#21. Is Higher Math Really Undiscovered Physics? [physics]

PH

Red, theory; black, fact.

This post was inspired by the realization that to progress in physics, we need to accept the Newtonian position that absolute space exists. Not only that, but that it is complicated, like a network, crystal, or condensate. Too many fundamental constants of nature (20, according to Lee Smolin) are required to explain the behaviour of supposedly elementary particles with no internal structures to which such constants could refer.

Thus, the constants must refer to the vacuum between the particles, now more readily understood as a complex medium. Looking at the pattern set by the rest of physics and cosmology, such a medium is more readily understood as a condensate of myriad "space-forming entities." Matter would be flaws in this condensate, entropy left over from its rapid formation. Energy may have the same relation to time: irregularities in its rate of progression.

To theorize about how space formed and what came before it, we have to give up visualization, obviously. I suspect this will be a big deal for most physicists. However, the abstractions of higher math may be an island of understanding already existing on the far side of the spatial thought barrier.

In other words, sets, integers, categories, mappings, etc., may be concrete things, and not abstractions at all. Presumably, our spatial and temporal reality still bears the properties it had from the very earliest stages of the universe, co-existing with later-developed properties, which have enabled mathematicians throughout history to access the deepest levels of description of reality, deeper than space time itself.

Consider set theory. Can the familiar concepts of set, union, intersection, and complement be placed into correspondence with physical processes and objects in today's space time to make a case that set theory is pre-spatial physics, so primordial as to be literally unimaginable if thought of as the rules of a real universe? To get started, we have to begin with Leibniz's monads, the "empty set," now considered a real thing. (If you must visualize these, visualize something ridiculous like Cheereos™ floating in milk, when the bowl has reached the single-layer stage.)

The physical process of binding is prefigured by the set-theoretical operation of union. In the simplest case, two monads combine to form a second-order set.

The physical process of pattern recognition, which is, in essence, energy release, is prefigured by intersection. Note that with intersection, the internal subset structure of the set is important, suggesting that the "operating system" of the universe at this stage must keep track of such structures.

We can associate a size measure with a set, namely the total of all the monads inside it once all subsets have been accounted for. The usefulness of numbers in dealing with the world is explained if this size measure is the basis of laws governing what sets may combine as unions and in what frequency (i.e., fraction of all sets extant.)

The fact that most of physics seems to be governed by differential equations may be prefigured by a tendency of these combining laws to depend on the difference of two sizes. The set-theoretical operation of complementation may prefigure the existence of positive and negative charge and the Pauli exclusion principle of fermions, on which molecular complementarity interactions depend.