15 research outputs found
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: , with
dimension of , and dimensionless , 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 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
Consistent use of paradoxes in deriving constraints on the dynamics of physical systems and of no-go-theorems
The classical methods used by recursion theory and formal logic to block
paradoxes do not work in quantum information theory. Since quantum information
can exist as a coherent superposition of the classical ``yes'' and ``no''
states, certain tasks which are not conceivable in the classical setting can be
performed in the quantum setting. Classical logical inconsistencies do not
arise, since there exist fixed point states of the diagonalization operator. In
particular, closed timelike curves need not be eliminated in the quantum
setting, since they would not lead to any paradoxical outcome controllability.
Quantum information theory can also be subjected to the treatment of
inconsistent information in databases and expert systems. It is suggested that
any two pieces of contradicting information are stored and processed as
coherent superposition. In order to be tractable, this strategy requires
quantum computation.Comment: 10 pages, latex, no figure
Leo Apostel Centre for Interdisciplinary Studies, Vrije Universiteit Brussel,
How to play two-players restricted quantum games with 10 card