The simplest theory of the attractive nuclear force was proposed by Yukawa in 1935, using an analogy with electromagnetic theory (a more exact, modern analogy is found by comparing quantum electrodynamics with quantum chromodynamics). Yukawa suggested that nucleons interact with each other by emitting and absorbing of a quantum of energy between them in a time span of about 10-24 seconds. These quanta are known as mesons (they have been experimentally-verified) and differ from protons by having a positive rest mass, e.g., mass remaining after accounting for kinetic energy,
E2 = (M0**2) * C**4 + P**2 * C**2 (18)
That both electromagnetic and the strong nuclear forces can be modeled similarly suggests that similar analogies may exist between the fundamental constants describing these forces. For example, quantum mechanical explanations of optical spectra and the fine-splitting of spectral lines occurring secondary to electron momentum due to the emission and absorption of photons by bound extranuclear electrons defines a fundamental constant known as the fine-structure constant, 2πe**2/hc, where e is the unit of natural charge. This constant can be thought of as the ratio of the speed of an electron in the first Bohr orbit to the speed of light. It is interesting that this constant is the ratio of relative motion corresponding to the doctrines of Heraclitus of the 6th century BCE.
Utilizing our analogy, the strong nuclear force should display a fundamental constant similar to the fine-structure constant. Using our analogy, we can define a fine-structure constant for the strong force of meson field theory, 2πg**2/hc, where g is the unit of chromodynamic charge for the nucleons. While our analogy is not exactly correct, it does suggest that a new fundamental constant of nature may exist as the ratio of the fine-structure constants for the strong and electromagnetic forces, g**2/e**2, can be derived.
The physical meaning of this quantity is that it represents the inverse ratio of the repulsive electromagnetic forces tending to separate the nucleons to the attractive strong, chromodynamic forces tending to maintain the integrity of the nucleus. Whenever the nuclear strong forces are such to compensate for the electromagnetic repulsion, stable atoms result. Consequently, the constant g**2/e**2 is the fundamental statement of the maximum number of protons that can be joined together to form an elemental nucleus. Using the current estimates for the fine-structure constant of 1/137 and about unity for the nuclear constant gives a current value of g**2/e**2 of about 137. However, we postulate that the actual value is equal to the maximum possible number of elements, 144. This provides an estimate for g**2 of 1.050768 which is very close to π/3, being greater by about 1/3rd of one percent, and g equals 1.025070 which is very close to the twenty-seventh root of two, 1.026004, for a major nine note, equally tempered musical scale, divided into 27 equal intervals.
Such agreement may be fortuitous, but it could represent an important universal law. For if g**2 equals π/3 at the Planck moment, then we have succeeded in relating a fundamental constant of nature to a purely mathematical number, π, which defines the circle.
The slight difference between the calculated value of g**2 and π/3 is likely due to our determining of constants as if they were truly independent of each other. Moreover, a slight difference is expected to exist between the value measured in the current universe of broken symmetries and the value at the unification point of more perfect symmetry.
Recently, chemists have filled the seventh row of the periodic table up to the element 118. However, the only stable elements found naturally terminate with element 104, Rutherfordium. The observation that less than 144 elements exist in nature suggests that the value of g**2/e**2 may have decreased as the universe has expanded over the past 13 billion years. Assuming an initial value of 144, and the current upper limit for naturally occurring elements of 104, suggests that this quantity has decreased about 28 %. This number is similar to the 30 % decrease in the gravitational constant that many relativistic physicists believe has occurred since the ‘big bang’. Whether this is accurate needs to be determined.
Although the answer remains theoretical, I suspect that the majority of the change has occurred in g**2 rather than e**2 since no strong evidence exists suggesting that charge have changed since the beginning of time.
Another interesting observation concerning nuclear structure is that an excess of neutrons are required to stabilize the nucleus once the atomic number (number of protons) is above 20. Looking at a x-y plot of proton number to neutron number demonstrates that the ratio of neutrons to protons very closely approaches the value of π/2. If the true asymptote is π/2, occurring for many of the higher elements , then another correspondence between the pure, irrational number π and the physical world exists. This suggests that elements with atomic numbers above 104 are not naturally observed because in the present universe it is not possible to provide sufficient neutrons for stabilization of such atoms except under extreme conditions.