#71. A Cosmological Setting for a GR-QM Unification [physics]

PH

Red, theory; black, fact

To unify these points most simply, you have to go outside the region of points.

“The Sphere,” campus of the National Research Council, Ottawa 

Figure 1. The expanding 5-ball

Figure 2. A wave packet

The Big Picture

The spacetime of general relativity (GR) is here considered to be an expanding 4D hyperball (4-ball) on the surface of an expanding 5D hyperball (5-ball). The latter is surrounded by subatomic-sized 5-balls ("paramorfs") that can fuse with the big, nearby 5-ball, which is the mechanism by which the latter enlarges. (See Fig. 1). Technically, a “sphere” is just a surface, with a dimensionality one less than the embedding space. I use “ball” here to refer to the embedding space dimensionality.

The Little Picture

Each fusion event sends out a ripple on the surface of the big 5-ball that travels at the speed of light in vacuum. A sequence of fusions happening in the correct order causes the ripples to add up to a shock wave at some point. At the maximum of the shock wave, the surface of the 5-ball is thrown out especially far into the surrounding emulsion of paramorfs, where it makes contact with yet another paramorf, resulting in yet another fusion event and another ripple, which has the correct phase to add to the shock wave. The result is a self-sustaining cycle that leads to persistence and thus observable particle-like phenomena. (See Fig. 2). The shock-wave speed, or “group velocity” will be somewhat less than the speed of light, or “phase velocity” so that ripples will be bleeding out the front continuously. This feature of the theory was introduced to prevent the amplitude of the particle from growing without limit. If the particle is travelling exactly along the time dimension, this bleed will be into the future direction. Therefore, “the future” will have a limited physical reality.

This mechanism was inspired by the superradiant nitrogen laser, in which nitrogen is excited by a zone of corona discharge travelling at nearly the speed of light. This mechanism is also based on Born's rule of quantum mechanics (QM). If wave curvature rather than displacement amplitude determines paramorf fusion probability, then we get something even closer to Born’s rule, which states that the square of the wave function is proportional to the probability of observing a particle. The curvature of a sine wave is not its square, but the resemblance is striking. Perhaps an experimental verification of Born’s rule with unprecedented accuracy is warranted to distinguish the two theories. 

Making It Messier, Like Reality

The big 5-ball may be filled with an emulsion of yin paramorfs in a continuous yang phase, as well as being surrounded by an emulsion of yang paramorfs in a continuous yin phase. Droplets of yin space could get injected into the interior as a side effect after each yang paramorf fusion event. This would explain why curvature alone dictates fusion probability: a concavity reaching interior yin paramorfs is as effective as a convexity reaching exterior yang paramorfs, and no depletion zone will develop over time. Yin and yang space are terms coined in a previous post, “The Checkered Universe.”

The Inflationary Era

Particle formation is entropically disfavored (requires a precise configuration unlikely to arise by chance) and thus only happens when paramorf fusions are frequent due causes other than the presence of particles. Postulating that spontaneous fusions are more frequent when the curvature of the 5-ball is greater, spontaneous fusions will be abundant when the growing 5-ball is still tiny and thus intensely curved. This would be seen in our 4-ball as the inflationary era of the Big Bang. 

A problem is that the paramorfs themselves are the most intensely curved elements in this system. Possibly, a binary paramorf fusion event releases so much energy in such a confined space that the fusion product immediately splits apart, resulting in no net effect overall. Analogously, in gas-phase chemistry, some two-molecule reactions will not go without a third “collision partner” to carry off some of the energy released. 

Time

The surface of our 4-ball would be formed by the stable particles radiating out of our local inflationary zone on the 5-ball into newly-created, blank 4-surface (see Figure 1). This radiation would define the post-inflationary era. Our time dimension would be one of the radii. These particles propagate in time the given, as opposed to time the clock reading. The position of the particle along its track is the clock reading.

