The Case for Planck Spherical Units

Throughout the universe, we find large hot spheres orbited by smaller cooler spheres. These are all composed of atoms that contain protons and neutrons at their center, both of which function as spheres. We’re surrounded by spheres and made of spheres. What if the universe at the most basic level is a vast array of spheres?

The evidence for this is much stronger than you might expect given the total obscurity of such a theory. Let’s begin with 3 fundamental constants of nature. First is the speed of light c, which represents the maximum rate of travel in the universe. Next is Planck’s constant h (also as h-bar = h/2π), which represents a minimum (electromagnetic) action. And third is the gravitational constant G, which relates the attractive potential between 2 massive bodies.

These empirically determined constants can be combined to yield a length of space known as the Planck length ℓP, which represents a minimum physical space. Another dimensional analysis of the same constants yields a particular mass, known as the Planck mass mP.

We’ll call a sphere with a radius equal to the Planck length a Planck Spherical Unit (PSU), a term first used by Nassim Haramein. Assuming space is composed of these spheres, we can now calculate 2 numbers with respect to the proton and its radius rp: V is the number of PSUs in its volume and S is the number of PSUs on its surface. We find that if the proton mass mp is evenly distributed among the PSUs on the proton’s surface, then that same fractional mass distributed among each of the PSUs in the volume of the proton would altogether have a mass equal to the Planck mass mP.

The above expression gives the same result for rp (0.84123 fm) as h/c = mp*rp*π/2, which is in perfect agreement with its current CODATA value of 0.8414(19) fm. But in addition to its simple theoretical framework, this new formulation has the great advantage of having no unexplained coefficients due to the natural factor of 4 difference between the area of the PSU equatorial disk and the surface area of the proton.

So to make sense of that h/c relationship we need only to posit a spherical unit (PSU) uniformly distributed throughout space with its size determined by the minimum length of space extrapolated from h, c, and G; and the spherical proton boundary extends just to the point at which the PSUs on the boundary total the observed proton mass and the PSUs contained inside it total the unique mass extrapolated from h, c, and G.

As the equilibrium point between the proton’s internal and surface PSUs, the proton radius makes for a natural measuring rod in the atomic domain. This is evident in the lowest energy state of the simplest atom, but with an important caveat. If the proton radius can be evenly divided into 20 subunits, then the number of them in the diameter of hydrogen in its ground state (2a0) is equal to the consecutive multiple of 135*136*137.

Of course, 1/137 is the approximate value of the fine-structure constant, which determines not only the size of an atom but also the electron’s anomalous magnetic moment. If instead of 137 we use the actual inverse fine-structure constant (~137.036) and the value for rp determined above, then we obtain a value for the Bohr radius a0 of 52,913 fm vs. a CODATA value of 52,917 fm — a close approximation given the uncertainty in the electron’s exact position at any given moment.

But let’s consider this fact from another angle. If the speed of an electron at a0 is equal to about c/137, as in the classical view, then in the time it takes a photon to complete an orbit of 2π*a0, an electron will travel 2π*a0/137. In units of rp this distance equals π*rp*135*136/20. And in terms of the proton-electron mass ratio, the electron’s partial orbit here is π*rp*mp/(2*me). This irreducibly simple description of the electron’s movement in relation to the proton is the result of a striking proportionality:

corrective for mp/me = 1.00008… and rp = 0.8415 fm

There are 3 ratios here representing the core attributes of the simplest atom: 1) the ratio of proton and electron rest masses (mp/me), 2) the ratio of the bound electron’s most stable radial distance to the proton’s charge radius (a0/rp), and 3) the fine-structure constant (~1/137) which is the classical ratio of the electron’s speed in this bound state to the speed of light (cα/c). No other proportionality relates these essential atomic parameters with such an economical use of terms.

Because the relationship mp/S = mP/V implies a direct link between the PSU and the proton radius rp and mass mp, and because the distance ratio of a0/rp and mass ratio of mp/me have a common factor of 135*136/20, these quantities may in fact express attributes of PSUs. We already know the multiple in the numerator is sequential with the inverse fine-structure constant. Now let’s take a closer look at the factor of 20 in the denominator.

The stability of an atomic nucleus depends on the number of protons and neutrons it contains. The heaviest stable atom with an equal number of protons and neutrons is atomic number 20. So aside from hydrogen, atoms with 20 or fewer protons are more stable when the nucleus contains either an equal number of protons and neutrons or just 1 extra neutron. However, atoms with greater than 20 protons are always more stable when the number of neutrons exceeds the number of protons. This break in the neutron-proton ratio at 20 protons may seem unremarkable, but it reveals an important limit for the structure of the atomic nucleus.

