According to Richard Feynman, physics is to mathematics as sex to masturbation. Jeeva suggests that, if we add philosophy to the equation, we will get an orgy. Odd as this may sound, it wasn't obvious from the start that Jeeva would want to engage in this orgy. After all, modern mathematics offers richer structures than any philosophical system. And physics is way ahead of mathematics and philosophy alike in how it engages reality. So, why go beyond mathematics and physics to philosophy and its "thinking without rules"? Here is a short answer: Philosophy helps address an unsolved and, for the time being, empirically unsolvable problem which concerns the very relation of physics and mathematics.
Jeeva's longer answer involves his modest claims for laws of nature and what they are.
After seven decades of intense deliberation and some experimentation, general relativity (space-time) is still physically and mathematically incompatible with quantum theory (Hilbert space). The political decision against the superconducting super-collider is only one indicator that there may not be any physical evidence forthcoming which would settle the question. For a solution Jeeva therefore turns to philosophy and to what Wigner has called "the unreasonable effectiveness of mathematics in the natural sciences." Why is mathematics so effective, Jeeva asks, and why is this effectiveness not at all unreasonable, but showing the way perhaps to a physical geometry which can unify general relativity and quantum theory?
Jeeva begins with a modest description of what scientists do. They do not explain what is, nor do they formulate laws of nature which govern all future events as they issue from some initial state of affairs. Instead, scientists see what remains invariant under transformations or what persists through change. f=ma, for example, describes an equality of results under various transformations of laboratory or measuring apparatus. Invariance under transformations, Jeeva argues, corresponds to symmetries in objects, and such symmetries are amenable to geometrical treatments (a geometry, after all, is the set of properties invariant under a group of transformations). If gauge-fields and gravity arise from transformations between wave functions, a geometrization of physics might hold the key to the unification of quantum theory and general relativity.
For the benefit of his philosophical audience Jeeva suggested that his principle of physical geometry ("the symmetry group of the laws of physics must be the same as the symmetry group of the corresponding physical geometry") is a synthetic a priori principle like the ones sought by Kant: it is not analytic (tautological) but pertains to experience without relying on it; it legislates how objects must be given in experience. Just like Kant's principles, to the extent that it assumes identity, reversibility, and transitivity it is a principle of physics and may not hold for chemistry or biology.
For the benefit of all those who are interested in the details of Jeeva's proposal, I must refer to
his dissertation on Reality and Geometry in Quantum Theory (University of Oxford, 1996). Here
are three references to related articles: "On the Hypotheses Underlying Physical Geometry"
(Foundations of Physics, vol. 10, 1980, pp. 601-629); (with H.R. Brown) "On the Reality of
space-time Geometry and Wave Function" (Foundations of Physics, vol. 25, 1995, pp. 349-360);
and "Classical and Quantum Gravity" (R.S. Cohen et al., eds., Potentiality, Entanglement and
Passion-at-a-Distance, Dordrecht: Kluwer, 1996, pp. 31-52).
Postscript
Alfred Nordmann
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