#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.

#52. Reality is Virtual but the Host Computer is Analog. [physics]

PH

Red, theory; black, fact

The nucleus around which a theory of everything will hopefully crystallize.

An Idea About What Exists

Existence may be something like a Turing machine, but with a multiplicity of tapes and a multiplicity of processors. Each tape corresponds to one elementary particle in space-time and the processors implement only Hebb’s rule, a rule of learning first discovered in neuroscience, and that governs correlations among signal sources. The tapes are polymer-like, and their ongoing elongation by polymerization at the ends causes the passage of time. This elongation is associated with a white-noise signal unique to each particle/tape/strand because the monomers are sampled from a population with a Gaussian size distribution.

A theoretical schema showing the basic strand-processor interaction. The theory borrows from the Turing machine concept, Hebb's rule of learning, and the chemistry of polymerization. Black, one information-bearing polymer strand; blue, processor; red, monomers.

A still more complex, three-strand scheme. At a given point, multiple strands may adhere to the same processor, and vice-versa.

Mechanism

The first illustration is my current best guess as to what a Hebb processor is like, but as we say in research, "Many questions remain." The short, black lines are the catalyzed ligation points between monomers, and these are the points of attraction to the processor. If the rear pull-off point encounters a big gap between ligation points, the processor will advance an unusually great distance in one step, creating an unusually long catalytic pocket at the front, which will have a selectivity for longer monomers, thereby implementing a copying mechanism. Causally, this is backwards, but the alternative explanatory plan seems to involve a messy discussion of chemical equilibria.

The Big Picture

This machine is presumed to be naturally occurring and to belong to a particular stage in the physical evolution of the universe. I make no appeal to arguments of intelligent design, even by space aliens. By the anthropic principle, the machine is not necessarily typical of all structures extant at that stage. In other words, we are living in a natural sub-world that is simulation-like in that the view from within is entirely unlike the view from without, but the two views are related by something that could be called a sub-world law, an example of which would be d = K/rxy. This concept is nothing new because it could also serve in outline as a description of human conscious experience, which is most unlike a mass of neurons signaling to each other in the dark.  Thus, the theory of everything could turn out to be a series of nested sub-world laws.

Mathematization

The length of a strand relative to some interior point is a Gaussian white-noise time-series signal with an upward trend just steep enough to eliminate negative slopes. I will deal here with the detrended version of this signal because, on the laboratory distance scale, both the observed system and the observer will share the same trend, preventing its direct observation. Moreover, the polymerization process is postulated to preserve a permanent record of the detrended signal. Therefore, while the future does not exist in this model of time, the past is perfectly preserved. A set of distinguishable time series is called panel data and is a Euclidean space by the mathematical definition and can therefore map onto and explain physical space, at least on the laboratory scale.

Imagine some panel data consisting of two time series, X and Y, representing two elementary particles. Take a slice of this data ten samples long and plot them as two ten-dimensional vectors, X and Y. The dot product of these vectors is then easily computed as x₁y₁ + x₂y₂ + … x₁₀y₁₀. A Euclidean space is defined as an affine space (i.e., containing no special points like the origin) where the vector dot product is defined. Recall that this dot product is equal to the length of X times the length of Y times cosθ, where θ is the angle between the vectors. Moreover, cosθ is here equal to rₓy, aka Pearson’s r, a measure of correlation between signal sources. Pearson's r is commonly used in the sciences, including neuroscience, and ranges from -1 for negative correlations to +1 for positive correlations; zero indicates no correlation.

rxy may represent distance in space-time, and vector length represents mass-energy in space-time. An rxy of 0 would represent infinite distance and an rxy of 1 would represent 0 distance, a state found only in black-hole singularities or the big bang singularity. 

The Illusion of Euclidian Space

Processes would be experienced as close together because they are correlated, not correlated because they are close together. The latter is the usual assumption, usually rationalized as being due to the easy exchange of synchronizing photons or virtual photons at close range. However, we seem to be moving here toward the elimination of the light/photon construct from physics.

