# The Anatomy of a Wave, Acceleration Density, and a Theoretical Synthesis

## In search of quantum foundations

Three of the fundamental equations of quantum physics are:

E=mc2,

w=P/mv,

and E=Pf,

where E=energy, m=mass, c=the velocity of light, w=wavelength, f=frequency, v=velocity, and P=Planck’s constant (Smolin, Einstein’s Unfinished Revolution).

If the first two equations are solved for mass then equated, with substitution and canceling such that the absolute minimum of variables remain, the simplest synthetic formulation is v=fw. This implies that all matter is in motion, and the structure of this fluxing matter takes the intrinsic form of a wave. It appears that since mass can be vacated from the hybrid expression in favor of a more essential form, namely a wave, the structurality we associate with mass, namely three dimensional particularity, is an epiphenomenon. Then we must inquire as to the sense in which this is true.

Regardless of how externalized particularity seems to an individual observer, it is fundamentally a perception, and this perception is a property of consciousness in its correlation to the body, a subject addressed with reference to neuroscience. The nervous system and brain are dazzlingly complex and premonitional, with our self-awareness constituting only a fraction of its functionality, so that the deceptiveness of introspection is well-documented, and a comprehension of the mind’s mechanisms must be preceded by a level of scientific modeling and insight into metaphysical concepts that has not been approached, which will probably induce a seismic shift in our picture of what substance and the existence it conjures consist in. But to the extent that this physical world we inhabit is analogous to current technology, it is not as much of an enigma, for technology interfaces our existence with nature on the much narrower scale of our quintessentially macroscopic bodies.

This spectral range of phenomena is much less complex than perception’s ultimate essence because it is parameterized by the overriding force of gravity on our planet, which makes all kinds of lifeforms and the objects they typically interact with relatively easy for science to handle, showing up in the simplicity of classical physics compared to neuroscientific psychology. This conglomeration of phenomena is also more transparent, for extremely prominent physiological structures, namely sense organs such as eyes, ears and noses, are exquisitely tailored for the most important factors in survival of our bodies, and operate in accordance with the principles of classical physics as well. This highly intuitive particularity, our sense-perception obeying the principles of classical physics, interacts with firmly established technological traditions based on the same principles to serve as the most crucial factor for sustaining and actualizing behavior by way of the baseline material requisites that must be met for reproduction, health, leisure and intellectuality to be attainable. Perceptions and technologies of Newtonian particularity intersect within the conceptual domain of spatiotemporality, simply amounting to three dimensional entities traveling in sequences. Mass is the most fundamental unit of this spatiotemporal portion of the experiential spectrum, a measure of three dimensional extension and its time-lagged relationships.

Many processes that are not directly observable can be described using this concept of particularized mass, an envisioning of matter as made up of self-contained, roughly spherical structures exerting pressure by collisions, or attracting such that the kinetic energy of their motions becomes contained as potential energy in chemical bonds. But quantum physics has unshrouded phenomena that do not conform to this mold. The behaviors of particles can be correlated across distances, where a manipulation of one produces almost instantaneous change in another by way of entanglement. Retroactive causality in elementary particles has also been observed, where perturbing a photon’s path after the measured particle passes the point of intersection results in a similar entanglement effect. Clearly there is something going on that transcends particularity, for particles exert causality by localized effects, whereas matter has been revealed to possess nonlocal properties.

Some matter appears particularized, but like a bouncing ball oscillates when perturbed until it again reaches inert equilibrium. Some material substances such as gases and light waves manifest as more nonparticularized, expanding and contracting on their own with no intrinsic spatial limitations, yet occupy definite spaces and move at specific rates, in effect behaving in a patterned way, as if comprised of regularized form, a particlelike symmetry. It seems that, roughly speaking, matter can be relatively more or less like a textbook particle such as a grain of sand, while in all cases capable of vibrating as a wave. A thrown baseball moves through three dimensional space like a particle, and flexes like a wave upon contact with the glove. During an earthquake, the ground moves as if a wave, and of course likewise for a perturbed liquid. Electrons can be made to flow in a wavelike current. They are also in constant motion within molecules, a phenomenon slippery enough to our present measuring devices that exact precision in the defining of either an electron’s position or momentum inhibits precision for the other. A beam of light behaves more like a wave, but is absorbed in discrete packets of energy by particles such as electrons, as if quantized.

