View source for Observations Support Spherically Closed Dynamic Space Without Dark Energy

{{Infobox paper
| title = Observations Support Spherically Closed Dynamic Space Without Dark Energy
| url = [http://www.naturalphilosophy.org/pdf/abstracts/abstracts_3207.pdf Link to paper]
| author = [[Tuomo Suntola]]
| keywords = [[Dark energy]], [[expansion of space large-scale structure of universe]], [[cosmological parameters]], [[distances and redshifts]], [[observations]]
| published = 2005
| num_pages = 12
}}

'''Read the full paper''' [http://www.naturalphilosophy.org/pdf/abstracts/abstracts_3207.pdf here]

==Abstract==

When interpreted with the standard theory of cosmology, recent observations of the apparent magnitude vs. redshift of Type Ia supernovae suggest an accelerating expansion of space. The acceleration is justified by assuming the presence of an unknown dark energy working against gravitation at cosmological distances. The assumption of dark energy is equivalent to Einstein's cosmological constant, which he originally proposed to prevent a collapse of spherically closed space which he assumed to be static. If Einstein's spherically closed space, the surface of a 4-sphere, is allowed to expand in a zero energy balance between the energies of motion and gravitation, no cosmological constant or dark energy is needed. In a thorough analysis of such expansion, the apparent magnitude, m, versus redshift, z, obtains the form m = M<sub>0</sub> + 5 log z + 2.5 log (z+1), which completely agrees with the Type Ia supernovae observations. Due to the assumed spherical geometry and the zero energy balance, the obtained magnitude prediction is absolute in its nature; it has no free parameters like &Omega;<sub>m</sub>, &Omega;<sub>&lambda;</sub>, or the Hubble constant H<sub>0</sub> that are needed in the corresponding equation derived from the standard cosmology model. In space, described as a dynamic 4-sphere, the fourth dimension is geometrical in its nature, allowing a universal time coordinate. The velocity of light becomes directly linked to the velocity of space in the direction of the 4-radius and the rest energy of mass gets the meaning of the energy of motion mass possesses mass due to the expansion of space. As further consequences of the zero-energy balance, buildup of mass centers in space result in local bending of space allowing solutions of the perihelion advance of planetary orbits, the bending of light and the Shapiro delay in closed mathematical form. The characteristic absorption and emission frequencies of atomic objects become linked to local motion and gravitation, which means that the concept of proper time is replaced by a direct effect of motion and gravitation on the frequencies of atomic oscillators. In dynamic spherical space the well known equality between the total gravitational energy and the rest energy of mass in space reflects the zero energy balance driving the expansion of spherically closed space.

==Overview==

This is Suntola's conference presentation of the Dynamic Universe model, given in the SPIE symposium "The Nature of Light: What is a Photon?" (San Diego, 2005) and published as Proc. SPIE Vol. 5866, pp. 160–170. The starting point is Einstein's 1917 picture of space as the three-dimensional "surface" of a four-dimensional sphere. Einstein needed the [[Cosmological Constant|cosmological constant]] to keep that surface static; Suntola's move is to drop the requirement of stasis and let the 4-sphere contract and expand under a '''zero-energy balance''' between the total energy of motion and the total energy of gravitation. If that balance is imposed, he argues, neither a cosmological constant nor [[Dark Energy|dark energy]] is required, and the acceleration inferred from Type Ia supernovae disappears as an artefact of the standard interpretation.

The consequences he draws are far-reaching and deliberately anti-relativistic. The fourth dimension becomes purely metric rather than time-like, which restores a universal time coordinate and a universal state of rest at the 4-centre. The [[Speed of Light|velocity of light]] is identified with the velocity of space along the 4-radius, so it decreases as space expands and is reduced locally near mass centres. Rest energy is reinterpreted not as a form of energy but as the energy of motion that matter possesses "due to the motion of space in the fourth dimension", with mass demoted to "the substance for the expression of energy". [[Time Dilation|Clock slowing]] becomes a real change in the frequency of atomic oscillators, determined by the clock's gravitational state and its velocity relative to its local energy frame — "neither a function of the velocity of the clock relative to an observer nor a function of the acceleration of the clock". Suntola states the conclusion flatly: "There is no place for the [[Lorentz Transformation|Lorentz transformation]] or the [[Equivalence Principle|equivalence principle]] in the Dynamic Universe... There is no place for the principle of relativity in the Dynamic Universe."