Mechanistic Variations

The illustrated mechanism of particle creation (see Figure 2) is periodic-deterministic and may account for photons and leptons. The corresponding chaotic mechanism may account for baryons, and the corresponding probabilistic mechanism may account for dark matter. The close relationship we see today between protons and electrons could have been due to their relationship during the inflationary era; the vicinity of one could have served as an incubator for the other.

Consistency with Relativity

The multitude of expanding spacetime ripples predicted to be around any massive object would comprise the spacetime curvature referred to by the Einstein tensor of the relativistic field equations. The asymmetry of the wave packet that leads to the shock wave accounts for momentum. According to special Relativity, mass-equivalent energy is just the spacetime component of the momentum along the time axis.

A Geometric Underpinning for this Theory

Fixing radius = 1, the 5-ball has the greatest volume of any ball dimensionality. (See the Wiki on “n-sphere”) Thus, this dimensionality could have been forced by some principle of minimizing the radius-to-volume ratio, call it a compaction principle (in a physical, not topological sense), the existence of which is already implied by the assumed ball shape. We cannot invoke gravity here to produce compaction because gravity emerges at a higher level of description than this. A surface tension-like effect related to the permittivity of free space may serve, which is already implied by invoking ripples on the surface. However, mention of ripples implies that the governing differential equation has oscillatory solutions, which seems to also require a medium with inertia, which may be related to the permeability of free space.

Beyond Geometry

If an overarching process of yin-yang separation existed, which would explain why all observations are ultimately observations of contrasts, this process would arguably have a smoothing effect on any resulting interfaces. Such smoothing would suggest surface tension when considered spatially and inertia when considered temporally. I suspect that electromagnetism and matter waves emerge from these simple ingredients. Conservation of paramorf volume would enter the mathematical proof as a constraint.

A limitation of this theory is that it does not explain the assumed presence of discrete, ancient inflationary zones on the surface of the 5-ball.

A Sixth Dimension Is Necessary

Close inspection of the volume versus dimensionality curve for n-balls of radius 1 suggests that maximum volume occurs at a fractional dimensionality somewhat above 5, which looks to be about five and a quarter. Under the compaction principle, this circumstance would lead to a squashed (oblate) 6-ball about one-quarter as thick as it is wide, with greatest curvature at the equator. (Here I am making an analogy with the Earth’s surface, which is an oblate spheroid.) This uneven distribution of curvature would result in the equatorial region losing its inflationary status later than at the poles, suggesting that the universal equatorial region spawned all the particles we can now see during the late inflationary era and that our familiar 3-space corresponds to a line of latitude on the oblate 6-ball travelling steadily toward a pole. 

This scenario allows the existence of ancient, dilute matter of non-equatorial origin coexisting with our 3-space. This ancient, dilute matter could account for cosmic rays and some of the diffuse cosmic gamma glow. Some of these ancient particles would by chance approach us in our future light cones and would therefore interact with our 3-space as antimatter. The resulting annihilation events would produce gamma rays and neutrinos. Those particles that escape annihilation could potentially re-emerge from our spacetime in our past light cones and at a different point, becoming matter cosmic rays. Cosmic particles following spacelike trajectories may not interact strongly with us, like two waves crossing at right angles, but Born's rule predicts some interaction.

A Second Limitation of this Theory

Relativity theory denies the existence of an absolute frame of reference, which I have just re-introduced in the form of the surface of a large ball. Perhaps this limitation can be addressed by showing that the concept of no absolute frame of reference can be replaced with the concept of space-tilted matter, in which the lengths of meter sticks change due to a tilt of the structure of Figure 2 so that propagation is no longer purely in time, but now has a component in space, and the length change must be to a degree necessary to guarantee the null result of the Michelson--Morley experiment.

