JRO 10 (2), 3186–3191 (2023) ISSN (O) 2589-9058 ISSN (P) 2589-904X
Explanation to Gravity
Jan Olof Jonson
DOI: 10.15520/jro.v10i2.166
Received 25 Jan 2023; Accepted 2 Feb 2023; Publish Online 6 Feb 2023
Reviewed By: Dr.
Daniel V.
Abstract
An explanation to gravity based on Coulomb’s Law is proposed. As application for the proof has been chosen the simplistic model of a hydrogen atom in its basic neutral state consisting of a positive nucleus surrounded by an orbiting electron. The electrostatic force according to Coulomb’s law between two such atoms is analysed. A net attractive force between the two atoms is attained by applying the Special Relativity Theory to the orbiting electrons. Since they are orbiting with a non-vanishing speed, due to the Lorentz contraction, the distance between the orbiting electron of one atom and the positive nucleus of the other is shorter than the distance would be if both were at rest. The magnitude of the difference depends on the component of the velocity directed along the perpendicular distance between the electron and the neighbouring nucleus. The consequence of the difference in distances is that the attractive force due to the first electron to the second nucleus is larger than the repulsive force between the two nuclei. Applying the same method to the rest of the atom-pair, will lead to a negative difference. Hence, there will be a resulting attractive force between the electrically neutral atoms.
Keywords: Coulomb’s law, gravity, hydrogen atom, special relativity theory, Lorentz contraction, electromagnetic force between electric currents, Lorentz force, Ampere’s law.
1.INTRODUCTION
Since it has not yet been possible to find a comprehensive understanding of the relationship between gravity and electrical forces, it is the goal of this article to find this. Beginning with Coulomb’s law, the analysis will proceed, with the ultimate goal to state a physical relationship between electricity and gravity.
Recent discoveries concerning the way Coulomb’s law shall be applied, when the effects of time delay of action and Special Relativity Theory are taken into account, will be used.
2. THEORY
2.1 Coulomb’s law
Coulomb’s law is the basic law of electromagnetism, historically believed to only describe the force between two electric charges being at rest with respect to each other. The electric force (the Coulomb force) between two point electric charges may be written as follows[1]:
(1)
2.2 Coulomb’s law used to describe electromagnetic forces between electric currents
Taking into account the effects of retarded action, it has been possible to explain the electromagnetic force that appears between electric currents [2]. This was done for an experimental series on Ampère’s bridge, performed by Pappas and Moyssides[3]. This force between electric currents is usually attributed the Lorentz force law (i.e. the magnetic force law) [1], [4], [5]. It constitutes a new term
that has to be added to the Coulomb force term, described above (1).In a rudimentary form, Grassmann explores the theoretical background of this term [5]. Nonetheless, parts of his derivation were inherited with calculation errors. However, it has been possible to prove that the Lorentz force is unable to explain the collinear force between electric currents, flowing along the same line [2].Other authors propose a model able to explain also this class of forces, using Ampère’s Law[6], [7], [8].A problem with respect to Ampère’s law, mentioned already by Maxwell [9], is that Ampère does not give any explanation to the two terms he defines in his law [10]. It seems that Ampère has constructed his law ad-hoc in order to fit with performed experiments. This is, to a certain extent, of course good science, but even better would be, if the agents behind the terms could be defined. The use of Coulomb’s law mentioned above, was, however successful in explaining the force between collinear currents [2].In fact, when also the Special Relativity Theory was applied, the theory became capable of explaining the attractive force between two parallel currents[11].
2.3. Previous efforts to explain gravity using Coulomb’s Law
In fact, efforts to apply electrostatics in order to explain gravitational forces, are absent in the literature. One effort may, however, be mentioned. In a comment paper it is proposed that nuclei consisting of quarks may be positioned in a way like a dipole, so that the part of a nucleus dominated by positive quarks will inevitably be oriented towards the negative side of a neighbouring nucleus [4], [12], [13]. A fundamental problem arises to explain gravity,
obeying the inverse-square law, when the typical force between electric dipoles obeys the inverse cube law. Hence, this approach must be abandoned.
2.4 The task to explain gravity, using the hydrogen atom model
The objective is now to apply the thus far most complete description of Coulomb’s Law [11],on two interacting hydrogen atoms. Below is a simple model aimed at visualizing the calculations.