==The argument==

===The zero-energy condition and the velocity of light===

The zero-energy condition for a homogeneous 4-sphere is written ''GM''&Sigma;''M''&Prime;/''R''<sub>4</sub> &minus; ''M''&Prime;''c''<sub>4</sub><sup>2</sup> = 0, where ''M''&Prime; = ''I''<sub>g</sub>&middot;''M''&Sigma; is the mass equivalence of the total mass in space and ''I''<sub>g</sub> = 0.776 is a numerical factor from integrating the gravitational energy of a 4-sphere. This gives the expansion velocity directly:

''c''<sub>4</sub> = &plusmn;(''GI''<sub>g</sub>''M''&Sigma;/''R''<sub>4</sub>)<sup>1/2</sup>

Inserting a mass density &rho; &asymp; 0.55&rho;<sub>c</sub> (where &rho;<sub>c</sub> is the Friedmann critical density), ''R''<sub>4</sub> = 14&times;10<sup>9</sup> light years and ''G'' = 6.7&times;10<sup>&minus;11</sup>, Suntola reports ''c''<sub>0</sub> = 300&thinsp;000 km/s — the observed speed of light. The check reproduces his number: with ''M''&Sigma; = 2&pi;<sup>2</sup>''R''<sub>4</sub><sup>3</sup>&rho; for the volume of a 3-sphere surface, the relation reduces to ''c''<sub>4</sub><sup>2</sup> = (3&pi;/4)&middot;''I''<sub>g</sub>&middot;(&rho;/&rho;<sub>c</sub>)&middot;(''R''<sub>4</sub>''H''<sub>0</sub>)<sup>2</sup>, and with ''I''<sub>g</sub> = 0.776 and &rho;/&rho;<sub>c</sub> = 0.55 the prefactor is 1.006, so ''c''<sub>4</sub> = ''R''<sub>4</sub>''H''<sub>0</sub> to better than one per cent. Equivalently, the model predicts a mass density of about 0.55 of critical rather than exactly critical.

Integrating the expansion gives ''R''<sub>4</sub> &prop; ''t''<sup>2/3</sup> and hence the age

''t'' = (2/3)''R''<sub>4</sub>/''c''<sub>0</sub>

which for a 14-billion-light-year 4-radius is 9.3 billion years — again reproducible from the stated inputs.

===Unified expressions of energy===

Section 3 rebuilds the standard energy relations on this basis. Because the buildup of a mass centre tilts local space, the local velocity of light is reduced by a chain of "cascaded" gravitational factors &delta;<sub>i</sub> = ''GM''<sub>i</sub>/''r''<sub>i</sub>''c''<sup>2</sup>, one for each nested system — the accelerator frame inside the Earth frame inside the solar frame inside the Milky Way frame, and so on out to hypothetical homogeneous space. Kinetic energy built at constant potential is obtained by transferring mass, giving ''E''<sub>k</sub> = &Delta;''m''&middot;''c''<sub>0</sub>''c'', which Suntola notes "is equal to the expression of the kinetic energy in the theory of special relativity, but for a completely different reason than that taught by relativity theory." The rest energy in an ''n''-th level frame carries the full product of gravitational and velocity factors, and the resulting statement that "expression of energy through motion in space reduces the energy the object expresses in the fourth dimension" is offered as "a quantitative expression of [[Mach's Principle|Mach's principle]]."

The same treatment is applied to radiation. Solving the dipole emission of a single oscillation cycle using the vacuum permeability rather than the permittivity gives an expression that "essentially has the form of [[Planck Constant|Planck's equation]] ''E'' = ''hf''", and an "intrinsic Planck constant" ''h''<sub>0</sub> = ''h''/''c'' independent of the velocity of light. A dimensionless factor &chi;<sub>&lambda;</sub> &asymp; 1.10492 appears, and from it the [[Fine Structure Constant|fine structure constant]] is presented as "a purely mathematical, dimensionless constant without connections to any physical constants" with the value 1/137.

===Cosmological predictions===

The cosmological section is the paper's core. Light travels along the tangential component of a path on the expanding sphere, so the optical distance equals the change in the 4-radius during transit, and the wavelength stretches in direct proportion to expansion. From Figure 5, an object seen at ''z'' = 5 emitted its light when ''R''<sub>4</sub> was 0.17 of its present value, having travelled 0.83''R''<sub>4</sub>.

