Realitivistic Relativity
| Scientific Paper | |
|---|---|
| Title | Realitivistic Relativity |
| Read in full | Link to paper |
| Author(s) | Robert L DeMelo |
| Keywords | relativity, quantum, scale relativity, fractal universe, space-time density, mass and charge |
| Published | 2007 |
| No. of pages | 27 |
Read the full paper here
Abstract
This paper examines the hypothetical possibility of relativistic symmetry between the celestial and quantum realms based solely on a scale difference between the two systems and the concept of space-time density derived from Einstein's curvature of space. The exploratory analysis presented in this paper derives two surprising mathematical coincidences including a new scale relativity mass equation which calculates Jupiter's relativistic mass (1.898x1027 kilograms) to the numerical value of an electron charge (1.6x10-19 Coulombs) exactly. This simple equation strongly suggests a direct mathematical relation between charge and mass, gives credence to the likelihood that the Universe is fractal in nature and that dimension changes with scale. Essentially this equation possibly unites our perception of mass at the celestial scale to that of charge at quantum scale which has enormous implications for all of physics.
Overview
Robert L. DeMelo's paper, first written in December 2007 and revised through October 2009, is presented by its author as an "exploratory analysis" rather than a finished theory. Its starting point is deliberately naive: the demotion of Pluto left the Solar System with four rock planets and four gas giants, and DeMelo takes the count of four gas giants as a signal that the Sol system is the scale-relative equivalent of a beryllium atom, whose nucleus is surrounded by four electrons. From that single observation the paper builds outward.
The hypothesis is stated flatly: "atoms and star systems are the same thing but exist in different velocity frames of reference." Gas giants are scale-equivalent to electrons; the inner planetary system to an atomic nucleus; the inner rock planets to neutrons; a star is composed of several fused celestial protons; the asteroid and Kuiper belts mark the boundary between inner and outer system. The departure from the mainstream account is total. Where standard physics treats mass and electric charge as independent properties governed by unrelated coupling constants, DeMelo proposes that they are the same property viewed at different scales, so that "dimension changes with scale," and that the universe is fractal and infinite, with each level related to the next by a single number he calls the Reality Scale Constant, S.
The argument
The Reality Scale Constant
S is obtained by comparing the radius of the beryllium atom with the radius of the Sol system. The displayed equations in the PDF are embedded as images and do not survive text extraction, but the surrounding prose states the result: S is a function of the speed of light c and of Euler's number e, a relation DeMelo finds significant because it joins "a dimensional constant relating to velocity" to "a mathematical constant relating to an infinite series and exponential growth." He reads this as evidence that scale is itself a function of velocity, the idea developed later under the heading of space-time density.
From volume to area: the mass transform
The paper's pivotal step concerns how mass should scale. Naively, shrinking a system by S should reduce mass by S3, the volume factor. DeMelo argues instead for S2. His reasoning is that the constituent atoms shrink along with the spacing between them, so that at the smaller scale they are no longer atoms at all but "sub-quantum point particles"; density is then counted by the number of point particles per volume, and the perceived mass-density rises by a factor of S, cancelling one power. The resulting relation is a quantum mass equal to the celestial mass divided by S2.
Applied to Jupiter (1.898 × 1027 kg) this yields the numerical value 1.6 × 10-19, which DeMelo identifies with the elementary charge in coulombs. Saturn gives a comparable figure. The mean mass of all four gas giants, run through the same equation, yields 2.691, which he notes is 98.99 per cent of e — the second of the paper's two "surprising mathematical coincidences." Earth, the most massive rock planet, gives a value he describes as small enough to be negligible against the electron charge, which he takes to correspond to the convention of ignoring the neutron's tiny charge moment while attributing to it a magnetic moment.
The lighter masses of Uranus and Neptune are handled by analogy with valence electrons: since valence electrons are shared in molecular bonds, DeMelo speculates that the Solar System may be in a "mass-sharing bond" with one or more neighbouring star systems.
Inverted quantum masses
An obvious objection is that if Jupiter is an electron and Earth a neutron, the mass ordering is backwards — real electrons are far lighter than neutrons. DeMelo's answer is that the measured invariant masses of quantum particles are themselves wrong. Detectors infer mass from the depth of penetration into a decelerating magnetic field, assuming that the particle arriving first carries more kinetic energy and hence more invariant mass. He argues this ignores "electromagnetic buoyancy," since particles of very different size and density do not penetrate a field in the same way, and concludes that the conventional masses are "actually flipped."
Space-time density and velocity frames
The relativistic half of the paper reinterprets inertial frames as velocity frames of reference defined against an approximately static universal frame — the observed near-fixity of stars and galaxies that astronomers use for celestial coordinates. Against such a frame, DeMelo says, "one object will always be traveling faster than the other," so velocity is not merely mutual. A faster observer sweeps through more space and encounters more particles per unit time; space-time is therefore literally denser for him, and to keep physics unchanged in his frame his physical structure must shrink, the ratio of space-time density to matter density being a universal constant.
From this he builds length, time and mass transforms parameterised by a scale factor s rather than by the Lorentz gamma, then modifies them (Eq. 8.1–8.5) to be, in his words, "suitably compliant with Einstein's relativity and the Lorentz Transformation" in the presence of persisting gravitational fields. The limiting case is a scale change of S corresponding to a velocity of c; a further level down, at the sub-quantum scale, the relative speed of light becomes c2 and the scale factor S2, while a super-celestial level would have √c as its light speed.
