Investigation of Coulomb’s law and the nature of the electric charge

This theoretical work investigates spin-spin energy in the hydrogen atom and its relation to Coulomb’s force law. Most elementary particles are assigned intrinsic properties of carrying electric charges, which leave us blundering about the essence of electric charge. The perplexity originated in Coulomb’s force law when the proportionality constant is expressed using the free vacuum electric permittivity constant ε 0 in units of. C2m−2. N−1. Introducing these units by the proportionality constant canceled any direct role for the electric charge. In this research, a genuine suggestion based on energy conservation redefines Coulomb’s force law. A new formula has been suggested for the force between two spinning particles. The results of energy and force calculations agreed with Coulomb’s law evaluations. The spin-spin energy is related to the electric potential energy, and the electric charge is found to be connected to the rotational energy of the mass.


Introduction
In a dynamic Universe, all entities that make up this Universe should be energetic entities with various forms of energy. Spin energy or rotational energy is one of these primary forms of energy needed to stabilize elementary particles. Physical spinning plays a vital role for all entities in self-structuring and balancing forces, thus maintaining a balanced proportionality of energy and mass. Energy exchange between entities crosses all boundaries with various mechanisms and involves all forms of energy and matter to sustain evolutionary life.
It is a common practice for researchers to apply graphical analysis to their experimental results and develop a fitting empirical equation between the variables by introducing proportionality constants. In the case of Coulomb's force law, Coulomb's proportionality constant K has units in Newton, meter, and Coulomb (N m 2 /C 2 ). The introduced charge unit cancels the formula's electric charge unit, obliterating any significance to the electric charge. Besides, the force unit (N) has been inserted into Coulomb's force law by the proportionality constant K [1,2]. This procedure conceals the direct role of the variables in the formula and communicates the result as the most significant.
The electric charge is defined as an intrinsic property of elementary particles and characterized into two types, 'positive and negative,' where alike charges repel each other, and opposite charges attract each other. The two types of charges can neutralize or cancel their effect if they meet, like the encounter between matter and antimatter or the destructive interference between out-of-phase waves. The lack of clear perception of the nature of electric charge created a state of vagueness, despite the notion that electric charge must be related to energy.
However, exploring the facts about 'electric charge,' physics' oldest mysterious intrinsic property, may change some conceptions and improve applications in the energy field. Electrical energy is essential for most activities in modern societies and the primary power source for today's technology.
This paper aims to explore an alternative approach to clarify the nature of the electric charge and determine its relation to mass and energy. The calculations of spin-spin energy for the electron and the proton in the hydrogen atom correlate well with the electrical potential energies. Besides, clockwise and counterclockwise spins are linked to the negative and positive electric charge, respectively. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.

Electron-proton interaction
All elementary particles, including photons, have rest mass energies and are characterized as dynamic entities with different forms of energy [3]. The existence of any particle requires the ability to interact and exchange energy with other particles. One type of these energies results from creating these particles, which take the form of a physical spin [4][5][6][7]. Spin-spin energies stabilize most entities, from the smallest particles to giant galaxies. Spin-spin interaction plays a significant role in the energy exchange between particles and contributes to combining particles to form atoms. The notion that these elementary particles are too small and should not have a physical rotation is an interminable argument. On the contrary, the size and complexity of these particles are relative perspective changes with the development of higher resolution instruments and improved measuring techniques. Spin-spin energy here implies the energy due to the physical rotation of particles and should not be confused with the intrinsic spin in quantum mechanics. Although, we should realize that quantum mechanics is an elaborate mathematical approach that deals with the same physical problems but discards human visual reasoning.
In this investigation, we considered the formation of the hydrogen atom due to the interaction between a proton and an electron. The electron and the proton are dynamic particles known to acquire different forms of energy, including spinning energy [8]. The electron's spin energy is I W 1 2 , where I 1 and W 1 are the moment of inertia and the angular velocity, respectively, of the electron. The stability of a two-particle system requires the lowest possible energy state, which implies the two particles should have opposite spins to minimize the total energy. If the proton is rotating counterclockwise in the hydrogen atom, it produces positive torque with positive energy. In contrast, the electron should rotate clockwise, producing negative energy to balance the proton spin energy. However, when an electron encounters a proton, the two free entities interact through the mediation of photon exchange, as shown in the Feynman diagram in figure 1.
In our case, we believe that the interaction involves phonon-electron coupling and phonon-proton coupling [9][10][11][12], where the phonon energy in each case is linked to the clockwise or the counterclockwise rotation. Most of the proton and electron energies are labeled as rest energies. These rest energies can come from rotational or vibrational energies, as seen from Plank's equation n = E h . The energy exchange between the electron and the proton is mediated through photons and phonons interactions. One may assume that electrons and protons can interact by exchanging energy bundles of photons and phonons. Since phonons are bosons carrying vibrational or rotational energy, the change in rotational energy occurs through energy exchange by phonons interactions. While on the other hand, photons act as the force carrier between the electron and proton, as shown in figure 1. Under this postulation, one can associate the drop of energy for the electron and the proton with the destructive interference between their respective coupled phonons. These phonons are out of phase due to their association with the opposite spins of the proton and electron. The drop of spin-spin energy leads to combining the two particles into a hydrogen atom through an equilibrium between the different forces. The two particles become locked in a constant state of energy exchange with each other while maintaining their energy by absorbing photons to maintain their stability. The equilibrium status led to the heavily dense proton occupying the center of the new system while the electron was forced into rotational motion with a radius equal to that of the hydrogen atom.
The superimposition of the two particles must be attributed to some attractive force between the oppositely spun particles. The negative rate of change in spin-spin energy for the two particles correlates to an attractive spin-spin force between the oppositely spined particles (F = −∇V).
Consequently, the electron acquired new kinetic energy through its clockwise rotation around the proton, equal to its spin energy, and amounts to half the spin-spin energy between the proton and electron. This energy formation is analogous to the energies formed by Coulomb's law, where spin energy replaces the electrical potential energy.
However, the hydrogen atom becomes stable, and the only way to free the electron is to overcome its binding energy by absorbing a photon with energy equal to or larger than its binding energy. Figure 2 illustrates the electron-proton interaction where photon-phonon coupling interlocks the two particles.
When the electron moves toward the proton, it loses energy and emits a photon with the exact lost energy. Figure 3 shows the photon-phonon coupling process, where a photon in energy state |1> interacts by scattering with a phonon, yielding a photon in energy state |2>, which interacts with another phonon and goes back to energy state|1>. Through repeated photon-phonon interactions, the photons travel forward in a different path, while each interaction satisfies the Bragg condition and the conservation of energy and momentum [13].

