The Unity of Coulomb's and Newton's Laws

Scientific Paper
Title	The Unity of Coulomb's and Newton's Laws
Read in full	Link to paper
Author(s)	Peter Kohut
Keywords	Coulomb's law, gravity, quantum dipole, dialectics, unification
Published	2010
No. of pages	11

Read the full paper here

Abstract

The nature of electrostatic and gravitational forces is derived by using a dialectical logic for finding the basic relations between fundamental physical characteristics of the Universe.

Overview

Peter Kohut, writing from Prešov in Slovakia, proposes that the universe is a growing network of quantum dipoles — elementary bipolar connections in which every positive pole is joined non-locally to every negative pole. At cosmic quantum state k the universe consists of k² such connections; the transition from k to k+1 creates 2k+1 new ones. Volume is the count of connections, and time is the count of transitions. From this single structure Kohut claims to derive both Coulomb's law and Newton's law of gravitation, and to show that they are two aspects of one relation.

What makes the paper unusual is its method. Kohut states explicitly that he is using "a dialectical logic", and the first third of the text is a Hegelian argument about quality, quantity and measure — quantity determined by its limit becomes a quantum, quantum without further determination is a number, and so on, with a nod to Pythagoras as the founder of objective idealism. Physics enters only after the categories are fixed. The departure from the mainstream account is therefore not a modified equation but a claim about where equations come from: constants and force laws are said to follow from the structure of being rather than from measurement. Along the way Kohut rejects the graviton as a particle, the phonon of BCS theory, and the virtual-particle account of the vacuum, replacing all three with direct non-local dipole connections.

The argument

Etalons

Because ordinary standards — the caesium second, for instance, defined by 9,192,631,770 periods of radiation — did not exist for most of cosmic history and themselves lose energy as the universe expands, Kohut argues they cannot serve as cosmic references. He therefore takes the elementary quantum jump as the standard of time and the quantum dipole as the standard of volume: "more elementary and shorter motion does not exist". Time dilation is recast as a counting statement — a process in a slower-running frame takes more cosmic jumps — so that "if the sky-rocket moves ... when its time flows twice slower", 14 billion years of expansion on Earth correspond to 7 billion in the rocket, but both correspond to the same number of jumps.

The universal relation

Dipoles differ in energy e_i; the counterbalancing quantity is their length d_i. Kohut posits that the product is the same for every dipole:

τ = e_id_i, with E = Σe_i summed over all k² connections

This constancy is the "universal law" of the paper, and Kohut suggests it is "why the geometry of the Universe is in relation to its energy, what Einstein intuitively disclosed".

Coulomb's law

Each dipole's energy splits into an attractive part and a repulsive part which, apart from a negligible remainder used to drive cosmic expansion, exactly balance: e_ia = e_ir, so e_i = 2e_ia. Hence e_ia = τ/(2d_i), which Kohut identifies with the Coulomb potential energy of a pair of elementary charges, q²/(4πεd_i). Using the definition of the fine structure constant α = q²/(2εhc) he rewrites this as e_ia = αħc/d_i, so that the universal relation becomes τ = e_id_i = 2αħc. Since force times length is energy, f_i = τ/d_i² and the attractive force per dipole is f_ia = αħc/d_i² — Coulomb's inverse-square law.

Why neutral bodies do not attract electrostatically

Two neutral bodies with k₁ and k₂ pole pairs are joined by 2k₁k₂ connections, giving a total attraction proportional to k₁k₂/d². Kohut's answer to why this is not observed is that at short range the attraction is "fully compensated by the repulsive spatial pressures of quantum dipoles coming out of these objects". Charging the bodies destroys the balance: for opposite charges q₁q₂ represents an excess of connections, for like charges a deficiency, and in each case the same Coulomb expression results — attraction being non-local pole-to-pole, repulsion being local spatial pressure.

Gravity

The compensation, Kohut asserts, "is valid only for small distances, for long ones it vanishes", because part of the universe's repulsive capacity is consumed in creating new connections during cosmic expansion. The residue is gravity: f_g has the same form as the neutral-body Coulomb attraction. Taking the external gravitational mass of a body to be proportional to its number of poles, m_j = γk_j, and substituting, he recovers f_g = Gm₁m₂/d² with the gravitational constant expressed in terms of α, h, c and γ. Inverting gives the density of connections in matter: "the object with a mass of one kilogram contains ... 1,446.10¹⁷ elementary quantum connections". The graviton is then not a particle but simply one of these connections, gravity is quantum in character, and gravitational energy cannot be localised because a body's connections branch to the whole universe.

