Related papers: Forms of Quantum Nonseparability and Related Philo…
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…
This paper addresses the question why quantum mechanics is formulated in a unitary Hilbert space, i.e. in a manifestly complex setting. Investigating the linear dynamics of real quantum theory in a finite-dimensional Euclidean Hilbert space…
We present a general formalism with the aim of describing the situation of an entity, how it is, how it reacts to experiments, how we can make statistics with it, and how it changes under the influence of the rest of the universe. Therefore…
The complex Hilbert space of standard quantum mechanics may be treated as a real Hilbert space. The pure states of the complex theory become mixed states in the real formulation. It is then possible to generalize standard quantum mechanics,…
The conceptual problems in quantum mechanics -- related to the collapse of the wave function, the particle-wave duality, the meaning of measurement -- arise from the need to ascribe particle character to the wave function. As will be shown,…
Some notes about quantum physics, an interpretation if one wishes, are put forward, insisting on `closely following the mathematics/formalism, the `nuts and bolts of what quantum physics says'. These, basically well-known, issues seem to…
Non-relativistic quantum mechanics for a free particle is shown to emerge from classical mechanics through an invariance principle under transformations that preserve the Heisenberg position-momentum inequality. These transformations are…
Algebraic approach to quantum non - separability is applied to the case of two qubits. It is based on the partition of the algebra of observables into independent subalgebras and the tensor product structure of the Hilbert space is not…
Quantum mechanics is formulated as a geometric theory on a Hilbert manifold. Images of charts on the manifold are allowed to belong to arbitrary Hilbert spaces of functions including spaces of generalized functions. Tensor equations in this…
Despite its enormous empirical success, the formalism of quantum theory still raises fundamental questions: why is nature described in terms of complex Hilbert spaces, and what modifications of it could we reasonably expect to find in some…
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…
In this article, the weakest possible theorem providing a foundation for the Hilbert space formalism of quantum theory is stated. The necessary postulates are formulated, and the mathematics is spelt out in detail. It is argued that, from…
Assuming the validity of the equivalence principle in the quantum regime, we argue that one of the assumptions of the usual definition of quantum mechanics, namely separation between the ``classical'' detector and the ``quantum'' system,…
Quantum mechanics, one of the most successful theories in the history of science, was created to account for physical systems not describable by classical physics. Though it is consistent with all experiments conducted thus far, many of its…
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…
The quantum mechanical formalism for position and momentum of a particle in a one dimensional cyclic lattice is constructively developed. Some mathematical features characteristic of the finite dimensional Hilbert space are compared with…
In this paper we attempt to discuss what has Kochen-Specker (KS) theorem to say about physical invariance and quantum individuality. In particular, we will discuss the impossibility of making reference to objective physical properties…
Nonseparability - multipartite states that cannot be factorized - is one of the most striking features of quantum mechanics, as it gives rise to entanglement and non-causal correlations. In quantum computing, it also contributes directly to…
Gaussian quantum systems exhibit many explicitly quantum effects but can be simulated classically. Using both the Hilbert space (Koopman) and the phase-space (Moyal) formalisms we investigate how robust this classicality is. We find…
The problem of understanding quantum mechanics is in large measure the problem of finding appropriate ways of thinking about the spatial and temporal aspects of the physical world. The standard, substantival, set-theoretic conception of…