High Dimensionality

The surface of a 6-ball is a 5-dimensional space. Particle propagation on this surface uses up one of these dimensions, turning it into time. However, the resulting spacetime has four dimensions of space and we see only three. What happened to the other one? Most likely it was largely suppressed by black hole formation shortly after the inflationary era. Black hole formation should be very facile in four spatial dimensions because gravitational orbits are unstable and radiative cooling is relatively efficient. This places us on the event horizon of one of these 4-D black holes and suggests that the event horizon actually is the membrane it seems to be in some theoretical studies. Considered geometrically, the event horizon is a surface and will therefore have a dimensionality one less than that of the bulk. Life on this surface will therefore be three dimensional.

 

In addition, this theory clearly provides a multiverse, because there can be many such hyper black holes, thereby answering the fine-tuning-for-life problem that inspired the anthropic principle.

String theory posits that a particle is a one-dimensional vibrating string embedded in three dimensions. However, my theory posits that a particle is a three dimensional system embedded in six dimensions. We are situated in a privileged location in 6-space in which three of these dimensions have an inward and outward direction. An analogous point in 3-space would be the corner of a cube. The wave component of particles would oscillate along a vector that can rotate in a wholly extradimensional plane, and with an axis of rotation perpendicular to all three dimensions of space, possibly coinciding with time. This would be the spin of the particle. In the cube analogy, one of the edges parallel to the time dimension is spiraling. If the vector rotates in a plane contained within 3-space, this would be the circular polarization of light. A baryon might consist of a trio of fermions, one on each of the three edges meeting at the cube corner and each offset a short distance back from the corner. This arrangement might create a tiny, semi-closed chamber where ripples are concentrated and thus intensified. This, in turn, would enhance paramorf capture, which would dynamically stabilize the structure.

See Figure 3. In this figure, the instantaneous structure resembles one edge of a cube merging with a surface. The line between points A may function as a closed chamber for fusion ripples because of the right-angle relationships at each end, leading to intensified shock waves inside and intensified paramorf fusion. This, in turn, dynamically maintains the geometry shown.

Etymology: "warped spacetime," Greek: paramorfoménos chorochrónos, thus: "paramorf."

Figure 3. A hyper-black hole progressing across the surface of the big 6-ball. The three spatial dimensions of relativity theory have been suppressed for clarity and are represented by points A; t is time.

Tilting at a Conceptual Unification

In general, spacetime structures would tend to evolve to greater efficiency in paramorf capture, and deviations from these structures will appear to be opposed by forces. This can be cited as a general principle in exploring the present theory.

For example, two fermions could capture paramorfs cooperatively: capture by one triggers an expanding ripple that reaches the other and triggers its own capture. This second capture then sends a ripple back to the first fermion, where it triggers a third capture, and so on. This duetting action is formally like light bouncing back and forth between parallel mirrors, as in the light-clock thought experiment of special Relativity, and recalling the Michelson—Morley interferometer. If duetting efficiency maintains the length of meter sticks, we have the beginnings of the long-sought explanation of the null result of the Michelson—Morley experiment in terms that allow the existence of a medium for the wave aspect of particles.

Velocity in space relative to the medium upsets the spatial relationships necessary for efficient duetting, triggering a compensatory reorganization of the spacetime structure to re-optimize paramorf capture efficiency, by the general principle enunciated above. This leads to the Fitzgerald contraction, one of the two basic effects previously explained in terms of special Relativity. The Fitzgerald contraction was recently proven to be directly unobservable; rather, a rotation of the front of the object away from the line of travel is observed, as predicted by Penrose and Tyrell. https://doi.org/10.1038/s42005-025-02003-6. If this rotation looks the same from all observation angles (elevations), it would have to be a rotation into extradimensional space, which the present theory allows, and it is easy to visualize how that would maintain the efficiency of duetting at high velocity. Therefore, close study of the relativistic rotation effect may provide a window on extradimensional space.

The other basic relativistic effect is time dilation; if fermions are always literally travelling along a time dimension as postulated here in connection with the space-tilted matter concept, a greater velocity along any spatial direction must come at the expense of a lesser velocity along the time dimension, leading to time dilation.

