Related papers: Hardy's Second Axiom is insufficiently general
We generalize the classical probability frame by adopting a wider family of random variables that includes nondeterministic ones. The frame that emerges is known to host a ''classical'' extension of quantum mechanics. We discuss the notion…
The extraction of classical degrees of freedom in quantum mechanics is studied in the stochastic variational method. By using this classicalization, a hybrid model constructed from quantum and classical variables (quantum-classical hybrids)…
The definitions of classical and quantum singularities in general relativity are reviewed. The occurence of quantum mechanical singularities in certain spherically symmetric and cylindrically symmetric (including infinite line…
Both classical and respectively quantum observables can be modeled as somewhat similar examples of random variables. In such a model the associated measurements preserve the values spectrum of an observable but change the corresponding…
The standard axiomatization of quantum mechanics (QM) is not fully explicit about the role of the time-parameter. Especially, the time reference within the probability algorithm (the Born Rule, BR) is unclear. Using a plausible principle…
Quantum mechanics is essentially a statistical theory. Classical mechanics, however, is usually not viewed as being inherently statistical. Nevertheless, the latter can also be formulated statistically. Furthermore, a statistical…
Quantum mechanics states that a particle emitted at point (x_1,t_1) and detected at point (x_2,t_2) does not travel along a definite path between the two points. This conclusion arises essentially from the analysis of the two-slit…
An analysis using classical stochastic processes is used to construct a consistent system of quantum counterfactual reasoning. When applied to a counterfactual version of Hardy's paradox, it shows that the probabilistic character of quantum…
The origin of nonclassicality in quantum mechanics (QM) has been investigated recently by a number of authors with a view to identifying axioms that would single out quantum mechanics as a special theory within a broader framework such as…
A new proof of the impossibility of a universal quantum-classical dynamics is given. It has at least two consequences. The standard paradigm ``quantum system is measured by a classical apparatus" is untenable, while a quantum matter can be…
The space P of pure states of any physical system, classical or quantum, is identified as a Poisson space with a transition probability. The latter is a function p: PxP -> [0,1]; in addition, a Poisson bracket is defined for functions on P.…
A new approach to quantum mechanics based on independence of the Continuum Hypothesis is proposed. In one-dimensional case, it is shown that the properties of the set of intermediate cardinality coincide with quantum phenomenology.
We consider the hypothesis that quantum mechanics is an approximation to another, cosmological theory, accurate only for the description of subsystems of the universe. Quantum theory is then to be derived from the cosmological theory by…
Elaborating on a previous work by Marolf et al, we relate some exact results in quantum field theory and statistical mechanics to the Bekenstein universal bound on entropy. Specifically, we consider the relative entropy between the vacuum…
The Hellmann-Feynman, virial and comparison theorems are three fundamental theorems of quantum mechanics. For the first two, counterparts exist for classical mechanics with relativistic or nonrelativistic kinetic energy. It is shown here…
How can quantum mechanics be (i) the fundamental theoretical framework of contemporary physics and (ii) a probability calculus that presupposes the events to which, and on the basis of which, it assigns probabilities? The question is…
Quantum particles and classical particles are described in a common setting of classical statistical physics. The property of a particle being "classical" or "quantum" ceases to be a basic conceptual difference. The dynamics differs,…
Hidden-variable models aim to reproduce the results of quantum theory and to satisfy our classical intuition. Their refutation is usually based on deriving predictions that are different from those of quantum mechanics. Here instead we…
We discuss that there is a crucial contradiction within quantum mechanics. We derive a proposition concerning a quantum expectation value under the assumption of the existence of the directions in a spin-1/2 system. The quantum predictions…
The geometry of the classical phase space C of a finite number of degrees of freedom determines the possible duality symmetries of the corresponding quantum mechanics. Under duality we understand the relativity of the notion of a quantum…