220 The Poetry of Physics and The Physics of Poetry
measure is 137 times the product of the uncertainty of measuring these
quantities it is quite evident that it will be impossible to detect the virtual
photon, and hence, our hypothesis of virtual photon exchange is not
inconsistent with the law of conservation of energy.
It is interesting to note that the distance R between the two charges
dropped out of the expression for Et. This result only occurs for the
inverse square law. If the force had any other form the expression for
E × t would have depended on R. It would then be possible to find
a value of R for which Et became greater than h and hence observable
in principle. If this were to occur then we would have to give up the
notion of virtual photon exchange and look for another explanation of
action at a distance. For example, if the force were e^2 /R^3 then the
potential energy would be e^2 /2R^2 and the product of energy times
lifetime would be Et = e^2 /2R^2 × R/c = e^2 /2Rc = h/274R. By considering
R small enough it would be easy to make Et greater than h and hence,
the photon detectable.
The hypothesis of virtual photon exchange gives us some
understanding of why the electric force goes like the inverse square of
the distance. It is the only dependence on the distance R that is consistent
with the uncertainty principle and the conservation of energy. The
uncertainty principle plays an extremely interesting role in the virtual
photon hypothesis. Rather than limiting our knowledge of the universe
the uncertainty principle enables us to understand certain aspects of basic
physics more deeply, namely the uniqueness of the inverse square law of
the electric force.
The hypothesis of virtual photon exchanges explains how action at a
distance occurs. Electrons interact through the exchange of virtual
photons. Individual electrons are continuously emitting and reabsorbing
virtual photons. They are surrounded by a cloud of virtual photons.
Whenever another charged particle enters that cloud it will interact
electrically (i.e. experience a force) by absorbing one of the virtual
photons. The electron whose virtual photon is absorbed will also
experience a force because the absorbed virtual photon will never return
to balance the momentum lost by its original emission.
Quantum electrodynamics is based on the hypothesis of virtual
photon exchange. Dirac’s theory is based essentially on the exchange of
a single photon between charged particles. Quantum electrodynamics
provides a more detailed description of charged particles by taking into
account the exchange of more than one photon. Multiple photon