Several results follow:

* '''Angular size.''' A rigid standard rod subtends &theta; &prop; (1+''z'')/''z'', but an object that expands with space subtends the Euclidean &theta; &prop; 1/''z''. Suntola compares the latter with Kapahi's median angular sizes of radio sources as reproduced by Sandage, and reports a straight Euclidean line fitting the data better than the ''q''<sub>0</sub> = 0, ''q''<sub>0</sub> = &frac12; or [[Tired Light|tired-light]] curves.
* '''Magnitude versus redshift.''' The parameter-free relation ''m'' = ''M''<sub>0</sub> + 5&thinsp;log&thinsp;''z'' + 2.5&thinsp;log&thinsp;(''z''+1) — equivalently a luminosity distance proportional to ''z''(1+''z'')<sup>1/2</sup> — is fitted to the Riess ''gold'' dataset plus HST points, with ''M''<sub>0</sub> the only adjustable quantity against the standard model's &Omega;<sub>m</sub>, &Omega;<sub>&lambda;</sub> and ''H''<sub>0</sub>.
* '''Expanding local systems.''' Unlike standard cosmology, the DU has planetary and galactic radii expanding with ''R''<sub>4</sub>. Suntola states that of the 3.8 cm annual increase in the Earth–Moon distance, 2.8 cm is expansion and only 1 cm is tidal. That figure is reproducible: ''H''<sub>0</sub>&times;384&thinsp;400 km at 70 (km/s)/Mpc gives 2.75 cm per year.
* '''Slowing atomic processes.''' Because rest energy dilutes as ''c'' falls, all internal atomic rates — including radioactive decay, which goes as ''t''<sup>&minus;1/3</sup> — slow with expansion. Correcting for the faster past decay rate turns a nominal 14-billion-year radiometric result into about 9 billion years, which Suntola offers as the resolution of the old-stars problem.
* '''Background radiation.''' The [[Cosmic Microwave Background|microwave background]] is radiation that has travelled a full 360&deg; path around the sphere, giving the specific prediction ''z'' = e<sup>2&pi;</sup> &minus; 1 = 534.5. The 4-radius at emission was then ''R''<sub>4</sub>/535.5 &asymp; 26 million light years, about 750&thinsp;000 years after singularity. Both figures follow correctly from the model's own ''R''<sub>4</sub> &prop; ''t''<sup>2/3</sup>.

The summary adds that Michelson–Morley-type experiments give a null result because electromagnetic resonators are closed energy systems, and that the Shapiro delay, [[Perihelion Precession of Mercury|perihelion advance]], [[Gravitational Lensing|light bending]], stellar aberration and the annual Doppler shift of pulsars all obtain closed-form solutions — these being derived elsewhere, in Suntola's 2004 book, rather than here.

==Assessment==

The Dynamic Universe is one of the more disciplined alternative cosmologies in this literature, and the reason is the zero-energy constraint. Once the total energy of motion is set equal and opposite to the total gravitational energy of the 4-sphere, the expansion velocity, the age, and the mass density are all fixed together; there is very little left to tune. That is why the magnitude–redshift relation comes out with a single normalisation constant instead of three fitted parameters, and it is a real methodological advantage over a model that can absorb a new observation by adjusting &Omega;<sub>&lambda;</sub>. The internal arithmetic holds up under checking at every point where it can be checked: the density ratio 0.55 is exactly what makes ''c''<sub>4</sub> = ''R''<sub>4</sub>''H''<sub>0</sub> given ''I''<sub>g</sub> = 0.776, the 9.3-billion-year age follows from ''t'' = (2/3)''R''<sub>4</sub>/''c''<sub>0</sub> at ''R''<sub>4</sub> = 14 Gly, the CMB redshift e<sup>2&pi;</sup> &minus; 1 = 534.5 is correct, and 750&thinsp;000 years is what ''R''<sub>4</sub> &prop; ''t''<sup>2/3</sup> gives at ''R''<sub>4</sub>/535.5. Suntola is also unusually forthright about what he is discarding, which makes the model easier to test than the more common approach of claiming to recover relativity in some limit.

