Red, theory; black, fact.
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| Natty dog/epiphany |
The basic theoretical vision
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| The givens assumed for this theory of everything. Since there are givens, it is probably not the real theory of everything but rather a simplified physics. (But maybe a stepping stone?) |
The dimensionality question
The foam is infinite-dimensional. Within the foam, interfaces of all dimensionalities are abundant. Following Hawking, I suggest that we live on a three dimensional brane within the foam because that is the only dimensionality conducive to life. The foamy structure of the large-scale galaxy distribution that we observe thus receives a natural explanation: these are the lower-dimensional foam structures visible from within our brane. The interiors of the domains are largely inaccessible to matter and energy. <03-12-2022: We have an infinite regress again, this time toward increasing dimensionality: we never get to the bulk. Is it time to censor again and postulate progressively lessened contrast with greater dimensionality, and asymptotic to zero contrast? No; the foam model implies a bulk and therefore a maximum dimensionality, but not necessarily three. But what is so special about this maximum dimensionality? Let us treat yin-yang separation as an ordinary chemical process and apply the second law of thermodynamics to see if there is some theoretical special dimensionality. Assuming zero free energy change, we set enthalpy increase (“work”) equal to entropy increase (“disorder”) times absolute temperature. Postulating that separation work decreases with dimensionality and the entropy of the resulting space foam increases with dimensionality, we can solve for the special dimensionality we seek. The separation process has no intrinsic entropy penalty because there are no molecules at this level of description. The real, maximum dimensionality would be greater than theoretical to provide some driving force, which real transformations require. However, is the solution stable? Moreover, the argument implies that temperature is non-zero.><06-26-2022: Temperature is here the relative motion of all the minute, primordial domains. This could be leftover separation motion. How could all this motion happen without innumerable checkerboard-rule violations and thus many fusion events? Fusion events can be construed as interactions, and extra dimensions, which we have here, suppress interactions. More on this below.><02-07-2023: That said, the idea of primordial infinite dimensionality remains beguiling in its simplicity and possibilities.>
12-23-2021: Since infinite dimensionality is a bit hard to get your mind around, let us inquire what is diminished upon increasing the dimensionality, and just set it to zero to represent infinite dimensionality. Some suggestions: order, interaction, and correlation. To illustrate, imagine two 2-dimensional Ardeans* walking toward each other. When they meet, one must lie down so the other can walk over them before either can continue on their way. That's a tad too much correlation and interaction for my taste.
03-03-2022: I suppose that as dimensions are added, order, correlation, and interaction decrease toward zero asymptotically. This would mean that 4D is not so different from 3D as 3D is from 2D. The latter comparison is the usual test case that people employ to try to understand extra dimensions, but it may be misleading. However, in 4D, room-temperature superconductivity may be the rule rather than the exception, due to extradimensional suppression of the interactions responsible for electrical resistance. The persistent, circulating 4D supercurrents, understood as travelling electron waves, may look like electrostatic fields from within our 3-brane, which, if true, would help to eliminate action-at-a-distance from physics. Two legs of the electron-wave circulation would travel in a Direction We Cannot Point. These ideas also lead to the conclusion that electrostatic fields can be diffracted. Bizarre, perhaps, but has anyone ever tried it? <03-21-2022: Yes, they have, and it is the classical electron diffraction experiment. The electrons are particles and are therefore not diffracted; they are accelerated in an electrostatic field that is diffracted, thereby building up a fringe pattern on the photographic plate. The particles, then, are just acting here as field tracers. Slight difficulty: neutrons can also be diffracted. A diffraction experiment requires that they move, however, so read on.>
Still to be explained: Newton's first law (i.e., inertia and motion).
How to accommodate the fact of motion
08-06-2012: Motion can be modelled as the array of ripples that spreads across the surface of a pond after a stone is thrown in. A segment of the wave packet coincides with the many minute domains that define the atoms of the moving object, and moves them along. The foam model implies surface tension, whereby increases in interface area increase the total energy of the domain. If the brane is locally thrown into undulations, this will increase the surface area of the interface and thus the energy. This accounts for the kinetic energy of moving masses. Momentum is the rate of change of kinetic energy with velocity and inertia is the rate of change of momentum with velocity.
