[FOM] Question about theoretical physics

[Joe Shipman]

My concern is simpler than this. I just want to know where there exists a computer program which takes as inputs the fine-structure constant and a desired output precision and returns a prediction of the magnetic moment of the electron to the requested precision, whether or not the program has good convergence properties. 

In other words, picking where to stop the sequence of approximations may be "cheating" in some way, but I haven't even seen a proper description of how to generate the sequence of approximations that is specific enough to allow a good programmer to implement it. I am sure that such a program EXISTS because the "predicted value" we read about, that is supposed to match experiment so well, must have been actually calculated at some point, but the only descriptions I can find are much too full of hand-waving.

I want a pointer to a reference work that tells how to enumerate the relevant Feynman diagrams, how to define and numerically approximate the relevant Feynman integrals when given a Feynman diagram, and which terms to calculate to which levels of precision, in order to obtain an answer to a specified number of decimal places. 

It doesn't need to be an actual program, just a good enough specification that computer scientists who do not have Ph.Ds in physics could agree "there must be a real algorithm in there" after enough shoveling is done.

Sent from my iPhone

On Feb 28, 2013, at 7:29 PM, "Timothy Y. Chow" <tchow at alum.mit.edu> wrote:

On Thu, 28 Feb 2013, Kreinovich, Vladik wrote:
> 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

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.

Sort of like tossing a needle a multiple of 213 times so that after 3408 trials one can "estimate" pi to 7 digits.

I think I know what the correct rejoinder is.  The situation is not like Buffon's needle because even if physicists have a whole array of different theoretical calculations that they could try, there's no reason a priori to expect *any* of the methods to agree with experiment to 10 digits. Admittedly, because the physicists can't precisely map out the space of possible theoretical calculations ahead of time, they can't make a precise quantitative statement about just how remarkable the agreement with experiment is.  But that is generally the case with scientific predictions anyway---we don't have any quantitative estimate of "how remarkable" Einstein's calculation of the perihelion precession of Mercury is. Though QED isn't mathematically rigorous, that doesn't mean it's infinitely malleable, and it's still possible to have an intuitive sense that there's something very remarkable about a particular non-rigorous calculation agreeing with experiment to that extent.

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?

Tim
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