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A recent understanding on how quantum effects may affect black-hole evolution opens new scenarios for dark matter, in connection with the presence of black holes in the very early universe. Quantum fluctuations of the geometry allow for…
Is quantum mechanics about 'states'? Or is it basically another kind of probability theory? It is argued that the elementary formalism of quantum mechanics operates as a well-justified alternative to 'classical' instantiations of a…
Non-relativistic quantum mechanics is reformulated here based on the idea that relational properties among quantum systems, instead of the independent properties of a quantum system, are the most fundamental elements to construct quantum…
When it comes to performing thought experiments with black holes, Einstein-Bohr like discussions have to be re-opened. For instance one can ask what happens to the quantum state of a black hole when the wave function of a single ingoing…
Heisenberg's uncertainty principle is formulated for a set of generalized measurements within the framework of majorization theory, resulting in a partial uncertainty order on probability vectors that is stronger than those based on…
A description of the motion in noninertial reference frames by means of the inclusion of high time derivatives is studied. Incompleteness of the description of physical reality is a problem of any theory, both in quantum mechanics and…
The present paper is based upon equations obtained in an earlier paper by the author devoted to a new formulation of quantum electrodynamics. The equations describe the structure of the electron as well as its motion in external fields,…
We formulate quantum mechanics in spacetimes with real-order fractional geometry and more general factorizable measures. In spacetimes where coordinates and momenta span the whole real line, Heisenberg's principle is proven and the…
We exhibit three inequalities involving quantum measurement, all of which are sharp and state independent. The first inequality bounds the performance of joint measurement. The second quantifies the trade-off between the measurement quality…
Two generalizations of Kempf's quadratic canonical commutation relation in one dimension are considered. The first one is the most general quadratic commutation relation. The corresponding nonzero minimal uncertainties in position and…
A generalization of the thermodynamic uncertainty relations is proposed. It is done by introducing of an additional term proportional to the interior energy into the standard thermodynamic uncertainty relation that leads to existence of the…
I review arguments demonstrating how the concept of "particle" numbers arises in the form of equidistant energy eigenvalues of coupled harmonic oscillators representing free fields. Their quantum numbers (numbers of nodes of the wave…
It is shown that q-deformed quantum mechanics (systems with q-deformed Heisenberg commutation relations) can be interpreted as an ordinary quantum mechanics on Kaehler manifolds, or as a quantum theory with second (or first)- class…
In static classical statistical systems the problem of information transport from a boundary to the bulk finds a simple description in terms of wave functions or density matrices. While the transfer matrix formalism is a type of Heisenberg…
The unified generalized non-local quantum kinetic and hydrodynamic theory is applied for mathematical modeling of objects in the giant scale diapason from the galaxy and Universe scale to atom structures. The principle of universal…
In the q-deformed theory the perturbation approach can be expressed in terms of two pairs of undeformed position and momentum operators. There are two configuration spaces. Correspondingly there are two q-perturbation Hamiltonians, one…
This work is a continuation of studies presented in the papers arXiv:0911.5597, arXiv:1003.4523. In the work it is demonstrated that with the use of one and the same parameter deformation may be described for several cases of the General…
The origin of black hole entropy and the black hole information problem provide important clues for trying to piece together a quantum theory of gravity. Thus far, discussions on this topic have mostly assumed that in a consistent theory of…
Classical statistical average values are generally generalized to average values of quantum mechanics, it is discovered that quantum mechanics is direct generalization of classical statistical mechanics, and we generally deduce both a new…
The question of general covariance in quantum gravity is considered in the first post-Newtonian approximation. Transformation properties of observable quantities under deformations of a reference frame, induced by variations of the gauge…