Wavepacket of the Universe and its spreading

Wavepackets in quantum mechanics spread and the Universe in cosmology expands. We discuss a formalism where the two effects can be unified. The basic assumption is that the Universe is determined by a unitarily evolving wavepacket defined on space-time. Space-time is static but the Universe is dynamic. Spreading analogous to expansion known from observational cosmology is obtained if one regards time evolution as a discrete process with probabilities of jumps determined by a variational principle employing Kolmogorov-Nagumo-R\'enyi averages. The choice of the R\'enyi calculus implies that the form of the Universe involves an implicit fractal structure. The formalism automatically leads to two types of "time" parameters: $\tau$, with dimension of $x^0$, and dimensionless $\varepsilon=\ln \epsilon_\tau$, related to the form of diffeomorphism that defines the dynamics. There is no preferred time foliation, but effectively the dynamics leads to asymptotic concentration of the Universe on spacelike surfaces that propagate in space-time. The analysis is performed explicitly in $1+1$ dimensions, but the unitary evolution operator is brought to a form that makes generalizations to other dimensions and other fields quite natural.Comment: v1 preliminary report, v2 includes sections on the explicit form of the evolution operator, v3 includes an explicit analysis based on Kolmogorov-Nagumo-Renyi averaging, v4 section on 1+3 generalization is corrected, v5 conflict of notation in Bernoulli and Renyi forms is fixed; v6 accepted in Int.J.Theor.Phy

How to play two-players restricted quantum games with 10 cards

We show that it is perfectly possible to play 'restricted' two-players, two-strategies quantum games proposed originally by Marinatto and Weber having as the only equipment a pack of 10 cards. The 'quantum board' of such a model of these quantum games is an extreme simplification of 'macroscopic quantum machines' proposed by one of the authors in numerous papers that allow to simulate by macroscopic means various experiments performed on two entangled quantum objectsComment: 4 pages, 3 figure

Leo Apostel Centre for Interdisciplinary Studies, Vrije Universiteit Brussel,

How to play two-players restricted quantum games with 10 card

Quantum morphogenesis : A variation on Thom’s catastrophe theory

Noncommutative propositions are characteristic of both quantum and nonquantum (sociological, biological, and psychological) situations. In a Hilbert space model, states, understood as correlations between all the possible propositions, are represented by density matrices. If systems in question interact via feedback with environment, their dynamics is nonlinear. Nonlinear evolutions of density matrices lead to the phenomenon of morphogenesis that may occur in noncommutative systems. Several explicit exactly solvable models are presented, including “birth and death of an organism” and “development of complementary properties.”Non UBCReviewedFacult