Basic Concept of 3-Dimensional Spiral String Theory (3D-SST)
| Scientific Paper | |
|---|---|
| Title | Basic Concept of 3-Dimensional Spiral String Theory (3D-SST) |
| Read in full | Link to paper |
| Author(s) | Vladimir B Ginzburg |
| Keywords | string theory, conservation laws, radiation, toryx, helyx, aether, elementary particles |
| Published | 2011 |
| Journal | Proceedings of the NPA |
| Volume | 8 |
| No. of pages | 12 |
| Pages | 209-220 |
Read the full paper here
Abstract
According to the 3-Dimensional Spiral String Theory (3D-SST), at the core of the universe are two polarized spacetime spiral string entities called toryces and helyces that form elementary mass and radiation particles respectively. Polarization of toryces is a result of a topological inversion of their spacetimes that enables them to absorb and release energy. Elementary mass particles are created from toryces by following the universal conservation laws. Helyces are created when their parental toryces are transferred from higher to lower quantum energy states. Depending on the type of their parental toryces, the helyces form elementary radiation particles having various frequencies and propagating at either luminal or superluminal velocities. The radiation particles are responsible for exchange of energy and communication between the matter particles. Physical properties of toryces and helyces are directly related to their spacetime properties. The theory requires a new interpretation of zero, number line and trigonometry.
Overview
This is a compact statement of the framework Vladimir B. Ginzburg has developed over some fifteen years of books and conference papers, presented to the 18th Annual Conference of the NPA at College Park in 2011. In place of point particles or the vibrating strings of conventional string theory, 3D-SST posits two spiral "spacetime string" objects: the toryx, a double-circular leading string with a double-toroidal trailing string wound around it, which builds all matter particles; and the helyx, a double-helical leading string with helical trailing strings, which builds all radiation particles. Every property a particle has — charge, inertial mass, gravitational mass, magnetic moment, density, even a Young's modulus of elasticity — is defined as a function of the string's geometry.
The organising trick of the theory is that all of a toryx's parameters can be written in terms of a single dimensionless variable, the relative radius of the leading string b1 = r1/ri, measured against a constant "real inversion" radius ri. As b1 is allowed to run "from negative to positive infinity", the toryx passes through four topological regimes — real negative, real positive, imaginary positive, imaginary negative — and these four regimes are what Ginzburg identifies with the different classes of elementary particle. Matter and antimatter differ by topological inversion, "turned inside out"; charge and mass differ by position on a circular number line.
Two features set it apart most sharply from the standard account. First, superluminal propagation is built into the formalism rather than excluded from it: the constraint that the spiral velocity of the trailing string equals c constrains only the resultant of its rotational and translational components, so "any one of them can be superluminal making the other one imaginary". Second, the theory does not merely use unconventional physics but unconventional mathematics: Ginzburg states plainly that 3D-SST "requires a new interpretation of zero, number line and trigonometry", introducing an "infinility" (the inverse of infinity) alongside infinity, a circular universal number line, and a "universal cosine" cosu.
The theory
Spacetime parameters of the toryx
A toryx consists of a double-circular leading string of radius r1 and a double-toroidal trailing string of radius r2. Three fundamental equations govern it:
- the length of one winding of the trailing string equals the spiral length of one winding of the leading string, L2 = L1;
- the difference of the two radii is the constant inversion radius, r1 − r2 = ri = const;
- the spiral velocity of the trailing string is the speed of light, V2 = (V2r2 + V2t2)1/2 = c = const.
When r1 = ri the toryx degenerates into a circular string propagating at c, the real inversion toryx. Two further constants follow: the inversion frequency fi = c/2πri and cycle time ti = 2πri/c. Everything else is then expressed relative to ri, fi, ti and c, and Tables 2 and 3 of the paper list closed-form expressions for the relative radius, spiral length, velocity, frequency, cycle time, number of windings, volume, wavelength and steepness angle of both strings as functions of b1 alone.
Because the constraint fixes only the resultant velocity, the peripheral velocities of the trailing string may exceed c. Ginzburg tabulates inner and outer translational and rotational velocities at the edges of the trailing string, and gives explicit ranges of b1 (roughly 0.544 to 1.0 for the inner case, 1.0 to 6.222 for the outer) within which the relative velocity exceeds unity — that is, becomes superluminal.
