Zero-Energy Space Cancels the Need for Dark Energy
| Scientific Paper | |
|---|---|
| Title | Zero-Energy Space Cancels the Need for Dark Energy |
| Read in full | Link to paper |
| Author(s) | Tuomo Suntola |
| Keywords | Cosmology, dark energy, supernova |
| Published | 2007 |
| No. of pages | 28 |
Read the full paper here
Abstract
A detailed analysis of a dynamic solution of the zero-energy condition of gravitation and motion in Einstein's original proposal of spherically closed space shows a precise match to the luminosity–redshift relation of Ia supernovae without dark energy, accelerating expansion, or additional parameters. In such a solution, Einstein's static 4-sphere is allowed to contract or expand instead of being forced to be stationary by means of a cosmological constant, the original formulation of dark energy. In spherically closed space the zero-energy condition determines the mass density and the development of the expansion velocity of space, allowing the derivation of predictions to cosmological observables like the angular size distance, the magnitude, the surface brightness of distant objects, and the orbital velocities in the vicinity of black holes in closed mathematical forms – all with excellent fit with observations without a cosmological constant, dark energy, or accelerating expansion.
Overview
This paper is Tuomo Suntola's presentation of the Dynamic Universe (DU) model, in which space is the three-dimensional surface of a four-dimensional sphere that expands along its 4-radius R4, and in which the total energy of the universe is exactly zero at every instant. Suntola takes two ideas Richard Feynman raised in his 1962–63 Lectures on Gravitation — that GMΣ2/R = MΣc2, so that "the total energy of the universe is zero," and that space may be "a tridimensional surface of a four sphere" — and joins them. Einstein's 1917 static 4-sphere required the Cosmological Constant precisely to prevent it from moving; release that constraint and the sphere must contract or expand, and the zero-energy balance then fixes both the mass density and the expansion velocity with no free parameters left.
The consequence Suntola presses hardest is that the rest energy of matter is not intrinsic but is the energy of motion that mass possesses by virtue of being carried outward at speed c4 in the fourth dimension. The time-like fourth dimension of relativity is replaced by a geometrical one, and the velocity of light in space is tied to the expansion velocity — so c is not a constant but decays as the universe grows. From this the paper derives magnitude, angular size and surface brightness as functions of redshift in closed form, and claims a fit to the Type Ia Supernova data equal to that of ΛCDM without Dark Energy, without acceleration, and without adjustable Ω parameters.
The argument
Zero-energy balance and the expansion law
Integrating Newtonian gravitational energy over mass uniformly spread on the 3-surface of a 4-sphere gives Eg = −GmM4/R4, where the mass equivalence M4 = 0.776 MΣ, the factor 0.776 being a geometric integral. Setting this against the rest energy — interpreted as the energy equivalence of momentum p4 = mc4 in the fourth dimension, so Erest = c4·mc0 — yields the zero-energy condition and solves for the expansion velocity c0 = ±√(0.776 GMΣ/R4). With R4 = 14 billion light years and mass density ρ = 5.0 × 10−27 kg/m3 — about half the critical density of the standard model — this returns c0 ≈ 300,000 km/s. The ± sign means the balance holds equally in contraction and expansion, and Suntola reads the two branches as a single history: rest energy is "built up against release of gravitational energy in a contraction phase before singularity and paid back to gravitational energy in the succeeding expansion phase."
Expansion decelerates as R4 grows, with dc0/c0 ≈ −3.6 × 10−11 per year at present, and the age of space becomes t = (2/3)R4/c0 ≈ 9.3 billion years for H0 = 70. Because atomic process rates — emission frequencies, radioactive decay — scale with the same declining c, locally measured c appears constant, and radiometric ages measured at today's decay rate overstate the true elapsed time.
Nested energy frames in place of the relativity principle
Rather than the Lorentz Transformation, DU distributes the total energy through a hierarchy of nested frames: Earth rotation inside the solar frame inside the Milky Way frame, and so on up to "hypothetical homogeneous space" as the universal rest frame. The locally available rest energy is Erest = c0m0c0 ∏(1 − δi)√(1 − βi2), where δi is a gravitational factor and βi = vi/c a velocity in the i-th frame. Relativistic effects therefore appear as reductions in the energy available to run local processes rather than as changes in metric. Suntola states explicitly that DU dispenses with the relativity principle, the Lorentz transformation and the Equivalence Principle, replacing the last by conservation of total energy, and traces the idea back past Newton to Leibniz's vis viva obtained against release of vis mortua.
Planck's constant from Maxwell's equations
A notable side result: starting from the standard dipole radiation power derived from Maxwell's Equations, and treating a point source at rest in space as a one-wavelength dipole in the fourth dimension, Suntola obtains the energy carried by one cycle of radiation as E = 2π2e2μ0cf, in which the factor 2π2e2μ0c has the dimensions of h and the numerical value 0.90506 h. Correcting by χλ = 1.1049 — a factor whose physical origin he says the analysis does not disclose — reproduces Planck's equation, and shows c to be "a hidden parameter in Planck's constant." Removing it defines an intrinsic constant h0 = h/c = 2.210 × 10−42 kg·m, conserved through the expansion. The Fine Structure Constant then reduces to α = 1/(2·1.1049·2π) ≈ 1/137.035, a purely numerical factor independent of c.