Every particle can be made to act as a wave, and every wave can be induced into particle behavior, so it seems that particularities and waves constitute opposite ends of a spectrum of substance, the forms of which are determined by degree of actual or possible oscillation. Particle behavior precludes nonlocality, so we can rule it out as fundamental, but even the most stable particles have wavelike properties, which agrees with our equation v=wf, so can the properties of a wave explain nonlocality? If we make the assumption that substance is one gigantic, amorphous wave of extreme complexity, does this account for our experimental observations while managing to avoid explaining away the apparent properties of inert, spatially differentiated, and plainly time-lagged particularity?

First of all, it has been established by experiment that the probability of finding a projectile electron in a specific location is proportional to the square of its wave function, which in terms of flow, simply means that the particle is most concentrated at a particular point in space, like the peak of a bell curve, with its structure thinning out in all directions while straying from the substantive core. Pilot wave theory models this: the function of a wavicle, approximative to the phenomenon in nature, is most particlelike where it is most localized, or rather where it has the least accelerative rate of change, at its apex, the crest of the hill so to speak. This point can be termed the maximum acceleration density. According to this definition, the wave becomes less particlelike as it approaches its base, with the acceleration density more diffuse, changing at a faster rate quantified as a limit, the slope of the tangent to the curve at a particular point along its length. The wave’s acceleration then levels off again as it approaches the next peak, meaning that it increases in density or concentrated motion.

This accounts for some significant phenomena. It is easily noted that at any particular point along the wave’s length, the acceleration density of the regions that immediately surround it are different in numerical value while also driving the wave out of its current state and towards a differing value. The motion of a wave is continuous but fundamentally disequilibrated. Yet given enough time, the wave will approximately duplicate any given state, so that as the topography or density contour of a wave increases in complexity, equilibrium arises. The more disequilibrations that exist in a wave as stimulated by phenomena such as interference, the more this disequilibrium is canceled out by its motions. At the most basic level, equilibrium in a wavelike structure is an emergent property of disorder, with greater quantities of relative disorder producing more equilibrated states as chaos theory suggests. A solar system is more heterogeneously complex than a miniature spinning model of a solar system one might find in a classroom, and though there is no precise scale by which to compare and contrast, the real thing in its dimension as a totality is obviously subject to much greater degrees of law-abiding behavior and perpetual motion, as evinced by the ease of mathematically modeling its revolutions over the course of an astounding billions of years, while in the case of a replica, the more complex the collection of factors involved in the structure and movement of a model itself, the more likely it is to spin on its own in an orderly way, all else being equal.

Acceleration density is noticeably lower or less concentrated at the wave function’s base than at its peak, leading to a statistically significant increase in relative motion, so it seems that a wave is moving faster the more approximately equidistant it is from the particlelike peaks. In a two dimensional wave, this effect is apparent but not all that extreme. However in nature, a wave’s oscillating movement is not occurring in two dimensions, but in all possible dimensions, which can be approximated as a wave function that vibrates in infinite dimensions, just as a circle can be thought of as a polygon with infinite sides. When a wave is vibrating in effectively infinite dimensions, the discrepancies between acceleration density at its most particlelike peaks and the positions located furthest away from surrounding peaks are magnified by a massive order of magnitude, so that motion near the peaks of the structure is almost stationary relative to the most equidistant troughs. As pilot wave theory approximates, acceleration is rapid enough between wave peaks that every particlelike position, though essentially diffuse, subsists within a single interconnected system, so wide swaths of wavicles respond to perturbation at any point almost instantaneously, as if their loci of motion are nearly standing still while the surrounding valleys oscillate in a relative flash.