The supernova fit deserves a closer look than the paper's "completely agrees" allows. Working in units of ''c''/''H''<sub>0</sub>, the DU luminosity distance ''z''(1+''z'')<sup>1/2</sup> and the flat &Lambda;CDM luminosity distance with &Omega;<sub>m</sub> = 0.3 differ by 0.03 mag at ''z'' = 0.1, rising to about 0.19 mag near ''z'' = 0.8–1.0 and falling back to 0.10 mag by ''z'' = 2. Since ''M''<sub>0</sub> is free, a constant offset of roughly 0.12 mag can be absorbed, leaving a residual shape difference of order &plusmn;0.09 mag across 0.05 < ''z'' < 2. Against the 2004 ''gold'' sample of about 157 supernovae with roughly 0.16 mag scatter apiece, that is genuinely hard to distinguish, and Suntola's claim of a fit as good as the standard model is defensible for the data he had. It is not a claim that survives unchanged: modern compilations of well over a thousand supernovae constrain the shape of the Hubble diagram at the few-hundredths-of-a-magnitude level, which is precisely the regime where a 0.09 mag curvature difference becomes decisive. The paper should be read as showing that the acceleration inference was not forced by the 2004 data, not that the DU curve is indistinguishable in principle.

Three difficulties are more serious. The first is the expansion of local gravitational systems. The 2.8 cm/yr figure for the Moon is arithmetically correct, but the same rule applied to the Earth's orbit gives ''H''<sub>0</sub>&times;1 AU &asymp; 10 metres per year, about 1000 metres per century. Planetary ranging — Mercury and Mars radar, then spacecraft tracking of MESSENGER and Cassini — constrains any secular drift of the astronomical unit to a few metres per century at most, two to three orders of magnitude below what the model requires. The lunar figure is also not free: the tidal recession rate is not a fitted residual but is independently fixed by the Earth's measured tidal dissipation, which shows up in the length-of-day increase of about 1.7 ms per century recorded in ancient eclipse timings and in satellite measurements of the tidal bulge; those give essentially the whole 3.8 cm/yr. Reassigning three-quarters of it to expansion requires the tidal torque to be four times smaller than the independent measurements of Earth's dissipation imply.

The second is the CMB. Fixing the background redshift at e<sup>2&pi;</sup> &minus; 1 by pure geometry is a bold and admirable prediction — it is a number that cannot be adjusted — but it implies an emission temperature of 535.5&times;2.725 K &asymp; 1460 K, and it makes the background a surface at a single sharp redshift. The observed background is a Planck spectrum accurate to a few parts in 10<sup>5</sup>, with an anisotropy power spectrum whose acoustic peak positions and heights encode the sound horizon at decoupling and the baryon-to-photon ratio; the paper offers no account of that structure, and a 360&deg;-path origin would have to explain why the spectrum is thermal and why the peaks fall where they do. The related prediction of a 26-million-light-year emission radius is likewise not confronted with any observation.

The third is the treatment of the fine structure constant. Equation (14) presents &alpha; as "purely mathematical... without connections to any physical constants", but the factor &chi;<sub>&lambda;</sub> = 1.10492 on which it rests is obtained in equation (12) by inserting the measured value ''h'' = 6.626068765&times;10<sup>&minus;34</sup>. A constant derived by substituting a measured constant is not a mathematical one; the result is a rearrangement, not a prediction, and presenting it as the latter is the weakest rhetorical move in the paper.

Two further tests are simply not addressed here, though they bear directly on the central claim. The Type Ia light curves in the very datasets Suntola fits show a (1+''z'') stretching of their time axis, established out to ''z'' &asymp; 1 and confirmed independently by the (1+''z'') broadening of supernova spectral-feature evolution; any model that reproduces the magnitude–redshift relation must also produce that dilation, and the paper does not show that its wavelength-stretching mechanism does. And the reduction of radiometric ages by a ''t''<sup>&minus;1/3</sup> decay-rate correction, which Suntola uses to bring 14 Gyr down to 9, does not obviously extend to the ages that actually create the old-stars problem: globular cluster ages come primarily from main-sequence turnoff fitting against stellar-structure models, not from radioactive dating, so the correction would have to be shown to propagate through nuclear reaction rates and opacities in the same way. Neither omission is fatal, but both are places where the model makes a commitment it has not yet cashed.

==See also==

* [[Tuomo Suntola]]
* [[Dark Energy]]
* [[Cosmological Constant]]
* [[Expanding Universe]]
* [[Hubble Constant]]
* [[Redshift]]
* [[Supernova]]
* [[Cosmic Microwave Background]]
* [[Tired Light]]
* [[Mach's Principle]]
* [[Fine Structure Constant]]
* [[Speed of Light]]
* [[Big Bang]]

[[Category:Scientific Paper|observations support spherically closed dynamic space dark energy]]

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