper in Phys. Lett. B
244: 95, 1990.
Osher Doctorow
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