Carezani Frame Reduction

Scientific Paper
Title	Carezani Frame Reduction
Read in full	Link to paper
Author(s)	David de Hilster
Keywords	Compton, Bohr, Lorentz, Einstein, Newton, Speed of Light, Autodynamics, frame reduction, particle propellant, simplified Lorentz equations
Published	2008
No. of pages	18

Read the full paper here

Abstract

In the early 1940s, Ricardo Carezani, an Argentinean engineering student who later received his doctoral in physics, found that more than one frame in the Lorentz Systems in Relative Motion's derivation was, one of them, mathematically, and physically redundant. The removing the redundant frame and using a single one resulted in a new set of equations that are, conceptually in motion, Newtonian, have a logical explanation, even does not blow up at the velocity "c", and presents no paradoxes. The new "Autodynamics" equations have been subsequently used to improve current mainstream equations such as the Compton Effect, to derive Bohr's Atom without the need for wave equations, and to describe subatomic interactions without the need for the neutrino, etc. The math behind the redundant frame will be shown, the derivation of the new Autodynamics equations, as well as the mismatching exponent form Einstein's attempt to generate the Lorentz equations from special relativity.

Overview

This 2008 paper by David de Hilster, written with excerpts from Ricardo Carezani and reproduced with his permission, is the compact statement of the foundational claim of Autodynamics: that the derivation of the Lorentz equations in special relativity uses one coordinate frame more than the physics requires, and that removing the superfluous frame yields a different and simpler set of transformation equations with different dynamical consequences.

The paper has three parts. The first is biographical and programmatic — Carezani's life from Tucumán in 1939 through the Perón years, his emigration, the Stanford episode, and the founding of the Society for the Advancement of Autodynamics by de Hilster in 1994 — together with a summary of the claims Autodynamics makes across atomic and cosmological physics. The second is the technical core: the parallel derivations of the relativistic and the Autodynamics transformation equations, with the two errors Carezani identifies in Einstein's own derivation. The third is an appendix of Carezani's original writing, including a piece published under the name "Dr. Lucy Haye" — a pen name Carezani himself used, not a separate author — giving a geometrical version of the same argument.

The programmatic claims are stated bluntly. "There is only one frame of reference or one three dimensional space and we can only move the origin. This nullifies special relativity that requires more than one frame." "Frames are mathematical, not physical and having no physical reality, cannot be part of any physical theory." Motion "is not for free and requires energy"; the neutrino "is an invention to conserve energy because of the superfluous mass that introduced by special relativity"; "the speed of light is a number but is not a speed limit."

The argument

Why one frame is superfluous

Carezani's appendix "Frames in Relative Movement" sets up three parallel Galilean frames F, F' , F with a point P of abscissa x in F. If F moves relative to F' at v and F' relative to F at v₁, then x'' = x + (v + v₁)t. If instead P moves within F at v_x, its coordinate in F' is x' = x + (v_x + v)t. The two expressions are formally identical, and Carezani's conclusion is that the extra frame is doing no work: one of the three is always "useless, inoperative, and superfluous."

The physical principle behind this is stated as an impossibility of self-observation. "With point P and a geometrical system F linked to it, we have no physics whatsoever. We need another system, one not linked to P … in which we place an observer describing the physical alternatives which P is undergoing. In this case, frame F is superfluous." A physical system, on this definition, "consists of two points in relative movement, P and F or the origin of F" — the observed and the observer — and nothing more.

The "Lucy Haye" appendix restates it geometrically. A phenomenon occurs at A and an observer at B receives its signal. Relativity holds between A and B already: inertial systems in relative motion and constant light velocity are both satisfied. Lorentz then introduces a third system C, at rest relative to A, and it is this C that Carezani rejects: "an Observer at B will see the phenomenon directly, and System C is totally superfluous."

