From: jbaez@riesz.mit.edu (John C. Baez)
Subject: I'm no radical
Organization: MIT Department of Mathematics, Cambridge, MA
Date: Sun, 4 Oct 92 22:35:46 GMT

Paul Budnik writes:
>In article <1992Oct2.202249.21453@galois.mit.edu>, jbaez@riesz.mit.edu (John C. Baez) 
writes:
>(Budnik writes:)
>> >But my formalism makes the same predictions of quantum mechanics with
>> >the exception of tests of Bell's inequality. 
 
>> Let's see your formalism - where are the equations?  What precisely does
>> it predict in situations where QM violates Bell's inequality?  Not
>> words, numbers.  Show how to do some QFT-type calculations using this
>> formalism (since QFT combines relativity and QM) - say electron-electron
>> scattering.  

>If I could do that I would not be wasting my time posting this stuff. I
>would be publishing it and patiently waiting for the Nobel committee to call.

>I should not have said `my formalism'.

Yes, that was my point.  I think your ideas are interesting enough
without having to oversell them.  Overselling them will attract
crackpots but repel the sort of people you might want to become interested.
You have a rough idea for an alternative formalism.  Very few people
who might have the chops to turn it into a working
alternative to QM are likely to be interested in spending their energy on
such a project, which has (IMHO) a very low chance of success.  Of
course, you think it has a high chance of success and are trying to convince
others of that.  If you don't have the ability to turn your ideas
into a fully functioning formalism, I guess that's a good
approach.   Even better would be convincing or paying someone to
do the crucial experimental test of Bell's inequality.  (I should add
that I have simply been taking your word all along on the claim that
existing tests fail to ensure spacelike separation.  Shows how nice I
really am.   :-))

I should emphasize though, that until you spend a lot of energy trying
to turn your ideas into a real formalism, you will never really know
how reasonable they are.

>The alternative to the existing theory
>I am proposing is to add locality as an additional constraint to that
>theory.  This implys that we do not know how the wave function changes
>before and after an observation. The multiparticle wave function cannot,
>in general, change in a local fashion when an observation is made, but that
>is not the issue. It must change in such a way that there are no nonlocal
>macroscopic effects. No one knows how it does change. I think it is a
>chaotic-like process that cannot be modeled by an equation. The underlying
>laws can be modeled and the whole process could in theory be simulated on
>a computer. But one cannot give a simple equation that models this behavior,
>Just as one cannot give a simple equation that models the atmosphere in
>enough detail to predict the weather. That can only be done to
>a limited degree by large scale simulations.

>A few months ago you gave an argument why quantum mechanics may not be
>completely valid at very small distances.

Huh??  I never gave anything of the sort, although I can imagine what
you are referring to.  I am more worried about your tendencies to
overstate things when you are describing MY work than your own.
In any case, let me state that I am working on the assumption that
quantum mechanics is completely valid at very small distances, 
simply because I see no evidence against this, and a huge amount of evidence
for QM in general, together with its tremendous mathematical elegance.

>You do not have an alternative
>theory worked out. You would like to develop such a theory that combines
>gravity with QFT but you know it will be hard problem and take a long time.
>I do not think you expect to be able to do it by yourself.

Let me clarify what I was referring to.  Typically in quantum theory
the inner product is fixed by the requirement that symmetry groups act
unitarily, together with the requirement that the Hamiltonian be
nonnegative.  In quantum gravity it is well-known by now that neither
of these requirements are applicable, at least when space is taken as
a compact manifold, say S^3.  I have developed a mathematical
formalism whereby certain "nonnegative" states of quantum gravity on S^3
determine Hilbert spaces for "quantum gravity on D^3", where D^3, the
closed unit ball, is one of the halves of the S^3.  This is rather
radical because of the state-dependence, and I imagine that's what
you're talking about when you say I'm claiming that "quantum mechanics
is wrong on small distance scales."  However:

1) I am not proposing dropping what I see as the key principles of
quantum mechanics, namely the use of Hilbert spaces to calculate
probabilities via inner products.  To do so in the absence of
compelling experimental evidence would be nuts.

2) I have worked out a mathematical formalism which led me to this
notion.  It is only because I have worked out lots of the details
that I have dared mutter anything about such ideas on sci.physics, and
even so, I believe that in my original post I said "take this with a
mongo grain of salt."

3) This formalism, far from being all my own, is simply the result of
applying ideas from knot theory and Chern-Simons gauge theory to the
Ashtekar-Rovelli-Smolin loop variables approach to quantum gravity. 
The latter approach, I should add, is extremely conservative in that
it is simply using a change of variables to simplify the constraints
that typically make quantum gravity so hard.  It is not, like string
theory, a whole new theory - it simply combines quantum mechanics and
general relativity in a mathematically clever way.  

4) I'm not working on my own; I'm constantly checking my ideas with
people who know infinitely more about general relativity than I do,
and I'm submitting papers to refereed journals and rewriting them to
correct errors and tone down any unsupported claims.  

In short, I am not doing anything nearly as radical (hence
likely to fail) as you seem to think.  I think that, in the absence of
compelling experimental evidence, it is best to take a conservative
approach.  

The above is sort of an over-reaction to Budnik's remark, but I think
it's important for people not to get an over-romanticized notion of
how progress in science typically works.  

>Tests
>of locality can be done using existing technology. Perhaps you should
>consider changing your area of research. :-)

Alas, I'm a mathematician, not an experimentalist.  I had enough
trouble trying to light a Coleman stove last weekend.  


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