Unified Equation of Fundamental Forces’ Coupling Values, and the Existence of Subsequent, Fifth and Other, Forces

This paper provides an equation to entangle all known fundamental forces by employing their coupling constants, i.e., strong ( s α ), electromagnetic ( α ), weak ( w α ), and gravitational ( g α ) interaction coupling values. The constant coupling formulation is further indicative of many other fundamental forces with significantly weaker coupling values. As an example, the fifth fundamental force, Kashi’s Force, is found to have a coupling constant of 10 −1446 , which is significantly smaller than the smallest known fundamental force, gravitational force, with an approximate coupling constant value of 10 −38 . Addition-ally, the paper finds the sum of all fundamental forces based on the equation proposed is equal to 0.0117, which is within the range of effective world value of the strong coupling constant 0.1


Journal of Applied Mathematics and Physics
cuses on a few mathematical findings associated with them. Such findings intend to present a unique formulation to bound the forces to a single nature. It appears a mathematical equation can entangle the magnitudes of the four fundamental forces.
The mere existence of such a relationship can have significant implications for our understanding of the universe as a whole. One of the primary outgrowths of such a relationship can shed light on the actuality of other fundamental forces. The current paper insinuates one such formula, in which a single formula presents the relative magnitudes of all the forces. The submitted article focuses on mathematical findings rather than the physical implication of such a formulary. It is imaginable that provided the obtained results are acceptable, many compelling determinations could be made to advance our knowledge of our physical surroundings further. Discussion of such conclusions is beyond the scope of the presented paper, yet the author provides some hints for interested readers.

Math and Equations
In order to compare the magnitude of the known fundamental forces and ultimately formulating the relationship between them, the coupling constants are applied. The dimensionless electromagnetic coupling strength, α , is employed and presented as follows [1].  The strength of the dimensionless electromagnetic coupling can increase [2] in specific conditions that are in the focus of the presented paper; however, it would be utilized in proceeding approximation and formulation.
On the same note, the dimensionless coupling value of the strong interaction, s α , is outlined bellow [3].
Similarly, the value of weak coupling, w α , can be circumscribed as follows. 6 10 w α − ≈ Ultimately, the coupling strength for the gravitational force, g α , can be determined by the following equation.  Table 1 summarizes the obtained value, along with their approximation used in the current paper [1].  For a more simplified formulation, the fundamental forces are ranked in an ascending order based on their strength, with the strong force being 1 α . Table 2 depicts the approximate relative coupling strength values for the known fundamental forces.

K. Mozafari Journal of Applied Mathematics and Physics
where n x is the approximate power of the n th coupling value, provided 1 0 x = ( Figure 1).
That is, the following calculations can be interpreted for the coupling values.
Note the n can only take integer values, and for its similarities with quanta concept, it can be called "Quanta Fo".
The strong force coupling value can be retrieved using the following equation.   where erf is defined as the error function.
That is, the sum of all possible forces found in Equation (3) is within the range of most accurate experimental effective strong interaction coupling constant of [17]. It is also possible to find 0 x by extracting the n x from Equation (2) as presented in the following line.    Therefore, the quanta fo that generates the strong coupling interaction value is 2 i ± .

Discussion
The methods of ascertaining values of coupling constants are subject to a lot of complexion; hence, variation [7] [19] [20]. Moreover, these values are restricted to specific conditions and physical properties. Therefore, a coherent conclusion is not the most logical approach, yet ignoring the findings is illogical.
The concept of formulation of coupling constants represented in Equation (1) indicates the possibility of other fundamental forces that are far weaker in nature than the proceeding known fundamental forces. As an example, provided the quanta fo, n, value is equal to 5, the coupling constant of the fifth force, Kashi's Force, can be achieved by utilizing Equation (1), which is an entirely different concept from other proposed fifth forces [21]. The mere existence of such a relationship can have significant implications for our understanding of the universe. One of the primary outgrowths of such a relationship can shed light on the actuality of other fundamental forces. The current paper insinuates one such formula: a single formula presents the relative magnitudes of all the forces. The submitted article focuses on mathematical find-Journal of Applied Mathematics and Physics ings rather than the physical implication of such a formulary. It is imaginable that provided the obtained results are acceptable, many compelling determinations could be made to advance our knowledge of our physical surroundings further. Discussion of such conclusions is beyond the scope of the presented paper, yet the author provides some hints for interested readers.

Conclusion
The purpose of the presented article was to seek a possible mathematical formulation between the known fundamental forces coupling values. Another interesting correlation could be discovered by overviewing the additional suggested fundamental forces and the proposed dark force in astrophysics.