[FOM] Question about theoretical physics
Walt Read
walt.read at gmail.com
Tue Jul 2 11:04:35 EDT 2013
So where is the FOM question here? Maybe we need a reverse
mathematical physics, with a less-shaky notion of mathematics than the
usual naive view. (Call it "what do physicists want?"). "Algorithm"
sounds right, under some reasonable interpretation, but "to any
desired precision" sounds too strong, given that the experimental
measurements to which the predictions will be compared won't be made
with unbounded precision. Do we need to say something about the reals
or real complexity? ("... and the prediction can be made before the
end of the world as we know it") Any experimental measurement would
seem to be to a limited precision and within a bounded range so it
would seem that we could generally assume that physical theories will
have finite models. Do we expect any interesting consequences from
adding an Axiom of Infinity, or of infinite precision, to a physical
theory? (At least any non-paradoxical ones?)
Physicists have a lot of difficult questions and grab whatever pieces
of math that seem to help (and even to make up stuff that makes
mathematicians squirm!). But the difficulties have also led them to
debate the nature of physical theory and to look more seriously at the
recent developments in logic and foundations. FOM has greatly
clarified the nature of mathematics and even brought new results. If
FOM is to have any effect on physical theory, we have to find a way to
connect traditional physics practice with 20th-century mathematical
developments.
-Walt
On Sat, Jun 29, 2013 at 1:40 PM, Joe Shipman <JoeShipman at aol.com> wrote:
> Physicists don't have in mind the same kind of theory that mathematicians do, and that's understandable. The reason I asked about this was that I felt that physicists ought to have, in any well-defined experimental situation, an algorithm to predict the experimental results to any desired precision, or at least to within a rigorous error term, if they were to claim any notion of correctness for their theory. That is a much less complex requirement then the kind of fully mathematized theory you described, and it seems to be the minimum requirement for a theory to be capable of experimental falsification.
>
> Prof. Neumaier confirmed for us that even for the supposedly well understood theory of QED, no such algorithm exists. This is contrary to what all of the popular books about it say, and physicists ought to admit this and make it known more widely.
>
> Note that I am not talking here about the failure of QED to converge in the limit as you pass to higher degree Feynman diagrams. This phenomenon, the "Landau pole", is a logarithmic divergence that has been understood for 60 years. I am talking about the failure to derive algorithmically even the finite-order partial sums in this series.
>
> I will point out that the physicist Lubos Motl disagrees with professor Neumaier and insists that a uniform algorithm exists for each order of Feynman diagrams that gives a well-defined real number at each stage that is recursive relative to the fine-structure constant.
>
> -- JS
>
> Sent from my iPhone
>
> On Jun 28, 2013, at 5:39 PM, Walt Read <walt.read at gmail.com> wrote:
>
> Physical theory is hard enough but invoking "professors of
> mathematics" turns it in another direction. Before we can ask whether
> a physical theory is consistent in a mathematical sense, we have to
> ask whether it's a theory in the mathematical (formal) sense. If so,
> what is the language? First order, second order, restricted second
> order? Have we agreed on symbols, wffs, rules of inference? Do we have
> effective axioms? If we're going to discuss specific values of special
> constants, it should include some theory (elementary?) of the reals.
> Of the integers? (At least for quantum theories?) Since the usual use
> of a physics theory is to compute values of real-valued functions,
> presumably a theory of such functions and such computation should be
> included in the physics theory. Of course, in principle this could all
> be done and the consistency question approached, if not necessarily
> answered, but I don't think this kind of formal theory is what
> physicists have in mind when they talk about a theory of, e.g., QED.
>
> -Walt
>
> On Fri, Jun 28, 2013 at 10:47 AM, Lukasz T. Stepien
> <sfstepie at cyf-kr.edu.pl> wrote:
>> I have read this very interesting discussion about fine structure
>> constant, QED etc., on FOM, in February and March, but just now I have a
>> leisure to join the discussion.
>>
>> Namely, I have a remark that as far as fine structure constant is
>> concerned, a theory, explaining the value of this constant, i.e. what is
>> the nature of the electric charge of electron, was constructed by Andrzej
>> Staruszkiewicz (Marian Smoluchowski Institute of Physics, Jagiellonian
>> University, Krakow, Poland).
>>
>> I give here the references to several his papers, devoted his theory:
>>
>> 1. Ann. Phys. (N.Y.) 190, 354 (1989).
>> 2. Acta Phys. Pol. B 26 (7), 1275 (1995).
>> 3. BANACH CENTER PUBLICATIONS, VOLUME 41, 257 (1997), INSTITUTE OF
>> MATHEMATICS POLISH ACADEMY OF SCIENCES, WARSZAWA 1997.
>> 4. Tr. J. of Physics 23, 847 - 849 (1999) - also published in "New
>> Developments of Quantum Field Theory", NATO Science Series: B: Vol. 366,
>> 179 (2002), Editors: Poul Henrik Damgaard and Jerzy Jurkiewicz, Plenum
>> Press, New York.
>> 5. Acta Phys. Pol. B 33(8), 2041 (2002).
>> 6. Found. Phys., 32 (12), 1863 (2002).
>>
>>
>> This my remark refers somewhat also to a question of Jay Sulzberger,
>> cit. "Is there a consistent theory of QED, consistent to the usual
>> standard of professors of mathematics?".
>>
>>
>> Łukasz T. Stępień
>> --
>> Lukasz T. Stepien
>>
>> The Pedagogical University of Cracow
>> Chair of Computer Science and Computational Methods,
>> ul. Podchorazych 2
>> 30-084 Krakow
>> Poland
>>
>> tel. +48 12 662-78-54, +48 12 662-78-44
>>
>> URL http://www.ltstepien.up.krakow.pl
>>
>>
>>
>>
>> On 1 March 2013, 10:38 pm, Fr, Arnold Neumaier wrote:
>>> On 03/01/2013 07:22 AM, Joe Shipman wrote:
>>>> 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.
>>> No. There is no program where you could specify a desired accuracy in
>> advance. Quantum field theory is too difficult a subject to allow that at
>> the present time.
>>> Nobody has written any code for getting higher than alpha^6
>>> approximations for QED (and far less for other quantum field theories),
>> and even the alpha^6 term is currently incomplete (and gives a result of
>> unknown accuracy), as for tractability only the contributions deemed most
>> relevant are included.
>>>> I want a pointer to a reference work
>>> The pointers that exist (and are given in my FAQ entry mentioned before)
>> point to far less, but point to what is common practice in reporting high
>> precision physics calculations.
>>> Arnold
>>> _______________________________________________
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>>> FOM at cs.nyu.edu
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>>
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