Global Relativity Establishes Absolute Time and a Universal Frame of Reference

Scientific Paper
Title	Global Relativity Establishes Absolute Time and a Universal Frame of Reference
Read in full	Link to paper
Author(s)	Tuomo Suntola
Keywords	Relativity, unification, cosmology
Published	2009
No. of pages	21

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Abstract

It has been known for several decades that the rest energy of all matter in space is essentially equal to the total gravitational energy in space. The Dynamic Universe model introduced in this paper studies the equality as a dynamic zero-energy balance of motion and gravitation in spherically closed space. In such a solution time is absolute, the fourth dimension has metric nature, and relativity appears as the measure of the locally available share of total energy in space. The study of the zero-energy balance in spherically closed space can be based on few postulates and the derivation of predictions for local physical phenomena and for cosmological observations can be carried out with fairly simple mathematics essentially free of additional parameters.

In all interactions in space the total energy is conserved. A clock in motion in space does not lose time because of slower flow of time but because motion in space diverts a share of the total energy of the device thus leaving less energy for the oscillation running the clock. In the DU framework a local state of rest can be related to the state of rest in hypothetical homogeneous space, which serves as a universal frame of reference for all local phenomena in space. The Dynamic Universe model discards the space-time marriage, the relativity principle, the Lorentz transformation, the equivalence principle, and dark energy. The DU model also discards the postulation of the constancy of the velocity of light but explains why the velocity of light is observed as being unaffected for observers in motion and for observers at different gravitational potentials.

In celestial mechanics, the Dynamic Universe leads to stable orbits down to the critical radius of local singularities (black holes), shows the perihelion shift of eccentric orbits, the Shapiro delay, the bending of light, etc. In the Dynamic Universe, gravitationally bound systems like planetary systems, galaxies and galaxy groups expand in direct proportion to the expansion of space. As a consequence, the Euclidean appearance of the angular sizes of galaxies is predicted. The DU's prediction for the magnitude versus redshift of standard candles is in an excellent agreement with recent supernova observations without assumptions of dark energy or free parameters.

The Dynamic Universe means a major change in the paradigm but offers a platform - with relativity built in and a firm anchor to human conception - to doctrines like Maxwell's equations and electromagnetism in general, thermodynamics, celestial mechanics, and quantum mechanics.

Overview

Tuomo Suntola's paper presents the Dynamic Universe (DU) model, in which space is the three-dimensional surface of a four-dimensional sphere contracting and expanding in an infinite four-dimensional universe. Its starting point is an old numerical coincidence — that the total rest energy of matter in space is essentially equal to the total gravitational energy — which Suntola treats not as a mystery but as a dynamic zero-energy balance to be solved. The consequence is that the rest energy of matter is the energy of motion of space itself along the fourth dimension, and the velocity of light is nothing other than the velocity of that expansion.

The framework is deliberately anti-relativistic in its foundations while claiming to reproduce relativity's results. Suntola discards the space–time union, the relativity principle, the Lorentz Transformation, the Equivalence Principle, the postulate that c is constant, and Dark Energy. In their place stand absolute time, a metric fourth dimension, and a universal frame of reference — the state of rest in "hypothetical homogeneous space," space as it would be without the accumulation of mass into centres. Relativity survives, but as a bookkeeping statement: it is "the measure of the locally available share of total energy in space." A moving clock does not run slow because time flows slowly; it runs slow because motion "diverts a share of the total energy of the device thus leaving less energy for the oscillation running the clock."

The argument

Zero-energy balance and the velocity of light

Suntola quotes Richard Feynman's lectures on gravitation twice: once on space as "a tridimensional surface of a four sphere," and once on the equality GM²/R = Mc², which Feynman called "one of the great mysteries." Suntola's answer is that Feynman "did not take into consideration the possibility of a dynamic solution." Starting from rest in homogeneous space of essentially infinite radius, both energies vanish; the release of gravitational energy drives a contraction, motion is gained, and after passing a singularity the motion is paid back into gravitation in an expansion phase — "like that of a spherical pendulum in the fourth dimension."