Cosmological predictions
Because light propagates tangentially at the same speed as R4 grows radially, its path is a four-dimensional spiral and the optical distance equals the increase in the 4-radius: D = R4(1 − e−α), giving D = R4·z/(1 + z) and an observed recession velocity that approaches but never exceeds c.
Two departures from standard cosmology follow. First, gravitationally bound systems — galaxies, quasars, orbital radii — expand in proportion to R4, whereas atoms do not, because the Bohr radius and the characteristic emission wavelengths are conserved. (Suntola attributes about 2.8 cm of the 3.8 cm annual increase in the Earth–Moon distance to this expansion, leaving 1 cm to tidal effects.) Expanding galaxies then subtend angles following the Euclidean 1/z law, which he matches against the 540 Fanaroff–Riley type II double radio sources of Nilsson et al. rather than the turn-up in angular size predicted by FLRW models above z ≈ 1.
Second, the "energy effect" is deleted from the flux dilution. Since a quantum's energy is the energy carried by one cycle, and the mass equivalence mλ = h0/λ is conserved as the wave stretches, redshift dilutes energy density but does not destroy energy. Only Hubble's "number effect" survives, so flux falls as (1 + z)−1 rather than (1 + z)−2. The resulting magnitude prediction is m = M + 5 log(R4/d0) + 5 log z + 2.5 log(1 + z), a parameter-free curve that Suntola shows tracking the Riess gold dataset as closely as the Ωm ≈ 0.31 / ΩΛ ≈ 0.69 fit, diverging from it only above z ≈ 2. The Tolman surface brightness law is correspondingly softened from (1 + z)−4 to (1 + z)−1, because the objects themselves expand. He also notes that the standard treatment of the CMB implies roughly 10% of the total energy of space has been lost to redshift, which he regards as a violation of energy conservation, and observes that DU does not by itself fix R4 at CMB emission.
Assessment
The model's chief attraction is economy. Where ΛCDM fits the supernova Hubble diagram with adjustable Ωm and ΩΛ, DU produces a magnitude–redshift curve containing no free cosmological parameter at all: once R4 is fixed by H0, the curve is determined. That such a curve should lie on top of the ΛCDM best fit across z = 0 to 2 is a real and non-trivial result, and it is the single strongest thing in the paper. The derivation is internally disciplined — every quantity is expressed as a mass equivalence times c0c, so the energy bookkeeping can be checked — and the criticism that the standard treatment applies two (1 + z) factors, one of which is a genuine energy loss with no accounting entry, is a longstanding and legitimate question rather than a misunderstanding. The prediction of Euclidean angular sizes at high z is likewise a genuine prediction rather than a retrofit, and it addresses a dataset the standard model handles only by invoking source evolution. Suntola is also careful to state what the model does not deliver, for instance leaving the 4-radius at CMB emission undetermined and leaving the surface-brightness comparison "outside the scope of this paper."
The difficulties are real. Several key steps are asserted rather than derived. The interpretation E = mc2 = c4·p4 is a postulate about what rest energy is, not a result; the factor χλ = 1.1049 needed to turn the Maxwell dipole result into Planck's equation is admitted to have no explanation, and since α is then defined in terms of that same factor, the apparently striking derivation of 1/137.035 is not independent of the number it fits. The claim that gravitationally bound systems expand with space while atoms do not is the hinge on which the angular-size and surface-brightness predictions turn, yet it is imposed by the energy-conservation requirement rather than demonstrated dynamically, and it carries a heavy observational burden. Specifically, the assertion that 2.8 cm of the 3.8 cm annual lunar recession is cosmological expansion conflicts with lunar laser ranging, where the measured recession is accounted for to within a few tenths of a centimetre per year by tidal dissipation independently constrained by the Earth's measured length-of-day change and by satellite-tracked ocean-tide models; planetary radar and spacecraft ranging bound any secular expansion of solar-system orbits far below the required rate.
The most serious test is the one Suntola meets directly rather than avoids, and it deserves to be stated precisely. The (1 + z) stretching of Type Ia supernova light curves is standardly read as cosmological time dilation. DU reproduces the same (1 + z) factor, but as a consequence of the declining velocity of light: a wave sequence emitted when c was higher arrives lengthened in the same ratio as the wavelengths. This is a genuine alternative account of the same number, and it should be credited as such. What the paper does not do is show that the two mechanisms are observationally equivalent in detail — the light-curve stretch and the wavelength stretch are made to share one cause, so any measurement that separated spectral-feature ageing from photometric stretch would discriminate between them, and no such comparison is offered. Similarly, the deletion of the "energy effect" changes the predicted flux by a full factor of (1 + z), which is why the parameter-free curve can imitate an accelerating universe; whether that substitution or dark energy is correct cannot be settled by the supernova magnitudes alone, since both were tuned against the same data. Finally, a model in which c and all atomic rates decline together is difficult to falsify locally by construction, and the paper does not identify a laboratory measurement that would distinguish it from constant-c physics.
On its own terms the paper is coherent, unusually explicit about its postulates, and free of the arithmetic inconsistencies that afflict much alternative cosmology. Its central claim — that a zero-energy, spherically closed, decelerating space fits the supernova data without dark energy — is established as a fit; it is not yet established as the better explanation, because the decisive discriminating tests have not been carried out here.