A Toolkit for Improving the Understanding of Relationships between Physical Parameters based on Adjusted SI units and a New Planck Unit Framework

Scientific Paper
Title	A Toolkit for Improving the Understanding of Relationships between Physical Parameters based on Adjusted SI units and a New Planck Unit Framework
Read in full	Link to paper
Author(s)	Michael Jefferson Lawrence
Keywords	Units, Eliminating G, parameters, light speed, c, dimensionality, charge, superluminal
Published	2009
Journal	Unpublished
No. of pages	15

Read the full paper here

Abstract

This paper presents new ways of understanding the relationships between parameters. The novel insights and predictions include: A self-contained and consistent new Planck unit set of maximal sized parameters from which all observed values can be compared and easily combined in equations. A self-contained and consistent new Planck unit set of electron-charge based parameters, some of which are directly observable in experiments. The interpretation of the gravitational constant G as a dimensionless ratio and its relegation from gravitational to permeability use and the elimination of the need to test the equivalence of gravitational and inertial masses. That all parameters can be displayed in terms of only h and c for the Planck maximal parameter set and in terms of only h, c and alpha for the electron-charge based set (other than permeability and permittivity which have G content), and which was previously considered impossible. There exists a new hypothetical dimensional analysis that can be used to describe parameter dimensions and to uncover any law of nature or any universal constants. That all electron charge based Planck parameters can be described solely in terms of ratios of the R_k and K_j, and so will benefit from the precision of measurement of these two parameters. That the experimentally observed value of R_k implies either that the velocity of a current within certain electromagnetic materials could be in excess of light speed, the patterns produced by subluminal physical objects have a maximum velocity of c times twice pi divided by alpha or that such a velocity is required in order to pass through those material. That most electromagnetic parameters can be reinterpreted in terms of mechanical parameters. By adjusting currently misaligned SI units to be self-consistent and consistent with DAPU units, greater clarity will ensue. This is a toolkit for providing a better understanding of the fundamentals of physics.

Overview

Michael Jefferson Lawrence (Maldwyn Physics) offers this fifteen-page paper not as a theory of anything in particular but as a toolkit — a rebuilt system of natural units together with a rule for translating between it and SI, designed so that mechanical and electromagnetic quantities sit on the same footing. The complaint driving it is one that professional metrologists also voice: SI's electromagnetic base is inherited from pre-relativistic electrodynamics, permeability and permittivity are carried around as separate dimensioned constants, and the result is that D, H, E and B end up with four different dimensions. Lawrence quotes Okun to this effect and offers his own image of the situation — a marionette whose strings are attached in the right places but cut to the wrong lengths, so that "the marionette can dance - but only after a fashion."

His repair proceeds in two stages. First the 2π is removed from the usual Planck definitions, giving "adjusted Planck units" (APU) with h = M_ocL_o and M_o = (hc/G)^1/2. Then, crucially, the factor √G is absorbed into both mass and length rather than mass alone, giving "double-adjusted Planck units" (DAPU): M_* = M_o√G = Q_*c and L_* = L_o/√G. The force and angular-momentum equations then read F_* = M_*²/L_*² = Q_*²c²/L_*² and h = M_*cL_*, with G gone. Lawrence is careful to say this is not the familiar move of setting G = 1: absorbing √G symmetrically "stretches" parameter space, where setting G = 1 leaves its topology untouched. He is also alert to how the exercise will look, and says so directly: "This paper is emphatically not an exercise in numerology."

The argument

Two parameter sets and two SI corrections

Two families of units emerge. The Q_* set is built on a hypothetical maximal Planck-scale charge and every member has DAPU value 1; expressed as constants they are pure powers of h and c — mass √(hc), velocity c, force c⁴, pressure c⁷/h, and so on. The q_e* set is built on the observed electron charge, and every member picks up a power of the single ratio d = q_e*/Q_* = (α/2π)^1/2, where α is the fine structure constant. Two tables give both sets in the proposed adjusted SI ("NSI") units.

