Re: Connes & Marcolli paper on renormalization

From: Chris Oakley (coakley_at_cgoakley.demon.co.uk)
Date: 10/07/04 

Date: Thu, 7 Oct 2004 12:04:56 +0000 (UTC)

> Well, you can throw out the theory, but that seems a bit drastic.

I believe that one has no choice. One can in any case find holes in the
cutoff procedure. Supposing, for example, we were to choose Lambda as a
function rather than a constant. Furthermore, let us make it a function of
variables that never even entered the original equations. There is no reason
in principle why we should not be allowed to do this. We then very rapidly
get nonsense. You will then say that it was my own fault for not making it a
constant, but all that means is that you can find a path through the
minefield. It does not mean that the minefield has ceased to exist.

There is no such thing as "reasonable" in theoretical physics, there is only
mathematical logic. The pillars of our current understanding of physics,
namely quantum mechanics and special relativity, both defy common sense. One
becomes aware of this very quickly when one tries to explain them to an
intelligent non-physicist. You and Dr. Neumaier say that it is
"unreasonable" to have four-momentum integrals extending to infinity,
leading you to want to cut them off. I say that if the mathematical logic
leads one there, then one has no choice other that to accept it, and if this
leads to nonsense then one has to accept that that something is
fundamentally wrong with the approach.

Let me be clear on this - I could not do any better. All my attempts to find
a rigorous way of doing Feynman-Dyson perturbation theory failed. This puts
me in good company with Dirac, Pauli, Feynman, the axiomatic field theorists
and many others. But in the end, I just decided that it was not worth
rescuing, tore everything up and started again. And - intermittently, at
least - I am still working on that.