3 The Dirac Electron and Basic Physical Concepts
63
electron, the metastable hydrogenoid species positronium (τ ∼ 0.1 ns) would be
viewed as a couple of oppositely charged vortices rotating around a barycentre. As
in hydrodynamics, the two vortices would attract each other if they spin in the same
direction and eventually merge into a single vortex, which would be our compound
photon (in fact, both para and ortho positronium decay into several lower-energy
photons). There results a charge oscillating along an axis orthogonal to the motion [22], generating an electromagnetic field.
Thus, Zitterbewegung is what relates a real electron and a virtual positron, their
mass and spin being linked by a wave beat between the two states; positronium is
a Bohr-like structure associating a real electron and a real positron, with resulting
spin S = 0/1; and a photon is what results for S = 1 when the fermion pair merges.
3.4 Rest Mass and Spin Motion
The essential idea in this paper is that the rest mass of the electron stems from the
spinning motion of a massless charge at light speed, in a confined region defined
by the Compton radius. That a mass may stem from motion already appears in the
increase of inertial mass with increasing speed: m v = m 0 /(1 − v 2 /c 2 ) 1/2 . And that
a massless entity moving at light speed may display mass properties also appears in
the photon showing kinetic momentum: p = h/λ (e.g. in the Compton effect) and
gravitational mass: m = p/c (e.g. in a Mössbauer shift).
Rewording in classical terms the interpretation of Zitterbewegung resulting from
Eq. (3.19), one may say that the intrinsic orbit (Sect. 3.3), which defines the ‘internal
structure’ of the electron, is described at velocity c, whereas the external orbit, in
an atom for instance, is described at velocity v. This makes it necessary to consider
that the charged entity describing the intrinsic orbit has zero rest mass. The rest
mass observed with respect to an external body, such as an atomic nucleus, must
then arise from the intrinsic motion of the charged entity at velocity c.
Rest mass induction by space confinement also holds for massless bosons like
photons. It has been shown [39, 47] that photons trapped in optical resonators acquire mass properties similar to those of fermions. For a similar reason, light trapped
on the photon sphere of a black hole or a neutron star acquires a rest mass much
larger than that resulting from the finite size of the Universe, R U ∼ 1.3 × 10 26 m.
Its total energy would be given by:
E
2
= m
2
0 c
4
+ p
2 c
2
=
2 c
2 /4r
2
C +
2 ω
2 .
(3.30)
For a blue radiation (λ ∼ 4.10 −7 m) trapped around a stellar black hole (M ∼
2.10 31 kg, R ∼ 3.10 4 m), the ratio of the two contributions in Eq. (3.30) would
be: E 1 /E 2 ∼ 10 −12 .
However, a rest mass induced by a confined motion must draw its energy from an
immaterial source which, for a massless charge, should be an electromagnetic field
(A 4 , A). For immaterial particles, the expression for the energy reduces to: E = p ·c.
For photons, one has: p = h/λ, yielding: E = hν. For a spinning charge, one would
63
electron, the metastable hydrogenoid species positronium (τ ∼ 0.1 ns) would be
viewed as a couple of oppositely charged vortices rotating around a barycentre. As
in hydrodynamics, the two vortices would attract each other if they spin in the same
direction and eventually merge into a single vortex, which would be our compound
photon (in fact, both para and ortho positronium decay into several lower-energy
photons). There results a charge oscillating along an axis orthogonal to the motion [22], generating an electromagnetic field.
Thus, Zitterbewegung is what relates a real electron and a virtual positron, their
mass and spin being linked by a wave beat between the two states; positronium is
a Bohr-like structure associating a real electron and a real positron, with resulting
spin S = 0/1; and a photon is what results for S = 1 when the fermion pair merges.
3.4 Rest Mass and Spin Motion
The essential idea in this paper is that the rest mass of the electron stems from the
spinning motion of a massless charge at light speed, in a confined region defined
by the Compton radius. That a mass may stem from motion already appears in the
increase of inertial mass with increasing speed: m v = m 0 /(1 − v 2 /c 2 ) 1/2 . And that
a massless entity moving at light speed may display mass properties also appears in
the photon showing kinetic momentum: p = h/λ (e.g. in the Compton effect) and
gravitational mass: m = p/c (e.g. in a Mössbauer shift).
Rewording in classical terms the interpretation of Zitterbewegung resulting from
Eq. (3.19), one may say that the intrinsic orbit (Sect. 3.3), which defines the ‘internal
structure’ of the electron, is described at velocity c, whereas the external orbit, in
an atom for instance, is described at velocity v. This makes it necessary to consider
that the charged entity describing the intrinsic orbit has zero rest mass. The rest
mass observed with respect to an external body, such as an atomic nucleus, must
then arise from the intrinsic motion of the charged entity at velocity c.
Rest mass induction by space confinement also holds for massless bosons like
photons. It has been shown [39, 47] that photons trapped in optical resonators acquire mass properties similar to those of fermions. For a similar reason, light trapped
on the photon sphere of a black hole or a neutron star acquires a rest mass much
larger than that resulting from the finite size of the Universe, R U ∼ 1.3 × 10 26 m.
Its total energy would be given by:
E
2
= m
2
0 c
4
+ p
2 c
2
=
2 c
2 /4r
2
C +
2 ω
2 .
(3.30)
For a blue radiation (λ ∼ 4.10 −7 m) trapped around a stellar black hole (M ∼
2.10 31 kg, R ∼ 3.10 4 m), the ratio of the two contributions in Eq. (3.30) would
be: E 1 /E 2 ∼ 10 −12 .
However, a rest mass induced by a confined motion must draw its energy from an
immaterial source which, for a massless charge, should be an electromagnetic field
(A 4 , A). For immaterial particles, the expression for the energy reduces to: E = p ·c.
For photons, one has: p = h/λ, yielding: E = hν. For a spinning charge, one would