View source for Dynamic Space Converts Relativity Into Absolute Time and Distance

{{Infobox paper
| title = Dynamic Space Converts Relativity Into Absolute Time and Distance
| url = [http://www.naturalphilosophy.org/pdf/abstracts/abstracts_3210.pdf Link to paper]
| author = [[Tuomo Suntola]]
| keywords = [[Dynamic Space]], [[Relativity]], [[Absolute Time]], [[Absolute Distance]]
| published = 2002
| journal = [[Episteme]]
| volume = 6
| number = 2
| num_pages = 10
}}

'''Read the full paper''' [http://www.naturalphilosophy.org/pdf/abstracts/abstracts_3210.pdf here]

==Abstract==

A confusing feature in the theory of relativity is the use of time and distance as parameters in explaining the constancy of the velocity of light and the reduced frequencies of atomic clocks in fast motion and in high gravitational field. It is well known that a radio signal passing a mass center is delayed compared to a signal from same distance through free space. Instead of stating that the velocity of the signal were reduced the theory of relativity explains that time close to mass centers flows slower thus saving the basic assumption of the theory, the constancy of the velocity of light. Same is true for atomic oscillators and the characteristic absorption and emission frequencies of atoms, an atomic clock loosing time when in fast motion is not considered as running slower but as experienced slower flow of time.

A key demand of a physical theory is its capability to create an understandable picture of the reality we observe. Instead of just introducing mathematical expressions for observations, a physical theory should explain the logic behind the phenomena observed. The old Ptolemy astronomy worked well for calendar and eclipses but failed in serving as a basis for a physical view of celestial motions. A key in Copernicus' findings was the realization of the observer's state in the system - instead of defining the observer's state as the origin at rest Copernicus identified the Sun as the origin of the planetary system with Earth orbiting and rotating like any other planet. Such a structure gave basis for a physical approach of motions in the system thus opening a new era for the understanding of celestial mechanics and the laws of nature.

The Dynamic Universe approach takes a further step in reorienting the observer. The observable three-dimensional space as whole is considered as a closed spherical structure with its dynamics determined by a zero energy balance between gravitation and motion in the structure. Such approach links local phenomena to the state and motion of whole space and gives physical explanations to several postulates like the velocity of light, the rest energy of matter and the Mach's principle. It also explains the dependence of the velocity of light on the gravitational environment and the dependence of the ticking frequencies of atomic clocks on the state of local motion and gravitation - not by distorting time and distance coordinates but in absolute time and distance.

==Overview==

Tuomo Suntola — a Finnish materials scientist best known outside physics as the inventor of Atomic Layer Deposition — published this compact statement of his '''Dynamic Universe''' (DU) model in Umberto Bartocci's journal ''Episteme'' in 2002, the same year as his book of that title. The paper is a summary rather than a full derivation: it states the model's postulates, quotes the resulting equations, and points to the book for the integrations.

The central proposal is that observable three-dimensional space is the ''surface'' of a four-dimensional sphere, and that this surface is moving along the fourth-dimensional radius at velocity ''c''. Everything else follows from a zero-energy condition: the rest energy of all mass in space is exactly balanced by its own gravitational energy. Rest energy ''E'' = ''Mc''<sup>2</sup> is then not a postulate but the energy of motion of matter carried along the 4-radius, ''E'' = ''cp'' = ''M''<sub>Σ</sub>''c''·''c''. Where [[Special Relativity|relativity]] modifies the time and distance coordinates, DU keeps them absolute and instead modifies the ''local velocity of light'' and the ''internal energy'' of matter. "The velocity of light is not a constant but a function of the local gravitational state." Suntola frames the move as a Copernican one: reorient the observer, and relativistic effects become consequences of the state of whole space rather than of coordinate distortion.

==The argument==

===Space as the surface of a 4-sphere===

Suntola starts from the long-noticed near-equality between the total rest energy of matter and its Newtonian self-gravitational energy, ''E'' ≈ ''GM''<sub>Σ</sub><sup>2</sup>/''R'' with ''R'' = ''c''/''H'' the Hubble radius. He adopts the 3-sphere geometry Einstein used in 1917 and argues it was abandoned only because Einstein wanted a static universe and had already assigned the fourth dimension to time.

