On the Fractal Nature of Existence: Difference between revisions

Scientific Paper
Title	On the Fractal Nature of Existence
Read in full	Link to paper
Author(s)	[[]]
Keywords	Quantum Gravity, dark energy, dark matter, expansion of the universe
Published	2012
No. of pages	29

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Latest revision as of 09:58, 21 July 2026

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Abstract

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Overview

On the Fractal Nature of Existence is a 29-page monograph by Christopher A. Laforet that attempts to replace the four fundamental interactions of standard physics — gravity, electromagnetism, and the strong and weak nuclear forces — with a single Universal Force that is repulsive and whose magnitude grows without bound as the separation between bodies shrinks. The paper's starting point is not a new field equation but a re-reading of Special Relativity: Laforet proposes that the geodesics of space-time are literally waves, that mass is "a vibrating point of space" which is the source of those waves, and that what physics calls the time dimension is nothing but the arc length of the wave wrapped around the spatial dimensions. From those premises he derives a force law, then applies it in turn to falling bodies, electric charge, nuclear binding, magnetism, electron orbitals, the double-slit experiment, galactic rotation curves, antimatter, the arrow of time and cosmic expansion.

The departure from the mainstream account is deliberate and total. There is no charge, no photon, no force-carrying particle, no wave-particle duality, no dark matter, no dark energy and no singularity. Attraction — including the fall of Newton's apple and the binding of the electron to the proton — is not a force at all but a shadowing effect: nearby bodies screen one another from the much larger repulsion exerted by the rest of the universe, so that the residual, unbalanced push from outside drives them together. This places the paper squarely in the Push Gravity tradition, though Laforet arrives at it from relativistic kinematics rather than from a corpuscular flux, and he combines it with an appeal to the bulk universe that is explicitly Machian. The concluding section pushes the scheme to its limit: because the model fixes no smallest or largest length, the same structure must repeat at every scale, so that "our universe may be an electron in the DNA strand of a much larger entity."

The argument

Time as a derived quantity

Laforet opens by denying that time is a property of the world. Position, he argues, is something observers construct by choosing a centre and measuring separations from it; time is then constructed by comparing the rate of change of one set of separations against another, which "is how we use clocks." Time is therefore a bookkeeping device for changes in distance, and the temporal dimension appearing in the mathematics of special relativity must be something else — in his model, a spatial "sub-dimension" of three-dimensional space.

Geodesics as waves

Mass is defined as a point of space that vibrates, the vibration occurring in a fourth dimension while the resulting waves spread through the three familiar ones. The rest-frame wavelength of this "geodesic wave" is a universal constant, taken equal to c in natural units. Length contraction is reinterpreted as a reduction in the wavelength of the geodesic, and time dilation as the corresponding increase in its arc length; the constancy of the speed of light becomes the constancy of the ratio of wavelength to arc length. Laforet asks the reader to picture the wave not as a transverse ripple but as a coil wound around the straight-line dimension, the number of coils varying with relative velocity. The relativistic Doppler factor for a photon emitted by A, reflected from B and returned,

λ_BA = λ_AB (1 + V) / (1 − V),

with c = 1 and V negative for approach, is said to already contain both effects.

The Universal Force

Combining Planck's relation E = h/λ with inverse-square spreading and a factor s/c counting how many wavelengths separate the bodies, the energy stored between two points is

E = (h / sc²) · (1 − V) / (1 + V),

and the force is minus its derivative with respect to separation s. Because each extended body is a collection of such points, and every point is assumed to interact with every point of the other body, the force is scaled by the product of the point-counts, which Laforet defines to be the masses M₁ and M₂. Mass in this scheme is therefore not a measured quantity but a tally of vibrating points. He concedes the product is a slight over-estimate because not every point has line of sight to every other, and argues that since atoms are mostly empty this correction is small. Two limits follow immediately: the force diverges as s → 0, and it diverges as the approach speed tends to c — which he offers as the reason nothing in the observable universe can reach light speed, since in any direction one is approaching something.

Attraction as shadowing

If the only force is repulsive, why do apples fall? Laforet invokes the cosmological principle: an isolated Earth in a homogeneous, isotropic universe feels equal repulsion from every direction and does not move. Introduce an apple, and each body screens the other from part of the cosmic push. Provided the surrounding universe's enormous mass more than compensates for its distance, a blocked cosmic line of force is replaced by a weaker apple–Earth line, leaving a net inward push on both. Because the Earth's shadow on the apple is far larger than the apple's on the Earth, the apple does nearly all the moving. In the low-velocity limit this yields

F = (M_eM_a/r²) · [ r²M_u / s²M_e − 1 ],

and Laforet identifies the bracketed quantity with Newton's G, arguing that the effective mass of the universe M_u itself scales with the mass of the central body (each added point blocks one more cosmic line) and falls off as r⁻², so that the bracket is approximately constant for the Earth or the solar system. Gravity is attractive only while r²M_u > s²M_e.