The inherent gravitational energy is Newtonian, E_g = −GM″m/R₄, where M″ = 0.776M is the mass equivalence at the centre of the 4-sphere; the inherent energy of motion is E_m = c₄p = mc₄², a form Suntola notes is Leibniz's vis viva. Setting their sum to zero gives c₄ = √(GM″/R₄) ≈ 300,000 km/s, using ρ = 5×10⁻²⁷ kg/m³ (about 0.55 times the Friedmann critical density) and R₄ ≈ 14 billion light years, corresponding to H₀ ≈ 70 (km/s)/Mpc. The Hubble Constant is thus not a free parameter but the expansion rate of the 4-radius. Because the balance is dynamic, c decreases as space expands, at dc/c ≈ −3.6×10⁻¹¹/year — but atomic clock frequencies degrade at the same rate through the loss of rest momentum, "thus disabling the detection."

Unified expressions of energy

Treating an emitting atom as a one-wavelength dipole in the fourth dimension, Suntola applies the standard dipole solution of Maxwell's Equations and obtains E = h₀c₀c/λ, where h₀ ≡ h/c is an "intrinsic Planck Constant" with dimensions [kg/m]. The claim drawn from this is that "the velocity of light appears as a hidden factor in the Planck constant." Coulomb energy is written in the same form with a mass equivalence Δm_C, and the Fine Structure Constant then "appears as a purely numerical factor without linkage to any physical constant." Rest energy, radiation energy and Coulomb energy thus all take the form E = c₀c·(mass equivalence), and the wavelength equivalence of a mass turns out to be its Compton wavelength. Planck mass and Planck distance are recovered from h₀ and the balance equations, with the Planck distance being the wavelength equivalence of the Planck mass — a relation Suntola credits Ari Lehto with using as a basis for building elementary particles as sub-harmonics.

Six postulates are stated: spherically closed 3-space free to contract and expand; time as a universal scalar with a metric fourth dimension; homogeneous initial mass distribution with conserved total mass; dynamics set by the zero-energy balance; inherent energies defined in the hypothetical homogeneous and rest environments; and conservation of the zero-energy balance through all subsequent buildup of motion, radiation, particles and mass centres. Force is not postulated but derived as the gradient of energy.

Nested energy frames, and relativity recovered

Building a mass centre tilts space locally; the local fourth dimension turns, and the tilt both creates the momentum of free fall as an orthogonal component and reduces the local velocity of light, c = c₀(1 − δ). The Shapiro delay and the bending of light are attributed to this reduction plus the extra path length through the dent. Real space contains many such centres nested inside one another, so a chain of gravitational frames runs from a laboratory on Earth through the Earth, solar, Milky Way and Local Group frames to hypothetical homogeneous space — which Suntola suggests "may be presented by the Cosmic Microwave Background as the universal reference at rest."

Kinetic energy behaves differently in the two cases, which is why the Equivalence Principle is rejected. In free fall, velocity is bought against a reduction in the local velocity of light and kinetic energy against a reduction of rest energy. At constant gravitational potential, energy must be supplied externally; the momentum then adds orthogonally to the rest momentum in the fourth dimension, and the mass increase works out as m/√(1 − β²) — formally the relativistic mass, but reinterpreted: "relativistic mass is not a consequence of the velocity in space but it is the mass contribution needed to build up velocity at constant gravitational potential." The corresponding reduction in rest momentum, and hence in the object's own global gravitational energy, is offered as "a quantitative expression of Mach's Principle."

Chaining the factors over n nested frames gives the locally available rest energy as E_rest = c₀c₀m∏(1 − δ_i)√(1 − β_i²). Inserted into Balmer's equation this makes atomic frequencies functions of motion and gravitational state; Suntola sets his expansion beside the general-relativistic one for a Schwarzschild frame and reports that on Earth and in near space "the difference in the frequencies ... appears in the 18th decimal at most, which is too small a difference to be detected." The Doppler formula derived classically in a shared propagation frame is "essentially the same as the equation for Doppler effect in the general theory of relativity," and because the momentum of radiation is conserved when source and receiver share a frame, "conservation of the momentum of radiation in the interferometer frame guaranties zero-result in Michelson–Morley experiment."

Celestial mechanics and cosmology

The DU critical radius is r_c = GM/c₀c₀, exactly half the Schwarzschild radius. Where Schwarzschild geometry forbids stable circular orbits inside 3r_c, DU orbital velocity falls smoothly to zero at r_c, giving stable slow orbits throughout 0 < r < 4r_c(DU) — which, Suntola argues, is what "maintains the mass of the black hole." He offers a test: for Sgr A* the shortest observed period is 16.8 ± 2 minutes, against a Schwarzschild minimum of about 28 minutes (requiring a rotating Kerr hole to fix) and a DU minimum of 14.8 minutes at r = 2r_c(DU). Perihelion advance comes out with the same expression in both frameworks, 6πGM/c²a(1 − e²), but in DU in closed form.

