The Three Elements Theory

Scientific Paper
Title	The Three Elements Theory
Read in full	Link to paper
Author(s)	Frederic Lassiaille
Keywords	gravity, unifying theory
Published	2010
No. of pages	20

Read the full paper here

Abstract

This is a short description of the Three elements theory (20 pages). The complete document (150 pages) is available in french language only, on the internet site http://lumi.chez-alice.fr/3elt.pdf. The three elements theory is a unifying theory.

Overview

Frédéric Lassiaille's paper is the English extract (version 0.05a, September 2010) of a 150-page French document setting out what he calls the three elements theory. It is a unification programme in the same ambition as string theory, but with a very different starting inventory. Where string theory builds everything from vibrating strings, Lassiaille builds everything from exactly three constituents: the luminous point, the bubble, and space-time itself, treated as an element in its own right rather than as a stage.

The luminous point is the sole carrier of energy — a point moving perpetually at the fixed speed c₀ = √2·c along space-time geodesics. A bubble is a surface, either a sphere or a torus, which constrains any luminous point that touches it to move within that surface. A bubble alone, with no luminous point in it, has no energy at all — and this, Lassiaille says, immediately explains "the mystery of the neutrino, the only particle of standard model without any energy." Spherical bubbles make bosons; torus-shaped bubbles make fermions, and the toroidal constraint is what prevents them from reaching c and therefore gives them mass.

The departure from the mainstream lies less in rejecting relativity than in re-reading it. Lassiaille recasts the space-time metric in Euclidean rather than Minkowski form, ds² = dx² + dy² + dz² + c²dt², insisting this is "nothing more than a different mathematical vision of relativity" — harder for perihelion calculations, but revealing of connections between relativity, quantum mechanics and Newton's law. He then generalises the first principle of general relativity — that gravity is a space-time deformation — to all four forces, distinguishing them by the shape of the deformation. And he breaks with special relativity on one specific point: the constancy of c holds only in privileged inertial frames, those whose origin coincides permanently with a massive particle.

The argument

The wave function as a propagated deformation

Each luminous point deforms the space-time around it and that deformation propagates outward at c₀ as a wave. Because a luminous point confined to a bubble surface must follow cyclic trajectories, the single wave becomes, on a larger scale, a continuous train of waves — and this train "corresponds exactly to the wave function of quantum mechanics." Wave-particle duality is thus a composite structure rather than a complementarity: the particle is the point in its bubble, the wave is the deformation it broadcasts.

The uncertainty principle follows as a measurement argument. Any detector close enough to localise the particle superimposes its own wave on the particle's, producing an uncertainty in frequency and hence in energy; measure from far enough away to avoid that pollution and the position becomes uncertain instead. Lassiaille presents this as a mechanism rather than a postulate.

Deformation shape as the source of force

The central generalisation is that every force is a space-time deformation, distinguished by the highest non-null curvilinear derivative of the luminous point's trajectory — effectively a Taylor decomposition of the trajectory. His table (Illustration 4) assigns them explicitly: energy is degree 0 and generates the gravitational field (degree 2, "space time curve"); charge is degree 4, "curve of torsion", and generates the electrostatic field at degree 6, "curve of torsion of torsion"; electric current is degree 5 and generates the magnetic field at degree 7, "torsion of torsion of torsion". Gravity, by contrast, comes from a deformation without torsion, generated by a luminous point in localised Brownian motion confined inside a particle — so mass is simply the energy of such a confined set of points. He notes, fairly, that general relativity's mathematics already permits deformations with non-null torsion but assigns them no meaning, calling this "a bizarrery of relativity."

A striking consequence: gravitational waves in this theory are not exotic and rare. "These waves are nothing else than electromagnetic fields, noticeably those fields generated by each moving particle" — so we see gravitational waves every day.

Recovering the Lorentz factor

A moving massive particle tilts the local tangents to space by an angle α = arcsin(v/c). Dilation and contraction coefficients are then simply cos α = √(1 − v²/c²), reproducing the standard factor. Lassiaille treats length contraction and time dilation as symmetrical to one another under the exchange of the time axis with a single space axis — and shows the same symmetry unifying potential and kinetic energy, so that alongside F_p = grad(E_p) there stands a kinetic counterpart F_i = grad(E_c).

The restriction to privileged frames is where he parts company with Einstein. In such a frame the origin coincides permanently with a non-null mass; only these frames are tangent to the local space and time axes, and only in these does light travel at c. He argues that a non-privileged inertial frame "does not have a concrete physical sense since one will never be able to place an observer or a detector in this frame", and that the Euclidean metric this permits is "perfectly physically exploitable" where the Minkowski signature is not.

Two superposed metrics

Locally, space-time is Euclidean with four dimensions, embedded in a larger Euclidean space of seven. Two Riemannian metrics are superposed: a macroscopic one, globally Euclidean, in which geodesics are straight lines; and a microscopic one in which geodesics are helices of roughly the electron radius. Zooming out, each helical geodesic collapses to its own axis and the macroscopic metric is recovered — which Lassiaille identifies as the point of similarity with string theory. The three extra dimensions are not curled up inside our space but are dimensions of the surrounding space in which our four are embedded.

