cosmology of twin universes Cosmology of twin universes (p. 11)
14) The problem of light emission
...Assume that the energy production by light sources occurs via collisions. The collision frequency can be written as :
(103) where n is the number density, Q the collision cross-section and v the thermal velocity. Assume that all these quantities obey our set of relations, that is:
(104)
which gives :
...Assume now that the characteristic amount of energy Ei, associated with this energy production reaction, varies like R(t). The energy emission rate then varies like :
(105)
...Thus, the emission rate would have been higher in the past. Since, in this model, the energy is conserved during the photon's journey, the receiver would measure a higher luminosity, which would vary like (1+z)1/2.
...If we examine the data presented by Barthel and Miley, and plot Log(P) – 0.5 Log(1+z) as a function of z, we obtain something relatively constant.
15) Some remarks regarding possible comparisons with observational data.
15.1) Local relativistic effects.
...From the classical model of General Relativity, many tests have been devised. The first ones concerned local tests, such as the precession of the perihelion of Mercury or the time delay of radar echoes. There is no a priori incompatibility between these tests and the model presented here. Indeed, according to the results of the numerical simulations, the matter density in the region of the twin fold corresponding to the vicinity of the Sun is highly rarefied, because the antipodal mass is pushed away by the mass. Thus, the second term on the right-hand side of equation (1) can be neglected:
(106) S = c ( T – A(T) ) » c T
so that, locally, the Einstein equation becomes an approximate form of equation (1). Under these conditions, from equation (1), we recover the classical local observational features, such as the precession of the perihelion, etc.
15.2) Regarding strong field tests from binary pulsars.
...A pulsar is supposed to be an object located in our galaxy. If we again assume that the antipodal matter is very rarefied in the conjugated adjacent fold, the field equation becomes:
(107) S » c T
that is, the Einstein equation. Thus, the observed effects [30] are compatible with both equation (1) and equation (2).
16) The problem of electromagnetism and other aspects of physics.
...We propose a new cosmological model. As mentioned earlier, this model fundamentally does not contain electromagnetic phenomena, nor strong or weak interactions, just like the classical model does not either. Only a fully unified field theory could incorporate them. In these conditions, is it legitimate to apply gauge analysis to the charged particle, that is, to determine how the Bohr radius varies with R? This question is debatable (hence the examination of this question by the author in his formal paper [13], section 9). The same applies to the strong and weak interactions and their associated characteristic lengths (in order to provide a complete and new description of cosmic evolution, including nucleosynthesis, one would have to introduce, in this constant energy model, time-dependent "constants").
Personally, I think that the cosmological model is far from being complete. For example, the so-called cosmological constant Λ could be added, according to the suggestion of J.M. Souriau:
(108) S = c ( T + Λ g – A(T) – Λ A(g))
or:
(109) S = c ( T + Λ g – T* – Λ g*)
where T* and g* = A(g) are respectively the stress tensor and the metric tensor associated with the conjugated antipodal region.
...This work simply suggests that the geometry of the universe could be somewhat different from our standard view. Perhaps a unified model (gravitation + electromagnetism) could be constructed, by introducing complex tensors S, T and A(T) in equation (1). On the other hand, one could move from a geometry S³ × R¹ to a twin geometry based on the covering of a projective P⁴ by a sphere S⁴. It would then perhaps be possible to address CPT symmetry, and thus take into account the matter-antimatter duality (the antipodal matter would behave like antimatter and constitute the missing "cosmological antimatter," as suggested by Andrei Sakharov and Novikov in 1967 [36,37], as well as the authors [38,39 and 402]). But this, we acknowledge, is a difficult mathematical task.
...In a Kaluza model, a five-dimensional manifold is considered. Thus, electromagnetism can be introduced, although it is still unclear what this fifth dimension exactly represents. Note that, locally, the model is equivalent to a Kaluza model with a fifth dimension limited to the values ±1.
In this model, the status of the Klein-Gordon equation is the same as in classical General Relativity.