[FOM] Question about theoretical physics

Arnold Neumaier Arnold.Neumaier at univie.ac.at
Fri Mar 1 05:50:51 EST 2013

On 03/01/2013 01:29 AM, Timothy Y. Chow wrote:

> Again, allowing me to caricature the situation for simplicity, I'd say
> that the objection is this.  If the sequence of approximations is not
> believed to converge, then this looks like "cheating" to an outsider.  I
> compute the first approximation, and it's not so good.  So I compute the
> second approximation, and it's better, but still not great.  I compute
> the third approximation, and wow!  It matches to 10 digits.  I collect
> my Nobel Prize and conveniently forget to mention that if I had computed
> the fourth approximation, it would have matched only 5 digits.

The Nobel prizes for QED were awarded for the leading (first order) 
approximation. No such fudging was involved. Note that all stuff 
computed in physics is an approximation only.

High accuracy tests of a theory are very hard work for dedicated 
scientists, not something to be lightly dismissed by outsiders who don't 
know the traditions.

> Having said that, I think that popular accounts do sometimes give the
> impression that the large number of digits of agreement makes this the
> most remarkable agreement between theory and experiment of all time, and
> maybe that is overstating the case?  It's not like every digit of
> agreement exponentially increases our confidence in the correctness of
> the theory?

It just means that one understands the phenomenon extremely well if 
accuracy is that high. Deviations would point to corrections, generally 
referred to as ''new physics''. They would open new avenues for research.

Arnold Neumaier

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