From Local to Global Relativity

Scientific Paper
Title	From Local to Global Relativity
Read in full	Link to paper
Author(s)	Tuomo Suntola
Keywords	newton, relativity
Published	2008
No. of pages	39

Read the full paper here

Abstract

Newtonian physics is local by its nature. No local frame is in a special position in space. There are no overall limits to space or to physical quantities. Newtonian space is Euclidean until infinity, and velocities in space grow linearly as long as there is constant force acting on an object. Finiteness of physical quantities was observed for about 100 years ago — first as finiteness of velocities. The theory of relativity introduces a mathematical structure for the description of the finiteness of velocities by modifying the coordinate quantities, time and distance for making the velocity of light appear as the maximum velocity in space and an invariant for the observer. Like in Newtonian physics, no local frame, or inertial observer, is in a special position in space. Friedman-Lemaître-Robertson-Walker (FLRW) metrics derived from the general theory of relativity predicts finiteness of space if a critical mass density in space is reached or exceeded.

In the Dynamic Universe approach space is described as the three-dimensional surface of a four-dimensional sphere. Finiteness of physical quantities in DU space comes from the finiteness of total energy in space — finiteness of velocities is a consequence of the zero-energy balance, which does not allow velocities higher than the velocity of space in the fourth dimension. The velocity of space in the fourth dimension is determined by the zero-energy balance of motion and gravitation of whole space and it serves as the reference for all velocities in space. Relativity in DU space means relativity of local to the whole — relativity is a measure of locally available share of the primary rest energy, the rest energy of the object in hypothetical homogeneous space. Atomic clocks in fast motion or in high gravitational field do not lose time because of slower flow of time but because part of their energy is bound into interactions in space. There is no space-time linkage in the Dynamic Universe; time is universal and the fourth dimension is metric by its nature. Local state of rest in DU space is the zero-momentum state in a local energy frame which is linked to hypothetical homogeneous space via a chain of nested energy frames.

Predictions for local phenomena in DU space are essentially the same as the corresponding predictions given by special and general theories of relativity. At extremes, at cosmological distances and in the vicinity of local singularities differences in the predictions become meaningful. Reasons for the differences can be traced back to the differences in the basic assumptions and in the structures of the two approaches.

Overview

This paper was presented at PIRT XI (Physical Interpretations of Relativity Theory), Imperial College, London, 12–15 September 2008. It is a compact statement of Tuomo Suntola's Dynamic Universe (DU) model, developed at book length in Theoretical Basis of the Dynamic Universe (2004), and it argues its case by direct side-by-side comparison: five tables set the definitions and predictions of special and general relativity against those of the DU, quantity by quantity.

The central move is to replace one kind of finiteness with another. Relativity secures the finiteness of velocities by making the coordinate quantities — time and distance — functions of velocity and gravitational potential, so that c emerges as an invariant limit by construction. Suntola instead makes the total energy of space the primary finite quantity and derives everything else from its conservation. Time and distance remain universal; there is no spacetime linkage; the fourth dimension is metric, a geometrical radius rather than a time axis. The model is explicitly built on two remarks of Richard Feynman quoted at length in the paper: that the total gravitational energy of the universe appears to cancel its rest energy, GM²/R = Mc², so that "the total energy of the universe is zero"; and that three-dimensional space might be "a tridimensional surface of a four sphere." The DU, Suntola writes, "is just a detailed analysis of combining Feynman's 'great mystery' of zero-energy space to the 'intriguing suggestion of spherically closed space' by the dynamics of a four-sphere."

The argument

Space as a spherically closed zero-energy system

Space is the three-dimensional surface of a 4-sphere of radius R₀. Its dynamics are those of a pendulum in the fourth dimension: in a contraction phase gravitational energy is converted into energy of motion, in an expansion phase the motion is returned to gravitation. The balance condition is written

E_rest + E_grav = Mc₀² − GM″M/R₀ = 0

with M″ = 0.776M the mass equivalence of total mass concentrated at the centre of the 4-sphere. Solving for the contraction/expansion velocity gives c₀ = (0.776 GM/R₀)^½. Taking R₀ ≈ 14 billion light years and a mass density ρ = 5.0 × 10⁻²⁷ kg/m³ — "about half of the critical density in the standard cosmology model" — yields c₀ ≈ 300,000 km/s. The rest energy of matter is thus not intrinsic but is the energy of motion that all mass possesses by virtue of being carried along the 4-radius.

