View source for The Cosmic Expansion and Its Consequences

{{Infobox paper
| title = The Cosmic Expansion and Its Consequences
| url = [http://www.naturalphilosophy.org/pdf/abstracts/abstracts_5366.pdf Link to paper]
| author = [[Peter Kohut]]
| published = 2010
| journal = [[General Science Journal]]
| num_pages = 16
| keywords = cosmic expansion, quantum dipole, gravitation, mass, cosmic pulsation, dark matter
}}

'''Read the full paper''' [http://www.naturalphilosophy.org/pdf/abstracts/abstracts_5366.pdf here]

==Abstract==

Many consequences, manifestations and characteristics of the cosmic expansion are derived from the basic cosmic equations. The exact values of the whole cosmic expansion an gravitational forces as well as elementary quantum of time are calculated. Also other characteristics like the period of one cosmic pulse (expansion and contraction) or relation E = mc<sup>2</sup> are deduced.

==Overview==

[[Peter Kohut]], writing from Presov in Slovakia, presents this as one instalment of a connected series developing what he calls the dialectic model of the universe. The starting point, taken over from his earlier paper "The basic space-time equation of the Universe", is that the universe is not made of particles in a container but is itself "an increasing network of elementary quantum relations (connections) — quantum dipoles", each dipole a bonded pair of a positive and a negative pole. Every positive pole is connected to every negative one and reciprocally, so a universe with ''k'' poles of each sign contains exactly ''k''<sup>2</sup> connections. Expansion is the successive addition of poles: the transition from state ''k'' to ''k''+1 creates 2''k''+1 new connections. Volume is identified with the number of connections and time with the number of jumps, giving the single founding equation ''V''<sub>''k''</sub> = ''k''<sup>2</sup>, or in dimensional form ''V'' = ''zt''<sup>2</sup>.

Everything else in the paper is presented as consequence rather than assumption. From that one equation Kohut claims to derive the deceleration of expansion, the nature of [[Mass|mass]] and [[Gravity|gravitation]], ''E'' = ''mc''<sup>2</sup>, a numerical value for the total force of the universe, a quantum of time, the period of a full cosmic pulse, and a dissolution of both the entropy death and the [[Dark Matter|dark matter]] problem. The departures from the standard account are sweeping: the universe expands and then contracts in an eternal pulsation with no thermodynamic end state; the expansion is decelerating, not accelerating; the total mass of the universe ''increases'' as ''t''<sup>2/3</sup>; there are three distinct kinds of mass rather than two; the [[Equivalence Principle|equivalence principle]] holds only for slow motion; and no dark matter exists.

==The argument==

===The basic law of motion===

Treating the universe as the three-dimensional surface of a four-dimensional sphere — closed, unbounded, but of finite volume — Kohut relates volume to circumference by ''V'' = ''o''<sup>3</sup>/(4π) and differentiates. Combined with ''V'' = ''zt''<sup>2</sup> this yields what he calls the basic law of motion of the universe:

(d''o''/d''t'')<sup>2</sup> = −2''o'' · d<sup>2</sup>''o''/d''t''<sup>2</sup>

He stresses that this holds not only for the circumference but for ''every'' length parameter, including the length of any individual quantum dipole. Its solution is ''o'' = ''ut''<sup>2/3</sup>, so that d''o''/d''t'' = (2/3)''ut''<sup>−1/3</sup> and d<sup>2</sup>''o''/d''t''<sup>2</sup> = −(2/9)''ut''<sup>−4/3</sup>: the circumference grows, its rate of growth falls, and the acceleration is negative. Hence ''H'' = (d''o''/d''t'')/''o'' = (2/3)''t''<sup>−1</sup> and ''t'' = (2/3)''H''<sup>−1</sup>.

===Mass as resistance to expansion===

During each quantum jump every dipole forms connections to the new poles and passes a small part of its internal energy to them, so it lengthens as its energy falls, according to ''e''<sub>''i''</sub>''d''<sub>''i''</sub> = constant. The dipole's resistance to this stretching ''is'' its mass. Since a deceleration is an acceleration in the opposite direction, Kohut identifies the deceleration of expansion with gravitational acceleration outright: "The mass is manifested by the deceleration of cosmic expansion, which appears as a mass." Short, energetic dipoles resist strongly and are massive; long, weak ones are nearly massless.