Particles and the standard model

Illustration 3 gives the catalogue. A neutrino is a bare bubble. A photon is a luminous point on a circular path on a spherical bubble; in space-time that circle becomes a helix, and since luminous-point trajectories determine the metric, the helices imprint a torsion on space-time which in turn forces all photons onto helical paths. The photon's observed speed is the axial projection of c₀ onto a "balanced" helix: √2·c/√2 = c. Bosons therefore have null mass in the macroscopic metric; fermions, on toroidal bubbles, cannot reach c and so have non-null mass. An electron is a torus crossed by a single luminous point; a down quark is qualitatively the same shape, an up quark the same but with helicity reversed, principal circle radius twice the orbital radius, and luminous-point energy larger by roughly the mass ratio (~2000). Cross-sections showing quark positions in the proton and neutron are given.

Paradoxes and dark matter

The EPR paradox is explained by a space-time "tunnel" — a narrow line joining the two particles in which the metric is very different from the global one and length contraction is extreme, so the particles are effectively adjacent and interact only through it. Lassiaille notes this "could lead to a validation experiment."

The twin paradox is resolved by asymmetry of mass: since it is mass and hence energy that determines the shape of space inside space-time, the spaceship's mass is negligible against the Earth's or the galaxy's, so the two brothers' situations are not symmetric. The time-dilation equation is calculated in each frame and yields identical results by wholly different routes. He remarks pointedly that "the mass do not appears in general relativity in order to explains the brothers paradox."

The claimed validation is dark matter. Lassiaille derives a correction to Newton's law at high matter density and short inter-mass distances, giving a larger effective gravitational constant outside a galaxy than within it. He reports that global galaxy rotation-speed profiles come out very close to measurement, with calculated stellar rotational speeds for NGC 3310 and NGC 1068 respectively "10% and 64% close to experimental measurements."

Proposed tests

Two are named. The first is to measure the electromagnetic fields near a twisted optical fibre carrying a powerful light beam — a direct probe of the helical photon trajectory and of the identification of electromagnetic fields with 5th- and 7th-degree deformations. The second is the relation c₀ = √2·c: show that light can move faster than c but never beyond √2·c. He states that "it seems that today a part of this experiment has been realized." He is candid that "in its actual state, the predictions of this theory are few. There are no foreseen particles," and that development is "difficult and slowed down today for a lack of means : 1 part-time person and no money."

Assessment

What is genuinely interesting here is the organising idea that different forces correspond to different orders of curvilinear derivative of a single underlying trajectory. Taken as a classification scheme, it is neat and non-arbitrary: it gives a reason why there should be a small fixed number of interactions rather than an open list, and it correctly notes that the Riemannian formalism admits torsion which general relativity leaves unused. The observation is fair and is one an orthodox reader can engage with. Equally, the derivation of the Lorentz factor from a geometrical tilt angle α = arcsin(v/c) is clean, and the insistence that the twin paradox is resolved by the mass asymmetry rather than by an appeal to acceleration alone is a real point about how the paradox is usually taught. The author's frankness about the theory's incompleteness — that momentum conservation, Maxwell's equations, QED and even E = hν "still remains to be calculated" — is more honest than most work of this kind.

But the difficulties are fundamental rather than incidental. The paper repeatedly asserts results it does not derive, and says so: of the central tilt-angle formula, "this results from the postulates after calculations. Those calculations are not easy to do and still remains to do." That is the load-bearing step of the entire special-relativity recovery, and it is unperformed. The same holds for electromagnetism ("immediately found qualitatively, complicated to demonstrate rigorously"), momentum conservation, and the standard model correspondence, which is conveyed by figures rather than equations. A unifying theory whose unifications are all pending is not yet a theory.

Internally, the numbers do not cohere. The claim that dark matter is explained "each dark matter mystery is solved" is placed alongside the reported agreement figures — 10% for NGC 3310 and 64% for NGC 1068. A 64% discrepancy is not a validation; it is a failure, and describing the pair as "a strong validation" is the paper's clearest internal inconsistency. Two galaxies is in any case not a test of a rotation-curve model: the standard dark-matter and MOND fits are assessed against samples of hundreds, with the baryonic Tully-Fisher relation as the discriminating regularity, and neither is engaged with here. Nor is a larger gravitational constant outside galaxies reconciled with solar-system and binary-pulsar constraints on any variation of G.

Two conflicts with measurement are decisive as stated. First, the postulate that luminous points travel at √2·c and the proposed experiment "showing that the light can move at a speed strictly higher than c" run against the direct timing of neutrinos and photons from SN 1987A, which arrived together to within hours after 168,000 years of flight, and against the OPERA superluminal-neutrino result of 2011, which was traced to a loose fibre-optic connector and withdrawn. The hint that "a part of this experiment has been realized" is not substantiated. Second, the identification of gravitational waves with ordinary electromagnetic fields is now directly contradicted: LIGO's 2015 detection of GW150914 and the 2017 multi-messenger event GW170817 measured a quadrupolar strain signal, at a frequency and amplitude matching binary inspiral templates, in instruments that are not sensitive to electromagnetic fields of that magnitude — and in the GW170817 case the gravitational and electromagnetic signals were separately observed with a 1.7-second offset. This is a case where a 2010 claim has since been settled by experiment.

Finally, the treatment of the quarks and of the proton and neutron is pictorial only. Assigning the up quark a mass ratio of "approximately 2000" relative to the electron is roughly right for a constituent quark mass but bears no relation to the measured current-quark masses (a few MeV for up and down), and the model offers nothing on colour, confinement, or the deep-inelastic structure functions that established the quark picture in the first place.

The author's own summary — "this unifying physical theory is in development phase" — is the right description. The paper is a sketch of an ontology with some appealing structural instincts, presented before the mathematics that would make it testable, and its most quotable claim, "the absence of proven nonconformity ... of this theory with any physics field," is only sustainable because so little of it has been calculated far enough to conflict with anything.