Two cosmological predictions follow with no free parameters. Because gravitationally bound systems — planetary systems, galaxies, galaxy groups — expand in direct proportion to space while atomic objects keep their dimensions, angular size goes as θ ∝ d_R/R₄√z rather than turning over: the appearance is Euclidean at all redshifts. Suntola compares this with Nilsson's largest-angular-size dataset for galaxies and quasars over 0.001 < z < 3, against FLRW curves for both Ω_Λ = 0 and Ω_Λ = 0.73. Second, the distance modulus becomes m − M = 5log(R₄/10 pc) + 5log(z) − 2.5log(1 + z), which he plots against the Riess "high-confidence" and HST supernova samples: indistinguishable from FLRW over 0 < z < 2, diverging above z > 3, and requiring no Dark Energy and no fitted density parameters.

Assessment

The DU is among the more disciplined alternatives in this literature, and several features deserve credit. It is genuinely parameter-free where the standard model fits Ω_m and Ω_Λ: the same R₄ that sets c sets the distance modulus and the angular-size relation. The reinterpretation of the Feynman coincidence as a dynamical balance rather than a numerical accident is elegant, and the derivation of c₄ from G, M″ and R₄ landing on 300,000 km/s is a real result of the scheme rather than an input. The system of nested energy frames gives a concrete, non-mystical reading of why a moving clock ticks slowly, and the recovery of the relativistic mass factor and the perihelion formula from energy conservation alone, without the Lorentz Transformation, is a substantial technical achievement. Suntola is also unusually careful to state where his predictions coincide with relativity — the 18th decimal remark, the Doppler formula, the perihelion advance — rather than manufacturing disagreements. The Euclidean angular-size prediction and the Sgr A* orbital period are both stated as falsifiable discriminants, which is exactly how a rival model should present itself.

The difficulties are correspondingly specific. The most serious is that several key steps are asserted rather than derived. The claim that "the velocity of light is equal to the velocity of space in the fourth dimension" is supported only by the remark that an object moving at c is on a "satellite orbit" around M″; the numerical coefficient 0.776 relating M″ to M is used throughout without the integral being shown. The dipole derivation of h introduces a fitting factor A = 2.3049, chosen precisely so that the result matches the CODATA value of Planck's constant — so the "breakdown of the Planck constant" is a re-parameterisation, not a prediction, and the accompanying claim that the fine structure constant thereby becomes "purely numerical" inherits that circularity. The postulate that c decreases at 3.6×10⁻¹¹/year is, by Suntola's own argument, undetectable in principle because clock rates track it; a quantity constructed to be unobservable does no explanatory work, and its introduction weakens rather than strengthens the model.

Three points of contact with measurement should be named. First, the abandonment of the equivalence principle is the model's boldest move and its most exposed: torsion-balance and lunar-laser-ranging tests confirm the universality of free fall to a few parts in 10¹³–10¹⁵, and the paper does not compute what its asymmetry between gravitational and non-gravitational acceleration predicts at that precision. Second, the claim that gravitationally bound systems — planetary systems and galaxies — expand in proportion to space is the mechanism behind the Euclidean angular-size prediction, but it conflicts directly with lunar-laser-ranging and planetary-radar constraints on the secular expansion of the Earth–Moon and Earth–Mars distances, which are consistent with zero at the millimetre-per-year level; the paper cites no such test. Third, the supernova comparison is presented as an "excellent agreement," yet Suntola states himself that the DU and FLRW curves are effectively indistinguishable below z = 2 — which is where nearly all the data lie — so the fit does not discriminate, and the model's real cosmological test remains the angular-size relation, where a fair assessment must contend with the substantial and well-documented selection effects in the Nilsson largest-angular-size sample. Finally, the Sgr A* argument rests on a single quoted 16.8 ± 2 minute periodicity in a compact source whose interpretation as a circular orbit at the innermost stable radius is not established; the paper treats a contested observation as a clean discriminant. None of this is fatal to the programme, but it marks the places where the DU's parameter-free elegance has been bought by leaving quantities unspecified rather than by predicting them.