The universal law of motion
From the relative-velocity relation β1 = (2b1 − 1)1/2/b1, Ginzburg extracts what he calls the universal law of motion, and shows that the classical law β1 = (2/b1)1/2 — the relation obeyed by planets and by atomic electrons — is simply its large-b1 limit. For b1 > 20 the two agree closely. Below about b1 = 2 they diverge sharply: the classical law sends β1 to positive infinity as b1 → 0, whereas the universal law has β1 rise to a maximum of exactly 1 (the speed of light) at b1 = 1 and then fall away toward "infinility" (+0), the inverse of infinity. This recovery of the classical orbital relation as a limiting case is the paper's main claim of continuity with established physics.
Two polarizations: vorticity and reality
Toryces are polarized in two independent ways. The vorticity V is the ratio of trailing to leading radius, equal to the relative rotational velocity of the trailing string; positive and negative vorticity define positive and negative toryces. The reality R is the square root of the relative outer radius b = 2b1 − 1; in a real toryx all spacetime parameters referred to the middle of the trailing string are real numbers, while in an imaginary toryx some of them are imaginary.
Both quantities are displayed on circular universal number lines divided into an "infinility domain" and an "infinity domain", with the numbers in different quadrants "either reversely or inversely related to one another". This is where the new arithmetic enters, together with the universal cosine cosu(φ2), which equals the ordinary cosine on 0°–180° and its reciprocal on 180°–360°.
Metamorphoses of the topology
Section 5 walks the toryx through a full circuit of the steepness angle φ2, describing four quadrants:
- Real negative (outverted) toryces — trailing string begins as two infinitely long straight lines (the negative inversion toryx) and contracts through a toroidal spiral until it merges with the leading string at b1 → 1, the real inversion toryx.
- Real positive (inverted) toryces — as b1 falls below 1 the number of windings grows; at b1 → 0.5 the opposite windings touch, the "toryx eye" disappears, and the windings become infinite in number: the positive inversion toryx.
- Imaginary positive (inverted) toryces — the windings become imaginary and overlap; at the end of the range the trailing string reduces to a circle, the imaginary inversion toryx, lying in the plane perpendicular to that of the real inversion toryx.
- Imaginary negative (outverted) toryces — the leading string radius turns negative, the string is "turned inside out", and the sequence closes back on the negative inversion string.
Antiparticles, Ginzburg states, are particles whose constituent toryces are "topologically inverted inside out" relative to their partners.
Physical properties
Where electric forces dominate gravity, the inversion radius and frequency are given in terms of the electron rest mass and elementary charge, ri = Ze02/8πε0m0c2 and correspondingly for fi. The physical properties then follow directly from vorticity: the relative charge, relative inertial mass and relative gravitational mass of a toryx are each equal to V/2. Further tables give the relative density, a relative Young's modulus of elasticity, and relative magnetic moments referred to the Bohr magneton μB and the nuclear magneton μn, with distinct expressions for real and imaginary toryces.
The exchange energy Ex is the sum of a toryx's relative kinetic and potential energies; a positive sign means absorption of energy and a negative sign release. Most toryces can perform only half of a "breathing cycle" and are called mutually-sustainable — they "need partners to complete their breathing cycles" — while a few are self-sustainable.
Quantum energy states
Toryces change state in quantum steps by two distinct mechanisms. In oscillation the inversion radius ri itself varies inversely with an oscillation factor Qp whose plot against the oscillation quantum number p is a bell-shaped curve. In excitation ri stays constant while the leading-string radius changes; excitation may be exponential or harmonic, with the quantization parameter z built from ΛM, an exponential quantum number m and a linear quantum number n.
ΛM is the matter level constant, depending on a matter level M, and is assumed to be given by a series whose first four terms are Λ0 = 1, Λ1 = 6, Λ2 = 137 and Λ3 = 6841. Ginzburg states that ordinary matter corresponds to M = 2 — so the constant governing the quantum states of ordinary matter is 137, the familiar reciprocal of the fine structure constant.
Trons: the elementary particles
Each elementary particle, or tron, is made of two polarized matched toryces. Reality-polarized trons pair a real toryx with an imaginary one; charge-polarized trons pair toryces of opposite charge. Any physical property of a tron is the sum of the corresponding properties of its two toryces.
- E-trons are reality-polarized. Negative e-trons "reveal themselves as conventional atomic electrons", positive e-trons as nuclear positrons. Muons and tau leptons are interpreted as oscillated electrons and antielectrons.