Relativity as locally available energy

Local structure enters through tilting. Building a mass centre converts part of the gravitational interaction in the fourth dimension into interaction in a space direction, and part of the velocity of space into velocity of free fall. This gives a system of nested energy frames, each frame seeing the space around it as "apparent homogeneous space." The local velocity of light is not constant but is the product of the cosine-like tilting factors of every frame in the chain, and the locally available rest energy is

E_rest(n) = c₀mc₀ ∏(1 − δ_i) √(1 − β_i²)

with δ the gravitational factor and β = v/c the velocity factor for each frame. The physical reading Suntola gives is blunt: "the greater is the energy used for motions and gravitational interactions in space the less energy is left for running internal processes." A clock in motion or deep in a potential well is not experiencing slowed time — it is running on a reduced energy budget. Crucially, the model needs neither the relativity principle, the equivalence principle, the Lorentz transformation, nor any postulate about the velocity of light.

An asymmetry follows that has no counterpart in general relativity: kinetic energy builds up differently in inertial acceleration (by mass insert at fixed potential) than in free fall (by tilting of space against a reduction of the local rest energy). The two cases are equalised by the equivalence principle in GR; in the DU they are physically distinct.

Mass as wavelike substance; the Planck constant broken down

In the DU "mass is not a form of energy but the substance for the expression of energy." Radiation, Coulomb energy and localised matter are all given a common mass equivalence, so that a cycle of radiation carries mass m = h₀/λ. Suntola solves for the energy emitted in one cycle by treating a point emitter, moving at c in the fourth dimension, as a one-wavelength dipole in that dimension, obtaining E₀ = 1.1049 · 2π³e²μ₀c'f and hence an intrinsic Planck constant h₀ = h/c with units kg·m rather than kg·m²/s. Two consequences are claimed: the quantum is tied to mass rather than momentum, and the fine structure constant becomes "a purely numerical or geometrical factor without linkage to any physical constant."

A localised mass object is then a closed standing mass-wave structure whose motion in space is carried by a parallel wave front — offered as "a physical explanation to the double-slit experiment," the deflection of a single object being fixed by the phase difference between wave fronts from the two slits.

Why the velocity of light looks invariant

Here the paper is at its most economical. Treat moving frames as momentum frames rather than velocity frames. When a mass object is caught by a moving frame, the momentum change appears as a change of velocity; when radiation is caught, the momentum change appears as a Doppler change of frequency and wave number, at conserved phase velocity. "The constancy of the observed (phase) velocity of light in moving frames is a consequence of the change of momentum via the Doppler shift of frequency ... instead of change in the velocity." Studying the Michelson–Morley interferometer as a momentum frame, Suntola concludes, "guarantees a zero result."

Points of divergence: black holes, Shapiro delay, cosmology

The critical radius in DU space, r_c(DU) = GM/c², is half the Schwarzschild value. In Schwarzschild space orbital velocity exceeds free-fall velocity inside 3r_c, so stable orbits end there; in DU space orbital velocity falls smoothly to zero at r_c(DU), permitting slow stable orbits over 0 < r < 4r_c(DU) which "maintain the mass of the black hole." For Sgr A* at the centre of the Milky Way the DU minimum orbital period is 14.8 minutes against the Schwarzschild minimum of about 28 minutes; the shortest observed period cited from Genzel et al. is 16.8 ± 2 min. Perihelion advance and light bending come out identical in the two frameworks, so gravitational lensing does not discriminate. Shapiro delay differs by a constant term of about 20 μs, which the Mariner 6 and 7 experiments could not detect for lack of an absolute reference.

