The Oscillating Planck Spherical Unit
Either there is 1 physical unit that fills space and connects all points within it or there is not. It’s one or the other and nothing in between. Here I’ll make the case that there is and it has intrinsic features that are evident in the atomic particles and the natural structures they form.
In 2012, Nassim Haramein published a paper titled “Quantum Gravity and the Holographic Mass.” There he defines a theoretical unit called the Planck Spherical Unit (PSU). Its diameter is equal to the Planck length, the singular unit of space derived from combining the fundamental physical constants for gravity G, the speed of light c, and Planck’s constant h. Its mass is equal to the Planck mass which is derived from the same set of constants.
With the PSU filling space as a “quantum foam,” he devised a formula for computing the holographic mass of a spherical object by counting the number of (red) PSUs in its volume and dividing that by the number of (white) PSU equatorial disks on the object’s spherical surface area. Multiplying this quantity by the Planck mass gives the object’s holographic mass. He then applied this concept to the proton mass, which is measured with high precision, and successfully calculated the less precisely measured proton charge radius. The value obtained through this method has been corroborated by the most precise measurements of the proton radius while the Standard Model gives a value that is about 4% too big, which is a significant deviation. So with space composed of PSUs and through the application of holographic mass, Haramein was able to provide a physical explanation for the following empirical relationship:
The formula was then applied to the electron mass in a subsequent paper titled “The Electron and the Holographic Mass Solution.” At the distance known as the Bohr radius a0, which is the minimum stable distance between a single electron and a single proton, the electron’s holographic mass emerges in proportion with the fine-structure constant α.
So at a distance of a0 from the proton, α is the ratio of the electron’s expected velocity cα to the PSU’s surface velocity c. But this dimensionless constant α, which is equal to about 1/137, appears in multiple contexts related to the atomic and subatomic domains. To take just 2 examples: it is the coupling constant that determines the strength of the interaction between electrons and protons, and it determines in part the electron’s anomalous magnetic moment. Yet despite its ubiquity, α is a quantity of unknown provenance. If space is indeed composed of a fundamental unit, then the successful application of the holographic mass ratio to both the proton radius and Bohr radius establishes the PSU as a legitimate candidate, and we should expect further investigation to shed light on this mysterious quantity of 137.
Although a static PSU is sufficient to account for the holographic mass solutions described above, Haramein often refers to the unit as the “oscillating PSU” or “PSU oscillator” without specifying the nature of this action. As we will see, there is substantial evidence that the oscillation of the PSU occurs within well-defined proportional limits. Let’s now explore the possibility that each PSU oscillates by a factor of 1/20 the size of its radius, expanding and contracting with 1 oscillation cycle per half rotation of the PSU. The surface of each PSU naturally rotates at the speed of photon transmission c. So the regular oscillation of the PSU by a factor of 1/20 not only generates a natural unit of time, but also implies a linear subdivision of space throughout. This is certainly evident in the proportional relationship between the 2 essential distances for which the holographic mass solution applies: the proton radius rp and Bohr radius a0.
Dividing the proton radius into 20 subunits, we find exactly (135)(136)(137) of them in the diameter of hydrogen in its ground state. Of course, the numbers 135 and 136 are consecutive with 137, which is the integer approximation of the inverse fine-structure constant. This intrinsic order in the simplest atom is quite striking, yet we might dismiss it as an amusing coincidence if not for the fact that the same proportion of (135)(136)/20 also appears directly in the proton-electron mass ratio (mp/me):
So the PSU provides the physical basis for the mathematical relationships in the holographic mass solution of the proton mass with the proton radius, and the electron mass with the Bohr radius. The ratios of the 2 complementary masses (mp/me) present in the simplest atom and the 2 distances (a0/rp) that define its core spatial dimensions share a common proportion of (135)(136)/20, which may reasonably be inferred to have some physical connection to the PSU. Furthermore, to obtain more precise values for the proton and electron masses we can apply a version of this ratio as follows:
Let’s leave aside the quantity of 22 for now. The ratio of (135)(136)/20² resembles a perfect square. This is important because both masses here have units of GeV/c², in which c² refers to the squared speed of light — a squared unit of space divided by a squared unit of time. As the primary participants in photon exchange, protons and electrons have an integral relationship with light, so perhaps the ratio that defines this universal speed limit is connected physically via the PSU to the numerical ratio that relates these 2 complementary masses.
Since the PSU oscillation factor of 1/20 occurs with perfect regularity, 20² may function here as the squared unit of time. However, despite its evident association with the fine-structure constant, the multiple of (135)(136) is not quite a perfect square nor do we yet understand its connection to the PSU. If the ratio of (135)(136)/20² is functionally equivalent to the squared speed of light in this relationship, converting our arbitrary units of space and time (i.e. meters²/second²) into proportionate terms, then we must be able to attribute a physical basis to the multiple of (135)(136), just as the quantity of 20 corresponds with the PSU oscillation. Let’s continue with the analysis and then return to this idea.