From the constancy of ''e''<sub>''i''</sub>''d''<sub>''i''</sub> and ''m''<sub>''i''</sub>''d''<sub>''i''</sub>, and from the law of motion written per dipole as ''c''<sub>''i''</sub><sup>2</sup>/2 = ''g''<sub>''i''</sub>''d''<sub>''i''</sub>, he obtains three quantities that are the same for every dipole in the universe at a given time — ''m''<sub>''i''</sub>''g''<sub>''i''</sub> (the expansion or gravitational force), ''m''<sub>''i''</sub>''c''<sub>''i''</sub> (momentum), and ''m''<sub>''i''</sub>''d''<sub>''i''</sub>. Because ''f''<sub>e</sub> = ''m''<sub>''i''</sub>''g''<sub>''i''</sub> is universal, the total expansion force is simply ''F''<sub>e</sub> = ''f''<sub>e</sub>''k''<sup>2</sup> = ''Mg''<sub>a</sub>, and it equals the total gravitational force ''G'' in magnitude and opposes it in direction. Since ''m''<sub>''i''</sub> and ''g''<sub>''i''</sub> both fall as ''t''<sup>−4/3</sup> while ''k''<sup>2</sup> grows as ''t''<sup>2</sup>, the total mass ''M'' grows as ''t''<sup>2/3</sup> — at the same rate as the length scale, so that ''M''/''r'' is "the basic unchanging cosmic constant during the whole existence of the Universe."

===Deriving E = mc<sup>2</sup>===

The longest possible dipole spans half the circumference, ''o''/2 = ''r'', and the rate at which it lengthens is the maximum speed — the [[Speed of Light|speed of light]]. So ''r'' = (3/2)''ct'' and ''c'' = ''o''/(3''t''), while ''g'' = −d''c''/d''t'', giving ''c''<sup>2</sup> = ''g''·''o''. Kohut notes that had expansion proceeded at constant speed the average speed would exceed the present one by the factor 3/2, so ''c''<sub>a</sub> = (3/2)''c'' — the same 2/3 that appears in the Hubble relation, which he calls the deceleration factor of the universe.

Splitting each dipole's energy into equal attractive and repulsive halves, ''e''<sub>''i''</sub> = ''f''<sub>''i''</sub>''d''<sub>''i''</sub> with ''e''<sub>i''a''</sub> = ''e''<sub>i''r''</sub> = ''e''<sub>''i''</sub>/2, he argues that for the longest dipoles the internal attractive force exactly balances the expansion force, ''f''<sub>i''a''</sub> = ''f''<sub>e</sub> = ''m''<sub>min</sub>''g'' — which is why they are the longest and set the size of the universe. Then ''e''<sub>min</sub> = 2''e''<sub>i''a''</sub> = ''m''<sub>min</sub>''g''·''o'', and substituting ''c''<sup>2</sup> = ''g''·''o'' gives ''e''<sub>min</sub> = ''m''<sub>min</sub>''c''<sup>2</sup>. Because ''e''<sub>''i''</sub>/''m''<sub>''i''</sub> is the same for every dipole, ''e''<sub>''i''</sub> = ''m''<sub>''i''</sub>''c''<sup>2</sup> universally, and by summation ''E'' = ''Mc''<sup>2</sup> for any body and for the universe entire.

===The magnitude of cosmic gravity===

Drawing on his earlier "The unity of Coulomb's and Newton's laws", Kohut expresses the gravitational constant γ in terms of ''h'', ''c'' and the [[Fine Structure Constant|fine structure constant]] α, and defines an elementary gravitational charge ''M''/2''k'' per pole. Because the attractive force per dipole goes as 1/''d''<sub>''i''</sub>, the short dipoles inside particles dominate the total attraction ''F''<sub>a</sub>; gravitation is visible only over long distances because there the attractive forces are not cancelled by the repulsive spatial pressures of dipoles. He recovers a Newtonian form for the universe as a whole, ''G'' = γ(''M''/2)(''M''/2)/(''o''/2)<sup>2</sup>, with the mass divided into two halves separated by the maximum cosmic distance, and shows that the dipole of average energy has length ''d'' = ''r''/4 and therefore four times the average energy and mass of the longest ones. Combining ''Mg'' = ''c''<sup>4</sup>/(4γ) with ''G'' = ''Mg''/4 gives the paper's headline number:

''G'' = ''F''<sub>e</sub> = ''c''<sup>4</sup>/(16γ) = 7.566 × 10<sup>42</sup> N

===Entropy, dark matter, and three masses===

Because attraction and repulsion are in permanent dynamic rather than static equilibrium, Kohut holds that the universe "will never come to its total cosmic death predicted by the law of entropy increase". The entropy law, derived from mechanical motion in a closed system, cannot handle the constantly growing network of connections, nor the widening energy gap between the very short dipoles inside atoms and the very long [[Vacuum|vacuum]] dipoles between bodies.

