New Cosmology Model Shows Relativity in Universal Time and Distant Observations in Euclidean Geometry

Scientific Paper
Title	New Cosmology Model Shows Relativity in Universal Time and Distant Observations in Euclidean Geometry
Read in full	Link to paper
Author(s)	Tuomo Suntola
Keywords	Cosmology, relativity, zero-energy principle, Dynamic Universe
Published	2001
Journal	Apeiron
Volume	8
Number	3
No. of pages	35
Pages	97-131

Read the full paper here

Abstract

It is natural to think of space as finite but without edges. The simplest geometry that eliminates the edges of a structure is a sphere, and to close a three-dimensional space we need a 4-sphere, the surface of a four-dimensional ball. Describing space as the surface of a four-dimensional sphere contracting and expanding in the direction of the 4-radius gives a view of closed dynamic space where relativistic phenomena appear as consequences of the zero-energy balance in the structure. Instead of being defined as a physical constant the velocity of light appears as the velocity of space in the fourth dimension. The rest energy of mass appears as the energy of motion that mass possesses due to the motion of space and the time-like line element, cdt , in Minkowski space and Schwarzschild metrics shows the distance the 4-radius of space increases in time differential dt.

The spherical geometry together with the changing velocity of light in dynamic, spherical space converts distant observations into Euclidean geometry. Clocks in motion or subject to local gravitational interaction do not lose time because time is distorted; they actually run slower as a result of their state of motion and gravitation in space. The Dynamic Universe model(1) based on the balance of the energies of motion and gravitation in spherically closed space gives precise mathematical expression to relativistic effects and cosmological observations and shows the energy build-up and release of space as a continuous dynamic process from infinity in the past to infinity in the future.

Overview

Published in Apeiron 8(3), July 2001, this is Tuomo Suntola's compact presentation of the Dynamic Universe (DU) model, developed at greater length in his book of the same year. The paper's proposal is that three-dimensional space is the surface of a four-dimensional sphere which contracts and then expands along its 4-radius, and that the fourth dimension is purely geometrical — a real spatial direction, not the "time-like" dimension of relativity. Time, in consequence, becomes a universal scalar shared by the whole of space.

The consequences Suntola draws are systematic rather than piecemeal. The velocity of light is not a defined constant but the velocity at which space moves along the 4-radius, fixed by a zero-energy balance between the energy of motion and the energy of gravitation of all mass in space. The rest energy of a body is then not a property of its mass but the energy it possesses by virtue of being carried along by that motion. Clocks in motion or deep in a gravitational well genuinely run slow — because the energy available for their internal oscillation has been spent elsewhere — rather than measuring a distorted local time. The Michelson–Morley null result follows from the Doppler behaviour of radiation without any length contraction. And at cosmological scale the geometry produces a modified Hubble law and an angular-size relation in which distant objects appear in flat Euclidean geometry, with no accelerating expansion and no need for a repulsive term.

The argument

Spherical space and the origin of c

Suntola begins with the historical point that in 1917 Albert Einstein came close to a space closed through the fourth dimension, computing the volume as that of a 4-sphere surface, V = 2π²R³. He was looking for a static model, which required a cosmological constant, and relativity subsequently made the fourth dimension time-like. Had the choice been made after Hubble, Suntola argues, it would have gone differently: a 4-sphere expanding along its radius explains the Hubble law immediately. Writing a distance in space as an arc D = R₄α, the recession velocity is v = v₄D/R₄, which identifies the Hubble constant as H₀ = v₄/R₄ and the Hubble radius with the 4-radius, so that v₄ = c.

The velocity of light is then derived rather than postulated. The energy of motion of all mass carried along the 4-radius, E_m = mc₀², is balanced against the gravitational energy integrated across spherical space, E_g = −G_EGmM_Σ/R₄, with a geometrical factor G_E = 0.776. The zero-energy condition E_m + E_g = 0 gives c₀ = (GM"/R")^1/2. Substituting R₄ = 14×10⁹ light years (for H₀ = 70) and a mass density ρ = 0.55ρ_c yields c₀ = 300 000 km/s — the velocity of light recovered from the mass content of the universe. Because the radial motion works against gravitation, c declines slowly, at about Δc₀/c₀ ≈ 4×10⁻¹¹ per year. Suntola immediately notes why this is not observed: the frequencies of atomic clocks and the wave numbers of spectral lines are themselves proportional to the internal momentum arising from motion at c₀, so the change cancels in any measurement referred to atomic standards.

