On a New Mathematical Framework for Fundamental Theoretical Physics
| Scientific Paper | |
|---|---|
| Title | On a New Mathematical Framework for Fundamental Theoretical Physics |
| Read in full | Link to paper |
| Author(s) | Robert E Var |
| Keywords | speed of light, elementary particles, light propagation |
| Published | 1975 |
| Journal | Foundations of Physics |
| Volume | 5 |
| Number | 3 |
| No. of pages | 26 |
| Pages | 407-431 |
Read the full paper here
Abstract
It is shown by means of general principles and specific examples that, contrary to a long-standing misconception, the modern mathematical physics of compressible fluid dynamics provides a generally consistent and efficient language for describing many seemingly fundamental physical phenomena. It is shown to be appropriate for describing electric and gravitational force fields, the quantized structure of charged elementary particles, the speed of light propagation, relativistic phenomena, the inertia of matter, the expansion of the universe, and the physical nature of time. New avenues and opportunities for fundamental theoretical research are thereby illuminated.
Overview
Robert E. Var wrote this paper at the Charles Stark Draper Laboratory and published it in Foundations of Physics in 1975. Its thesis is that the branch of mathematics best suited to fundamental physics is not tensor geometry but compressible fluid dynamics, and that a single substance — which he calls space-energy — can serve as the medium whose flow, compression and shock behaviour account for electric and gravitational fields, the structure and quantization of charge, inertia, the speed of light, the expansion of the universe, and time itself. The paper takes E = mc2 as its only basic assumption and treats every other relativistic relation as a consequence.
What makes the paper unusual is that it is not an attack on relativity. Var repeatedly invokes Einstein in support: Einstein's insistence that "space is endowed with physical properties, without which there not only would be no propagation of light, but also no possibility of existence for standards of space and time", and Dirac's remark that a theory able to explain charge would need "a new mathematics that happens to work". The break with the mainstream account is interpretive rather than predictive. Var restores an absolute frame — the space-energy continuum — and with it absolute simultaneity, a universal rate of time, and a real, physically caused length contraction and clock slowing. Time dilation, on his reading, is a superfluous equation of physics: a derived consequence of mass increase and structural contraction, not an independent fact about time. This makes the paper an Aether-theoretic reconstruction of relativity in fluid-dynamic clothing, of a family with Lorentz ether theory but pushed much further, into charge structure and cosmology.
The argument
The absolute principle of relativity
Section 2 begins from the classical power equation dE/dt = F·v and Newton's F = dP/dt, and, inserting E = mc2, obtains E/E0 = m/m0 = γ. From this together with c = 1/(ε0μ0)1/2 Var derives what he names the absolute principle of relativity (APR): "The laws of nature are invariant with respect to an observer's constant velocity through a single physical space-energy continuum of the universe." Every inertial observer is therefore empirically entitled to believe he is at rest in the continuum, even though he is not.
The key working equation is the phase-velocity relation c′ = w·n = c(1 − β·n): the speed of light relative to a moving point is anisotropic. Requiring the period of a light-clock to be independent of its orientation then forces L∥ = L∥0/γ with L⊥ unchanged, and requiring velocity-invariance of c forces all clock periods to satisfy T = γT0. A "disk-clock" argument then shows that the spin-rate reduction ω = ω0/γ and the moment-of-inertia increase m/m0 = γ are the same fact seen twice, so that at least one of the five relations must be dependent on the rest. Var elects time dilation as the redundant one, and states a clock principle (CP) corollary: a clock's period lengthens by γ "due to velocity-dependent changes that have occurred in the pertinent physical phenomena", not because time itself dilates. Among his six methodological principles is the flat statement "(i) Time advances at the same 'rate' throughout the entire universe."
Gravitation as accelerating space-energy
Section 3 reads Einstein's equivalence principle as an equivalence between accelerating a body relative to the continuum and holding it stationary against a flow of the continuum. Gravity is then the fluid acceleration ag = ∂q/∂t + ∇(½q2) − q×ξ, with ξ = ∇×q the vorticity. A static Newtonian field is the steady, irrotational case, and the identity ∇(−φ) = ∇(½q2) fixes the potential as φ(r) = −½q2(r): the gravitational potential is the inflow speed of space-energy, squared. Defining u = q/c and the field factor Y(r) = 1/(1 + 2φ/c2)1/2, Var obtains c′ = c(1 + u·n), m = Ym0, L∥ = L∥0/Y, T = YT0, and hence the gravitational blue- and red-shifts. He then constructs a velocity-metric wik(u), argues it plays the role of gik, and shows that for a radial field it reproduces exactly the Schwarzschild interval — and with it the perihelion precession and light bending. A black hole becomes the condition q → c, "a macroscopic shock singularity in space-energy."
