Biomedical Engineering Reference
In-Depth Information
dilations are real effects rather than 'hidden' variables. According to
SFT relativity involves both the internal and the external motions
of the photon. Relativity sees all space as expanding since the
big bang. According to SFT this is incorrect and only the external
distance must be considered, not the internal or hidden distance.
Thus there may be a central point in space-time corresponding
to the big bang; there is no reason to assume it has moved. In
1905, Einstein via the photoelectric effect observed that radiation
itself, not just its frequency, acted as discrete quanta or particles of
energy
E
/
h
ν
termed photons. Bohr, recognising the Plank-Einstein
=
ν
equation
E
held for emitted and absorbed energy, proposed a
quantum theory of atomic spectroscopy in which angular momenta
were whole numbers of Planck's quantum
h
=
/
π
. Over the next
two decades the methods of quantum theory evolved via Bohr's
classical theory of the atom as a heuristic eigenvalue method based
on examiningtheLagrangian associated witha singleparticle.
The history of QFT began with the evolution of Schrodinger's
non-relativisticequationtoDirac'srelativisticequation.Schrodinger
expressed the phase of a plane wave as a complex factor, Eq. (2.2a).
The Klein-Gordon equation, Eq. (2.2b), is a relativistic version of
Schrodinger's equation. Using Feynman notation, Eq. (2.2c), we see
how the Klein-Gordon equation can be analytically factorised to
yieldthepositiveandnegativeenergyversionsoftheDiracequation,
Eq.(2.2d),wherethe
γ
μ
are4
×
4bi-spinorsofmathematicalnature.
Thus Dirac predicted the electron's anti-particle, the positron.
Although Dirac's equation is first-order it is derived from a second-
order wave equation, and it is this that demands gauge symmetry
and invarianceunder conformaltransformations.
i
∂
h
2
H
∂
t
(
x
,
t
)
=
(
x
,
t
)
(2.2a)
m
2
c
2
2
∇
+
ψ
(
r
)
=
0
(2.2b)
2
∂
m
2
ψ
=
2
+
0
→
(
i
∂
+
m
)(
i
∂
−
m
)
ψ
=
0
(2.2c)
γ
μ
∂
μ
+
im
γ
μ
∂
μ
−
im
ψ
=
0
(2.2d)
