Biomedical Engineering Reference
In-Depth Information
Figure 1.3
The coupled spherical coordinate system at the electron's
electric and magnetic centres of motion, coupled via the ML equations.
The electron performs a combined motion consisting of two rotations, one
orbital and the othercyclotron.
In this form each of the two spinors refers to a centre of motion.
For an electron performing a double rotation around an orbital or E
field centre of rotation and a cyclotron or H field centre of rotation
(Fig. 1.3), its E andH fields can bewritten as
1
q
r
o
e
j
φ
o
r
=
E
(1.3)
4
πε
0
1
q
e
j
φ
c
ˆ
H
=
φ
c
(1.4)
πε
0
μ
0
θω
r
c
4
sin
There is a lot of mathematical history in Eqs. (1.1a-f), and we
shall briefly unpick a tiny part of it. Looking at Eqs. (1.1a-d) there
are three independent equations in four scalar unknowns. This
is in fact the Maxwellian basis of the quantum field equations,
which are normally posed as integral equations, a Lagrangian
formulation, which is basically symmetric and quadratic. At this
stage we cannot solve these equations in only one particle; they are
underconstrained—toomanyunknownsandnotenoughequations.
This is the reason for the probabilistic basis of quantum theory. In
this form the equations are incomplete. We need to examine pairs
of particles that can form a dynamic balance; to solve the equations
deterministically we need the added information in Eq. (1.1e). It is
thismathematicalrealitythatEinsteintriedtopointout.Despitethe
deafening silence of those who had formulated quantum theory he