Synchronization and anti-synchronization of fusion events between adjacent particles could account for the narrowness of the time slice we seem to be living in.

Duetting could account for attractive forces between fermions and duetting with destructive interference could account for repulsive forces. A difficulty is that the simple ripple model is one-sided whereas destructive interference assumes sinusoidal disturbances, which are two-sided. This could be remedied by assuming that the ripples have profiles like wavelets or the Laplacian of the Gaussian.

At the Limit of this Vision

Paramorf-ripple dynamics looks remarkably biological, featuring elementary processes that recall feeding and natural selection. Their cosmological setting cannot be the end of the story, however, because one naturally wonders where the entire ensemble of yin and yang space came from and why it has a bipartite nature. To answer these questions, it may be necessary to conceive an elemental version of the ultimate power of living things: reproduction. The ineffably great multiplicity of things demands an explanation.

Questions Arising 

• Do we need a new representation system to tackle the question of ultimate origins? 
• Do we merely need to shift from visual to verbal? 
• Is the concept of differentiation valuable here? For example, primordial undifferentiated space and time, primordial undifferentiated time and causation, or primordial undifferentiated somethingness and nothingness. 
• Is entropy increase the ultimate source of all differentiation? 
• Is the concept of primordial fluctuations valuable here? For example, should I proceed as I did in the abiogenesis post, from vacuum fluctuation to persistence by self-repair to growth to reproduction? 
• What is the effect of a vacuum fluctuation in the background of a previous fluctuation?
• Is circularity a key concept here? 
• Is positing an ultra-simplified version of something well known in other disciplines, a kind of consilience, a useful operation? 
• Is the concept of a primordial less-structured space valuable? For example, a topological space is less structured than a Euclidean space. 
• Is the strategy of bringing the observer into the system under study valuable here?
• The further back I go, the fewer the raw materials, but the fewer the constraints. How do I keep from losing my way?

Snail universe beside the Rideau canal. There may be perspectives in which what we consider our own universe looks no grander than this.

Zen weeds in the Rideau Canal. No explanation.

#32. Big-electron Theory [physics]

PH

Red, theory; black, fact

The Particle Model is an Approximation 

Some of the paradoxes and weirdness of quantum mechanics can be dispelled if we assume that any particle that can be diffracted isn't really there: we are only looking at the center of spherical symmetry of a much larger, possibly cosmologically large, wave function. Furthermore, this center of symmetry is only an abstraction, like the north pole of the Earth. Like the fields that we impute to them, quantum particles would have a wave function amplitude that decreases asymptotically to zero with distance from the centre, and thus would have no well-defined outer boundary: particles or wave functions would be "expansive."

Why Does the Illusion Hold?

Elementary particles seem submicroscopic in size because the wavelength of the corresponding wave functions is often submicroscopic, which imposes a requirement for the centers of symmetry of two such "particles" to coincide with very great precision before an interaction can be observed. This would be the case if the default interaction were characterized by destructive interference almost everywhere, which only switches over into constructive interference when the centers nearly coincide. An assumption needed for further development of this theory is that interaction is contingent on the development of expansive constructive interference. 

Why the Illusion Usually Holds In the Presence of Acceleration 

The common presence of  accelerations in our universe combined with a finite speed of light might suggest that expansive wave functions would quickly fill up with incoherence, destroying their usefulness as explanatory causes. However, if there are no non-expansive elementary particles, we just have expansive interacting with expansive to produce every acceleration. Once you get entirely away from the tiny-electron idea, it is not at all clear that any incoherence could ever develop. Such may well occur to a limited extent under some conditions, however. Relativity theory may be based on such limited incoherences.

Specific Experiments 

Two baffling kinds of experiment seem amenable to the big-electron treatment: diffraction of "particles" of matter like electrons, and entanglement experiments.