A Second-iteration Theory

A simpler possibility is d = K/rxy and rxy = K/d. This change advantageously limits how small space-time distances can become, thereby eliminating infinities from gravity calculations. K is this minimum length. With this revision, the dot product of two vectors in the simulation becomes equal to gravitational binding energy.

How Known Physics Comes from the Model

Orderliness

Each strand would have a Hebb processor on each end that may catalyze the polymerization process. Each processor would also be connected to a random point within the mass of strands. This connection moves along the associated strand like a phonograph needle,  reading the recorded signal while keeping pace with the growing end. The processor also has a front read-point in the present. The two read points may or may not be on the same strand. If a correlation is detected between the two read points, the correlation is permanently enhanced by a modification of the polymerization process, per Hebb’s rule. All the orderliness of the universe is supposed to emerge from this one type of calculation.

Space

At this point, we have not eliminated space from physics; we have merely replaced Euclidean space by another kind of space that is less structured, in which the spaghetti machine has its being. The new space is a metric space but has neither norm nor dot product axiomatically, although they can be present in simulation. The metric is bijective with the counting (natural) numbers and is equal to the number of primordial time elements (PTEs) in a polymer of same. The metric space may itself be a simulation running on a processor situated in a still simpler space, namely a topological space, in which only a few distinctions matter, such as inside-outside and closed-open.

Speed of Light

Degrees of correlation less than maximal are encoded in the processor as the number of strands adhering to the processor above the minimum for inter-strand copying, namely two. One of these middle strands is illustrated in the sketch of the three-strand scheme, and they putatively degrade the fidelity of the copying process and reduce Pearson's r in proportion to their numbers, while also introducing a time delay into the copying process, due to changes in the length of the processor. A reduction in Pearson's r, which increases the encoded distance, simultaneous with an increase in the copying time delay is responsible for the finite speed of light.

Hydrogen Spectrum

If N is the number of middle strands on a processor, then a reasonable guess as to its effect on Pearson’s r would be r = 1/(N + 1). Units analysis requires that the electron binding energy equal the length of the projection of the electron vector on the proton vector. This is not the dot product and it has the correct units, namely mass-energy. Rydberg's formula for predicting the energies of the spectral lines of hydrogen can thus be reproduced as:

ΔE = ||e||*(1/n₁ – 1/n₂), n₂ > n₁

Equation (1)

Gravity

The default interaction implemented by Hebb’s rule would be gravitational attraction. Black hole formation illustrates that gravitation has a built-in positive feedback, and this would derive from the positive feedback built into simple forms of Hebb’s rule.

To provide the hypothetical Hebb processors with such a positive feedback, I postulate the following: Middle strands come and go in an energy-dependent excision/reintegration process and have a small loop of processor adhering to them when free, which explains how the processor length changes occur. A high-fidelity copying process releases more energy than does a low-fidelity copying process, and excision requires energy input. These ingredients, together with the fidelity-degrading property of a middle strand, should be sufficient for a positive feedback.

Mass

If the two read points are on the same strand, the result will be an oscillation. Electromagnetism could be the set of interactions peculiar to oscillating strands. The variance needed to express the oscillation would be deducted from a fixed total, resulting in less variance available to represent distances by its correlations. A smaller distance signal will be more rapidly modified by the Hebb processors, resulting in faster responses to forces and a smaller mass according to Newton’s a = F/m. Thus, we expect neutral particles to be more massive than charged particles, and this tendency is indeed found among the mesons and when comparing the proton and neutron. The relatively great mass of the proton and neutron and the nuclear strong force itself may emerge from a cyclic pattern of three strands (the quarks) connected by three processors. The example of the benzene molecule teaches us to expect novel results from cyclization. The great mass of the baryons may come from the chaos inevitable in the celestial-mechanics version of the three-body problem, but the three bodies would be the three quarks. In the present theory, noise amplitude corresponds to mass-energy, and fast chaos looks like noise. 

An extension of this idea would be that chaos is the source of all mass and the properties of a timeline depend on how many highly-correlated others (HCO) there are and the degree of this correlation. One HCO produces an oscillation but no mass; two or more produce chaos and some amount of mass. High correlation can be understood as relative, leading to a hierarchy of relationships. 