These 2 relations demonstrate the narrow and well-ordered constraint on the proton mass in its natural units. It is extremely improbable that the first 7 digits of the (2*mp) proton mass, a supposedly random number, would match the series 2–0.123456 by chance. But given that fact, it is unfathomable for the electron mass to also reduce the ratio of (135)(136)/20² proportionally to about 0.02345 without any coordination between the two. For both proton and electron masses to be so clearly associated with this series demonstrates their inherent complementarity and hints at the fundamental nature of mass in relation to the PSU.
Absolute proof this is no mere numerical coincidence is found in the muon-electron mass ratio. The electron has an unstable form known as a muon which has a mass measured with a precision on par with the atomic particles. Due to their lack of composite particles and nearly identical magnetic moments, the difference in mass is the only significant difference between electron and muon. The muon mass (mμ) can be accurately expressed in terms of the electron mass (me) as the surface area of a torus (π²):
Like the proton mass, we again obtain the first 7 digits of the muon mass through an irreducibly simple relation. And because 19/20 is equal to half of 2–0.1, the muon-electron mass ratio has a direct link to both the upper and lower bounds on the proton mass. Furthermore, the emergence of the rational number 20+19/20 in this limit strongly supports the notion that PSUs oscillate by a factor of 1/20, as the PSU radius divided into 20 subunits would have a maximum extent of 21, exactly 1/20 greater than 20+19/20. And the factor of π² is a clear indication that 20+19/20 indeed refers to a radius as the surface area of a quarter torus is equal to π²*R*r.
So with respect to the rest masses of the proton, electron, and electron-related muon, we reject the view of the Standard Model that these are independent physical constants with no meaningful proportionality between them. This conclusion is based not only on the exceptional precision and the economy of terms in the individual equations, but their interrelation and the ability to associate the proportional terms with physical processes in a logical manner.
The highly precise equations above demonstrate an intrinsic order that places specific, proportional limits on the rest masses expressed by electrons and protons. Now, we know that electrons behave as point particles while protons are composite particles. With the universe fundamentally composed of the PSU, we may deduce that an electron conveys a disturbance of a single PSU that travels to the next PSU along its QED-defined trajectory at a rate always less than the speed of light. Naturally, the PSU disturbance represented by a single electron may be collectively present in the proton. Because the ratio of (135)(136)/20 reduces to 918, the proton mass may be expressed in terms of the electron mass as follows:
This formulation presents an intriguing possibility for the composition of a proton. 6 spheres aligned in a plane, all surrounding a central sphere, form a hexagon with 1 sphere per side. A hexagon with 17 spheres per side contains 918 spheres, excluding the central sphere.
The proton mass is obtained when each sphere is a PSU with a disturbance representing approximately double the electron rest mass (2*me). An elegant consequence of this model is that when a proton captures an electron it transforms into a neutron and its new mass is obtained simply by including the central sphere and marginally increasing the 2*me multiplier.
What might be the “disturbance” in the PSUs that would express mass as either me or ~2*me to signify the presence of a massive particle? To transmit photons in accordance with observations the PSUs must spin at 1 rate: the speed of light. A disturbance to this natural rotational rate may thus produce what we perceive to be a massive particle. For instance, a neutrino, which has an immeasurably small mass and typically travels very near the speed of light, would represent a minuscule decrease in the rotational rate that moves from 1 PSU to the next in accordance with the trajectory of the particle; an electron would represent a similar but more substantial decrease; and the nucleons would be hexagonal collections of PSUs with each PSU slowed by about double the amount of an electron.
But this is somewhat backwards. Since the 2–0.123456 relation for the (2*mp) proton mass obtains 7 of its 9 well-established digits — an extraordinary 99.99999% match — we may reasonably infer that, as a first order effect, the overall proton mass mp aligns with this value, yielding its total diminished PSU rotation. Consequently, the 918 PSUs that compose the proton each have a diminished rotation of mp/918; the PSUs that compose a neutron each have a slightly more diminished rotation than those of a proton; and the diminished rotation of a PSU transmitting an electron is about halfway between that of a proton’s component PSU and a PSU with undiminished rotation. The fact that it is not exactly half is analogous to the anomalous magnetic moment in the electron’s g-factor (~-2.002319). It has an expected absolute value of 2, however due to higher order effects it is slightly greater than 2. And the electron’s anomalous magnetic moment is actually greater than its anomalous mass differential with respect to both proton (~2.000166) and neutron (~2.000744). Because the electron’s anomalous magnetic moment can be calculated using corrections from higher order effects, a future area of investigation would be to see if a similar approach can be applied to the anomalous mass differential in protons and neutrons.
Let’s review: The holographic mass solution posits the physical existence of the oscillating PSU to explain the relationship between the proton radius and proton mass, as well as the Bohr radius and electron mass. The ratios of the 2 distances and the 2 masses share a common proportion of (135)(136)/20 which reduces to 918. A perfect hexagon is formed from 918 spheres surrounding a central sphere in a plane. The ratio of (135)(136)/20² that yields exceptionally precise values for the electron and proton masses reduces to 918/20, where both terms have a natural physical basis — the numerator refers to the hexagonal arrangement of PSUs that form a proton and the denominator refers to the oscillation factor of PSUs.
