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Re: virtual particles preferred frame?



Hi all-
I'll put in my 99 cents here:
Glenn A. Carlson writes:
*****************************************************************
I'm sorry, but John's comments re "why the virtual particles don't
propagate very far" and "Because they have zero total energy. They've
got negative kinetic energy
which just cancels their rest-mass energy" strike me as a misread of
the theory of virtual particles.

Virtual particles don't go very far because they cannot exist longer
than a time interval defined by the uncertainty principle; not because
they have "imaginary momentum." E.g., creation of a virtual
electron-positron pair violates conservation of energy by an amount at
least 2mc^2 (m=electron mass=positron mass) which is a very positive
amount, but which is allowed only for a time interval delta-t =
h-bar/2mc^2. Hence, the electron or positron can move at most a
distance c*delta-t = h-bar/2mc from their point of creation; any
farther is prohibited by the uncertainty principle. "Advanced Quantum
Mechanics," Sakurai, p. 138.
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The notion of "virtual particle" is part of the poetry of physics
that is used to describe the covariant perturbation theory that is
describable in terms of Feynman diagrams. I'll try to explain.
In the old-fashioned, time independent perturbation theory
(that is taught in 1st year QM to describe the Zeeman effect, for example)
there is a perturbing term that allows transitions to intermediate states.
These intermediate states are described as states with on-the-mass-shell energies.
Actual transitions to these states are not permitted because the transitions
would not conserve energy. In that sense the states are "virtual" because the
system cannot end up in those states.
In a more careful, time-dependent treatment (which I have never seen
done), a system can live briefly in a such a state because the uncertainty
principle does not require strict conservation of energy for short times. That
statement is the essence of Sakurai's remark.
The covariant perturbation theory of Feynman-Dyson demands that the
transitions to the intermediate states conserve energy-momentum. How do they
do this? They take the intermediate particles off of their mass shells. That
is, they describe the particles in the intermediate states as particles with
unphysical masses. Does Sakurai's description apply to such states? The question
is, strictly speaking, meaningless because in the Feynam-Dyson description one
is calculating an S-Matrix. The S-Matrix is not a time-dependent object.
Nevertheless, when low order perturbation theory is accurate, we talk as though
the intermediate state "really" exists (like speaking of single photon exchange).
Note that the foregoing description avoid discussing transitions to
states of <lower> energy than the initial state. Such transitions are realized,
but the initial state is unstable and one has to torture the S-Matrix formalism
to calculate transition probabilities.
So the answer is that "virtual states" are fictional, but the fiction
has created its own reality.
Regards,
Jack


"I scored the next great triumph for science myself,
to wit, how the milk gets into the cow. Both of us
had marveled over that mystery a long time. We had
followed the cows around for years - that is, in the
daytime - but had never caught them drinking fluid of
that color."
Mark Twain, Extract from Eve's
Autobiography