Electrons fired in a vacuum at a pair of closely-spaced slits, with a photographic plate situated on the other side of the slits, will produce a diffraction pattern on the developed plate consisting of alternating exposed and unexposed bands. These are interpreted as locations of constructive and destructive interference between "matter waves" emanating from the two slits under the stimulation of the electron beam. If the intensity of the beam is lowered to the point where only one electron is "in the chamber" at a time, thereby eliminating inter-electron interactions inside the chamber, the diffraction pattern develops just as before. It merely takes longer. All this could happen only if each electron goes through both slits at once. This is weird if we try to use the traditional tiny-electron picture, but much easier to visualize using the big-electron picture.

Entanglement of two particles that persists over distances measured in kilometers is also easier to understand if we remember that the experimental apparatus is itself made up of expansive wave functions and is therefore mostly overlapped with the two particles being studied throughout the experiment.

Conclusion 

If all this is true, then we live in a vast web of inter-validating illusions called the particle model.

#30. The Russian-dolls--multiverse Part II [physics]

PH

Red, theory; black, fact

Continuing from the previous post, leptons may arise as electromagnetic wave functions originating in p2 that are transported into our p3 universe/condensate by ordinary diffusion and convection. Wave functions in p2 that are already leptons become our baryons when they are transported in. The only kind of wave functions that are "native" to a given frame of reference are electromagnetic (photonic) in that frame of reference. If they subsequently propagate towards increasing p (inwards) they gain mass as matter; if they propagate towards decreasing p (outwards), they first lose mass as matter until they are photonic (i.e., massless) and then gain mass as antimatter.

To produce stable leptons from in-migrating photons, the first condensates, the p2s, would have had to be rotating simultaneously about three mutually perpendicular axes. If this is impossible for p3 physics, we have to appeal to the possibility of a different physics in p1 for any of these ideas to make sense.

A "universe" is something like an artist's canvas with a painting in progress on it. First, nature makes the blank canvas, and then, in a second stage, puts the information content on it. Consider the moon. It formed out of orbiting molten spray from the collision of two similarly-sized planetesimals. In the molten state, its self-gravity could easily round it up into a perfect sphere which could have solidified with a mostly smooth surface. Call this smooth surface the "canvas." Subsequently, the very same force of gravity would have brought down meteors to cover the surface in an elaborate pattern of craters. Call this the "painting." 

Now consider the neutronium core of a neutron star, viewed as a p4, or small universe. The tremendous energy release of the catastrophic gravitational collapse in which it forms homogenizes all the matter into pure neutrons, thought to be a superfluid. This creates the "canvas." Subsequently, matter and energy from our p3 migrate into the superfluid, producing a "painting" of leptons (our photons), baryons (our leptons), and "uberbaryons" (our baryons). Indeed, the neutron-star core is actually thought to be not pure neutronium, but neutronium containing a sprinkling of free protons and electrons (as seen in p3, of course).

#29. The Russian-dolls--multiverse Part I [physics]

PH

Red, theory; black, fact

A Matryoshka

The space we live in may have an absolute frame of reference, as Newton taught, and which Einstein taught against. This frame of reference may be a condensate, like the water a fish swims in.

The divide-and-conquer strategy that has served science so well thus far can continue with the conceptual disassembly of this space into its constituent particles. The question arises if these particles are situated in yet another space, older and larger than ours, or if we go direct to spacelessness, where entities have to be treated like Platonic forms. In the former case, does that older, larger space in turn comes apart into particles situated in a still older and larger, etc, etc, ad infinitum?

Infinities are the death of theories. Nevertheless, let us continue with the Russian-dolls idea, merely assuming that the nesting sequence is not infinite and will not be infinite until the entire multi verse is infinitely old, because the "dolls" form one by one, by ordinary gravitational collapse, from the outside in.

Wave functions would be the basic building blocks, following quantum mechanics. In the outermost space, previously called #, the wave crests always move at exactly the speed of light.

This speed is not necessarily our speed of light, c, but more likely some vastly greater value.

