SUPERFORCE – the Fundamental Force of Unification

Salvatore Cezar Pais, SUPERFORCE – the Fundamental Force of Unification, preprint, Open Science Framework, 24 July 2023. Dedicated to the public domain under CC0 1.0 by the author and reproduced in full; the record is at doi.org/10.31219/osf.io/9kebt.

(On this site, the devices this theory sits under are Pais’s own: the inertial mass reduction craft at /library/stm-4678f2e210, the electromagnetic field generator at /library/stm-791a62522c, the plasma compression fusion device at /library/stm-99473476f3 and its journal write-up at /library/stm-a1c7e0936f, the room-temperature superconductor at /library/stm-43f730a83f, the piezoelectric high-temperature superconductor at /library/stm-ac45e5fd5e and the high-frequency gravitational wave generator at /library/stm-630831fa55. The Navy’s own operability attestation for that patent family is at /library/stm-3edb229bab.)

Abstract

It is found that it is the Planck Force, the speed of light to the fourth power divided by the gravitational constant, that is the ruling force of unification, named the Superforce, which also is found in the field equations of Einstein’s General Relativity theory. In this manner, the Superforce unites the world of the very small, quantum field theory, with the world of the very large, general relativity, thus accounting for a feasible theory of Quantum Gravity. Moreover this Superforce indicates that it is by its very action on the local spatial-temporal geometric structure that Energy Density and hence Matter is created.

Keywords: Quantum Gravity; spacetime structure; Superforce; force of unification; quantum vacuum engineering; quantum field theory; General Relativity; quantum mechanics; quintessence; vacuum energy density.

I. Introduction

The best theoretical model of physical reality we have to date is known as the Standard Model of particle physics and it describes physical observations quite well, however there are several shortcomings to it. For example, the Standard Model does not explain the origin of dark matter, nor does it explain the origin of neutrino masses. However its greatest failure is its inability to account for the unification of the four known fundamental forces, including gravity.

This fact may be due to the best model of gravity being a non-linear theory described by General Relativity, while quantum field theory, from which the Standard Model sources, is based on the linear theory of quantum mechanics. Hence a theory of Quantum Gravity is not given by the Standard Model, thus letting us pose the question: what if unification of the forces is not achieved by quantizing the gravitational field, nor by geometrizing quantum spacetime, but by something completely different, namely the Superforce.

II. A path to Quantum Gravity?

If you carefully observe Einstein’s gravitational field equations, general relativity, you note that the stress-energy tensor is coupled to the geometry of curved spacetime by a scalar factor, on the order of the gravitational constant divided by the speed of light to the fourth power, where the gravitational constant is universal and the speed of light is the speed of light in a given medium.

A simple dimensional analysis shows that the inverse of this coupling scalar constant has the units of energy divided by length, thus as an energy gradient the scalar, the speed of light to the fourth power divided by the gravitational constant, has the units of a force — we shall call it the Superforce. Mathematically, general relativity can be re-written as the Einstein tensor being proportional to the stress-energy tensor divided by the Superforce.

Moreover, if you carefully look at the mathematical structure of the Planck Force, you realize that this is the Superforce, and it does not contain h-bar, namely the modified, reduced, Planck constant, therefore it can relate to a quantum phenomenon exhibiting macroscopic classical behavior, namely a macroscopic quantum phenomenon.

Equation 1 in the source states that the Superforce is approximately the Planck mass times the speed of light squared divided by the Planck length, which is approximately the mass of the observable universe times the speed of light squared divided by the radius of the observable universe.

Equation 1 shows that the Superforce equals the energy gradient for both the Planck scale and the horizon, that is cosmic, scale, in that the Superforce is approximately ten to the forty-fourth, which is approximately ten to the fifty-third times ten to the seventeenth, divided by ten to the twenty-sixth, where the mass and radius of the observable universe supply the first and last of those figures. This fact cannot be a mere coincidence and shows that indeed the Superforce acts as the bridge between general relativity and quantum mechanics, namely the realms of the very large and that of the very small, quantum gravity.

III. Force of unification

Consider the relation that the strong nuclear force divided by the electromagnetic force equals one over the fine structure constant, where the fine structure constant is approximately one over one hundred and thirty-seven.

We can write the strong nuclear force as one over the fine structure constant times the electromagnetic force, and by recalling that the fine structure constant is the squared electric charge divided by the product of the constant four pi times the electrical permittivity of free space, h-bar and the speed of light, and also that the electromagnetic force is one over that same constant times the squared charge divided by the squared length, then at the Planck scale — namely where the squared length is the squared Planck length, which is the gravitational constant times h-bar divided by the speed of light cubed — we obtain the strong nuclear force equal to the speed of light to the fourth power divided by the gravitational constant, namely the formula for the Superforce.