Charge, the nucleus and the absence of singularities

The same geometry, Laforet claims, produces the phenomena attributed to charge. A light electron near a large, massive proton is in the apple's position and is pushed inward; two identical particles cast equal shadows and settle at an equilibrium separation where the mutual repulsion balances the averaged external force, F_AB = (F_A + F_B)/2. Like charges repelling and unlike charges attracting are thus two cases of one geometry, with no charge property required. The strong nuclear force is the proton–proton force at that equilibrium point; an incoming neutron that disrupts the equilibrium can tip the force back to repulsion, which he offers as fission, while larger nuclei have equilibria more easily disturbed by stray particles, which he offers as spontaneous decay. Because the repulsion rises without limit at short range, no accumulation of mass can collapse: the singularities of General Relativity are excluded by construction.

Magnetism, orbitals and the double slit

Magnetism is treated as a velocity effect on the Universal Force. A bar magnet is modelled as circulating conduction electrons; evaluating the force at ±V and ±2V for a magnet facing a plain metal bar, a south pole and a north pole gives F₂ < F₁ < F₃, so opposite poles attract and like poles repel, with the differences proportional to electron speed. An unmagnetised metal has an opposite circulation induced in it and is therefore attracted to either pole. Iron filings around a current-carrying wire align tangentially because the end nearer the wire has faster-circulating electrons, producing a radial force difference and hence a torque. In the atom, two electrons of opposite spin orbiting in a common plane are stable; a third necessarily shares a rotation sense with one of them, generating a non-tangential force that ejects it from equilibrium — offered as a derivation of the Pauli exclusion principle and of two-electrons-per-orbital, with subsequent shells sitting farther out because the filled inner shell raises the nucleus's effective mass. For the double slit, Laforet argues that repulsion from the slit edges deflects each electron, that passing exactly centred and unrotated is very improbable, and that the overlap of the resulting high- and low-probability bands from two slits produces fringes one particle at a time without any self-interference. Light needs no photon either: the electromagnetic wave is the geodesic wave, and the photoelectric threshold is simply the wavelength at which the force on a bound electron becomes sufficient to free it.

Cosmology, antimatter and scale

Flat galactic rotation curves are addressed by balancing centrifugal force against the galactic core's push and the universe's push, giving V² = M_ur/s² − M_G/r; Laforet notes he lacks the mass-distribution data, but observes that if galactic mass grows linearly with r while the effective universal mass falls as 1/r, the velocity is constant and no dark matter is needed. On antimatter he is explicitly tentative, suggesting that a positron track may be electrons stripped from the detector itself by the collision. The arrow of time follows from the impossibility of reversing a purely repulsive expansion; accelerated cosmic expansion is galaxies "pushing off each other," and as the surrounding universe thins, the confining push weakens and structures come apart in sequence — galaxies, then solar systems, then atoms. Since the model sets no scale, the same physics recurs at every magnification: observed speeds depend on the ratio of a system's mass to c, so electrons appear fast and galaxies slow, and the Big Bang is displaced by "a continuous outward expansion from infinity to infinity." Laforet closes by extending the scale argument to human society, where growing population and interconnection amount to a contraction of the effective length scale and hence a faster observed rate of change.

Assessment

The paper's genuine attraction is its economy of ambition. A single force law, one geometrical mechanism (shadowing) and one reinterpretation (time as arc length) are asked to cover gravity, charge, nuclear binding, magnetism, orbital structure and cosmic expansion. Several of the reinterpretations are elegantly posed: identifying the electromagnetic wave with the geodesic rather than placing a field in space-time is a clean move; the short-range divergence of the repulsion disposes of singularities without ad hoc cut-offs; and the shadowing account of attraction is a coherent modern restatement of the screening tradition in Push Gravity, with the additional virtue that it makes G a derived, environment-dependent quantity rather than a brute constant. The treatment of the double slit, whatever its ultimate merit, at least attempts a definite mechanical picture rather than an appeal to formalism.