Local metrics, tilted space and complex energy

Near a mass centre, local space is "tilted" out of the direction of homogeneous space by an angle φ, giving a local light velocity c = c₀cosφ = c₀(1 − δ) with the gravitational factor δ = GM/rc². The resulting line element resembles the Schwarzschild metric but with the modification factor (1 − GM/rc²)² in place of (1 − 2GM/rc²). Tilting lengthens radial line elements while leaving transverse ones untouched.

The energetic bookkeeping is done with complex quantities: the imaginary axis is the fourth dimension, the real axes are the three space directions. The total energy of motion becomes E*_tot = c₀(p' + ip") and the rest energy E*_rest = c₀m(β + i(1−β²)^1/2)c. Their scalar values reproduce the familiar relativistic expressions E_tot = mc²/(1−β²)^1/2, and Suntola states plainly that "equations (20), (21), and (23) are essentially the same as their counterparts in the theory of relativity." The interpretive difference lies in the imaginary component: the imaginary part of kinetic energy is the work done in reducing the gravitational effect of all mass in space on the accelerated object, which Suntola offers as a quantitative expression of Mach's principle. Inertia thus becomes an attribute of the gravitational state rather than a property of mass.

Gravitational frames are cascaded: an object sits in a local frame, which is itself an object in a parent frame, and so on, so that c = c₀Π(1−δ_i) and m = m₀Π(1−β_i²)^1/2. The rest energy is then E_rest = mc₀c, differing from E = mc² by a frame conversion factor which on Earth is about 1 + 10⁻⁶¹ — absorbed in practice into the measured mass.

Radiation and the Planck constant

Energy conservation requires that the Planck constant be proportional to the velocity of space: h = h₀c, where the intrinsic Planck constant h₀ has dimensions of mass×length rather than momentum×length. The quantum of action becomes a quantum of mass — of "substance for the expression of energy." Radiation momentum is p_rad = (h₀/λ)c, so conservation of momentum is equivalent to conservation of frequency: radiation crossing between gravitational states keeps its frequency and changes its wavelength, whereas an atomic oscillator's frequency tracks the local c. Gravitational shift is therefore a frequency shift for oscillators and a wavelength shift for radiation in flight.

Analysing Schrödinger's equation, Suntola concludes that atomic dimensions are independent of c and so of the expansion, but that the Bohr radius depends on the object's velocity through the reduction of electron rest mass, a₀ = a₀₍₀₎Π(1−β_i²)^1/2. Through Balmer's formula this shifts emitted wavelengths with velocity — which is, on his reading, what special relativity calls time dilation or the transverse Doppler effect. He gives a general oscillator-frequency formula covering both gravitational and velocity factors across all parent frames, and a Doppler expression closely related to the general-relativistic one, from which the Michelson–Morley null result follows without length contraction.

Cosmological predictions

At cosmic distances light follows a spiral path in four dimensions, since space expands while the signal travels. The Hubble law becomes z = e^α − 1 = e^D/R₄ − 1, departing from the linear form only at large distance. The angular separation of two objects works out to θ = d/D = dα/z — that is, distant separations appear in Euclidean geometry, with no dependence on a deceleration parameter.

For surface brightness Suntola derives F_obs = F₀/(z(1+z)ⁿ) with 0 < n < 2, n depending on how the emitting area develops with the object's radius, and reports that the best fit to the supernova magnitude–redshift data available at the time (citing Perlmutter et al., 1998) is n ≈ 1.5. This is the point at which the model claims to dispense with accelerating expansion: the observations are said to be "in a complete agreement with the DU prediction without new assumptions."

The microwave background is reinterpreted as light that has travelled a full 360° around spherical space and returned to the observer's own location. That path gives a redshift z = e^2π − 1 ≈ 534.5, placing the emission about 750 000 years after singularity, when R₄ was around 23–26 million light years and c was some 23 times its present value.

Energy build-up and release

The largest-scale claim replaces the Big Bang with a symmetric zero-energy history. Space contracts by free fall from infinite 4-radius, converting gravitational energy into energy of motion, culminating in a singularity where infinite momentum throws the process into expansion; the expansion then returns that energy to gravitation as the 4-radius runs back out to infinity. Total energy M_Σc₀² − GM_ΣM"/R" = 0 at all times. The universe therefore "began in emptiness at infinity in the past and returns to emptiness at infinity in the future," and no antimatter is required to balance the rest energy of matter. A secondary build-up produces mass centres by local free fall; conversion of unstructured matter into radiation is taken to begin where the free-fall velocity reaches the local c, at r = 3.414r_c — a figure Suntola checks against neutron stars of about 1.5 solar masses and 8 km radius. In this scheme dark matter is simply matter in its basic energised form, before secondary build-up converts part of it into radiation, particles and structured material.

