Back to the Basis – Observations Support Spherically Closed Dynamic Space
| Scientific Paper | |
|---|---|
| Title | Back to the Basis – Observations Support Spherically Closed Dynamic Space |
| Read in full | Link to paper |
| Author(s) | Tuomo Suntola |
| Keywords | Cosmology models, relativity, absolute time, fourth dimension, dynamic space |
| Published | 2005 |
| Journal | ArXiv |
| No. of pages | 19 |
Read the full paper here
Abstract
A holistic view of the cosmological appearance and development of space is obtained by studying space as a spherically closed surface of a 4-sphere in a zero energy balance between motion and gravitation. Such an approach reestablishes Einstein's original view of the cosmological structure of the universe but instead of forcing space to be static with a cosmology constant, it lets it contract or expand while constantly maintaining a balance between the energies of motion and gravitation within the structure. In spherically closed dynamic space the fourth dimension, the direction of the 4-radius of the structure, is purely metric in its nature; time can be treated as a universal scalar, and the line element cdt in the fourth dimension gets the meaning of the distance that space moves at velocity c in time differential dt. The rest energy of matter appears as the energy of motion due to the motion of space in the fourth dimension, in the direction of the 4-radius of the structure. The dynamic universe approach converts Einsteinian spacetime in variable time and distance coordinates into dynamic space in absolute coordinates. All velocities in space are related to the 4-velocity of space, and the local state of rest appears as a property of the local energy system rather than as the state of an observer. Based on the zero-energy balance of whole space and the conservation of energy in interactions in space, the dynamic space approach allows the derivation of relativistic phenomena and cosmological predictions in closed mathematical form without relying on the Lorentz transformation or the relativity and equivalence principles. Mach's principle gets a quantitative expression, and the picture of cosmology is cleared: no dark energy or free parameters are needed to explain the magnitude/redshift relations of distant objects. Local systems expand in direct proportion to the expansion of whole space which results in a Euclidean appearance of distant space and explains the observed development of the surface brightness of galaxies. The rate of internal atomic processes is tied to the velocity of light which is determined by the expansion velocity and local geometry of space. All processes, like radioactive decay or buildup of large scale structures in space, have been faster in the young expanding universe. The ongoing decelerating expansion of space continues to infinity by gradually releasing the rest energy of matter. In the dynamic universe, the cycle of observable physical existence begins at cessation at infinity in the past and ends at cessation at infinity in the future.
Overview
This paper is Suntola's presentation to the 1st Crisis in Cosmology Conference (CCC-I), held at Monção, Portugal in June 2005. It is a compact statement of his Dynamic Universe model, in which three-dimensional space is the closed "surface" of a four-dimensional sphere, and the whole structure is in free motion along the 4-radius under its own gravitation. The rest energy of matter is not a separate postulate but the energy of motion that mass possesses because space itself is moving at velocity c in the fourth dimension. The zero-energy balance between that motion and the gravitation of the whole structure — the condition Feynman had called "one of the great mysteries" when he noticed that GMΣ2/R ≈ MΣc2 — becomes the governing equation of the model rather than a coincidence.
The departure from the standard account is at the level of what the fourth dimension is. In relativity the fourth coordinate is time-like; here it is purely metric and geometrical, and time is restored as a universal scalar. Consequently the model needs neither the Lorentz transformation, the relativity principle, nor the Equivalence Principle: the slowing of moving clocks and clocks deep in a gravitational potential is derived instead from the reduction of the locally available rest energy of matter. Suntola's cosmological claim is that this framework reproduces the observed magnitude/redshift relation of supernovae with a single free parameter and without Dark Energy, and simultaneously accounts for the Euclidean angular sizes of radio sources and the surface brightness of high-redshift galaxies.