The two errors in Einstein's derivation

Carezani identifies two specific steps. In the relativistic derivation, differentiating the Lorentz position equation and dividing dx' by dt' produces the velocity-addition formula, but "the velocity v_x appears spontaneously through the mathematical operation of the derivative" even though P was posited at rest in F. "There is no energy to move point P … with respect to the F coordinate system." Then, in going from acceleration to the force law, one must set v_x = v to recover the standard result: "this simplification has no physical sense. There is no reason for setting these two velocities equal." He adds a pointed observation — if the two velocities really were equal, then substituting that back into the earlier velocity equation gives either 0 or an absurdity, "which emphasizes again the utter irrelevance of setting the two velocities equal."

The second charge is arithmetical: the exponent obtained in Einstein's route is 3/2 where the target Lorentz form requires 1/2, "so that even with the strange assumption that v_x must equal v, it still does not match the desired Lorentz exponent."

The Lucy Haye appendix presses the same point through the position coordinate. In the Lorentz form, x is divided by √(1 − v²/c²), so the transformed distance grows with velocity — "yet this is not true: x is a constant distance because A is at rest in System C." A worked example using Feynman's Lectures (Vol. I, Fig. 15-1, Eq. 15.3) takes x = 100 m, u = 0.8c, t = 10⁻⁷ s, so ut = 24 m, and finds the transformed coordinate at 126.67 m — the traveller moves toward P while his distance from it increases. "This increasing distance represents a velocity and this creates an artificial energy that later needs to be subtracted artificially using the Neutrino."

The Autodynamics equations

With a single frame, position and time are functions of t alone rather than of (x,y,z,t), so a single coefficient a relates them: x' = avt, t' = at. Matching the coefficient of t² in the light-sphere condition, c² = a²c² − a²v², gives a = 1/√(1 − v²/c²) and hence the "Simplified Lorentz Equations". Differentiating and dividing gives v' = v — "the observer velocity IS the object velocity", which de Hilster notes is unsurprising once F has been collapsed onto F' . Because "Einstein's equations had four variables … he had to solve four equations simultaneously. AD on the other hand has only one variable t, and thus has to solve only one equation."

Differentiating again for the acceleration and inserting it in F = dp/dt yields the mass in motion

m = m₀√(1 − v²/c²)

— the reciprocal of the relativistic factor. "This makes complete physical sense: when energy is expended, mass is expended!" The kinetic energy follows as

E_k = m₀c²[1 − √(1 − v²/c²)]

which rises to a maximum of m₀c² rather than diverging at c, and a momentum that increases and then decreases as mass is spent. The paper's comparison table sets these against their relativistic counterparts and adds a fourth row: in Autodynamics, "if a charged particle decays, its charge gets smaller."

The physical mechanism offered for the decreasing mass is particle propellant: "mass moves when quanta from that mass is expelled in the opposite direction of the path of acceleration … Particle propellant is the basis for all movement in the universe," so that "a mass will eventually turn into smaller particles and disappear as a mass when all the mass is expelled in creating velocity."

Consequences claimed

De Hilster lists what Autodynamics is claimed to deliver: Bohr's atom derived without wave equations, the Cherenkov relations recovered from AD equations, accounts of muon and pion decay, nucleus–nucleus collisions and proton–proton annihilation, a modified Compton relation, and the elimination of the neutrino from beta decay. Cosmologically: no big bang, a universe "eternal in time, finite in mass" in a cycle of birth and death, no infinite-density singularities though "super dense objects" exist, and mass increase as part of universal gravitation, invoked to account for lunar distancing, perihelion advance, the Pioneer anomaly and the Allais pendulum effect.

De Hilster also pre-empts two standard objections. To the complaint that the AD equations do not reduce to classical mechanics at low velocity, he answers that agreement with the classical limit "is characteristic of special relativity that is by no means a principle in itself." To the complaint about velocity addition, he answers that "both Newton and Einstein assumed in their equations that velocity appears instantaneously," whereas in AD "velocity does not come for free and … mass must be used to move itself to a velocity."