He then distinguishes three masses. ''Internal'' mass is the summed energy of a body's own dipoles; ''external gravitational'' mass is fixed by its number of poles; ''inertial'' mass expresses its resistance to acceleration relative to other objects. At rest all three coincide. In motion the gravitational mass is unchanged, the inertial mass rises, and the internal mass ''falls'' — the dipoles lengthening so the body can better "puncture" the resistance of the surrounding vacuum, with the slowing of all internal processes appearing as [[Time Dilation|time dilation]]. The [[Equivalence Principle|equivalence]] of inertial and gravitational mass therefore holds only at low speed, and fails altogether for [[Photon|photons]] and [[Neutrino|neutrinos]], which have zero rest mass but a gravitational mass set by their pole count. From this he concludes that [[Dark Matter|dark matter]] is an artefact: counting the gravitational mass of all photons and neutrinos, "no mass is missing for the explanation of a whole amount of gravitational forces in the observed system, e.g. galaxy."

===The cosmic pulse and the quantum of time===

Treating a free photon as a pulsating dipole with ''e''<sub>''i''</sub> = ''hν''<sub>''i''</sub> = ''hc''/λ<sub>''i''</sub>, and combining this with the Coulomb-type relation ''e''<sub>''i''</sub>''d''<sub>''i''</sub> ∝ ''hc''/α, Kohut obtains ''d''<sub>''i''</sub>/λ<sub>''i''</sub> ∝ 1/α and ''d''<sub>''i''</sub>/''t''<sub>''i''</sub> = ''c''. Applying this to the longest dipole makes its pulse period the period of one complete cosmic cycle. The result is a factor 3π/(4α) = 322.88, so that

''T''<sub>cyc</sub> = 3π''t''/(2α) = 9,040 billion years, ''T''<sub>exp</sub> = 3π''t''/(4α) = 4,520 billion years

If the present age is 14 billion years, expansion has 4,506 billion years still to run. He also derives an elementary quantum of time Δ''t'' = 1.228 × 10<sup>−44</sup> s, so that one second contains 8.144 × 10<sup>43</sup> quantum jumps, and insists the causal order is the reverse of the usual one: "the quantum jump is not measured by elapsed time, but contrarily, the time is measured by the number of elementary quantum jumps." The corresponding counts are ''k'' = 3.6 × 10<sup>61</sup> poles of each sign, ''k''<sup>2</sup> = 1.295 × 10<sup>123</sup> connections, a maximum ''n'' = 1.16 × 10<sup>64</sup> jumps to the turnaround, an average dipole energy ''e'' = 9.29 × 10<sup>−54</sup> J and average length ''d'' = ''c''/(4''H'') = 4.97 × 10<sup>25</sup> m. In the contraction phase the time arrow reverses, each symmetric jump annihilating a pole pair, the contractive force being balanced by antigravity, until the universe is again a single dipole and a new [[Big Bang|Big Bang]] begins.

==Assessment==

The attractive feature of this paper is the severity of its starting point. One combinatorial premise — a fully connected bipartite network of ''k'' positive and ''k'' negative poles, hence ''k''<sup>2</sup> links — is asked to generate everything else, and Kohut is consistent in applying it. The identification of mass with resistance to cosmic expansion is a genuinely Machian idea, in the tradition of taking [[Inertia|inertia]] to be a relation to the whole universe rather than an intrinsic property, and the invariants ''m''<sub>''i''</sub>''d''<sub>''i''</sub>, ''m''<sub>''i''</sub>''c''<sub>''i''</sub>, ''m''<sub>''i''</sub>''g''<sub>''i''</sub> are internally coherent given his premises. His numerical results are also self-consistent where they can be checked: ''G'' = ''c''<sup>4</sup>/(16γ) does evaluate to about 7.6 × 10<sup>42</sup> N, 1/(1.228 × 10<sup>−44</sup>) is indeed 8.14 × 10<sup>43</sup>, ''k''<sup>2</sup> matches ''k'', and ''c''/(4''H'') with ''t'' = 14 billion years gives his 4.97 × 10<sup>25</sup> m. Nor is he shy about the model's most vulnerable predictions, which he states in plain figures rather than hedging them.