The argument
Space as the surface of a 4-sphere
Suntola takes up Einstein's 1917 closed spherical space, with Riemann volume V = 2π2R43, but drops the requirement that it be static. Where Einstein needed the Cosmological Constant to hold the sphere up, Suntola lets it contract and expand freely. Hubble's law is then read directly as the expansion of the 4-radius at velocity c4 = c, with R4 = c/H0 — the same quantity the standard model calls the Hubble radius, about 14 billion light years (see Hubble Constant).
The rest energy of matter as motion in the fourth dimension
Rewriting the Minkowski line element ds2 = −c2dt2 + dx2 + dy2 + dz2 in vector form, d s = ic4dt + dr, lets c4 be a genuine velocity of space rather than a conversion factor on time. Mass at rest in space then carries a momentum p4 = i mc4 in the fourth dimension, whose energy equivalence is
- E4 = c4p4 = mc2
so that E = mc2 arises as the "energy equivalence of momentum in the fourth dimension." Adding momentum in space orthogonally gives Etot = c√(p2 + m2c2), formally the familiar total-energy expression of special relativity but reached, as Suntola stresses, "through a completely different reasoning." Kinetic energy splits into two terms, cΔm for acceleration at constant gravitational potential and mΔc for free fall, where local space is tilted.
The zero-energy balance
Integrating Newtonian gravitational energy over the whole 3-surface gives Eg = −0.776 GmMΣ/R4; the factor 0.776 defines a "mass equivalence" M″ = 0.776 MΣ sitting at the centre of the 4-sphere. Setting the energy of motion against it,
- mc42 − GmM″/R4 = 0, hence c4 = ±√(GM″/R4)
With R4 = 14 billion light years and a mass density 0.55 times the Friedmann critical value, this returns c4 ≈ 300,000 km/s. Space behaves as a "spherical pendulum in the fourth dimension": contraction from infinity, a singularity, then decelerating expansion back to rest at infinity. The Speed of Light is therefore not constant but declines at dc/c ≈ −3.6×10−11 per year, and the age since singularity is t = (2/3)R4/c0 ≈ 9.3 billion years for H0 = 70 (km/s)/Mpc.
Tilted space, cascaded energy frames
Local mass concentrations tilt the 3-surface in the fourth dimension by an angle φ with cos φ = 1 − δ, where δ = GM″/Rc2 is the "gravitational factor." The local velocity of light is reduced accordingly, cδ = c0δ(1 − δ), and motion reduces the "internal mass" available for expressing rest energy by √(1 − β2). Chaining these through nested frames — extragalactic space, Milky Way, solar, Earth, accelerator, ion — gives the rest energy of an object as a product over all its parent frames. This replaces proper time and proper distance: a clock runs slow because of its energy state relative to the rest state of the frame it moves in, "not the velocity relative to an observer as taught by the relativity theory," and acceleration as such has no effect. Suntola computes that in the Earth frame his prediction and that of General Relativity differ by less than 10−18 in relative frequency.
Electromagnetism and the intrinsic Planck constant
Treating a point source as a dipole one wavelength long in the fourth dimension, the Maxwell dipole solution yields an emitted quantum E = 2π3e2μ0cf, a factor 1.1049 below Planck's constant; multiplying by that transition factor recovers E = hf exactly and defines an "intrinsic Planck constant" h0 = h/c with dimensions of [kg·m]. Because h is then proportional to c, and because the Fine Structure Constant becomes α = 1/(2×1.1049×2π2) ≈ 1/137, a purely geometrical number, both "constants" inherit the time dependence of c. Rest energy, Coulomb energy, quantum energy and kinetic energy are then written in a single unified form E = c0cm, with m a mass or mass equivalence — Suntola's central formal result (see Planck Constant, Maxwell's Equations).