A similar limit appears in electrons. High energy collisions can cause electrons to gain a discrete amount of mass and enter into a transitory state known as a muon. The only meaningful difference between muon and electron is their difference in mass. For instance, their magnetic moments are nearly identical: the ratio of muon g-factor to electron g-factor is equal to 1.00000626, a small difference accounted for by their difference in mass. Furthermore, muons are sufficiently similar to electrons to form a simple atom known as muonic hydrogen. And because the muon mass is measured with the same high degree of precision as the electron mass, the muon-electron mass ratio mμ/me offers rare insight into the nature of mass at the most basic level. What we find is astonishing.

If we stipulate that the muon is a toroidal transformation (π*π) of the electron mass, then the main factor that emerges is 20+19/20, with a corrective factor of only 1.00000034. And this minuscule factor, which is only necessary to correct the 8th and last significant digit of the muon mass, effectively disappears if we further stipulate that nature does not produce absolutely perfect circles. So the most extraordinary feature here is the rational number 20+19/20. Not only is the integer the lowest common denominator of the fraction, but the number is just 1/20 less than a whole integer greater than 20. The high precision, basic geometry, and unusual coordination between integer and fraction make /me extremely compelling as evidence of an underlying proportional limit centered around a factor of 20.

So the internal and external components of an atom both exhibit a distinct structural change at a critical threshold of 20. Inside the nucleus it occurs when the number of protons exceeds 20, and for electrons subjected to an extreme acceleration, their mass increases toroidally by a discrete factor of 20+19/20. The limiting quantity of 20 that marks the transformation of the nuclear and electronic structures is consistent with the core parameters of the simplest atom, in which the atomic mass ratio of mp/me and the atomic distance ratio of a0/rp share a common proportion of 135*136/20. This connection to the proton is significant because our PSU model uniquely establishes rp as the equilibrium point between a proton’s internal PSUs, which total 1 Planck mass, and its surface PSUs, which total the observed proton mass.

Now, to account for the anomalies involving the factor of 20, we can posit a dynamic modification to the PSU: in their natural state, PSUs oscillate in size at a constant rate by a factor of 1/20 the size of their radius. The pervasive effect of the PSU’s regular oscillation is the linear subdivision of space by a factor of 20. So it is this perpetual, proportional vibration of the PSU that reproduces the factor of 20 in the essential atomic ratios of mp/me and a0/rp, as well as the critical limits of /me and the neutron-proton ratio. If the static PSU model accurately describes the proton radius, then the oscillating PSU is the most natural means of accounting for these other observations in the atomic domain.

Nature provides a crude but powerful test of this hypothesis. If the atom containing 20 protons were irrelevant or played only a minor role in the organization of matter, then that fact alone could sufficiently falsify the notion of a ubiquitous quantum oscillation by a factor of 1/20. But what we find is quite the contrary. It is no surprise that the 4 most abundant atoms in the human body are hydrogen and the 3 heavy atoms of nucleosynthesis — carbon, nitrogen, and oxygen. But after that it’s not magnesium or silicon or iron but calcium, most of it stored in bone. Out of all the elements to choose from, including several with very similar chemical properties, nature selects the atom with 20 protons as its base material for solid construction.

Yet nature’s use of calcium goes far beyond its role as a skeletal mortar. In a process known as calcium signaling, our cells store and release calcium ions in pulsating waves that effectively control all muscle contraction and neuronal transmission. Every movement and every thought, from cell fertilization to cell death, requires this active, highly coordinated flow of calcium ions. In contrast with the more passive regulatory functions of other atomic ions, calcium is a vital messenger in the system that translates the low level activity of the cell into the higher level function of the organism.

Now obviously not every instance of the number 20 is a “sign,” but the unique structural and signaling role of calcium in living organisms can at least partially be accounted for in this model as a harmonic resonance with the PSU oscillation. Indeed, a true description of nature at the most basic level should not only account for small scale phenomena but also provide insight into the organization of matter at higher levels. Thus we find the indelible mark of the PSU in both the proton radius and the proportionally larger Bohr radius, and not just in simple muons but more complex calcium atoms as well.

The case for the PSU relies on a pattern of facts that are impossible to reconcile in its absence. The direct physical evidence — the equivalent of finding traces of DNA at a crime scene — must be the calculation of rp as the spherical boundary between internal and surface PSUs. The 4 ratios of a0/rp, mp/me, /me, and the neutron-proton ratio function as fact witnesses. None are sufficiently compelling on their own but together they paint a consistent picture of the PSU and its signature oscillation. Finally, calcium serves as a character witness that can credibly testify to the suspect’s behavior outside the narrow domain of particle physics, which further affirms our theory of the case.

Although there will always be reasonable doubt as to the fundamental composition of the universe, the case for PSUs is quite substantial on its own terms, and all the more plausible when compared to alternatives that leave even the proton radius a total mystery. In this universe of spheres — hot and cold, big and small — the oscillating Planck Spherical Unit may ultimately prove to be its most fundamental sphere.

For more information on this topic, see my previous article The Oscillating Planck Spherical Unit.