The space-forming particles of # are themselves aggregates with enough internal entropy to represent integers and enough secondary valences to form links to a set of nearest neighbors to produce a network that is a space. This space acts like a cellular automaton, with signals passing over the links to change the values of the stored integers in some orderly way. The wave functions are the stereotyped, stable figures that spontaneously develop in the automaton out of the initial noise mass left over from catastrophic gravitational collapse. 

The dimensionality of a space would increase steadily over time, because the number of links emanating from each node in the underlying network increases slowly but surely. Macroscopically, this dimensionality increase could look something like protein folding. 

Let us label the Russian-dolls universes from the outside in, in the sequence 1, 2, 3,...etc, and call this number the "pupacity" of a given frame of reference. (From the Latin "pupa," meaning "doll.") Let us further shorten "pupacity" to "p" for symbol-compounding purposes. Thus, the consecutively labelled spaces can be referred to as p1 (formerly "#"), p2, p3,... etc.

pn can exhibit global motions ("n" is some arbitrary pupacity), such as rotation, in the frame of reference of p(n-1): a whole universe rotating as a rigid unit. Probably, it can drift and vibrate as well.

Global motions must be subtracted from the true, outer, speed-of-light speed of the wave crest to produce its apparent speed and direction when seen from within pn. Thus, the universe's love of spinning and orbiting systems of all sizes is explained: a spinning, global-motion vector is being subtracted from the non-spinning, outermost one. As the pupacity of the frame of reference increases, more and more of these global vectors are being subtracted, causing the residual apparent motion to get progressively smaller. We would assume under current physics that the wave functions are acquiring more and more mass, to make them go slower and slower, but mass is just a fiction in this scenario. However, the reliance of current physics on the mass construct is an opportunity to determine the pupacity of planet Earth: it is three.

Three, because physics describes three broad categories of particle mass: the photon, leptons, and baryons. The photon would be native to p1, leptons, such as electrons and positrons, would be native to p2, and baryons, such as protons and neutrons, would be native to p3, our own sub-world. 

The positron atom would be a standing-wave pattern made up of oppositely rotating wave functions, an electron and a positron, both native to p2. A neutron would be exactly the same thing, but native to p3. 

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

PH

Red, theory; black, fact

Back to the Aether Theory 

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 absolute space is complicated, like a network, crystal, or condensate.

The Reasons

1) 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. 

2) The wave model and the particle model of mass and energy are both very useful in Quantum Mechanics, our best theory of the very small. The wave model demands some kind of medium and thus an absolute frame of reference. The particle model, however, does not demand its absence. For example, observing frictionless motion of a particle could be due to the absolute frame of reference being a region of superfluid. Relativity theory uses the particle model exclusively and denies the existence of an absolute frame of reference, but this conclusion comes at the end of a long and convoluted chain of reasoning and is thus weaker than the claim made by use of the wave model.

3) The importance of the speed of light in Relativity is highly consistent with the wave model: it could be the propagation speed of the waves underlying both matter and energy.

The Medium is Complex

Thus, I assume that the fundamental constants 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 may more readily be 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.

The Thought Barrier 

To theorize about how space formed and what came before it, we have to give up visualization. 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.

Beyond the 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.

Set Theory as Physics Beyond the Barrier

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 unimaginable if thought of as the rules of a real universe? 

Development 

1) 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 unpretentious like Cheereos™ floating in milk, when the bowl has reached the single-layer stage.)

2) 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.

3) 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.

4) 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.)

5) 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. 

6) 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.

#19. The Two-clock Universe [physics]

PH

Red, theory; black, fact

Is This Reasonable?

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

Background 

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, a concept that was originally introduced to explain why the distribution of matter in the universe is smoother than predicted by the original version of the big bang.

Cosmological Expansion by Two Clocks

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.

Mechanistic Details

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.

The Fate of the Universe 

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 re-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.

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

PH

Red, theory; black, fact

Detail of a mural by Barbara Vermer

Alocia and Anaevia

Can you make a case for the existence of absolute space and even suggest 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 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.