Nesvizhevsky et al.[1] performed an experiment to study the problem of gravitational quantum well. The “well” in which a quantum particle (neutron was used in the experiment) bounces back and forth, was formed by placing a horizontal reflecting mirror in the Earth’s gravitational field. The experimental results were in reasonable agreement with the theoretical results. So if there is any noncom...

We discuss various symmetry properties of the reparametrization invariant toy model of a free non-relativistic particle and show that its commutativity and noncommutativity (NC) properties are the artifact of the underlying symmetry transformations. For the case of the symmetry transformations corresponding to the noncommutative geometry, the mass parameter of the toy model turns out to be nonc...

The relationship between the noncommutativity of operators and the violation of the Bell inequality is exhibited in the light of the n-particle Bell-type inequality discovered by Mermin [Phys. Rev. Lett. 65 (1990) 1838]. It is shown, in particular, that the maximal amount of violation of Mermin’s inequality predicted by quantum mechanics decreases exponentially by a factor of 2 whenever any m a...

We revisit the question of microcausality violations in quantum field theory on noncommutative spacetime, taking O(x) =: φ⋆φ : (x) as a sample observable. Using methods of the theory of distributions, we precisely describe the support properties of the commutator [O(x),O(y)] and prove that, in the case of spacespace noncommutativity, it does not vanish at spacelike separation in the noncommutin...

We study the noncommutative version of the extended ADHM construction in the eight dimensional U(1) Yang-Mills theory. This construction gives rise to the solutions of the BPS equations in the Yang-Mills theory, and these solutions preserve at least 3/16 of supersymmetries. In a wide subspace of the extended ADHM data, we show that the integer k which appears in the extended ADHM construction s...

As we look around, the orientation of our eyes depends on the order of the rotations that are carried out, a mathematical feature of rotatory motions known as noncommutativity. Theorists and experimentalists continue to debate how biological systems deal with this property when generating kinematically appropriate movements. Some believe that this is always done by neural commands to a simplifi...