Assessment

The paper is admirably direct about where its disagreement lies. Rather than attacking relativity's conclusions, it goes to a specific line of a specific derivation and says: this step is unmotivated. That is the right kind of criticism to make, and the particular step identified — setting v_x = v partway through a chain-rule calculation for the force law — is genuinely a place where textbook presentations often move faster than they explain. The observation that a frame attached to an object cannot itself observe that object is also a real philosophical point about what a reference frame is for, and Carezani's insistence that "frames are mathematical, not physical" is a defensible position that has been argued in various forms by others. The account of Carezani's career is valuable in its own right, and the paper is honest about the state of the evidence, conceding that the SLAC experiment arranged with Noyes "did not do that because it was designed incorrectly" and that a definitive experiment "has been designed but yet to be performed."

The technical difficulties are, however, substantial and they concentrate at the point where the derivation is replaced rather than where relativity is criticised. Setting x' = avt and t' = at does not "collapse two frames into one"; it restricts attention to a single worldline, that of a point moving at exactly v from the origin. Those two equations describe the transform of one particular event, not a coordinate transformation, because they contain no free x. Any transformation law must tell you what happens to an event at arbitrary position, and the AD relations simply do not have the parameter needed to do so. This is why the argument that "AD has only one variable t, and thus has to solve only one equation" understates rather than simplifies the problem: the four equations in relativity are four because four numbers are needed to label an event.

The consequences are then unavoidable. v' = v means that Autodynamics has no velocity transformation at all — velocities are the same for every observer — and, combined with an invariant c, that is Galilean kinematics with a preferred frame smuggled back in, which is the position the Michelson–Morley result was taken to exclude. The mass law m = m₀√(1 − v²/c²) conflicts directly with measurement, not with theory: every circular accelerator on Earth is engineered around increasing inertia with speed, and the momentum of an electron in a storage ring would, on the AD law, fall above v = c/√2, which would make the machines inoperable in a way no operator could fail to notice. The kinetic energy ceiling of m₀c² is contradicted by the routine acceleration of protons to energies thousands of times their rest energy. And the claim that a decaying charged particle loses charge conflicts with the exact charge conservation observed in every decay channel measured.

De Hilster's reply to the classical-limit objection is the weakest passage. It is true that agreeing with Newtonian mechanics at low speed is not a logical requirement on a theory; but it is an empirical requirement, because Newtonian mechanics is what low-speed experiments measure, and a theory whose predictions differ there is refuted by ordinary mechanics rather than by relativity. The Feynman worked example likewise misreads what the transformation says: the Lorentz x' is the position of the same event in a frame whose rulers are differently calibrated and whose clocks are differently synchronised, so comparing 126.67 m with 100 m as though both were lengths in one frame is comparing quantities that the theory does not equate. The relativity of simultaneity is the piece that makes the comparison meaningful, and it does not appear anywhere in the paper's treatment.

Finally, the neutrino argument runs against a large body of direct evidence. Even granting that special relativity created the energy deficit in beta decay, neutrinos have since been detected in their own right — from reactors, from accelerator beams, from the Sun, and from SN 1987A — and their flavour oscillations have been measured. An argument that the neutrino was invented to patch a bookkeeping error has to account for those detections, and this paper does not attempt to.

What the paper does establish is the shape of the Autodynamics programme and the exact point at which it parts company with the standard derivation. It is the clearest single statement of Carezani's frame-reduction claim, and for that reason it is the right place to begin for a reader who wants to evaluate the theory on its own terms rather than through summaries.

See also

• David de Hilster
• Ricardo Carezani
• Autodynamics
• Society for the Advancement of Autodynamics
• Special Relativity
• Lorentz transformation
• Neutrino
• Muon
• Mass
• Speed of Light
• Simultaneity
• Time Dilation
• Michelson-Morley Experiment