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# Retrograde Motion - Virtual Particles

All the planets (other than Earth) exhibit retrograde motion during a portion
of their synodic period. The superior planets (those orbiting the Sun outside
the Earth's orbit) display retrograde motion near opposition when the Earth
passes between them and the Sun. The inferior planets (those orbiting the
Sun inside the Earth's orbit) display retrograde motion near inferior
conjunction when they pass between the Sun and the Earth. (This motion is
difficult to see as one has to look into the glare of the Sun when looking at
an inferior planet whose phase goes from waning crescent to new to waxing
crescent as the planet passes from being an evening star to being a morning
star.)

Virtual Particles

The gauge bosons responsible for carrying the interactions between the sources
for unbroken gauge symmetries are massless, and those carrying the
interactions between the sources for broken gauge symmetries are massive. The
Strong, EM, and (presumably) Gravitational interactions have massless gauge
bosons (which are the gluons, photons, and the gravitons respectively) and the
Weak interaction has massive bosons (which are the Z_0, W+, and W- which
acquired their mass via the Higgs mechanism). These gauge boson particles
mediate their respective interactions via *virtual* processes. This means
that the amplitude for the interaction between two sources includes
contributions from all possible 4-momenta for the mediating gauge bosons since
each of the components of the 4-vector of the (argument of the propagator for
the) mediating boson are integration variables in the multidimensional
integrals which contribute to the amplitude and which are represented by
Feynman Diagrams. Since all 4-vector components are integrated over, the
constraint that m^2 = E^2 - p^2 (the on-mass shell condition) is violated for
nearly all of the values of the integrands in the Feynman integrals. Since
E^2 - p^2 takes on all real values in the integrals one can imagine that the
virtual processes include contributions from all possible time-like (ordinary
masses), spacelike (tachyonic masses) and null (massless) 4-vectors. These
violations of the on-mass shell condition violate the conservation of energy
(over a time scale short enough to be allowed by the Heisenberg Uncertainty
Principle) and also display the intrinsic nonlocality present in quantum
theory. After all these off-mass shell contributions are added up however,
the overall asymptotic interaction between the sources is causal and
propagates at speed c for the massless gauge boson case, and propagates with a
group velocity slower than c for the massive gauge boson case. It is the
nonzero mass of the Weak gauge bosons which gives the Weak interaction its
very short range of operation. The other interactions have an "infinite"
range of operation (1/r^2 force counts as infinite here). The Strong force
is only noticed strongly inside hadrons and slightly in nuclei (but strong
enough to bind the nucleons into the nucleus) not because it is a short ranged
force, but because its potential energy *grows* with distance and this causes
confinement of its sources (colored quarks) into color-neutral particles (such
as the mesons and the baryons) and the strong interaction between these color-
neutral composite particles does fall off rapidly with distance.

David Bowman
Georgetown College
dbowman@gtc.georgetown.ky.us