Getting SI to fit requires two corrections. The first is a factor √10⁻⁷ between the charge and mass sides of the force equation, marked by a cedilla on the affected unit (so watts W become W̃ = √10⁻⁷ W). The second concerns permeability: using u_* = 4π × 10⁻⁷ introduces the factor 4π × 10⁻⁷/√G = 6.501 into quantities such as the farad, so Lawrence proposes redefining u_* = √G. G is thereby "relegated from gravitational to permeability use" — a measure of interaction strength within materials rather than between masses. He draws the corollary that the apparent weakness of gravity relative to electrostatics is not intrinsic: it "is due to the relative size of the electron charge versus the electron mass, in the electron. But the inherent strength of their underlying actions is identical."

The dimensionality scheme

To justify treating G as a dimensionless number, Lawrence introduces a one-parameter "hypothetical dimensionality" Y. Each quantity is assigned a single integer: mass Y⁺¹, velocity Y⁺², length Y⁻³, charge Y⁻¹, time Y⁻⁵, energy Y⁺⁵. The scheme is internally consistent — h (kg m² s⁻¹) gives Y⁺¹Y⁻⁶Y⁺⁵ = Y⁰, and G (m³ kg⁻¹ s⁻²) gives Y⁻⁹Y⁻¹Y⁺¹⁰ = Y⁰. The claim is that every fundamental constant except c has total dimensionality zero, and hence that "producing a law of nature" reduces to writing an equation whose Y powers balance: F = Ma works because Y⁸ = Y¹Y⁷. Lawrence suggests the product of volume and viscosity, being Y⁰, would represent a new constant of nature. He concedes the tool cannot fix numerical coefficients, since those "depend on the specific context".

R_k, K_j, and the superluminal claim

The most striking results concern the von Klitzing and Josephson constants. In the q_e* set the maximal resistance equals R_k and the maximal magnetic flux equals 2/K_j, so both measured constants fall out of the framework rather than being inserted. Since mass and magnetic flux share value and dimensionality in the Q_* set, and resistance shares them with velocity, Lawrence proposes a systematic mechanical reading of electromagnetism: magnetic flux is mass, inductance is distance, magnetic inductance is acceleration, current density is mass density. He then shows the whole q_e* set can be written as ratios of R″_k and K″_j/2 alone — h = 1/[R″_k(K″_j/2)²], c = R″_kd², current ι_e* = R″_k², voltage ∨_e* = R″_k³ — and suggests the ampere could be defined from R″_k² alone, and other constants gain precision from the exceptional accuracy of R_k and K_j.

Because resistance is read as a velocity, and because R_k = c/d² = 2πc/α ≈ 2.58 × 10¹¹ m/s, the framework yields a speed some 861 times c. Lawrence does not assert that objects travel this fast. He lists three readings — that currents in certain materials exceed c, that patterns produced by subluminal sources have this maximum, or that this is the minimum velocity required to cross a maximal medium — states a preference for the last, and says the question "should be investigated", citing Ardavan et al. on superluminal pattern motion. A resistance, on this reading, measures the velocity needed to get through a material: zero resistance passes any current, maximal resistance is impassable.

Simplifications

Three worked examples close the paper. The Bohr energy levels E_n = −(1/n²)(k²me⁴/2ℏ²) become, in DAPU form, the transparent ratio E_n/E_* = −½mv_e²/n² — "simply different variations in the kinetic energy of the electron". The magnetic moment recasts as nμ_e = ½ev_er_e, formally parallel to nℏ = mv_er_e, so that charge in motion carries "orbital magnetic momentum" as mass carries angular momentum, with [ec] replacing m in the kinetic-energy form. From this Lawrence extracts a testable prediction: the ½ is only a low-energy approximation, and in atoms with fast electrons the levels should diverge from it by δ = (γ_v − 1)/v_e² − ½. The third example derives Ohm's law by splitting v_e² = v_Rv_I into a material-limited velocity and an average current velocity, and checks it on a 240 V, 20 A, 12 Ω circuit in both unit systems.