Furthermore, considering the gravitational force at the Planck scale as the gravitational constant times the squared Planck mass divided by the squared Planck length, namely where the squared mass is the squared Planck mass, which is h-bar times the speed of light divided by the gravitational constant, we obtain the gravitational force equal to the speed of light to the fourth power divided by the gravitational constant, once again the formula for the Superforce.

Therefore this simple yet elegant proof shows that the strong nuclear force equals the gravitational force which further equals the Superforce at the Planck scale. Since the strongest of the known forces equals the weakest of the forces at the Planck scale, this proves that the Superforce is indeed the force of unification.

IV. Finding the Superforce in the Schrödinger and Dirac equations

Consider the Schrödinger equation, given as Equation 2 in the source: the imaginary unit times h-bar times the time derivative of the wave function equals minus h-bar squared over twice the mass, times the second spatial derivative of the wave function, plus the potential energy times the wave function. Here the wave function belongs to a particle of a given mass travelling through a field of potential energy.

This mathematical formalism does not take into account special relativity, which when considered, by coupling that equation with the total energy relation — the squared total energy equals the squared rest mass times the speed of light to the fourth power, plus the squared momentum times the speed of light squared — yields the Dirac equation.

We can think of the structure of equation 1, and re-write it as x equals y plus z, with these respective terms given as the corresponding terms of equation 1. Performing a simple dimensional and scaling analysis on the previous relation we note that from x being of the order of z we obtain the potential energy of the order of the Planck constant times the angular frequency, considering that time goes as one over that frequency. This expression for the potential is the Planck-Einstein relation, wave-energy theory, the frequency being the vibrational frequency of the particle.

Moreover by considering x of the order of y we can obtain the wavelength as the Planck constant divided by the mass times the velocity, namely the de Broglie wavelength of the particle, where a reference length is written as the velocity times the time, also given that the reference length is the wavelength.

Furthermore, by considering y of the order of z, given that the Superforce can be written in gradient form as the potential energy divided by the reference length, and that the Planck length is the reference length, we can obtain the relation that the Superforce is of the order of the speed of light to the fourth power divided by the gravitational constant, since one over the squared spatial increment goes as one over the squared reference length, which is one over the squared Planck length.

Thus we see that the Superforce relation arises in the Schrödinger equation and hence in the Dirac equation, once special relativity is brought into play.

V. Engineering the Superforce?

Consider the linearized relation that the squared speed of light equals one divided by the product of the vacuum and non-vacuum magnetic permeabilities and the vacuum and non-vacuum electric permittivities, the latter being the dielectric constant. In this case the speed of light is the speed of light in a non-vacuum medium, that is, the relative permeability and the relative permittivity are not equal to one.

Given the fact that the Superforce can be written as the speed of light to the fourth power divided by the gravitational constant, we can see that by engineering the electric permittivity and the magnetic permeability of a given medium, we can engineer the Superforce itself. This realization has great potential insofar as affecting the very nature of our reality at the most fundamental level. The military and commercial implications of this fact are unbounded, to say the very least.

VI. Conclusion

To recap, the Superforce is the Planck Force, hence it represents the energy gradient at Planck scales, thus it can be written as Planck energy divided by Planck length. Therefore the Superforce is quantum in nature, and thus fundamental, even though the modified, reduced, Planck constant does not feature in its mathematical formalism. In a nutshell, in view of the possible existence of the Superforce, which equals the Planck Force and exists at every point in space and time at the Planck scale, general relativity may have a new interpretation, namely Einstein’s gravitational field equations can be re-arranged to state that: it is the Superforce that, when acting locally on the spacetime geometric structure, gives birth to energy density, hence generates matter.

This may mean that the cosmos is filled with a superfluid-like substance.

Acknowledgments

I thank my mother Florina Hristescu for the inspiration to write this paper. Tanto nomini nullum par elogium.

References

1. S. Bertolini, L. Di Luzio and M. Malinsky, Physical Review D 85, 095014, 2012, arXiv 1202.0807.
2. H. Georgi and S. L. Glashow, Physical Review Letters 32, pages 438 to 441, 1974.
3. H. Fritzsch and P. Minkowski, Annals of Physics 93, pages 193 to 266, 1975.
4. H. Murayama and A. Pierce, Physical Review D 65, 055009, 2002.
5. J. Armas, Conversations on Quantum Gravity, Cambridge University Press, 2021.
6. E. Schrödinger, Space-Time Structure, Cambridge University Press, 1950.
7. K. Huang, A Superfluid Universe, World Scientific Press, 2017.

Salvatore Cezar Pais signs the paper as Aerospace Engineer, AIAA member.

(Reference-number markers in the running text have been dropped and display equations rendered in words with their source equation numbers; the equations in their original form are at the source.)