Integrating the gravitational energy properly over the three-dimensional surface introduces a geometrical factor ''G''<sub>E</sub> = 0.776 and gives the zero-energy balance ''G''<sub>E</sub>''GM''<sub>Σ</sub><sup>2</sup>/''R''<sub>4</sub> = ''M''<sub>Σ</sub>''c''<sub>0</sub><sup>2</sup>, whence

''c''<sub>0</sub> = ±√(''G''<sub>E</sub>''GM''<sub>Σ</sub>/''R''<sub>4</sub>).

With the total mass of the closed surface ''M''<sub>Σ</sub> = 2ρπ<sup>2</sup>''R''<sub>4</sub><sup>3</sup>, a mass density of 5 × 10<sup>−27</sup> kg/m<sup>3</sup> — "0.55 times the Friedmann critical mass" — and ''R''<sub>4</sub> = 14 × 10<sup>9</sup> light years, he reports that ''c''<sub>0</sub> comes out at 300 000 km/s. The whole history of the universe is then a single zero-energy process: contraction from infinity through a singularity, then expansion back to infinity, with gravitational energy and energy of motion trading places (his Figure 3). Because expansion works against the structure's own gravitation, ''c''<sub>0</sub> is slowly falling — by about 4 × 10<sup>−11</sup> per year — but atomic frequencies fall in proportion, so the change is undetectable by any clock.

===The fourth dimension and relativistic dynamics===

Written as a four-vector, ''i''''c''d''t'' + d''x'' + d''y'' + d''z'', the Minkowski line element is reinterpreted: ''c'' in the imaginary direction is not motion ''in'' space but motion ''of'' space. The rest momentum of any object is therefore ''p''<sub>4</sub> = ''imc'', and the total energy is the orthogonal sum

''E''<sub>tot</sub> = ''c''√(''p''<sub>4</sub><sup>2</sup> + ''p''<sup>2</sup>),

which reproduces the special-relativistic energy expression "without the use of the Lorentz transformation as a correction of the coordinates."

Motion in space is, relative to the mass equivalence ''M''" in the fourth dimension, central motion; the resulting centrifugal term reduces the object's gravitational coupling to the total mass of space, and hence its "internal mass". The consequence is that the characteristic frequency of an atomic oscillator moving at β = ''v''/''c'' is reduced by √(1 − β<sup>2</sup>). Suntola stresses the reinterpretation: the Lorentz factor is "not a correction of time coordinate but a factor reducing the internal energetic response of a moving object to the gravitation of the total mass in space." Correspondingly, the kinetic energy of acceleration is the work done in reducing that gravitational energy — a concrete realisation of [[Mach's Principle|Mach's principle]].

===Tilted space and gravitation===

Where mass clumps, conservation of total gravitational energy requires the 4-sphere's surface to dip, forming "dents". In a dent the local fourth dimension is tilted by an angle φ, and since the expansion velocity is fixed in the global fourth dimension, the ''local'' velocity of space and hence of light is reduced: ''c'' = ''c''<sub>0</sub>cos φ ≈ ''c''<sub>0δ</sub>(1 − ''GM''/''rc''<sup>2</sup>). Locally ''E'' = ''mc''<sup>2</sup> becomes δ''E'' = ''c''δ(''mc''), and free fall gains kinetic energy against a release of rest energy through the falling velocity of light. Suntola attributes the Shapiro delay, light bending and the perihelion rotation of elliptical orbits to this tilting, though he computes none of them here.

Real space is a hierarchy of "cascaded gravitational frames" — Earth inside the Solar System inside the Galaxy inside the Local Group — and each contributes a factor, giving the compound expressions

''E''<sub>rest</sub> = ''mc''<sub>0</sub><sup>2</sup>∏(1 − δ<sub>i</sub>)(1 − ... β<sub>i</sub><sup>2</sup>),  ''f'' = ''f''<sub>0</sub>∏(1 − δ<sub>i</sub>)√(1 − β<sub>i</sub><sup>2</sup>).

A notable consequence is that the rest frame for light propagation near Earth is the Earth-centred non-rotating frame — "the local ether" — which Suntola identifies with the Earth Centred Inertial frame of general relativity. He estimates the local velocity of light on Earth to be about one part in 10<sup>6</sup> below its value in hypothetical homogeneous space.

