Dear Aldo Filomeno,
While many essays speak of Grothendieck's 'dessin d'enfants', or the Langlands program, or the Monster group, etc. in hopes that these will answer some questions, you address probably the most significant mathematics of the last 60 years, gauge theory – and you properly put it in its place.
As no other general field of math has had the impact on physics as has...
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Dear Aldo Filomeno,
While many essays speak of Grothendieck's 'dessin d'enfants', or the Langlands program, or the Monster group, etc. in hopes that these will answer some questions, you address probably the most significant mathematics of the last 60 years, gauge theory – and you properly put it in its place.
As no other general field of math has had the impact on physics as has gauge theory, I'd say you have your priorities right. Also, you rightly include "(and vice versa)" when you note the relation of symmetry principles for every continuous global symmetry of the Lagrangians to which corresponds a conservation law.
It seems to me that if one had to classify these entities, the conservation laws would be ontological facts, while the symmetry principles would be epistemological effervescences.
The really amazing thing, to me, is that
none of the basic symmetries are exact, from iso-spin to SUSY. You mention 'astonishing success' such as the prediction of the Omega minus. But have there really been that many such? Perhaps I'm jaded, but when it comes to trying various hierarchical layouts of the known particles, just how hard was it to notice "one seems to be missing here"?
I very much enjoyed your "
Elegant but contingent…" analysis of gauge symmetry. I particularly liked that (B) assumes "
a language full of non-actualized possibilities, and that the mathematics constituting our best physical theories is only one of the infinite possible mathematical descriptions of the regularities of the world."
My essay begins by 'extracting' regularities from measurement data to find a 'best' [in a max entropy sense] feature vector that represents the measured properties. Your analysis of the strong force leads again to the particular final choice being made among an extremely vast space of possibilities.
[I have suggested another possibility in
The Chromodynamics War in which SU(3) is based on
structure, not color. You might enjoy some of the ideas in this 'hard sci-fi' novel.]
It is not insignificant that the gauge fields are put in 'by hand' to a large extent.
But, to return to your "
Elegant but contingent…", I have made the same argument against the Bell's basic model: it is '
Elegant but contingent' in the sense that it is contingent on a constant field, which leads to a null experimental result, and hence begins with a contradiction. There is much more to the story which is presented in
my essay . I invite you to read it and would welcome feedback.
Thanks again for your very well written and quite on-target essay.
My best regards,
Edwin Eugene Klingman
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Dear Eugene Klingman,
I very much appreciate your compliments and especially the comments.
Your point about the inexactitude of the symmetries seems to me particularly appealing: scientific or philosophical research should be carried out pursuing this line. So far I do not know which side I would bet on. I envisage arguments refusing the importance of such inexactitudes as well as arguments that might employ such inexactitudes against a too idealized view of the laws of nature.
I also agree that one could interpret symmetries and conservation principles as you suggest (being the latter more fundamental). Then, we face questions regarding the conservation principles: Are they a plausible unexplained primitive of our ontology, or should the postulation of the conservation of some property be somehow explained?
Finally, I'll read your essay which looks really interesting!
Warm regards,
Aldo Filomeno