Bookmark 8: Free motion of the Dirac particle with a constant CM velocity
v
z
=0.1 along OZ axis, and the CM spin orientation is θ=180∘ and ϕ=45∘. In the right hand side we see the zitter motion of the CC (blue) and the CM trajectory (dotted red). The two components of the angular velocity
ω
p
and
ω
u
(magenta), are also drawn. The component
ω
u
has in this case the same direction than the velocity of the CC
u
, because the angle α between the vector
ω
p
and the velocity
v
, formula (36), is α<π/2.

13. Dirac Hamiltonian


14. Natural Units


15. The Internal frequency of the electron


16. Time dilation

The time of an electron can be understood as its period, the time it takes the Center of Charge to complete a turn, adding a tick to its clock for each completed turn.If the CM is moving (
v
>0) its internal frequency decreases.When the particle is moving with a velocity
v
, like in the Bookmark 9 below along the Y axis, the velocity of the CC
u
=
u

+
u
⟂
has a longitudinal component
u
y
=
u

=
v
and a transversal component
u
⟂
, that as 
u
= c, is 
u
⟂
=
2
c
-
2
v
​Then the component 
u
⟂
, which is the one making the CC turn is always 
u
⟂
⩽ c. It takes more time to complete a cycle, the moving clock goes slowly, and more slowly as
v
increases.The time
T
0
of the motion of the CC when the CM is at rest during a zitter turn is
T
0
=
2π
R
0
c
=
πℏ
2
mc
= 4.05 ×
-21
10
s Now the period, the time taken during a turn is T(
v
)=
2π
R
0
u
⟂
=γ(
v
)
T
0
​​