Hello Prof. Politzer,

I'm a physics student with a quick question.

Are virtual off mass particles really out there, do they really exist or
are they just mathematical artifacts of perturbation theory and thus
fictitious?

(I got confused by people on the Internet who were saying that if we
would do non-pertubative quantum field theory, then virtual particles
would not come up and thus they are dependent on the calculation scheme
being used and can't be real or physical.)


And I replied:

This is precisely the kind of question you should be asking as
you're learning about relativistic quantum mechanics.  And in 
trying to find answers, you'll surely learn quite a bit of
physics.

However, as you work on it, I suspect that the more of the
physics you understand, the less relevant the initial question  
becomes.

I do not mean to be cryptic just for its own sake, but, in
finding answers, you'll first find that there are problems with
the question.

In particular, the most problematic words and concepts in your
note to me are: exist, fictitious, and real.

You probably already know that there is some quantum funny
business that concerns the relation of energy uncertainties and
time intervals (or at least those are the terms that are usually
used).  So is your question just a matter of degree?  Are rho
mesons real particles? Or are they just mathematical artifacts
whose role is to simplify our account of the behavior of "real"
particles?  How about the rho''?  Pions?  W's?  Protons are known
to live much longer than the current age of the universe.  But 
what if they're unstable, too?  Are quarks mathematical
artifacts?  Some people would insist yes.  But where does that
get them?  Some people will tell you that you can't construct a
gauge invariant, correct state of a single electron.  In some  
sense they're right, and one can imagine structuring all physical
calculations in terms of space-time correlations between gauge
invariant sources.  But insisting on that is just plain foolish.

In practice, you will be in a better position to confront and
answer questions of the sort you asked me all by yourself once
you have mastered the rudiments of the theoretical calculations  
under discussion and (very importantly) how those calculations  
are used to confront the physical (i.e., real)  world.

If you really and absolutely believe that quantum mechanics 
fundamentally involves uncertainties and probabilities and that wave
functions collapse upon the making of observations (as opposed to
all of those being conveniences for us who are not all that
smart after all), then you believe that quantum mechanics doesn't
apply to you.  However, the only argument in favor of that
proposition is that it makes you comfortable.  There is not a  
shred of experimental evidence.  Rather, there is an enormous
body of evidence to the contrary.

We are all Schroedinger's cats!

D.P.