===Cosmological predictions===

Because the zero-energy principle applies at every scale, Suntola holds that expansion occurs inside bound systems too: of the observed 3.8 cm per year increase in the Earth–Moon distance, he attributes 2.8 cm to the expansion of space and only 1 cm to tidal interaction.

At cosmological distances light follows a spiral path in four dimensions, with equal velocity components along the 4-radius and tangentially. This yields a Hubble law and a flux–redshift relation

''F''<sub>obs</sub>/''F''<sub>e</sub> = 1/[''z''<sup>2</sup>(1 + ''z'')],  ''m'' = ''m''<sub>0</sub> + 5 log ''z'' + 2.5 log(1 + ''z''),

which he says gives "a perfect match" to the [[Supernova|supernova]] magnitude–redshift data of Perlmutter et al. over ''z'' = 0.01 to 1, so that "recent confusion regarding the redshift versus magnitude observations becomes solved without any new assumption or parameter" — that is, without a [[Cosmological Constant|cosmological constant]] or [[Dark Energy|dark energy]].

Finally he gives a combined gravitational and Doppler formula whose DU form carries (1 − ''GM''/''rc''<sup>2</sup>) where general relativity carries √(1 − 2''GM''/''rc''<sup>2</sup>), and notes correctly that in the Earth's field the two differ by only about 10<sup>−18</sup> — far below the sensitivity of the Vessot–Levine Scout D rocket clock experiment he cites.

==Assessment==

This is one of the more disciplined alternative cosmologies in the literature, and its central arithmetic is correct. Working the numbers of section 1 independently: ''R''<sub>4</sub> = 14 × 10<sup>9</sup> ly is 1.324 × 10<sup>26</sup> m; the 3-sphere surface volume 2π<sup>2</sup>''R''<sub>4</sub><sup>3</sup> is 4.59 × 10<sup>79</sup> m<sup>3</sup>; at 5 × 10<sup>−27</sup> kg/m<sup>3</sup> that is ''M''<sub>Σ</sub> = 2.29 × 10<sup>53</sup> kg; and √(0.776 × ''G'' × ''M''<sub>Σ</sub>/''R''<sub>4</sub>) = 2.995 × 10<sup>8</sup> m/s. Suntola's 300 000 km/s is right to better than a tenth of a per cent. The critical-density comparison also checks: with ''H'' = ''c''/''R''<sub>4</sub> = 69.8 km/s/Mpc, ρ<sub>c</sub> = 3''H''<sup>2</sup>/8π''G'' = 9.16 × 10<sup>−27</sup> kg/m<sup>3</sup>, so the stated density is 0.546 of critical, matching his "0.55". His decay rate for the velocity of light checks too: since ''c''<sub>0</sub> ∝ ''R''<sub>4</sub><sup>−1/2</sup> at fixed total mass and d''R''<sub>4</sub>/d''t'' = ''c''<sub>0</sub>, the fractional rate is ''H''/2 = 3.6 × 10<sup>−11</sup> per year, his 4 × 10<sup>−11</sup>. And the magnitude relation ''m'' = ''m''<sub>0</sub> + 5 log ''z'' + 2.5 log(1+''z'') follows exactly from the quoted flux law. It is refreshing to be able to say plainly that a paper's numbers reproduce.

It is worth being clear, though, about what the ''c''<sub>0</sub> = ''c'' result is. Substituting ''M''<sub>Σ</sub> = 2π<sup>2</sup>ρ''R''<sub>4</sub><sup>3</sup> and ρ = ''f''ρ<sub>c</sub> = 3''fc''<sub>0</sub><sup>2</sup>/8π''GR''<sub>4</sub><sup>2</sup> into the balance equation makes ''c''<sub>0</sub> cancel identically, leaving ''f'' = 4/(3π''G''<sub>E</sub>) = 0.547. The agreement is therefore not a numerical coincidence between three independently measured quantities; given the definition ''R''<sub>4</sub> = ''c''/''H'', it is a theorem, and its whole content is the single prediction Ω = 0.55. That is a genuine and testable prediction — but it should be read as one, not as a triple coincidence. Measured against it, the Planck value for the total matter density is Ω<sub>m</sub> = 0.315, and DU has no dark-energy component to make up the difference; the model predicts about 1.7 times more matter than is observed.

