[FOM] Question about theoretical physics

[Arnold Neumaier]

On 02/28/2013 11:59 PM, Kreinovich, Vladik wrote:
> 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.

The situation is not as good. The Nobel prize was awarded for results 
obtained in 1948, just after QED was made to give sensible predictions 
at all. At that time the accuracy needed was low, and a first order 
expansion in the fine structure constant was enough. This is essentially 
what can be found in today's textbooks on quantum field theory.

Today, calculations have to be done to order alpha^5 and alpha^6,
to match the experimental accuracy for the anonmalous magnetic moment of 
the electron. But higher order calculations are messy and give little 
insight; hence they are done only by those few physicists specializing 
in high accuracy tests of QED.

For other applications, in particular to relativisitc quantum chemistry, 
the situation is very mixed. A recent article by
    Werner Kutzelnigg,
    Solved and unsolved problems in relativistic quantum chemistry,
    Chemical Physics 395 (2012), 16-34.
describes what the title promises. One cannot calculate well many things 
of interest. A prime example is the Helium fine structure; cf.
    Ingvar Lindgren,
    The helium fine-structure controversy
    http://arxiv.org/abs/0810.0823

Anyone who wants to understand the complexity of QED calculations and 
see the inadequacy of accusations such as ''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.''
(quoted form a mail by Timothy Chow in this thread) should read these 
articles and perhaps leaf through the book
    Ingvar Lindgren
    Relativistic Many-Body Theory: A New Field-Theoretical Approach,
    Springer 2011.
    online copy at http://fy.chalmers.se/~f3ail/Publications/BoundQED.pdf


Arnold Neumaier