Related papers: Quantum mechanics on profinite groups and partial …
The uncertainty relation of three quantities in quantum mechanics is estimated in terms of commutators. The Pauli matrices are used to find a contribution of third-order commutators. The resulting inequality refines the Heisenberg…
The theory of quantum mechanics is examined using non-standard real numbers, called quantum real numbers (qr-numbers), that are constructed from standard Hilbert space entities. Our goal is to resolve some of the paradoxical features of the…
The purpose of this paper is to show that the mathematics of quantum mechanics (QM) is the mathematics of set partitions (which specify indefiniteness and definiteness) linearized to vector spaces, particularly in Hilbert spaces. That is,…
In a previous preprint (quant-ph/0012122) we introduced a ``contextual objectivity" formulation of quantum mechanics (QM). A central feature of this approach is to define the quantum state in physical rather than in mathematical terms, in…
In the tradition of toy models of quantum mechanics in vector spaces over finite fields (e.g., Schumacher and Westmoreland's "modal quantum theory"), one finite field stands out, 2, since vectors over 2 have an interpretation as natural…
In this paper we develope the main ideas of the quantized version of affinely-rigid (homogeneously deformable) motion. We base our consideration on the usual Schr\"odinger formulation of quantum mechanics in the configuration manifold which…
The properties which give quantum mechanics its unique character - unitarity, complementarity, non-commutativity, uncertainty, nonlocality - derive from the algebraic structure of Hermitian operators acting on the wavefunction in complex…
We propose terminology to classify interpretations of quantum mechanics and models that modify or complete quantum mechanics. Our focus is on models which have previously been referred to as superdeterministic (strong or weak), retrocausal…
The development of the new logic of partitions (= equivalence relations) dual to the usual Boolean logic of subsets, and its quantitative version as the new logical theory of information provide the basic mathematical concepts to describe…
Non-relativistic quantum mechanics is shown to emerge from classical mechanics through the requirement of a relativity principle based on special transformations acting on position and momentum uncertainties. These transformations keep the…
Quantum mechanics is a special kind of description of motion. The concept of wave function itself implies the openness of quantum system. We show that quantum mechanics describes the quantum correlation, i.e., entanglement, and information…
Wigner distributions for quantum mechanical systems whose configuration space is a finite group of odd order are defined so that they correctly reproduce the marginals and have desirable transformation properties under left and right…
In the past decade, the toolkit of quantum information has been expanded to include processes in which the basic operations do not have definite causal relations. Originally considered in the context of the unification of quantum mechanics…
Mathematical core of quantum mechanics is the theory of unitary representations of symmetries of physical systems. We argue that quantum behavior is a natural result of extraction of "observable" information about systems containing…
Four level quantum systems, known as quartits, and their relation to two- qubit systems are investigated group theoretically. Following the spirit of Klein's lectures on the icosahedron and their relation to Hopf sphere bra- tions,…
New status in quantum mechanics is connected with recent achievements in the inverse problem. With its help instead of about ten exactly solvable models which serve as a basis of the contemporary education there are infinite (!) number,…
For an arbitrary preparation, quantum mechanical descriptions refer to the complementary contexts set by incompatible measurements. We argue that an arbitrary preparation, therefore, should be described with respect to such a context by its…
It is shown that the independence of the continuum hypothesis points to the unique definite status of the set of intermediate cardinality: the intermediate set exists only as a subset of continuum. This latent status is a consequence of…
Incompatibility between conjugate variables and complementary pictures comes in two kinds, exclusive of one another. The first kind is unconditional, and the second conditional on quantum's indivisibility. We employ this distinction to…
In this paper we will present tha main features of what can be called Schwinger's foundational approach to Quantum Mechanics. The basic ingredients of this formulation are the \textit{selective measurements}, whose algebraic composition…