Supporting phenomena

Kohut offers Cooper pairs and the Casimir effect as evidence for attraction between like-charged and between neutral objects respectively. Electrons, he suggests, are "probably structures with one positive and two negative poles", and BCS theory's phonon is "a non-existing particle" invoked out of ignorance of direct connections. He also holds that strong and weak forces differ from the electromagnetic only in intensity, being short and energetic connections.

Assessment

The paper has a genuine architectural idea: one relation, τ = e_id_i, from which an inverse-square law follows immediately because energy divided by length is force. And Kohut is consistent — attraction non-local, repulsion local, expansion drawing on the repulsive budget — rather than assembling ad hoc rules. The philosophical framing is unfashionable but honestly declared rather than smuggled in.

The arithmetic is correct. The chain α = q²/(2εhc), e_ia = q²/(4πεd) = αħc/d, f_ia = αħc/d² is exact SI algebra with no dropped factor. The headline number checks out too: with G = 6.674×10⁻¹¹, α = 7.2974×10⁻³ and hc = 1.9865×10⁻²⁵ J·m, πG/(αhc) = 1.446×10¹⁷, exactly the figure printed for one kilogram. (A caution for readers: this PDF loses Greek letters and superscripts on extraction, so α, π, ε and squares vanish from the printed equations in text form — they have been reinstated here from the numerical consistency of the chain.)

But Coulomb's law is not derived; it is substituted in. The step from e_ia = τ/(2d_i) to the Coulomb energy is an identification, not a deduction — Kohut writes "as we can see it is a classical Coulomb's relation" and thereby fixes τ from the known value of the charge. Everything downstream, including the "unification", is the definition of α rearranged: αħc/d is q²/(4πε₀d). What the model supplies is the assumption that e_id_i is universal; what it takes from measurement is the value of that product.

One fitted parameter carries the whole result. The coefficient γ converting poles to kilograms is never derived from the dipole network; it is obtained by demanding that the answer come out equal to G. Since the electrostatic and gravitational strengths differ by about 10³⁶, γ is doing all the work that the physical mechanism — vanishing compensation at long range — is credited with. Worse, the mechanism is not quantified anywhere: no crossover distance is computed, no formula for the degree of compensation is given, and both the compensated and uncompensated forces have the identical 1/d² form, so there is nothing to distinguish them observationally. For the picture to work, the cancellation between attraction and repulsion between neutral bodies must be incomplete by a fraction of order 10⁻³⁶, uniformly, at every separation — and nothing in the paper sets that number.

Conflicts with measurement. Three are concrete. The Casimir force between parallel plates goes as 1/d⁴ per unit area, not 1/d², and its magnitude is predicted by QED and confirmed to a few per cent by Lamoreaux (1997) and Mohideen and Roy (1998); an uncompensated Coulomb-type residue would have the wrong distance law. Phonons are not hypothetical: they are observed directly in inelastic neutron scattering, and the superconducting isotope effect — T_c varying as M^−1/2 across mercury isotopes, measured in 1950 — is precisely the evidence that lattice vibrations mediate the pairing Kohut attributes to pole geometry. And the cosmology implied by his own counting is testable: with volume proportional to k² and time proportional to k, the scale factor grows as t^2/3, a decelerating expansion, which is what the Type Ia supernova magnitude-redshift measurements of 1998 ruled out.

Standard results treated as paradoxes. The remark that "Einstein's equations of gravitational field violate the law of energy conservation at local level" misstates the situation: general relativity enforces local conservation exactly, through the vanishing covariant divergence of the stress-energy tensor. What it does not admit is a local gravitational energy density, and that is a consequence of the equivalence principle — the field can be transformed away at a point — not a contradiction between non-locality and locality. Similarly, the claim that gravitational energy "cannot be localised" is the accepted position, not a discovery of the dipole model. Finally, the electron as "one positive and two negative poles" is asserted with no account of how it then carries unit charge, and the assimilation of the strong and weak interactions to short, energetic dipoles has nothing to say about the features that distinguish them — colour confinement, parity violation, or the measured W and Z masses.

See also

• Peter Kohut
• Coulomb's Law
• Gravity
• Casimir Effect
• Fine Structure Constant
• Superconductivity
• Expanding Universe
• Vacuum