#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.

#20. The Two-clock Universe [physics]

PH

Red, theory; black, fact.

The arrow of time is thought to be thermodynamic in origin, namely the direction in which entropy (disorder of an isolated system) increases. Entropy is one of the two main extensive variables of thermodynamics, the other being volume. I would like to propose that since we live in an expanding universe, the direction of cosmological volume increase makes sense as a second arrow of time; it's just not our arrow of time.

One of the outstanding problems of cosmology is the nature of dark energy, thought to be responsible for the recently discovered acceleration of the Hubble expansion. Another problem is the nature of the inflationary era that occurred just after the Big Bang (BB), introduced to explain why the distribution of matter in the universe is smoother than predicted by the original version of the BB.

Suppose that the entropy of the universe slowly oscillates between a maximal value and a minimal value, like a mass oscillating up and down on the end of a spring, whereas the volume of the universe always smoothly increases. Thus, entropy would trace out a sinusoidal wave when plotted against volume.

If the speed of light is only constant against the entropic clock, then the cosmological acceleration is explainable as an illusion due to the slowing of the entropic increase that occurs when nearing the top of the entropy oscillation, just before it reverses and starts down again. The cosmological volume increase will look faster when measured by a slower clock.

The immensely rapid cosmological expansion imputed to the inflationary era would originate analogously, as an illusion caused by the slowness of the entropy oscillation when it is near the bottom of its cycle, just after having started upward again.

These ideas imply that entropy at the cosmological scale has properties analogous to those of a mass-and-spring system, namely inertia (ability to store energy in movement) and stiffness (ability to store energy in fields). The only place it could get these properties appears to be from the subatomic particles of the universe and their fields. Thus, there has to be a hidden network of relationships among all the particles in the universe to create and maintain this correspondence. Is this the meaning of quantum-mechanical entanglement and quantum-mechanical conservation of information? However, if the universe is closed, properties of the whole universe, such as a long circumnavigation time at the speed of light, could produce the bounce.

These ideas also imply the apocalyptic conclusion that all structures in the present universe will be disassembled in the next half-period of the entropy oscillation. The detailed mechanism of this may be an endothermic, resonant absorption of infrared and microwave photons that have circumnavigated a closed universe and returned to their starting point. Enormous amounts of phase information would have to be preserved in intergalactic space for billions of years to make this happen, and here is where I depend heavily on quantum mechanical results. I have not figured out how to factor in the redshift due to volume expansion.&&

#4. My First Theory of Everything (TOE) [physics]

PH

Red, theory; black, fact.

The nucleus around which a TOE will hopefully crystallize.

Alocia and Anaevia

In my first post, I made a case for the existence of absolute space and even suggested that space is some kind of condensate (e.g., a crystal). The divide-and-conquer strategy that has served us so well in science suggests that the next step is to conceptually take this condensate apart into particles. The first question that arises is whether these particles are themselves situated in an older, larger embedding space, or come directly out of spacelessness (i.e., a strange, hypothetical early universe that I call "Alocia," my best Latin for "domain of no space." Going even further back, there would have been "Anaevia," "domain of no time." Reasoning without time seems even trickier than reasoning without space.)

What came before space?

The expansion of our universe suggests that the original, catastrophic condensation event, the Big Bang, was followed by further, slower accretion that continues to this day. However, the resulting expansion of space is uniform throughout its volume, which would be impossible if the incoming particles had to obey the rules of some pre-existing space. If there were a pre-existing space, incoming particles could only add to the exterior surface of the huge condensate in which we all presumably live, and could never access the interior unless our universe were not only embedded in a 4-space, but hyper-pizza-shaped as well. The latter is unlikely because self-attraction of the constituent particles would crumple any hyper-pizza-shaped universe into a hypersphere in short order. (Unless it spins?) Conclusion: the particles making up space probably have no spatial properties themselves, and bind together in a purely informational sense, governed by Hebb's rule. 

Hebb's rule was originally a neuroscience idea about how learning happens in the brain. My use of it here does NOT imply that a giant brain somehow underlies space. Rather, the evolutionary process that led to the human brain re-invented Hebb's rule as the most efficient way of acquiring spatial information. 

Hebb's rule pertains to signal sources: how could hypothetical space-forming particles come up with the endless supply of energy required by pumping out white noise, waves, etc., 24/7? Answer: these "particles" are the growing tips of time lines, that themselves grow by an energy-releasing accretion process. The chunks that accrete are variable in size or interrupted by voids, so timeline extension has entropy associated with it that represents the signals needed by Hebb's rule.

I am well aware of all the space-bound terms in the previous paragraph (underlined), supposedly about goings-on in Alocia, the domain of no space; however, I am using models here as an aid to thought, a time-honored scientific technique.

Is cosmological expansion some kind of accretion?

I imagine that Alocia is home to large numbers of space-like condensates, with a size distribution favoring the microscopic, but with a long tail extending toward larger sizes. Our space grows because these mostly tiny pre-fab spaces are continually inserting themselves into it, as soon as their background signal pattern matches ours somewhere. This insertion process is probably more exothermic than any other process in existence. If the merging space happens to be one of the rarer, larger ones, the result would be a gamma ray burst bright enough to be observed at cosmological distances and generating enough pure energy to materialize all the cosmic rays we observe.

The boundary problem

I suspect that matter is annihilated when it reaches the edge of a space. This suggests that our space must be mostly closed to have accumulated significant amounts of matter. This agrees with Hawking's no-boundary hypothesis. The closure need not be perfect, however; indeed, that would be asking a lot of chance. Imperfections in the closure of our universe may take the form of pseudo-black holes: cavities in space that lack fields. If they subsequently acquire fields from the matter that happens to hit them, they could evolve to closely resemble super-massive black holes, and be responsible for nucleating galaxies.

Conclusions

• Spatial proximity follows from correlations among processes, and does not cause them.
• Any independence of processes is primordial and decays progressively.
• The universe evolves through a succession of binding events, each creating a new property of matter, which can be interpreted as leftover entropy.
• Analysis in the present theoretical framework proceeds by declaring familiar concepts to be conflations of these properties, e.g., time = change + contrast + extent + unidirectional sequence; space = time + bidirectional sequence.