So what we might call the global wave is amorphously oscillating in effectively infinite dimensions, amounting to ensembles of waves within waves which are altogether interfering in ways so variable as to be thus far structurally inconceivable. Nonlocality is transcendently complex to humanity’s notions of logical form, beyond anything which can be directly represented as spatiotemporality. But as we have seen, in terms of a wave function, and as an approximation to a real wave, the properties of a two dimensional idealization are roughly congruent with the whole, and so even as the exact quantitative specs such as ratios differ, the idealization is like a microcosm, a model of the real thing scaled down to manageable proportions, just as a circle displays many of the same properties as the sphere it inheres in, with a sphere categorizable in a sense as an extremely complex circle.

If all substances are infinite waves, why the disjunctions we experience in the material world, such as between radio waves, visible light and gamma rays, or electrons, atoms, molecules and all the larger corpuscles? Every substance is entangled nonlocally in some as yet unmodeled way, but superposition or wave synthesis only occurs, to the large and still unspecifiably constrained extent it is possible, between waves of similar enough scale. This is apparent from how wavelengths of the visible spectrum blend to create a diverse color palette, but do not blend as substantially with radio waves, and circumvent much interaction with even extraordinarily large collections of atoms. The sky is blue because of its vast absorption of light, but a room illuminated by white light filled with trillions of absorptive electrons is colorless. Visible light is similar enough in wavelength across its spectrum that it blends as superpositions into hybrid waves, just as electrons of different energies are similar enough in wavelength that they superposition into hybrid shapes, but light’s wavelengths differ so dramatically from the spectrum of electron arrangement in atoms that they travel through gas nearly as if in a vacuum. More condensed wavelengths of a liquid, corresponding to greater acceleration densities amongst interfering wave ensembles, are more absorptive, and most solids more absorptive still.

So we can set forth the principle that all else being equal, interference ensembles producing shorter wavelengths are more likely to transmit or deflect longer wavelengths of lower frequency, and closely packed wavelengths are more likely to absorb, but in order for the effects to be easily noted, discrepancies must be quite large. The atmosphere for instance does not transmit high frequency gamma rays as readily as radio waves, but this effect is only detectable over many miles, hence the greater range of radio waves than the gamma rays generated by a nuclear bomb. The superposed wavelengths in atoms are similar enough that they can exert blunt force as bodies when perturbed or dissolve each other. And gamma rays are a biologically borderline case, penetrating into an animal’s body as if somewhat reminiscent of blunt force, but not causing nearly the same level of damage to tissue as a solid such as a bullet, while ultraviolet radiation can damage the skin with heat, visible light illuminates it, and radio waves diffract around solids and to a limited extent through some kinds of solids with no appreciable effect.

The concept of acceleration density allows a simple qualitative synthesis of quantum mechanics with general relativity. All matter is made up of wavicle ensembles that interfere, which amounts to quantum fields within quantum fields, mixed and matched supradimensionally, with a fraction of these ensembles salient in various ways to human perception. The quantum field of the earth consists in a gargantuan range of ensembles and frequencies, some of which extend far beyond its surface. In general, the closer these ensembles are to the earth’s core, the more compact their acceleration densities and the stronger the force they exert on each other and their immediate surroundings, an outward thrust which is however partially resisted by a sort of surface tension that the greater amount of matter in outer regions of the spreading field reciprocally exerts, which does not constrain all of the wave but is sufficient to maintain Earth’s structural integrity in the atomic range of the spectrum. A portion of the quantum field that does apparently escape is gravity, and it exerts a force on objects within its range in proportion to how close to the core they are and thus subjected to higher acceleration density. A clock runs slower at lower altitude because the gravitational wave ensembles it is emulsed in have a higher acceleration density and thus are slightly more compact, causing a minuscule quantity of substance inertia due to permeating compression.

Why a wave to begin with? We can understand the existence of waves in nature by pondering the relationship between light and atoms. As soon as the wave starts to propagate, approaching its peak, it has entered an orbit, enveloped in an atomic quantum field while resisted by incoming fields, and just as the planets decelerate until reaching the extremity of their elliptical path, the acceleration density of light increases. As it passes the peak, it is whipped around the ellipse, ever closer to the center, but if its path is not impeded or channeled enough by atomic forces to merge with an ensemble, it flies out of superpositioned atomic structure at maximum acceleration. Then as soon as it leaves one ensemble’s orbit, it enters that of another, and whips around the opposite side to similar effect.

