Thu Feb 28 17:59:47 EST 2013

```Situation with \QED is not as bad as that. What physicists often do is that they use some first approximation, crudely speaking, the result of linearizing the corresponding equations. Often, the results of the first approximation fit the experiments well, i.e., the difference between the predictions and observations is smaller than 2-3 sigma, where sigma is the standard deviation of the measurement error. If the results are close but not that accurate, they try second approximation.

For QED, we get correct result with I think 10 digits or so, very accurate, by using the appropriate approximation, enough to explain most experiments, this is indeed a great achievement for which Nobel prize was awarded. Yes, we still have a problem of not being clear what to do 100 years from now, when the measurement accuracy willl increase so much that we will need to take equations into account more accurately.

In this case, we will still have the corresponding operator-valued differential equations as now, the question is hot to algorithmically solve them.

________________________________________
From: fom-bounces at cs.nyu.edu [fom-bounces at cs.nyu.edu] On Behalf Of Timothy Y. Chow [tchow at alum.mit.edu]
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
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