Figure. Model illustrating two hydrogen atoms (attached)
At first, it is necessary to mention that the so- called Standard Configuration [14] will be applied, where K denotes the coordinate system in which both nuclei are at rest. K’ denotes the coordinate system, in which the orbiting electron of the first nucleus is at rest when positioned in the orbit, while aligned along the x axis between the two nuclei. This holds also for the orbiting electron of the second nucleus. There will be four forces interacting in this configuration. At first glace there seems to be no net electric force between the two electrically neutral atoms. This has made it reasonable to define a special force named gravity, since there will inevitably be an attractive force between the two atoms. However,
it must be taken into account that the distance between an orbiting electron and the positive nucleus of the neighbour atom, due to the Lorentz contraction, is smaller than the force between the two positive nuclei of both atoms, respectively.
This, in turn, makes the attractive force between the electron and the nucleus to become larger than the repulsive force between the two nuclei. Hence, there will arise a net attractive force, when summing the two contributions. In total, there will be four contributions to the total electric force, involving two hydrogen atoms. These are the four combinations of the two charges of each atom, respectively. The task is now to define these four forces.
In the following analysis, the distances involved will be approximated with the their component along the x axis, respectively.
2.4.1 The electric force between the two nuclei The electric force between the two nuclei will easily be defined by Coulomb’s Law[1],writing:
(2)
2.4.2 The electric force between the first orbiting electron and the second nucleus
Due to the speed v of the orbiting electron of the first atom, the Lorentz contraction causes the distance to the nucleus of the second atom to shrink. Depending on the position in the orbit, the x component of the velocity varies, with a maximum value v. This affects the expression of the Coulomb force. Applying the Lorentz transformation for that case [15], it will accordingly be written:
(3)
For simplicity, the Lorentz factor[16] has been used:
(4) Always varying, due to the fact that
(5)
the mean absolute value of the force will be larger than the force between the two nuclei, , which are at rest with respect to each other.
(6)
2.4.3 The electric force between the first nucleus and the second orbiting electron
This case is in fact similar to the above-described case with the force between the first orbiting electron on the second nucleus. Hence, one may write:
(7)
Apparently, in analogy with the previous case (Section 2.4.2), the mean absolute value of the force will be larger than the force between the two nuclei, , which are at rest with respect to each other.
(8) 2.4.4 The electric force between the two orbiting electrons
Due to the speed v of both orbiting electrons, the Lorentz contraction causes the distance between them to shrink. Depending on the position in the orbit, the x component of the velocity varies, with a maximum value v. This affects the expression of the Coulomb force, so that its maximum value will accordingly be written:
(9)
Again, in analogy with the two previous cases (Section 2.4.2 and 2.4.3), the mean absolute value of the force will be larger than the force between the two nuclei, , which are at rest with respect to each other.
(10) 2.4.5 The sum of the four contributions
Performing the summation of the four terms above, Eq. (2), (3), (7), (9) gives a result that differs from zero and is negative. This implies that the force is attractive, a property that is similar to the effect of gravity. The sum is:
(11)
Serial expansion of , thereby neglecting higher order terms of , leads to
the following expression:
) (12)
which implies a net attractive force between the two electrically neutral atoms.
3. DISCUSSION
Since this is only the beginning of a new scope of investigation of gravity, it seems necessary to categorise all the phenomena that can be acquainted with gravitational effects, in order to plan the order of research that has to be undertaken. Among those to be mentioned is ‘dark matter’. Calculations based on Coulomb’s law would have to be planned for the interactions with
cosmic bodies as well as for the bodies in close vicinity. However, it is difficult to now foresee, what the long-terms consequences of this research would lead to.
4. CONCLUSIONS
The calculations above have shown that Coulomb’s law is able to account for the effects earlier attributed to gravity, when a simplistic two- atom interaction is analysed.
5. LIST OF VARIABLES
electric force (the Coulomb force) between two point electric charges
point electric charge point electric charge vacuum permittivity
separation distance between two point electric charges
electric force between the two nuclei electric force between the first orbiting electron and the second nucleus
electric force between the first nucleus and the second orbiting electron
electric force between the two orbiting electrons
total electric force between two hydrogen atoms
e electron charge
speed of the orbiting electrons Lorentz factor
distance between the two nuclei SI units have been used.
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