[FOM] Question about theoretical physics

[Timothy Y. Chow]

Joe Shipman wrote:
>> The complete failure of 
>> "constructive quantum field theory" to provide anything that is 
>> recognizably an effective algorithm to predict results of real 
>> experiments is a scandal, and the lack of awareness of this in all of 
>> the articles and books addressed to non-physicists is another scandal.

Arnold Neumaier wrote:
> The purpose of constructive quantum field theory was never to find an 
> effective algorithm to predict results of real experiments, just as the 
> purpose of the theory of partial differential equations was never to 
> find an effective algorithm to solve partial differential equations.

I don't really understand QFT.  However, I think I understand the gist of 
Joe Shipman's objection.  I'll caricature it somewhat because I think the 
caricature may be illuminating.

If a scientist wants to claim proudly that a certain theory has made 
predictions that have been subsequently confirmed by experiment, then it 
is important that the scientist say ahead of time precisely what the 
prediction is.  It's cheating if the scientist makes some kind of 
ambiguous statement that can later be weaseled to fit any experimental 
result that happens to turn up.

It seems to me that this is what Shipman's talk of an effective algorithm 
is getting at (and by this he doesn't mean a computationally efficient 
algorithm, just any precisely specified algorithm).  He's saying that the 
theoretical physicists ought to say precisely how they're calculating the 
digits (of the anomalous magnetic dipole moment of the electron, for 
example) that they're proudly claiming are confirmed by experiment.  If 
they can't say exactly how they're getting the next digit, then it looks 
(to the mathematician, at least) like they're pulling a fast one. 
Hypothetically, if the digit *hadn't* matched experiment, wouldn't they 
have just used the wiggle room afforded by their lack of rigor to come up 
with some other calculation that *did* give the right answer?  If they're 
making up the theory as they're going along so that it matches experiment, 
then doesn't this mean that the much-vaunted agreement between theory and 
experiment isn't so remarkable after all?

I'm not saying that this criticism is on target, but this is what I 
understand to be (most of) what bothers Shipman.

Tim