Related papers: Uncertainty Relations (UR) Have Nothing to do with…
Starting with a consideration of the implication of Bell inequalities in quantum mechanics, a new quantum postulate is suggested in order to restore classical locality and causality to quantum physics: only the relative coordinates between…
The momentum representation is seldom used in quantum mechanics courses. Some students are thence surprised by the change in viewpoint when, in doing advanced work, they have to use the momentum rather than the coordinate representation. In…
We discuss the no-go theorem of Frauchiger and Renner based on an "extended Wigner's friend" thought experiment which is supposed to show that any single-world interpretation of quantum mechanics leads to inconsistent predictions if it is…
Quantum theory demands that, in contrast to classical physics, not all properties can be simultaneously well defined. The Heisenberg Uncertainty Principle is a manifestation of this fact. Another important corollary arises that there can be…
A two boundary quantum mechanics without time ordered causal structure is advocated as consistent theory. The apparent causal structure of usual "near future" macroscopic phenomena is attributed to a cosmological asymmetry and to rules…
Uncertainty relations are fundamental to quantum mechanics, encoding limits on the simultaneous measurement of conjugate observables. Violations of joint uncertainty bounds can certify entanglement -- a resource critical for quantum…
For any ideal two-path interferometer it is shown that the wave-particle duality of quantum mechanics implies Heisenberg's uncertainty relation and vice versa. It is conjectured that complementarity and uncertainty are two aspects of the…
Uncertainty relations play a central role in quantum mechanics. Entropic uncertainty relations in particular have gained significant importance within quantum information, providing the foundation for the security of many quantum…
This paper aims at investigating the influence of space-time curvature on the uncertainty relation. In particular, relying on previous findings, we assume the quantum wave function to be confined to a geodesic ball on a given space-like…
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…
Epistemological consequences of quantum nonlocality (entanglement) are discussed under the assumption of a universally valid Schr\"odinger equation in the absence of hidden variables. This leads inevitably to a {\it many-minds…
Consider a statistical model with an epistemic restriction such that, unlike in classical mechanics, the allowed distribution of positions is fundamentally restricted by the form of an underlying momentum field. Assume an agent (observer)…
A concise review of various mathematical formulations of the uncertainty relations in quantum mechanics discovered since 1927 is given. Besides the traditional Heisenberg inequality, the modifications made by Schr\"odinger and Robertson, as…
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…
A generalized uncertainty relation for an entangled pair of particles is obtained if we impose a symmetrization rule for all operators that we should use when doing any calculation using the entangled wave function of the pair. This new…
Classically general covariance is found from the idea that a vector is a physical quantity which exists independently of choice of coordinate system and is unchanged by a change of coordinate system. It is often assumed that there exists…
A suitable unified statistical formulation of quantum and classical mechanics in a *-algebraic setting leads us to conclude that information itself is noncommutative in quantum mechanics. Specifically we refer here to an observer's…
(2+2)-dimensional quantum mechanical q-phase space which is the semi-direct product of the quantum plane E_q(2)/U(1) and its dual algebra e_q(2)/u(1) is constructed. Commutation and the resulting uncertainty relations are studied. ``Quantum…
The non-relativistic quantum mechanics with the generalized uncertainty principle (GUP) is examined when the potential is one-dimensional $\delta-$function. It is shown that unlike usual quantum mechanics, the Schr\"{o}dinger and Feynman's…
The correspondence between the integrability of classical mechanical systems and their quantum counterparts is not a 1-1, although some close correspondencies exist. If a classical mechanical system is integrable with invariants that are…