dub@pur-phy.UUCP (Dwight U. Bartholomew) (04/06/84)
I am not an expert in quantum field theory, but I do know that in the
recent past people working in the field DID have annoying singularities
in their calculations that made their calculated numbers worthless.
Then came Renormalization theory!!! It said that some of those
singularities (infinites, to those not into the jargon) were different
"kind" of singularities and by redoing the calculations one could make
these "odd" singularities drop out. The end result is that quantum
field theory can predict numbers like the fine structure constant to
zillions (a slight exaggeration) of decimal places.
Dwight Bartholomew
UUCP: {decvax,ucbvax,harpo,allegra,inuxc,seismo,teklabs}!pur-ee!Physics:dub
INTERNET: dub @ pur-phy.UUCPclt@pur-phy.UUCP (Carrick Talmadge) (04/06/84)
Also, continuing Dwight's defence of Q.E.D., one must distinguish
between infinities which arise as a consequence of the field theory,
and infinities which arise as a consequence of the method by which
we obtain solutions to that field theory (namely via the quantum
perturbation method). Infinities may be obtained even in classical
field theories, such as General Relativity, when one does a perturbation
expansion ( the usual example of this is in solving the two body
problem to determine the rate of precession of the perihelion as in the
case of the Sun-Mercury system). These infinities are eliminated via
"renormalization" just as in the case of a quantum field theory.
Carrick Talmadge
UUCP: {decvax,ucbvax,harpo,allegra,inuxc,seismo,teklabs}!pur-ee!Physics:clt
INTERNET: clt @ pur-phy.UUCPgwyn@brl-vgr.ARPA (Doug Gwyn ) (04/08/84)
Then there are REAL infinities caused by conceptual problems, such as the self-energy of the electron in classical electromagnetism. The problem with QED renormalization is that it smacks of an ad-hoc method to avoid a problem. The basic idea in simple terms is to consider the terms in the formulas as pertaining to an (unknown) "bare" quantity (mass or whatever) and reinterpret the theory so the "real" quantity is predicted. Unfortunately this pushes the difficulty into the unmeasurable "bare" quantity, much like sweeping dust under the rug. (To forestall flames: yes, I know about renormalization groups and the associated paraphernalia, but I don't want the critical concepts to get lost in a morass of technical details. I think this happens far too frequently these days.)