The model's most attractive feature is that it is a real expansion model, not a [[Tired Light|tired-light]] one. Because the redshift arises from genuine expansion of the 4-radius, DU inherits the (1 + ''z'') broadening of [[Supernova|supernova]] light curves that has been measured directly and that kills static-universe redshift mechanisms. Its supernova fit is likewise not empty: ''F'' ∝ 1/[''z''<sup>2</sup>(1 + ''z'')] means a luminosity distance ''d''<sub>L</sub> ∝ ''z''√(1 + ''z''), which at ''z'' = 1 is 1.41 ''c''/''H''<sub>0</sub> against 1.54 for ΛCDM and 1.17 for Einstein–de Sitter. DU sits much closer to the accelerating model than to the matter-only one, and the difference from ΛCDM at ''z'' = 1 is only about 0.19 magnitudes. Against the 1998 Perlmutter data Suntola cites, that is close to indistinguishable, so "a perfect match" overstates a fit that the paper presents as a curve through a scatter plot with no residuals or χ<sup>2</sup>. Discriminating the two requires the higher-redshift and much larger samples of the following two decades, which the paper predates.

The clearest failure is the Earth–Moon claim. Attributing 2.8 of the 3.8 cm/yr to expansion is exactly ''H''<sub>0</sub> × 3.84 × 10<sup>8</sup> m = 2.75 cm/yr, so the number is the naive product and not an independent calculation. But the lunar recession is not free to be reassigned: the tidal torque is measured independently, through the observed secular deceleration of Earth's rotation, and it accounts for essentially the whole 3.8 cm/yr. Worse, the same rule applied one step up is catastrophic. ''H''<sub>0</sub> × 1 AU is about 10 metres per year, whereas planetary ranging bounds any secular increase of the astronomical unit to of order 0.1 m/yr — two orders of magnitude smaller. A model in which expansion "occurs everywhere" including inside bound systems is refuted by Solar System ephemerides, and the paper does not confront this.

Several other steps are asserted rather than derived. The geometrical factor ''G''<sub>E</sub> = 0.776, on which the density prediction entirely rests, is stated and referred to the book. The claim that tilted space produces the observed light bending and the perihelion rotation is made in a single sentence with no calculation, which matters because the DU gravitational factor (1 − ''GM''/''rc''<sup>2</sup>) carries a coefficient of 1 where general relativity's metric carries 2 — precisely the factor that distinguishes the full Einstein light deflection from the naive Newtonian value, and that the Cassini measurement of the Shapiro delay now fixes to about one part in 10<sup>5</sup>. Suntola notes that both the path length and the velocity change contribute, so the accounting may work out, but until it is done the agreement is a promise rather than a result. His comparison of equations (17) and (18) is fair and correctly reasoned: in Earth's weak field the DU and GR Doppler predictions differ at order 10<sup>−18</sup>, so the Vessot–Levine experiment cannot separate them.

Two smaller points. The historical remark that spherical space "was rejected" in 1917 is not right — Einstein's 1917 model ''is'' a spatially closed 3-sphere, and it was abandoned for its instability and for Hubble's expansion, not because the fourth dimension was occupied. And the slow decrease of ''c''<sub>0</sub> is arranged to be unobservable by construction, since atomic frequencies are said to track it; that is internally consistent but removes what would otherwise have been the model's sharpest test.

Judged on its own terms, the paper does what it says: it recovers the standard first-order relativistic phenomenology from a global energy balance in absolute time and distance, and it does so with arithmetic that survives checking. Its exposed flank is not the relativistic sector but the cosmological one — Ω = 0.55, and expansion inside bound systems.

==See also==

* [[Tuomo Suntola]]
* [[Expanding Universe]]
* [[Hubble Constant]]
* [[Mach's Principle]]
* [[Speed of Light]]
* [[Time Dilation]]
* [[Dark Energy]]
* [[Cosmological Constant]]
* [[Supernova]]
* [[Umberto Bartocci]]
* [[General Relativity]]

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