Single-Particle Electrodynamics - Assassination Science

importantly, the hyperbolic tangent in the rate of polarisation, (6.154), is not
equivalent to the exponential rate of (6.141).
The difference between the classical and quantum field theoretical calculations
is most dramatic for a neutron initially polarised in the direction of
the field: the quantum result gives simply 1/τ TBK as the probability per unit
time of it flipping its spin; but the classical result (6.153) vanishes as the
polarisation approaches ±100%.
This behaviour can, in fact, be understood by recalling the assumptions
made as to the nature of the radiation being considered in each analysis.
A stationary neutron with its spin parallel to the magnetic field does not
precess; it merely sits there. Classically, if the neutron does not precess, and
its does not move, then it cannot possibly radiate, since it is simply a static
system. If it does not radiate, then clearly there cannot be any effects of
radiation reaction. The neutron therefore remains in this static state (albeit
perturbatively unstable).
Quantum field theoretically, however, the electromagnetic field is considered
to be quantised into photons. One therefore has the phenomenon of
spontaneous radiation coming into play. Classically speaking, with spontaneous
radiation the neutron effectively “anticipates” the radiation that it
will emit in making the quantum jump from spin-up to spin-down; the reaction
from this “anticipated” radiation is what, roughly speaking, causes the
neutron to flip its spin—and hence emit the anticipated radiation.
This manifestation of the photon’s discreteness would, of course, become
proportionally less important if the spin of the particle, s, were large compared
to the spin of the photon, ¯h, since then each radiated photon would
only “step” the spin vector of the particle by the then relatively small amount
1
of ¯h. Of course, for a spin of s = 2¯h, such a step represents a transition from
full polarisation to full antipolarisation!—and hence the discreteness of the
photon is maximally manifested. Thus, while we have, in the previous chapters
of this thesis, successfully dispelled some of the myths of the “large
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