The paper closes with a four-page point-by-point comparison table setting the DU against the theory of relativity and the standard cosmological model, covering basic assumptions, physics, metrics and celestial mechanics, and cosmology.

Assessment

This is one of the more disciplined alternative cosmologies in the literature, and the reason is methodological: Suntola works from a single stated principle — zero total energy in a spherically closed dynamic space — and lets the rest follow, rather than tuning mechanisms to match observations one at a time. Two results genuinely earn attention. The first is the derivation of c from the mass content of space: c₀ = (GM"/R")^1/2 returning 300 000 km/s for a mass density of 0.55ρ_c is a real quantitative achievement, since in relativity c is simply given. The second is the model's self-consistency about its own unobservability: having concluded that c declines at 4×10⁻¹¹ per year, Suntola does not evade the obvious objection but shows why atomic-clock and spectroscopic measurements cannot detect it, because the standards themselves scale with c₀. The intellectual honesty of the comparison table, which states the standard position fairly before giving the DU alternative, is also rare and makes the paper unusually easy to evaluate.

Several difficulties are nonetheless real. The most important is that the model's cosmological successes are precisely where it is hardest to distinguish assertion from derivation. The surface-brightness relation F_obs = F₀/(z(1+z)ⁿ) is offered as fitting supernova data "without new assumptions," but n is a free parameter running over the whole range 0 to 2, and the fitted value 1.5 is chosen after the fact. A model with a free exponent fitting a magnitude–redshift curve is not in the same evidential position as a model with none; the DU here trades one adjustable quantity (the cosmological constant) for another (n), and the paper does not acknowledge the trade. Relatedly, the paper's own claim to explain the supernova observations must be squared with the (1+z) time dilation of Type Ia light curves — supernovae at higher redshift are observed to evolve more slowly in exact proportion to 1+z. The DU may well accommodate this, since it does allow the expansion of space to stretch propagation paths, but the paper does not address the measurement, and a cosmology built on a redefinition of time owes an explicit account of it.

The microwave background reinterpretation is the boldest claim and the most exposed. A 360° return path gives a clean prediction, z = e^2π − 1, but light returning to the observer's own location by a great-circle path is light from a single direction-set determined by the geometry, and it is not obvious from the paper how that produces the observed near-perfect isotropy, nor how it produces a Planckian spectrum at 2.7 K, nor how it accounts for the acoustic peak structure of the anisotropies. None of these is discussed. Similarly, gravitational interaction is stipulated to be instantaneous rather than propagating at c — a substantial claim which the paper asserts in a table entry without argument, and which sits uneasily beside the subsequent (post-2015) direct detection of gravitational waves propagating at the speed of light.

Finally there is a question about what the model actually replaces. Suntola states that his scalar energy expressions "are essentially the same as their counterparts in the theory of relativity," and his light-deflection formula φ_d = 4GM/rc² is identical to the general-relativistic one. Where his metric differs from Schwarzschild — the factor (1−GM/rc²)² rather than (1−2GM/rc²) — the difference is second order and he notes the perihelion advance comes out the same, with an additional predicted ellipticity perturbation peaking at aphelion. That last item is the paper's one clean discriminating prediction in the solar system, and it deserved more than the two lines it receives. As it stands, a reader is left with a reinterpretation that reproduces relativity's confirmed numbers, adds a genuinely new derivation of c, and makes its strongest departures precisely where the observational tests are hardest to specify. That is a coherent research programme, and Suntola presents it with unusual rigour; it is not yet a demonstration.

See also

• Tuomo Suntola — the author; see also his companion paper in the same issue of Apeiron
• Ari Lehto — acknowledged for discussions on the theoretical basis of the model
• Apeiron — the journal of publication
• Cosmology and Big Bang — the standard model contested here
• Redshift and Tired Light — alternative accounts of cosmological redshift
• Special Relativity, General Relativity and Relativity
• Time and Time Dilation — reinterpreted here as real slowing of oscillators in universal time
• Michelson-Morley experiment — explained without length contraction
• Dark Matter and Dark Energy
• Gravity and Light