Related papers: Minimal length: A source of quantum non-locality
Hilbert space combines the properties of two fundamentally different types of mathematical spaces: vector space and metric space. While the vector-space aspects of Hilbert space, such as formation of linear combinations of state vectors,…
Here it is shown that the simplest description of Bell's experiment according to the canon of von Neumann's theory of measurement explicitly assumes the (Quantum Mechanics-language equivalent of the classical) condition of Locality. This…
A century after the advent of Quantum Mechanics and General Relativity, both theories enjoy incredible empirical success, constituting the cornerstones of modern physics. Yet, paradoxically, they suffer from deep-rooted, so-far intractable,…
The operational meaning of some measures of noise and disturbance in measurements is analyzed and their limitations are pointed out. The cases of minimal noise and least disturbance are characterized.
Temporal correlations in quantum mechanics are the origin of several non-classical phenomena, but they depend on the dimension of the underlying quantum system. This allows one to use such correlations for the certification of a minimal…
We elaborate an interpretation of quantum physics founded on the hypothesis that quantum particles are conceptual entities playing the role of communication vehicles between material entities composed of ordinary matter which function as…
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…
Quantum states can be subjected to classical measurements, whose incompatibility, or uncertainty, can be quantified by a comparison of certain entropies. There is a long history of such entropy inequalities between position and momentum.…
Quantum gravitational effects usually are assumed to be important on small scale (Planck scale), but actually these effects are also very significant on large (cosmological) scales. It is recognized that in curved spacetime, the existence…
We explain why and how the Hilbert space comes about in quantum theory. The axiomatic structures of vector space, of scalar product, of orthogonality, and of the linear functional are derivable from the statistical description of quantum…
Quantum mechanics introduces the concept of probability at the fundamental level, yielding the measurement problem. On the other hand, recent progress in cosmology has led to the "multiverse" picture, in which our observed universe is only…
It is shown how all the major conceptual difficulties of standard (textbook) quantum mechanics, including the two measurement problems and the (supposed) nonlocality that conflicts with special relativity, are resolved in the consistent or…
Non-locality is one of the hallmarks of quantum mechanics and is responsible for paradigmatic features such as entanglement and the Aharonov-Bohm effect. Non-locality comes in two flavours: a \emph{kinematic} non-locality -- arising from…
Ever since the work of Bell, it has been known that entangled quantum states can rise non-local correlations. However, for almost forty years, it has been assumed that the most non-local states would be the maximally entangled ones.…
We study the effects of a generalized uncertainty principle on the classical and quantum cosmology of a closed Friedmann Universe whose matter content is either a dust or a radiation fluid. More concretely, assuming the existence of a…
The existence of a minimum length and a generalization of the Heisenberg uncertainty principle seem to be two fundamental ingredients required in any consistent theory of quantum gravity. In this letter we show that they would predict…
We analyze the emergence of a minimal length for a large class of generalized commutation relations, preserving commutation of the position operators and translation invariance as well as rotation invariance (in dimension higher than one).…
We construct the states of maximal localization taking into account a modification of the commutation relation between position and momentum operators to all orders of the minimum length parameter. To first order, the algebra we use…
The mathematical notion of incompleteness (eg of rational numbers, Turing-computable functions, and arithmetic proof) does not play a key role in conventional physics. Here, a reformulation of the kinematics of quantum theory is attempted,…
Since the beginning of quantum mechanics, many puzzling phenomena which distinguish the quantum from the classical world, have appeared such as complementarity, entanglement or contextuality. All of these phenomena are based on the…