Now if we divide the PSU radius into 20 subunits (like we did for the proton radius), then its regular oscillation produces a photon pathway proportional with a distance of 22π from one end of the PSU to the other. So if a particle of light (photon) is represented by a point on the sphere along the plane of rotation, then for every half revolution around the main radius (20π) and full oscillation cycle (2π), the photon has moved to the opposite end of the sphere and traversed a distance of 22π. This conjecture is supported not only by this equation, modified from earlier, involving the masses of both electron and proton — the primary participants in photon exchange:
But also by the fact that the nucleon masses and g-factors closely align with 7π, which is approximately equal to 22:
Other than the electron g-factor, the Standard Model offers no means of calculating or otherwise understanding the proportional relations between these parameters. Yet here they are in another irreducibly simple and succinct relation that also happens to be dimensionless. It is an elegant expression of the intrinsic order contained within every PSU and, by extension, the atoms that give form to natural structures.
Beyond offering insight into the proportional constraints on the fundamental parameters that define the atomic particles, the projection of the PSU oscillation and its 22π photon pathway appears to produce a stabilizing resonance at increasingly larger scales:
- The Bohr radius, which we know from its proportionality with the proton radius, is also equal to the electron Compton wavelength scaled by a factor of 1/(2πα), which is about 21.81. So in the lowest energy and most stable state of the simplest atom, the expected length of space separating proton from electron is nearly 22 times greater than the photon wavelength with energy equivalent to the electron’s rest mass energy.
- 22 protons inside an atomic nucleus form titanium, the metal with the highest strength-to-weight ratio. So of the 94 naturally occurring elements, this 1 forms the strongest molecular bonds per unit of mass.
- 22 protons also appear in carbon dioxide. Of the prominent atmospheric gases — including hydrogen, helium, nitrogen, and oxygen — carbon dioxide is the heaviest. Yet it’s so stable that the atmospheres of Venus and Mars are about 95% CO2. More importantly though, CO2 provides the carbon necessary to create simple sugars during photosynthesis. It is the only gas absorbed by all plants and produced by all animals on Earth. So to breathe is to break apart and dissolve into the surrounding space 22 protons at a time.
- The conversion of adenosine diphosphate (ADP) into adenosine triphosphate (ATP) and back again carries an electric potential that powers most cellular activity. The additional phosphate group consists of 40 protons and releases a discrete amount of energy as it breaks away, converting ATP to its more stable form as ADP. This molecule serves as the basic unit of energy transfer in every living cell, and is therefore essential to the metabolic function of all life on Earth. It consists of 220 protons.
- Energy from the Sun is transformed into food on Earth through the action of chlorophyll. Certain wavelengths of red and blue light excite this molecule and cause it to split water into electrons, protons, and oxygen gas during the light dependent reactions of photosynthesis. At the core of every molecule of chlorophyll is a lone magnesium ion surrounded by a chlorin ring. The structure contains 1 magnesium ion, 20 carbon atoms, 16 hydrogen atoms, and 4 nitrogen atoms totaling 176 protons, which is exactly 8*22 protons. Furthermore, different types of chlorophyll molecules are associated with different side chains attached to the central ring, which alter the spectrum of light absorbed by the molecule. Chlorophyll a is the only type found in all photosynthetic organisms. It contains 2 protons less than 22², a 99.6% equivalence.
Proton number is the most important factor in determining the characteristics of an atom. For molecules it is less determinative, though even if proton number has a weak effect we should expect molecules to resonate with the natural harmonics of the PSU oscillators. Indeed, the pattern is unambiguous and the evidence is overwhelming.
The 5 examples above demonstrate how multiples of 22 convey stability from the simplest atom to successively larger structures, especially as it relates to their ability to store or transfer energy. Biologically, there are 3 molecules that are essential to the flow of energy through the global ecosystem. Chlorophyll absorbs sunlight, ADP receives and transports that energy within the cell, and CO2 provides the basic material to form nutrients that retain this vital energy. These nutrients are then consumed either directly or indirectly by every organism on Earth. The 3 molecules involved in this global process to store and transport energy all contain discrete multiples of 22 protons, with the largest consisting of just 2 protons less than 22². This unusual pattern of stability is evidence at the molecular scale of the oscillating PSU and its 22π photon pathway linking the particles that compose all these structures.
No fundamental unit of space can be observed directly. We may only infer its existence based on the objects it manifests. Perhaps there is no such unit and the set of parameters that define the atomic masses and g-factors are in essence just random numbers. But the best alternative to that baseless, chaotic universe is one filled with the oscillating PSU. With it we understand massive particles as minor deviations in PSU spin; we see the hexagonal composition of protons and neutrons; we recognize the harmonizing effect of its oscillation on the formation of natural structures. If there is an ultimate source to the order evident throughout the material universe, which brings to life cellular organisms and conscious beings like us, then we may with good reason attribute it to the intrinsic order within the oscillating Planck Spherical Unit.