Repulsive Forces

There may be an alternative kind of middle strand or mode of adhesion that enhances copying fidelity upon adhesion rather than degrading it. This amendment to the theory may be required to model interactions that appear repulsive.

The Transparency of the Universe

Hebb processors with their rear read points in the distant past would open up long-distance communication channels in space-time, giving us the by-now familiar experience of looking millions of years into the past through powerful telescopes, to see galaxies as they were when the universe was young. The communication would be instantaneous, but from an old source; not slow from a new source.

The big bang

The universe may have begun in a singularity for a trivial reason: it initially had no way to represent information, let alone correlations, because all the incoming monomers were PTEs, identical in size and having the smallest possible size. A slow direct condensation reaction in the monomer pool then gradually built up larger blocks of PTEs, causing the average size of the items adding to the strands by polymerization to increase progressively. The standard deviation of the size distribution would likewise have increased. 

Space would have expanded rapidly at first, as predicted by the inflationary hypothesis, because the first little bit of polymerization entropy to develop would have had a disproportionate effect on the system's ability to represent information. This predicts that the mass-energy of all particles has also been increasing ever since the big bang. Therefore, by equation (1), we expect that spectral lines from ancient luminous matter will be redder than comparable lines from contemporary matter, as found by Hubble, which explains the cosmological red shift.

#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.

#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. 

#25. The Phasiverse [physics]

PH

Red, theory; black, fact

The nucleus around which a theory of everything will hopefully crystallize.

The Concept

Our reality, the world of appearances, is encoded in the relative phases of an ineffably large number of oscillators, each of which is a kind of primitive clock.

Inspiration from Quantum Mechanics 

An early interpretation of the theory of quantum mechanics was that there is a harmonic oscillator somehow assigned to each point in space, and that these account for the matter fields of the universe. Examples of oscillators would be a mass bouncing up and down on a spring and an electronic device called a tank circuit, which is just one capacitor connected across the terminals of one inductor. 

Consider Huygens's Clocks

If a set of such oscillators can communicate with each other (exchange oscillatory energy), this is called coupling, and it can make the oscillators tend to pull each other in to the same, common phase. The Huygens's clocks experiment began with two old-school pendulum clocks in a case with their pendulums swinging in some random phase relationship. The next day, mysteriously, the pendulums were found swinging in opposite directions. The coupling is evidently due to tiny, rhythmic forces travelling through the common supporting beam from clock to clock.

Enter Positive Feedback 

If the coupling is positive, as assumed here, (it's negative in the above experiment), the phase pull-in effect becomes stronger the closer the two phases approach each other, causing a positive feedback effect. This is very reminiscent of Hebb's rule in neuroscience and the tendency of natural attractive forces such as gravity to depend inversely on distance. 

A Organizing Principle 

The phase pull-in effect provides a simple answer to questions such as where the organizing principle comes from. All you need to explain is where the oscillators themselves all came from, how they oscillate, and why they are coupled. Since the oscillators begin life in spacelessness, they cannot avoid interacting to produce a coupling effect. Second, oscillators need no past or future; they can arise as a succession of causally related nows that alternates between two contrasting forms. Figures in Conway's game of Life would seem to be examples of this alternation.

Enter Entropy

A great many oscillators all with the same phase is not an interesting universe. However, suppose that this is impossible because of "train wrecks" happening during the synchronization process that produce frustration of the synchronization analogous to spin frustration in spin glasses. An example would be a cyclic relationship of oscillators in which a wave goes around the loop endlessly. Such cycles may correspond to particles of matter in our universe, and the spiral waves that they would throw off into surrounding space may correspond to the fields around such particles.

Gravitational Lensing Explained

A black hole or galaxy would be surrounded by a tremendous number of such radiating fields. The resulting desychronization of the oscillators making up the surrounding space would increase the average phase difference between phasically nearby oscillators, thereby inhibiting their coupling, thereby inhibiting the travel of signals generally through the region. Result: the speed of light is reduced in the vicinity, resulting in the bending of light rays, called gravitational lensing.

Quantization is not explained, which is a limitation of the present theory.

#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.

#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.