- A-trons are charge-polarized. Real a-trons are very light particles Ginzburg names aetherons (from aether); imaginary a-trons are heavy particles named singletrons (from singularity). At high quantum energy states these form the quantum vacuum; at low states they form the cores of nucleons.
- Harmons are built from harmonically excited toryces. Reality-polarized harmons "serve as free electrons and positrons", while charge-polarized harmons reside in the nucleon shells.
Complex particles, including all known hadrons, are made of trons.
Three conservation laws
Formation and existence of stable atoms is governed by three laws, each stated as a sum over all constituent toryces that must approach infinility (that is, tend to zero from a limiting direction rather than equal zero exactly): conservation of charge, Σei → 0; conservation of reality, Σ(mgR2)i → 0; and conservation of energy, ΣExi → 0.
Helyces and radiation particles
The helyx is the radiation counterpart of the toryx: a double-helical leading string of radius r1 with helical trailing strings of radius r2 wound around each branch. Its four fundamental equations closely parallel the toryx's — the inversion radius obeys the same equation, and the spiral velocity of the trailing string is again c — and Tables 9 and 10 give the full set of relative parameters as functions of b1.
Helyces are created when a parental toryx drops from a higher to a lower quantum energy state; by conservation of energy the emitted helyx frequency equals the difference of the toryx exchange energies at the two states, and Ginzburg gives an explicit formula for fjk in terms of the leading-string radii and oscillation factors at states k and j. Radiation particles are then matched pairs of helyces, named after their parental matter particles: excited toryces yield electons, positons, aethertons and singletons; oscillated toryces yield electrinos, positrinos, aethertrinos and singletrinos.
The velocities are graded. Radiation from electrons, positrons and aetherons propagates at the velocity of light — more precisely, real helyces slightly slower than c and imaginary helyces slightly faster. But "the velocities of propagation of singletons and singletrinos are much greater than the velocity of light."
Assessment
What is attractive here is the economy of the ontology and the seriousness with which it is carried through. Two geometric objects, seven fundamental equations, and one free variable b1 are made to generate charge, mass, magnetic moment, particle taxonomy, antimatter, radiation and the vacuum. The recovery of the classical orbital law β1 = (2/b1)1/2 as the large-radius limit of the universal law is a genuine correspondence result, not merely an assertion of compatibility. The paper also sits in a real tradition of toroidal and helical models of the electron — Ginzburg cites Bostick, de Broglie, Gauthier, Lucas, Sarg and the NASA electron-spiral-toroid study — so its central geometric intuition has independent company.
The most serious limitation is that nothing in the paper is compared with a measured number. The framework produces equations for the toryx's charge, inertial and gravitational mass, and Bohr magnetic moment, and it asserts that muons and taus are oscillated electrons; but no mass ratio, no magnetic moment and no lifetime is computed and set against experiment. Since the whole scheme is parameterised by quantum numbers m, n and p that can be chosen freely, the reader has no way to judge whether the particle spectrum it generates is the observed one. The appearance of 137 as the matter level constant Λ2 for ordinary matter is the paper's most striking numerical claim, but Ginzburg introduces the series with the word "assumed", gives no derivation of it, and does not address the fact that the measured reciprocal fine structure constant is 137.035999…, not the integer 137. A near-coincidence with a famous number, presented without an error estimate or a mechanism, is exactly the kind of result that needs the most scrutiny.
The superluminal content conflicts directly with established measurement. Singletons and singletrinos are said to propagate "much greater than the velocity of light", and imaginary helyces to exceed c slightly; no account is offered of why such signals are not observed, why they do not violate causality, or how they escape the constraints from timing of astrophysical sources and from every accelerator and interferometric test of the light-speed limit. The move that permits this — reading V2r2 + V2t2 = c2 as allowing one component to exceed c while the other becomes imaginary — is an algebraic step given physical force without an argument that imaginary velocities correspond to anything measurable.
Finally, the paper's own closing point is also its heaviest prerequisite: 3D-SST "requires a new interpretation of zero, number line and trigonometry". The infinility, the circular universal number line and the universal cosine are used throughout — the three conservation laws are stated in terms of sums approaching infinility rather than equalling zero — but they are stated here, not established; the reader is referred to Ginzburg's books and earlier NPA papers. Asking a reader to accept revised arithmetic before the physics can be evaluated is a large demand, and it makes the theory difficult to check independently. This paper is best read as a summary map of the framework, a catalogue of definitions and tabulated relations, rather than as a derivation or a test of it.