#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.

#28. My Second Theory of Everything [physics]

PH

Red, theory; black, fact

How does wavelike, low-frequency light becomes particle-like, high-frequency light as frequency is smoothly increased? Waves are continuous, whereas particles are discontinuous; how, then, does the breakup occur?

You have to put the source in the picture. Recoil of the source atom sends the wave function off in a specific direction, but the wave function is known to expand (about its center of symmetry?) as it goes. Presumably, it is the vector sum of these two motions that must equal the speed of light; either one is presumably free to take on some lower speed, say, that of a pitched softball. I conjecture that as frequency increases, the particle-like drift of the center progressively dominates the mixture at the expense of the local, wave-like expansion of the wave function about its center. This is how I see waves morphing into particles as the frequency increases. 

• There is an absolute frame-of-reference, #.
• All motions seen in this frame of reference will be observed to occur at the speed of light (c); and only this frame of reference has this property.
• All speeds lower than c are illusions caused by the motion of the observer's frame of reference.
• That which moves always at c is not a wave function, but a phase marker of some sort within it, such as a zero crossing or a wave crest.
• The local wave function evolution relative to its center of symmetry combined with the drift of that center relative to # always travels at c relative to #.
• If local evolution is an expansion along all wave function radii, you have light; if it is a rotation about the center of symmetry (i.e., motion perpendicular to radii), you have matter.
• Light wave functions will be like nested spherical shells, whereas matter wave functions will have a lobar, angle-dependent structure like a p-, d-, or f-orbital in theoretical chemistry. The lobes are essential to provide a contrast pattern that could, in principle, be observed to spin.
• The presence of one axis of rotation produces the neutrino; two simultaneous axes of rotation produce the mesons; three produce the remaining stable particles, e, p, and n. If the three rotational rates are distinguishable, the resulting structure has a handedness.
• The matter/antimatter dichotomy arises from this handedness, when combined with a law of conservation of spin that would result from space initially being symmetrical. 
• The mesons should have an ability in 3-space to flip over into their corresponding antiparticles.

#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.