Spin-spin energy
The binding energy for the electron in the hydrogen atom is D = =´-E 13.6 eV 2.17 10 j, 1 18 ( ) and its frequency using Planck's formula is / n = =É h s 3.29 10 1 , 15 which corresponds to one of the observed lines in the Balmer series of the H spectrum. Assuming the electron is a point particle spinning in a shell model [14,15], the spin energy for the electron is:   1 which gives / =Ẃ 0.77 10 rad s. 1 21 Assuming that the electron is a point particle with a radius of´-2.82 10 m 15 [17,18]. The moment of inertia for the electron is = =´-I m r 7.24 10 kg.m , 1 11 2 60 2 and its spin energy from equation (2) is: =´-E j 2.15 10 4 18 ( ) The spin energy of the electron is almost equivalent to its binding energy in the hydrogen atom, which suggests that the spin energy plays the role of Coulomb's potential energy for the electron during the combining process. The moment of inertia for the proton, assuming a point particle model, calculated using the radius of proton r 2 = 0.831´-10 15 m [19], is = =´-I m r 11.5 10 kg.m . The proton's spin energy must counterbalance the electron's clockwise spin energy because of energy and momentum conservation in the interaction between the two particles. Therefore, =´- where W 2 is the proton's angular velocity, substituting for the moment of inertia, and solving the above relation gives W 2 = 0.61 × 10 20 rad s −1 .
Since the two particles spin in opposite directions, the spin-spin energy is equal to the difference between their energies (-´-2. 15  The same is true for the centripetal force on the electron.

Results
Since the electron and the proton have equal but opposite spin energies in the hydrogen atom, the spin-spin energy is equal I W . F is the force between the oppositely spinning electron and proton in the hydrogen atom. Substituting for the variables in equation (8) gives the expected electric charge value of ±1.6 ×10 −19 C, and substituting for the variables in equation (9) yields F = −0.81 × 10 −7 N, which is equivalent to Coulomb's force. Equation (9) states that the spin-spin force between spinning particles is proportional to the square root of the moment of inertia and the angular velocity and inversely proportional to the distance between the particles. Equation (9) has no proportionality constants and relates force to rotational energy. The force is attractive for particles spinning in opposite directions and repulsive between particles spinning in the same direction.
The Heisenberg exchange interaction for identical particles [20] pointed out that the exchange interaction between two electrons in the singlet state, where they have opposite spins, is different from that of the triplet state. The two electrons are farther apart in the triplet state than in the singlet state. They move as if they were under the influence of a repulsive force for a parallel spin and an attractive force for the antiparallel spins, but there is no final consensus on the subject. Furthermore, the presence of a Spin transverse force has been mentioned lately in several research papers, which is supported by experimental evidence [21,22]. However, the above calculations showed that mass rotation is the source to what is labeled as electric charge and provides the energy needed to form a stable hydrogen atom. The central hypothesis within the discussion is that the spin-spin energy between two interacting particles attests to an interactive force between them.
Using equation (8), one can derive all other formulas used in electricity and magnetism. For example, the Electric potential for any spinning particle can be written as = V W I k r and the electric current , where R is the resistance.

Conclusion
The paper represents a genuine attempt to understand the essence of the electric charge. The calculation reveals that what is known as an electric charge is equated to the energy of a rotating mass, which depends on the moment of inertia and the angular velocity of the involved particle. Numerical analysis showed that what is known as electrical potential energy is equivalent to spin-spin energy associated with physical spin. The paper hypothesizes that clockwise and counterclockwise rotations correspond to the two types of electric charges. Spin-spin energy and spin-spin force calculations ultimately agreed with the well-known obtained values by Coulomb's law. In this work, spin-spin energy replaces electric potential energy, and the force between oppositely spun particles replaces Coulomb's law by a new attractive force, This force between rotating particles correlates to the energy difference between these particles. The force is attractive for particles with opposite rotations and repulsive for particles rotating in the same direction. Further investigations are needed to explore elementary particles' rest mass energies and reveal their interaction mechanisms. Other studies are required to explore phonons' role as force carrier bosons.

Data availability statement
No new data were created or analysed in this study.