Cosmological predictions
Because emission wavelengths track the Bohr radius, which does not expand, while wavelengths in flight do, redshift follows as z = eα − 1 with optical distance D = R4z/(1 + z). The optical recession velocity then approaches but never exceeds c. Crucially, local gravitational systems do expand with space — Suntola attributes 2.8 cm of the Moon's 3.8 cm annual recession to expansion and only 1 cm to tides — so the observation angle of an expanding object takes the Euclidean form θ ∝ 1/z, matching Kapahi's radio-source angular sizes better than any q0 of the standard model or the Tired Light curve. The magnitude relation reduces to
- m = m0 + 5 log z + 2.5 log(1 + z)
with the single parameter m0, which Suntola reports fits the Riess "gold" Supernova dataset at least as well as the standard three-parameter fit. Surface brightness falls only as 1/(1 + z); radioactive dating corrected for a faster past decay rate pulls a 14-billion-year result down to about 9 billion, removing the oldest-stars age conflict; and the Cosmic Microwave Background is reinterpreted as radiation that has made a full 360° circuit of closed space, z = e2π − 1 ≈ 534.5, emitted when R4 ≈ 26 million light years, some 750,000 years after singularity.
Assessment
The distinctive strength of the paper is its economy of postulates. A single condition — zero total energy for the closed structure — fixes the expansion velocity, identifies it with c, and delivers rest energy, the total-energy expression, gravitational and kinematic clock rates, and the magnitude/redshift law without a metric tensor, without the Lorentz transformation and, most strikingly, without dark energy or tunable density parameters. Reducing equation (53)'s three fitted quantities to a single reference magnitude is a real claim of parsimony, and it is testable rather than rhetorical. The quantitative expression given to Mach's Principle — every local rest state referred through a chain of parent frames to rest in hypothetical homogeneous space — is more concrete than most invocations of that principle. The paper is also candid about where it is merely re-deriving familiar formulas by another route: it says outright that its total-energy expression is "equal to the well known expression … introduced by the theory of special relativity."
The difficulties are correspondingly structural. Several central steps are asserted rather than derived. The reduction of "internal mass" by √(1 − β2) is introduced with a "phenomenological explanation" appealing to central acceleration relative to the mass equivalence at the centre of the 4-sphere; the text then claims internal and effective mass "are not assumptions but consequences of the conservation of energy," which the argument as presented does not establish. The energy transition factor 1.1049 in the dipole derivation is fixed by comparison with Planck's constant, so the subsequent presentation of α as a purely geometrical factor is partly circular: the number that makes the geometry come out right was calibrated on the quantity it is meant to explain. The gravitational integral's 0.776 does real work throughout, but the transition from that homogeneous-space result to the local tilting formula cos φ = 1 − δ relies on an unstated conservation of "total gravitational energy in a mass center buildup."
There is also friction with measurement. A secularly decreasing c with dc/c ≈ −3.6×10−11 per year is defended as unobservable because atomic frequencies scale with c; but the model also makes h ∝ c and leaves the Bohr radius fixed, and the paper does not test that combination against the tight laboratory bounds on drift in α and on clock-comparison ratios between transitions with different α sensitivities. The claim that planetary and lunar orbits expand with space — 2.8 of the Moon's 3.8 cm/yr — sits against lunar laser ranging and planetary ephemerides, which constrain any anomalous secular increase in the astronomical unit and in GM far below that level; the tidal budget from ocean dissipation is independently measured and already accounts for the observed recession. The supernova fit is presented as magnitude versus redshift alone; the model does not here address the (1 + z) stretching of Type Ia light curves, which any redshift mechanism must reproduce and which a purely metric expansion in absolute time is not automatically guaranteed to give. Finally the microwave background account is the boldest and least developed part: a single-circuit redshift of 534.5 gives an emission epoch and radius, but the paper offers no calculation of the observed blackbody spectrum, its 10−5 anisotropies, or the acoustic peak structure — and a full 360° circuit through closed space would raise questions about the isotropy and imaging of that radiation that are not taken up.
Judged on its own terms as a conference statement rather than a complete theory, the paper does what it sets out to do: it shows that a zero-energy, spherically closed, dynamically expanding space reproduces a substantial list of observations with fewer free parameters than the concordance model. Whether the framework survives contact with the precision tests it does not yet engage is left open.