A retrospective view on the history of natural sciences in XX-XXI

Olkhovsky, V. S.

doi:10.4236/ns.2010.23035

Cited by 1 publication

(1 citation statement)

References 109 publications

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“…We did also analyzed in (Olkhovsky, 2010) these three problems in the context of other aspects, first of all regarding the increasing discussions between the supporters of two different meta-theoretical, meta-philosophical doctrines: either the beginning of the Universe formation from vacuum ("nothing") is either a result of the irrational randomness after passing from other space-time dimensions or from other universe, caused by some unknown process, or a result of the creation of the expanding Universe (together with the laws of its functioning) by the supreme intelligent design from nigilo.…”

Section: A Brief Review On the Problems Of The Universe Originmentioning

confidence: 99%

A Fully Quantum Model of Big Bang

Maydanyuk¹,

Popolo²,

Olkhovsky³

et al. 2012

Theoretical Concepts of Quantum Mechanics

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16www.intechopen.com 2 Will-be-set-by-IN-TECH (Vilenkin, 1994) could seem to be the most natural and clear description, where the wave function should represent an outgoing wave only in the enough large value of the scale factor a. However, is really such a wave free in the asymptotic region? In order to draw attention on the increase of the modulus of the potential with increasing value of the scale factor a and increasing magnitude of the gradient of such a potential, acting on this wave "through the barrier", then one come to a serious contradiction: the influence of the potential on this wave increases strongly with a! Now a new question has appeared: what should the wave represent in general in the cosmological problem? This problem connects with another and more general one in quantum physics -the real importance to define a "free" wave inside strong fields.T o this aim we need a mathematical stable tool to study it. It is unclear whether a connection between exact solutions for the wave function at turning point and "free" wave defined in the asymptotic region is correct. Note that the semiclassical formula of the penetrability of the barrier is constructed on the basis of wave which is defined concerning zero potential at infinity, i.e. this wave should be free outgoing in the asymptotic region. But in the cosmological problem we have opposite case, when the force acting on the wave increases up to infinity in the asymptotic region. At the same time, deformations of the shape of the potential outside the barrier cannot change the penetrability calculated in the framework of the semiclassical approach (up to the second order). An answer to such problem can be found in non-locality of definition of the penetrability in quantum mechanics, which is reduced to minimum in the semiclassical approach (i. e. this is so called "error" of the cosmological semiclassical approach). The problem of the correct definition of the wave in cosmology is reinforced else more, if one wants to calculate the incident and reflected waves in the internal region. Even with the known exact solution for the wave function there is uncertainty in determination of these waves! But, namely, the standard definition of the coefficients of penetrability and reflection is based on them. In particular, we have not found papers where the coefficient of reflection is defined and estimated in this problem (which differs essentially from unity at the energy of radiation close to the height of the barrier and, therefore, such a characteristics could be interesting from a physical point of view). Note that the semiclassical approximation put serious limits to the possibility of its definition at all (Landau & Lifshitz, 1989). Thus, in order to estimate probability of the formation of the Universe as accurately as possible, we need a fully quantum definition of the wave. Note that the non-semiclassical penetrability of the barrier in the cosmological problems has not been studied in detail and, therefore, a development of fully quantum methods for ...

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Section: A Brief Review On the Problems Of The Universe Originmentioning

confidence: 99%