[FOM] Question about theoretical physics

Arnold Neumaier Arnold.Neumaier at univie.ac.at
Mon Feb 25 05:26:58 EST 2013

On 02/22/2013 02:46 AM, Joe Shipman wrote:
> What is the official "algorithm for predicting experimental results?" Is it "keep adding terms for as long as they decrease in size, when you encounter a term which is larger than the previous term then ignore it and stop"?

In class, a one-loop calculation (first order Taylor expansion in 
alpha). This calculation made QED famous in 1948, as it explained
a discrepancy previously unaccounted for.

Already 2-loop calculations (giving the O(alpha^2) term) are very 
cumbersome and can be done only approximately. 4-loop calculations are 
feasible only for very few people.

> If this is the case (and I want to see a CITATION or a QUOTE that officially INSTRUCTS students where to truncate the calculation), then the theory is valid only to a fixed precision. Furthermore, it is mathematically foundationless. It is a much worse situation than simply saying that the theory provides no model of reality, just calculation of experimental predictions, because the experimental predictions are not really "provided" either!

The quantum field books by Peskin and Schroeder and by Weinberg both 
only give 1-loop calculations. For higher loops, one needs to consult 
the specialized literature. See the FAQ mentioned in my earlier mail.

Arnold Neumaier

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