The difficulties are substantial and mostly concern what is asserted rather than derived. The central identification — that the number of "points of space" in a body is its mass — is a definition, and nothing in the paper connects it to any measured inertial or gravitational mass, so equations 5 and 6 carry units and magnitudes that are never fixed. The bracketed expression said to equal G is argued to be constant only by stipulating that the effective mass of the universe scales as M_e/r²; no independent reason is given for that scaling, and it is introduced precisely because it delivers the required answer. The same manoeuvre reappears in the rotation-curve section, where the author openly concedes he has no mass-distribution data and then supposes exactly the distribution (galactic mass linear in r, universal mass inverse in r) that makes V constant. That is not a prediction; it is a fit chosen after the fact, and Laforet's candour about lacking the data underlines the point.

There are also unresolved tensions with measurement. Shadowing models of gravity have long faced the objection that screening depends on the amount of intervening matter, so gravity should not scale strictly with mass and should show measurable saturation in dense bodies; Laforet raises the transparency issue but treats it only qualitatively, and the resulting force is admitted to depend on "masses and densities" — which conflicts with the equivalence of gravitational and inertial mass tested to parts in 10¹³ by torsion-balance and lunar-laser-ranging experiments. The claim that antimatter is a detector artefact sits badly with the routine production of positrons in medical positron emission tomography and with the measured annihilation signature at 511 keV, and the author states plainly that he is "not very familiar with antimatter" — an honest disclaimer that nonetheless leaves the section as speculation rather than argument. The nuclear section identifies the strong force with a proton–proton equilibrium but offers no account of why binding energies per nucleon peak near iron, nor of the neutron's role beyond a single sentence about disrupted equilibria. Finally, the abolition of the photon must contend not merely with the photoelectric threshold, which the paper does address, but with photon antibunching and single-photon interference experiments in which detections are anticorrelated at a beamsplitter — a result a purely continuous geodesic wave does not obviously reproduce.

Read as a physical theory ready for comparison with data, the paper falls short: its key constants are not calibrated and its cosmological successes are constructed rather than derived. Read as what it more nearly is — a sustained attempt to see whether one repulsive interaction plus a screening geometry could in principle generate the phenomena usually assigned to four forces — it is internally consistent, unusually frank about its own gaps, and clear about which of its sections are argument and which are conjecture.

@@ Line 18: / Line 18: @@
 ''On the Fractal Nature of Existence'' is a 29-page monograph by [[Christopher A. Laforet]] that attempts to replace the four fundamental interactions of standard physics — [[gravity]], electromagnetism, and the strong and weak nuclear forces — with a single '''Universal Force''' that is ''repulsive'' and whose magnitude grows without bound as the separation between bodies shrinks. The paper's starting point is not a new field equation but a re-reading of [[Special Relativity]]: Laforet proposes that the geodesics of space-time are literally waves, that mass is "a vibrating point of space" which is the source of those waves, and that what physics calls the time dimension is nothing but the arc length of the wave wrapped around the spatial dimensions. From those premises he derives a force law, then applies it in turn to falling bodies, electric charge, nuclear binding, magnetism, electron orbitals, the double-slit experiment, galactic rotation curves, [[antimatter]], the arrow of time and cosmic expansion.
-The departure from the mainstream account is deliberate and total. There is no charge, no photon, no force-carrying particle, no wave-particle duality, no [[dark matter]], no [[dark energy]] and no singularity. Attraction — including the fall of Newton's apple and the binding of the electron to the proton — is not a force at all but a ''shadowing'' effect: nearby bodies screen one another from the much larger repulsion exerted by the rest of the universe, so that the residual, unbalanced push from outside drives them together. This places the paper squarely in the [[Push Gravity]] tradition, though Laforet arrives at it from relativistic kinematics rather than from a corpuscular flux, and he combines it with an appeal to the bulk universe that is explicitly [[Mach's Principle|Machian]]. The concluding section pushes the scheme to its limit: because the model fixes no smallest or largest length, the same structure must repeat at every scale, so that "our universe may be an electron in the DNA strand of a much larger entity."
+The departure from the mainstream account is deliberate and total. There is no charge, no photon, no force-carrying particle, no wave-particle duality, no [[dark matter]], no [[Dark Energy|dark energy]] and no singularity. Attraction — including the fall of Newton's apple and the binding of the electron to the proton — is not a force at all but a ''shadowing'' effect: nearby bodies screen one another from the much larger repulsion exerted by the rest of the universe, so that the residual, unbalanced push from outside drives them together. This places the paper squarely in the [[Push Gravity]] tradition, though Laforet arrives at it from relativistic kinematics rather than from a corpuscular flux, and he combines it with an appeal to the bulk universe that is explicitly [[Mach's Principle|Machian]]. The concluding section pushes the scheme to its limit: because the model fixes no smallest or largest length, the same structure must repeat at every scale, so that "our universe may be an electron in the DNA strand of a much larger entity."
 ==The argument==