Charge quantization from a shock limit
Section 4 is the paper's most striking construction. Var replaces the electric displacement D = εE with a momentum-density flux Ds = ρsq, assumes an equation of state ps = kρs3 and Euler's equations for irrotational flow, and finds that Ds has an intrinsic maximum Ds\* = ρs0c/2, attained where q = 0.707c equals the local speed of sound. Charge is thus quantized by choking, exactly as the mass flow through a converging–diverging nozzle is quantized once the throat goes sonic. Continuity through a surface enclosing the source gives a "course structure" constant 2π = es/(ρs0cr\*2), which combines with the far-field energy density to yield the fine-structure relation es = 2αh/r\*2 and h = 137.04πρs0cr\*4. Numerically he obtains an electron radius r\* = 1.56 × 10−15 m, a zero-point energy density φ0 = 4.14 × 1030 J/m3, and a free-space mass density ρs0 = 1.38 × 1014 kg/m3 — the last comparable, as he notes, to the density of nuclear matter. A conversion constant X = e/2πr\*2 = 1.05 × 105 C/m2 turns 1/ε0 into an energy density and μ0 into a mass density, so that all electromagnetic units reduce to mass, length and time; a field of 1 V/m corresponds to a flow of 2.5 × 10−13 m/s.
The hypershock cosmology and the nature of time
Section 5 embeds this in a four-dimensional cosmology. The universe is a spherically symmetric hypershock — a thin shell of thickness δ expanding in a four-dimensional continuum, with three-surface S3(R) = 2π2R3 and enclosed four-volume V4 = π2R4/2. Time is not a fifth spatial dimension but the growth of R: dR = kc dτ. Protons and electrons are literal sources and sinks of space-energy entrained on the leading and trailing three-surfaces of the shell, formed where the pressure and density gradients cross to generate vorticity (∂ξ/∂t = ∇ps × ∇(1/ρs)) and the vortex throat chokes at q = c′ = 0.707c. The convergent flow from S3(R) to S3(R − δ) requires a mean acceleration at = (−3k2c2/R)ξ, which Var names the time-field and identifies as the origin of gravitation as distinct from electromagnetism. He closes by anticipating a later paper in which "blurred point sources representing nth-order image poles of the radiation from galaxies" would produce the intensities, redshifts and spectra characteristic of quasistellar objects.
Assessment
The paper's attractions are real. Its economy is genuine: from E = mc2 plus momentum conservation it reconstructs the standard special-relativistic relations without postulating light-speed isotropy, and the velocity-metric wik(u) really does reduce to the Schwarzschild interval for a radial field, so the classical tests are not sacrificed. The charge-quantization argument is the most original thing in it. Quantization by a sonic choke is a mechanism rather than a postulate, and unlike most aether models it makes contact with numbers: it yields an electron radius of the right order (1.56 × 10−15 m, against the classical 2.818 × 10−15 m) and an expression for Planck's constant in terms of the medium's properties. Var is also unusually candid about status: he presents the fluid picture as a language worth exploring rather than a finished theory, and states plainly that the main obstacle is extending fluid mathematics to four or more dimensions.
The difficulties are correspondingly large. Several central steps are asserted, not derived. The equation of state ps = kρs3 is introduced without justification and does most of the work in Section 4; the identification of the maximum of Ds with a real electron radius is assumed and then, in effect, confirmed by the assumption; and the transition in Section 5 from "there is a finite statistical probability Q(R)" of vorticity generation to a universe of protons and electrons is admitted by Var himself to rest on "entirely intuitive considerations." The hypershock cosmology is qualitative throughout: no expansion history is computed, no value of R or δ is derived from observation, and the promised quasar paper is not delivered here. Because the fluid framework is built to reproduce the Schwarzschild results rather than to modify them, the theory as presented makes almost no independent predictions — the one clear exception, the anisotropy c′ = c(1 − β·n), is precisely what Var argues is unobservable, since the contraction and clock-slowing conspire to hide it.
Where it does touch measurement, the strain shows. The claimed free-space mass density of 1.38 × 1014 kg/m3 is a physical, gravitating medium filling all space; general relativity requires that a uniform energy density curve spacetime, and the observed cosmological constant corresponds to an energy density close to 40 orders of magnitude below Var's φ0. Var does not confront this — the paper predates the sharpest statements of the vacuum-energy problem, and unlike Hatch's later elastic-ether work it offers no gradient argument to neutralise a uniform density. The prediction that quasar redshifts arise from higher-order optical images of ordinary galaxies is not supported by later data: quasar host galaxies have been resolved directly, and their emission- and absorption-line systems do not behave as images of foreground sources. Finally, the reprint on file carries a garbled header, "Reprinted from FOUNDATIONS OF PHYSICS Vol. 5, No. 3, September 1915" — the correct year is 1975, as the copyright line and the December 1974 receipt date confirm.