Assessment

The paper's real merit is that it takes a genuine and under-discussed defect seriously. The mechanical/electromagnetic split in SI is an artefact of history, the 4π × 10⁻⁷ in the old μ₀ was a definition rather than a measurement, and the observation that R_k and K_j are now the most precisely realised electrical quantities — so that other constants might be expressed through them — is exactly the reasoning that led to the 2019 SI redefinition, in which h and e were fixed exactly and the ohm and volt became derived from R_k and K_j. Lawrence's instinct here was sound and, in the narrow metrological sense, has been vindicated. The δ = (γ_v − 1)/v_e² − ½ prediction for high-Z atoms is a real, checkable statement rather than a rearrangement. And the internal bookkeeping is careful: the tables are mutually consistent and the Y-exponent assignments do balance for every relation he tests.

But the central novelties do not survive inspection, and the superluminal result is the clearest case. R_k = h/e² = μ₀c/2α, and with the pre-2019 μ₀ ≡ 4π × 10⁻⁷ exactly, this is identically 10⁻⁷ × (2πc/α). The "velocity in excess of light speed" is therefore the numerical value of the ohm-defined resistance with the factor 10⁻⁷ stripped off — and that factor is precisely the arbitrary SI convention Lawrence himself has just removed by hand. Nothing physical has been discovered; a conversion factor has been deleted and the residue read as a speed. The paper even supplies the disproof, since Table 3 lists 10⁻⁷ as the DAPU translation factor for R_e*. That an ohm can be given the units of m s⁻¹ under a scheme that assigns every quantity a single integer is a fact about the scheme, not about currents in materials; Ardavan's polarisation-current work concerns superluminal phase patterns and supplies no support for a 861c bound.

The dimensionality tool has the same defect in general form. Assigning one integer per quantity is a linear map from the three-dimensional (M, L, T) space of dimensions onto a single integer line, and any such map has a large kernel: dimensional balance in Y is necessary for a correct equation but nowhere near sufficient, so the claim that it "can be used to uncover any law of nature" inverts the logic. Lawrence's own illustration shows the trouble. Volume × viscosity is Y⁰, but in real dimensions m³ × Pa s = kg m² s⁻¹, which is simply action — not a new constant of nature but Planck's constant's units over again. Relatedly, calling G dimensionless is not an insight but a choice of convention: the number 6.67428 × 10⁻¹¹ is not invariant, and the Duff–Okun–Veneziano "Trialogue" that Lawrence cites is precisely the debate over whether such a move has content. Absorbing √G, a dimensioned quantity, into M_* and L_* while declaring it dimensionless is the step that most needs an argument and receives an assertion.

Two further difficulties. The claim that eliminating gravitational mass makes the equivalence of gravitational and inertial mass a non-question is a definitional manoeuvre, not a physical result: relativistic gravitation makes equivalence an empirical statement about how bodies of different composition fall, tested to parts in 10¹⁵ by torsion-balance and lunar-laser-ranging experiments, and a unit convention cannot render such a measurement meaningless. And the assertion that the "inherent strength" of gravity and electromagnetism is identical, the difference lying only in the electron's charge-to-mass ratio, restates the problem rather than solving it — the ratio in question is the ~10³⁶ disparity itself, and calling it a consequence of the electron's parameters leaves untouched the question of why those parameters take the values they do. The claim throughout that particular displays "were previously considered impossible" is also overstated; expressing Planck quantities as powers of h and c after absorbing G is a familiar rescaling, and the cited authors deny not its possibility but its significance.

As a compact and self-consistent unit system with a clear translation table, the toolkit does what it says. As a source of new physics — superluminal limits, a universal law-generator, the dissolution of the equivalence principle — it mistakes properties of its own notation for properties of nature, which is the failure mode its author was right to worry about and did not escape.

See also

• Michael Jefferson Lawrence
• Planck Constant
• Fine Structure Constant
• Speed of Light
• Equivalence Principle
• Mass
• Electron