| 20 |
...One
considers a particle. If we move off at distance c and observe it, when
cruising at velocity v , everything looks as if, conversely, the particle
was orbiting around the observer, at velocity v and distance d (radial
distance r).
(286)
Now we have to explain
what is the "passage" f = m [ c - v Dt ].
It simply vanishes
when c = v Dt , i.e. when we link
the velocity v to the combined space-translation c and time
translation DDt.
(287)
Let us return to the
Poincaré's momentum, written in a system of coordinates, the the passage
f is zero :
(288)
...A
particle as a peculiar choice of the momtum's components, which depend on
the chosen systel of coordinates. There is always a peculiar system of coordinates
in which the passage f becomes zero, and in which the impulsion vector
p may reduce to a single component (for an example z-movement).
(289)
Then the object described
by the Poincaré's group corresponds to :
-
An energy E
-
An impulsion p
-
A proper spin l
...A
spin is a mass multiplied by a length and by a velocity. Then its dimension
is M L2 T-1 . It is the dimension of the Planck constant
(289b)
...The
geometric quantification, developped by J.M.Souriau ( See Structure des Systèmes
Dynamiques, Dunod 1983, or Structure of Dynamical Systems, Birkhauser Ed,
1997 ) shows that proper spin must be equal to :
(289b)
multiplied by n/2, n
being an integer. The proper spin s is unity for photon and is equal to1/2
for proton, neutron, electron and neutrinos and the corresponding antiparticles.
.
The photon.
...We
get two distinct photons, which own distinct helicities, right and left, event
if they cruise along the same direction, with the same energy.
(290)
The Energy Eand the
impulsion p of a photon are not independent quantities :
(291)
E = h
n
which gives :
(292)
...Besides
these characteristics (energy, path, helicity) the photon owns no more ones.
In particular it owns no "charge". In other terms we can consider that all
its charges are zero. So that the photon is identical to its anti-particle
(for + zero = - zero).
Index Dynamic Groups Theory