[FOM] Question about theoretical physics

Timothy Y. Chow tchow at alum.mit.edu
Sat Mar 2 00:23:31 EST 2013

Arnold Neumaier wrote:

> See the citations from ''Is QED consistent?'' mentioned above.

I took a brief look at a couple of these.  Now that Joe Shipman has 
clarified that his objection is simpler than the "caricature" that I 
painted in previous posts, I think that his complaint is analogous to the 
complaints that have been leveled against the Appel-Haken-Koch proof of 
the four-color theorem and against the Hales-Ferguson proof of the Kepler 
conjecture.  Namely, the excessively detailed computations involved have 
not been documented in a fully satisfactory manner.  For example, Passera
(hep-ph/0606174) writes:

   The exact expressions for these coefficients are rather complicated,
   containing hundreds of polylogarithmic functions up to fifth degree (for
   the light-by-light diagrams) and complex arguments (for the vacuum
   polarization ones). Indeed, they were too long to be listed in [19, 20]
   (but were kindly provided by their authors), although series expansions
   were given for the cases of physical relevance.

I interpret "kindly provided by their authors" to mean a private 
communication with Passera.

The fact that the computations involve non-rigorous mathematics arouses 
additional anxiety in a mathematician, who may wonder if a non-rigorous 
calculation is independently reproducible.  But it seems to me that the 
lack of rigorous mathematical foundation for QED is something of a red 
herring, if Shipman's main concern is being able to reproduce the 
calculation.  The real problem is that both the mathematics and the 
physics communities haven't completely solved the problem of adequately 
documenting extremely complicated calculations.  I think this is a 
legitimate concern, though Shipman's use of the term "scandal" in a way 
that implies that QFT is a particularly egregious offender seems a bit 
over-sensationalized to me.


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