The speed of light, which is the propagation of a quantum field ensemble in supradimensional space, is so rapid compared to the rates amongst atoms that it can only be slowed enough for absorption by vast quantities of shifting wavicles, so that under many conditions, such as in our atmosphere, absorption is rather minimal. Light traveling through a conventional gas is like trillions upon trillions of minutely fluxing elliptical orbits, sufficing in quantity to eventually lower the electromagnetic radiation’s speed such that absorption often occurs, an effect more pronounced as a general rule for liquids and solids with their tendency towards greater acceleration density. If the superpositioned ensemble of an atom is such that it complements an electromagnetic wave, it absorbs that wave into its structure. Energy input from a quantum field can be large enough to burst apart an atom, such as when metals conduct an electric current or oxygen combusts.

Acceleration density within entangled ensembles of interfering quantum fields and their effectively infinite dimensionality, variously superpositioned, may be adequate to model much of what happens in our universe.

Then the question is: why dimensionality? If matter is best described as practically infinite in dimension, how come particular dimensions exist? Basically, dimensions are like idealized cross sections of reality, frames of mathematical reference typically rendered into an intuitive two or three dimensional image for integrating diverse phenomena into an approximate but maximally coherent general picture. Three dimensionality itself is perfect for modeling position, objects at rest, and is probably the most intuitive cross section. Two dimensionality is perfect for modeling velocity, objects with a trajectory, and is the core of predicting linear motion in three dimensions, such as with a projectile or planetary revolutions. Acceleration is a special case of velocity, appropriate for measuring especially rapid changes, with torque or accelerating acceleration perhaps the most rapid rate of change necessary for most purposes of physical modeling. And four dimensionality or spacetime is appropriate for modeling material phenomena that encompass too large a spectrum to involve the intuition of objects at rest, a substrate in which everything is in a relationship of perpetual motion. Each higher dimension contains all the others, but may not be finely grained enough to register many phenomena unless we so to speak zoom in with a lower dimension and then reintegrate.

With entanglement and retroactive causality, three dimensionality itself is perceptive enough to register very simple correlations in a suitable experimental context, but the phenomena jump into existence as if by magic, without the foggiest notion of their causality, and from this perspective, the fundamental mystery of it all means that large ensembles of wavicles as manifest in three dimensions quickly exceed our capacity to predict precisely where to look and thus measure, though some biological systems such as photosynthetic reaction centers and enzyme active sites are almost a microcosm of nonlocal phenomena, like quantum machines, so that investigating them yields systematic insight. The spacetime fourth dimension provides an accurate theoretical framework for elucidating how relative velocities of objects correlate throughout the universe, so is perfect for defining phenomena on the galactic scale, which move without direct three dimensional contact, but it deals in smooth curvatures of space that proceed in particular directions to the exclusion of all alternatives, and so cannot transcend particularity, only contextualize its full scope. Its yardstick still includes the arrow of time, and so remains fundamentally disjuncted from the quantum scale, having nothing at all to say about the idea that wavicles move outside of time, which has become central to our image of atomic reality.

Modeling the universe as an amorphous topography of infinite wave structure with its acceleration densities gives a good approximation of how matter can exist beyond the boundaries of time, ricocheting across distances with an asymmetric rapidity that transcends the loci we intuitively recognize as particles, generating equilibrium from chaos, interacting as supradimensional interferences that scale up or down in infinite space, accommodating any material interaction regardless of how large, small or fractal, a causality that preserves relativity while clarifying the workings of matter from the galactic to the nanoscale. But despite its explanatory power and likely benefit for making predictions and designing experiments going forward, it is still a thought experiment, and must follow wherever the data leads. It will need to be qualified in the future as we design science and technology with the theoretical framework in mind, tweaking its parameters based on cumulative evidence, and eventually unchaining ourselves from the conceptual intuitions involved to assemble and perhaps synthesize with new or alternative paradigms.