Cosmologically the two models part company. In FLRW space expansion occurs only between galaxies or galaxy groups; in DU space all gravitationally bound systems expand with space, so galaxy radii are not standard rods and angular sizes take a Euclidean form, θ = d_R(1 + z)/R₀z. Suntola sets this against the Largest Angular Size data of Nilsson et al. for quasars and galaxies over 0.001 < z < 3 and reports that two Euclidean lines enclose the data uniformly across the whole range while both FLRW curves — Einstein–de Sitter, and Ω_m = 0.27 with Ω_Λ = 0.73 — deviate significantly. On the dilution of redshifted radiation, FLRW takes the power density to fall as (1 + z)⁻² because both the reception rate and the energy per quantum drop, which Suntola describes flatly as a violation of energy conservation; the DU conserves the mass equivalence of a cycle, giving (1 + z)⁻¹. The resulting magnitude–redshift prediction is fitted to the Riess "high-confidence" and HST Type Ia supernova data, and Suntola stresses that "unlike the FLRW prediction, the DU prediction has no adjustable parameters" — no dark energy, no free density parameters — the two curves diverging meaningfully only above z > 3.

Assessment

The genuinely attractive feature of this work is its discipline. Suntola does not merely object to relativity; he builds an alternative that reproduces the classical tests — perihelion advance, light bending, gravitational shift, the null result of the interferometer, the clock rates used by GPS — and then states precisely where and by how much it differs. The claim that DU and GR clock predictions on Earth and in Earth satellites differ by Δf/f ~ 10⁻¹⁸, "too small a difference to be detected with present clocks," is exactly the kind of honest quantification most dissident papers omit. The parameter-free supernova magnitude fit is a real strength: the standard fit requires Ω_m and Ω_Λ to be tuned, whereas the DU prediction is fixed once R₀ is set by the Hubble constant. The reinterpretation of clock rate as an energy budget rather than a flow of time is philosophically clean and, unlike many aether-style proposals, does not smuggle a preferred velocity frame back in through a detectable local anisotropy.

The difficulties are real too. The mass density ρ = 5.0 × 10⁻²⁷ kg/m³ is chosen so that c₀ comes out at 300,000 km/s; the paper presents this as consistency, but it is a calibration, and no independent determination of ρ is offered to make it a prediction. Likewise the factor M″ = 0.776M and the antenna constant A₀ = 1.1049 are stated without derivation in the text, so the breakdown of the Planck constant into "primary electrical constants" cannot be checked here — and since the fine structure constant is then computed from h₀, which itself contains A₀, the claim that α is "purely numerical" rests on a number that is itself geometric input. The redefinition of h₀ with units kg·m is a substantive change, not a bookkeeping one, and the paper does not show that the whole of quantum mechanics — where h appears as an action — survives it.

The sharpest test is the one the paper mentions only obliquely. The DU dilutes redshifted power as (1 + z)⁻¹ rather than (1 + z)⁻² because the quantum is held to conserve its mass equivalence. But the missing factor in FLRW is the reduced rate of arrival, and that rate is directly observed: the light curves of Type Ia supernovae are stretched by exactly (1 + z), a time dilation confirmed independently in supernova spectral evolution. Suntola's expansion does contain a cycle-time factor T_0(z), so the model is not obviously in conflict — but the paper does not confront the light-curve stretching directly, and given how much of the cosmological case rests on the dilution exponent, its absence is conspicuous. Similarly, the Largest Angular Size comparison is presented as bracketing lines around a scattered dataset spanning three decades in redshift; that is suggestive, but a dataset of quasar and galaxy sizes with intrinsic scatter of that magnitude is weak evidence against FLRW, and the paper offers no statistical measure of the comparison. Finally, the DU offers no account here of primordial nucleosynthesis or of the cosmic microwave background — an eternal contraction–expansion cycle "from infinity in the past to infinity in the future" must explain the light-element abundances and the blackbody background some other way, and the paper is silent on both.

On its own terms the paper is careful, quantitative and unusually candid about where its predictions coincide with the orthodox ones. It is best read as a serious research programme in the tradition of absolute-time, aether-adjacent cosmology rather than as a refutation, and it does not claim more than that.

See also

• Tuomo Suntola
• Ari Lehto
• Big Bang
• Dark Energy
• Redshift
• General Relativity
• Michelson-Morley experiment