03-08-2022: Brane surface tension would be a consequence of the basic yin-yang de-mixing phenomenon, because increases in interfacial area without volume increase (interface crumpling) can be construed as incipient re-mixing, which would go against the cosmological trend. Thus, the interface always tends to minimum area, as if it had surface tension. <03-04-2023: this tension provides the restoring force that one needs for an oscillation, which is important because waves figure prominently in this theory. However, a wave also needs the medium to have inertia, or resistance to change, and where is that in the present theory? It can be introduced in the form of a finite speed of light. For example, the permeability of free space, related to inductance, a kind of electrical inertia, can be expressed in terms of the speed of light and the permittivity of free space, related to capacitance, which inversely expresses a kind of electrical restoring force.>
Dark matter and how to introduce gravity into this theory
08-14-2021: Gravity is being difficult here. I don't want to replace it with a bunch of spiral branewaves, and I don't know why it has an inverse squared power law. Let's drill down on this: when two interstellar dust grains collide, some kinetic energy is converted to heat energy, which radiates away. Without this process, called inelastic collision, the gravitational accretion of mass, and thus gravity itself, will not be observed. (By the way, one illusion that we may need to shed to make progress is that the convex spaces of the universe, such as the spaces occupied by stars, planets, and galaxies, are fundamental and the negative, concave, between-spaces are just meaningless pseudo-structures, which are called "spandrels" by evolutionary theoreticians. But could it be the other way around? In this, I am using the word "space" in an architectural sense.
08-27-2021: Eureka! Let us suppose that each visible astrophysical object is surrounded by an invisible atmosphere-like structure consisting of mid-sized domains (larger than atomic scale but smaller than intergalactic voids). This could be dark matter. Let us further assume that minimizing the total interfacial area of this structure leads to sorting according to domain size, resulting in a gradient of domain sizes that places the smallest in the center. Therefore, lifting an object off the visible surface necessarily disturbs this minimum-energy structure, requiring an input of energy. This requirement would be the gravitational potential energy of an elevated object. The exact power law remains unexplained, but I think these assumptions bring us much closer to an explanation.
12-29-2021: Ordinary matter would be distinguished from dark matter by the ordinary domains being full of standing waves that store the energy of many historical merging events. The antinodes in the standing wave pattern would be the regular array of atoms thought to make up a crystal (most solid matter is crystalline). The facets of the crystals would correspond to the domain walls.
<02-10-2023: The waves could be confined inside the ordinary domains by travelling across our 3-brane at right angles, strictly along directions we cannot point. However, something has to leak into the 3-brane to account for electrostatic effects.><02-12-2023: Crossing the 3-brane perpendicularly is possible by geometry if each particle is a hypersphere exactly bisected by the 3-brane, and mass-associated waves travel around the hypersphere surface.><02-14-2023: Presumably, the neutron produces no leakage waves, which could be assured by the presence of a nodal plane coinciding with the spherical intersection of the particle hypersphere with the 3-brane. Electrons and protons could emanate leakage waves, a possibility that suggests the origins of their respective electric fields. However, the fact that these particles have stable masses means that waves must be absorbed from the 3-brane as fast as they exit, meaning that an equilibrium with space must exist. For an equilibrium to be possible, space must be bounded somehow, which is already implied by the foam model. Since we know of only two charged, stable particles, two equilibrium points must exist. This scenario also explains why all electrons are identical and why all protons are identical. If their respective leakage waves are of different frequencies, the two particle types could equilibrate largely independently by a basic theorem of the Fourier transform.><02-19-2023: Particles of like charge would resonate with each other's leakage wave, resulting in a tendency to be entrained by it. This would account for electrostatic repulsion. Particles of opposite charge would radiate at different frequencies and therefore not mutually resonate, leading to no entrainment. However, since each particle is in the other's scattering shadow, it will experience an imbalanced force due to the shadow, tending to push it toward the other particle. This effect could explain electrostatic attraction.><03-14-2023: Gravity may also be due to mutual scatter shadowing, but involving a continuum spectrum of background waves, not the resonant line spectra of charged particles. Note that background waves are not coupled to any domains, and so do not consist of light quanta, which, according to the present theory, are waves coupled to massless domain pairs.><04-21-2023: The bisected hypersphere particle model predicts that subatomic particles will appear to be spheres of a definite fixed radius and having an effective volume 5.71 x greater than expected from the same radius of a sphere in flat space. (5.71=1+1.5x🥧) Background waves that enter the spherical surface will therefore be slow to leave, a property likely to be important for physics.>
03-08-2022: There may be a very close, even mutualistic, relationship between domain geometry and interface waves, all organized by the principle of seeking minimum energy. Atomic nuclei within the crystal could be much tinier domains, also wave-filled but at much shorter wavelengths. The nuclear domains would sit at exactly the peaks of the electron-wave antinodes because these are the only places where the electron waves have no net component in the plane of the interface. Most particles will have the following structure as modelled with reduced dimensionality: a pair of prisms joined at the end-faces, the joint plane coinciding with the 3-brane of our world. Mass is standing waves in the joint plane. One prism is a plus domain and the other a minus domain. Both project out of our 3-brane into cosmologically-sized domains of opposite type. 09-04-2022: Neutrinos may violate this pattern if they are unpaired domains completely surrounded by the opposite type of space and having no obligatory presence in our 3-brane. This would explain the weakness of their interaction with other types of matter and the existence of more than one type of neutrino. This picture predicts two types but we know three exist, a difficulty for this theory.