Forces
Because charge and mass are identified, electrostatic force and gravity must be scale equivalents. Their enormous difference in strength is then attributed not to a difference in coupling but to the difference in the passage of time: Newton's force law contains time squared through the acceleration, and the gravitational constant likewise carries a squared time component, so transforming to a frame where time runs faster by the factor c amplifies the force accordingly. DeMelo reports that after this transformation a residual divergence of exactly 1498.5763 remains between the gravitational and electric field strengths, which he attributes to unmodelled changes in the properties of space and folds into a "complete gravitational formulation" (Eq. 9.5). Attraction and repulsion are then handled by wave superposition: destructive interference between the field waves of two objects of similar mass-density produces repulsion, constructive interference between objects of different mass-density produces attraction.
Reverse Uncertainty Principle
The final section argues that the unpredictability of an electron's path after measurement is the scale image of the unpredictability of planetary orbits far into the future. Because the quantum passage of time is faster by a factor of 3 × 108, predicting an electron's orbit is equivalent to predicting the Solar System over billions of years, during which rogue planets, asteroids and supernova blast waves make the outcome uncertain. Hence the "Reverse Uncertainty Principle."
Predictions
The paper closes with testable claims: gravity between two gas giants should be repulsive; objects of similar mass and density repel while objects of very different mass and density attract; all star systems should have gas giants and an equal number of rock planets; all should have inner and outer asteroid belts; and star systems should bond to one another as atoms bond into molecules.
Assessment
What is attractive here is the honesty of the framing. DeMelo repeatedly labels the work hypothetical and exploratory, lists the assumptions he cannot justify, appends a dated log of his own corrections — including the removal of a spurious factor of e from Eq. 8.2 — and ends with falsifiable predictions rather than with a claim of proof. The predictions are genuinely testable and genuinely bold: exoplanet surveys can in principle check whether every star system has four gas giants and matching rock planets, and the claim that two gas giants repel each other is refutable by ordinary celestial mechanics. Very few papers in this vein volunteer that much. The underlying intuition — that the universe may be scale-invariant, and that apparently independent constants may be linked — is respectable and has serious proponents; Laurent Nottale's scale relativity pursues a related idea with a different formalism.
The difficulties are severe, and they begin with dimensions. The transform divides a mass in kilograms by S2 and reads the result as a charge in coulombs. That is only possible because S is built from the numerical value of c with its units discarded — the paper says so explicitly, defining c = 3 × 108 "(no units)". A relation of that form is not scale-invariant at all; it is SI-invariant. Express c in cm/s, or km/s, or in natural units where c = 1, and the Jupiter–electron coincidence disappears entirely. The paper anticipates the objection only by observing that kilograms and coulombs are both metric, which is the problem rather than the answer. Everything downstream — the 2.691 ≈ e result, the residual factor 1498.5763, the whole force sequence — inherits this dependence on a particular choice of units.
The internal arithmetic does not always hold either. "Exactly" is too strong: the elementary charge is 1.602 × 10-19 C, not 1.6, so the agreement is to two figures at best. The paper states that Saturn is 41 per cent of Jupiter's mass; it is about 30 per cent (5.68 × 1026 against 1.90 × 1027 kg). More seriously, since Eq. 3.0 is linear in mass it preserves ratios exactly, so the Earth-derived figure must be smaller than the Jupiter-derived figure by Jupiter's mass ratio to Earth's, about 318 — not the "almost 33 times" the text reports. The step from S3 to S2 is the paper's decisive move and it is asserted rather than derived: the argument that constituents "become point particles" and so contribute a compensating factor of S is a verbal manoeuvre with no accompanying calculation, and without it the Jupiter result does not arise.
Against measurement the proposal fares badly. The claim that the invariant masses of quantum particles are "flipped" conflicts not with one experiment but with the whole of mass spectrometry and with Thomson's charge-to-mass determination, neither of which uses the deceleration scheme DeMelo criticises; the electron's e/m is measured directly and is not an inference about penetration depth. Electron scattering constrains any electron substructure to below about 10-18 m, leaving no room for an internal planetary architecture. The beryllium mapping is also imperfect on its own terms: beryllium has four protons and five neutrons, while the paper gives the Sun "4 or 5 celestial protons" and the system four rock planets, and its electrons occupy 1s and 2s orbitals rather than four coplanar orbits. The prediction that two gas giants repel is contradicted directly by the mutual gravitational perturbations of Jupiter and Saturn, which are measured to high precision and are attractive; the great inequality between their orbital periods is one of the classical results of celestial mechanics. Finally, the "Reverse Uncertainty Principle" describes deterministic chaos in the n-body problem — sensitive dependence on initial conditions — which is a different phenomenon from Heisenberg indeterminacy, and identifying them elides the distinction the Uncertainty Principle exists to mark.
Read as what it says it is — a record of a striking numerical coincidence and an attempt to see how far one could push it — the paper is a legitimate exercise. Read as a physical claim, it needs a dimensionally consistent version of its central equation before the coincidence can carry any weight.