The difficulties begin with the derivations that are presented as such. ''E'' = ''mc''<sup>2</sup> is not derived; it is arranged. The chain runs ''e''<sub>min</sub> = ''m''<sub>min</sub>''g''·''o'' and ''c''<sup>2</sup> = ''g''·''o'', so the result follows the moment one accepts that the longest dipole's attractive force exactly equals ''f''<sub>e</sub>. That equality is asserted, justified only by the circular remark that it is "the reason why they are the longest". The step from ''e''<sub>''i''</sub>''d''<sub>''i''</sub> = constant to ''m''<sub>''i''</sub>''d''<sub>''i''</sub> = constant likewise presupposes proportionality of energy to mass, which is what was to be shown. Similarly, "the deceleration of expansion is the gravitational acceleration" is a redefinition, not a mechanism: it explains why gravity has the magnitude it has only by having earlier fixed that magnitude from the same equation.

Several results are less novel than presented. ''H'' = (2/3)''t''<sup>−1</sup>, ''a'' ∝ ''t''<sup>2/3</sup> and monotonic deceleration are exactly the Einstein–de Sitter solution of standard matter-dominated cosmology; Kohut's network reproduces a known model rather than a new one, and inherits its problems. Chief among these is that expansion is not observed to decelerate in this way. The dimming of high-redshift Type Ia supernovae relative to an ''a'' ∝ ''t''<sup>2/3</sup> universe is the measurement that forced the [[Cosmological Constant|cosmological constant]] back into cosmology, and a model in which the acceleration is negative at all times contradicts it directly. The paper does not mention supernova cosmology at all. A second conflict is with the acoustic peak structure of the [[Cosmic Microwave Background|cosmic microwave background]], which the model does not address, and a third with the [[Big Bang|Big Bang]] nucleosynthesis abundances, which depend on the expansion rate at a specific epoch.

The claim that the total mass ''M'' of the universe grows as ''t''<sup>2/3</sup> is presented as a consequence, but it is a very large one: mass-energy is not conserved in this model, and no account is given of where it comes from or how local conservation, which is extremely well tested, survives. The dark-matter argument is the weakest part of the paper. Assigning [[Photon|photons]] and [[Neutrino|neutrinos]] a gravitational mass proportional to pole count, independent of energy, is not merely unorthodox; it is quantitatively hopeless as an explanation of galactic rotation curves, since what those curves require is a specific ''radial distribution'' of mass extending well beyond the visible disc, and nothing in the paper produces such a profile. No number is offered for the total photon and neutrino gravitational mass of a galaxy, so the claim that "no mass is missing" is unsupported arithmetic.

Finally, the three-mass scheme is asserted rather than developed — Kohut says twice that the mathematical relation between the three forms "will be derived in a separate article" — and the claim that internal mass ''decreases'' with speed while inertial mass increases has no derivation here and is hard to reconcile with the fact that the two are supposed to be equal at rest and that ''E'' = ''mc''<sup>2</sup> is supposed to hold generally. The pulsation period of 9,040 billion years hangs on the identification of the longest dipole's photon-like pulse with a cosmic cycle, an analogy rather than an argument, and the reversal of the time arrow in the contracting phase is stated without any account of how the thermodynamic asymmetry would reverse.

Judged on its own terms, the paper is a philosophically motivated construction — Kohut's repeated word is "dialectic" — that achieves impressive internal economy at the cost of leaving its central steps asserted, and whose one sharp cosmological prediction, permanent deceleration, is the one that observation has gone against.

==See also==

* [[Peter Kohut]]
* [[Expanding Universe]]
* [[Big Bang]]
* [[Dark Matter]]
* [[Gravity]]
* [[Mass]]
* [[Inertia]]
* [[Equivalence Principle]]
* [[Hubble Constant]]
* [[Fine Structure Constant]]
* [[Speed of Light]]

[[Category:Scientific Paper|cosmic expansion consequences]]

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