Related papers: How much complementarity?
In this talk we entertain the possibility that the synthesis of general covariance and quantum mechanics requires an extension of the basic kinematical setup of quantum mechanics. According to the holographic principle, regions of spacetime…
We determine the ring structure of the equivariant quantum cohomology of the Hilbert scheme of points in the complex plane. The operator of quantum multiplication by the divisor class is a nonstationary deformation of the quantum…
We describe a scheme of quantum mechanics in which the Hilbert space and linear operators are only secondary structures of the theory. As primary structures we consider observables, elements of noncommutative algebra, and the physical…
Unitarity is a pillar of quantum theory. Nevertheless, it is also a source of several of its conceptual problems. We note that in a world where measurements are relational, as is the case in gravitation, quantum mechanics exhibits a…
We reveal strong and weak inequalities relating two fundamental macroscopic quantum geometric quantities, the quantum distance and Berry phase, for closed paths in the Hilbert space of wavefunctions. We recount the role of quantum geometry…
The exponential modalities of linear logic have been used by various authors to model infinite-dimensional quantum systems. This paper explains how these modalities can also give rise to the complementarity principle of quantum mechanics.…
The mathematical model of orthodox quantum mechanics has been critically examined and some deficiencies have been summarized. The model based on the extended Hilbert space and free of these shortages has been proposed; parameters being…
The concept of quantum coherence, including various ways to quantify the degree of coherence with respect to the prescribed basis, is currently the subject of active research. The complementarity of quantum coherence in different bases was…
We present critical arguments against individual interpretation of Bohr's complementarity and Heisenberg's uncertainty principles. Statistical interpretation of these principles is discussed in the contextual framework. We support the…
Quantum theory and Lorentz structure are the twin pillars of fundamental physics today. With quantum theory kept and Lorentz structure replaced by Euclidean Jordan algebra --- a more fundamental structure, one naturally arrives at the…
A foundation of quantum mechanics based on the concepts of focusing and symmetry is proposed. Focusing is connected to c-variables - inaccessible conceptually derived variables; several examples of such variables are given. The focus is…
We start to develop the quantization formalism in a hyperbolic Hilbert space. Generalizing Born's probability interpretation, we found that unitary transformations in such a Hilbert space represent a new class of transformations of…
This paper outlines the common ground between the motivations lying behind Hans Primas' algebraic approach to quantum phenomena and those lying behind David Bohm's approach which led to his notion of implicate/explicate order. This…
In quantum mechanics, the selfadjoint Hilbert space operators play a triple role as observables, generators of the dynamical groups and statistical operators defining the mixed states. One might expect that this is typical of Hilbert space…
An algebraic structure underlying the quantity calculus is proposed consisting in an algebraic fiber bundle, that is, a base structure which is a free Abelian group together with fibers which are one dimensional vector spaces, all of them…
We attempt to contribute some novel points of view to the "foundations of quantum mechanics", using mathematical tools from "quantum probability theory" (such as the theory of operator algebras). We first introduce an abstract algebraic…
Standard particle theory is based on quantized matter embedded in a classical geometry. Here, a complementary model is proposed, based on classical matter -- massive bodies, without quantum properties -- embedded in a quantum geometry. It…
We derive fundamental constraints for the Schur complement of positive matrices, which provide an operator strengthening to recently established information inequalities for quantum covariance matrices, including strong subadditivity. This…
We argue that the demand of background independence in a quantum theory of gravity calls for an extension of standard geometric quantum mechanics. We discuss a possible kinematical and dynamical generalization of the latter by way of a…
On the base of years of experience of working on the problem of the physical foundation of quantum mechanics the author offers principles of solving it. Under certain pressure of mathematical formalism there has raised a hypothesis of…