Related papers: Causality, delocalization and positivity of energy
Positivity of the Hamiltonian alone is used to show that particles, if initially localized in a finite region, immediately develop infinite tails.
Theorems (most notably by Hegerfeldt) prove that an initially localized particle whose time evolution is determined by a positive Hamiltonian will violate causality. We argue that this apparent paradox is resolved for a free particle…
A theorem of Hegerfeldt (Instantaneous spreading and Einstein causality in quantum theory, Ann. Phys. Leipzig vol. 7, 716-725 (1998)) establishes, for a class of quantum systems, a dichotomy between those which are permanently localized in…
We investigate possible explanations of quantum correlations that satisfy the principle of continuity, which states that everything propagates gradually and continuously through space and time. In particular, following [J.D. Bancal et al,…
A family of wave packets with power law tails are employed to analyze the long time dependence of the corresponding probability density. The densities, associated to packets for free particles in the one-dimensional space, with sufficiently…
In relativity, there is no absolute notion of simultaneity, because two clocks that are in different places can always be desynchronized by a Lorentz boost. Here, we explore the implications of this effect for the quantum theory of unstable…
A theorem of Hegerfeldt shows that if the spectrum of the Hamiltonian is bounded from below, then the propagation speed of certain probabilities does not have an upper bound. We prove a theorem analogous to Hegerfeldt's that appertains to…
In nonrelativistic quantum mechanics the wave-function of a free particle which initially is in a finite volume immediately spreads to infinity. In a nonrelativistic theory this is of no concern, but we show that the same instantaneous…
Drawing from the theory of optimal transport we propose a rigorous notion of a causal relation for Borel probability measures on a given spacetime. To prepare the ground, we explore the borderland between causality, topology and measure…
It is argued that while quantum mechanics contains nonlocal or entangled states, the instantaneous or nonlocal influences sometimes thought to be present due to violations of Bell inequalities in fact arise from mistaken attempts to apply…
The notion of Einstein causality, i.e. the limiting role of the velocity of light in the transmission of signals, is discussed. It is pointed out that Nimtz and coworkers use the notion of signal velocity in a different sense from Einstein…
Quantum entanglement is the quintessential characteristic of quantum mechanics and the basis for quantum information processing. When one of two maximally entangled particles is measured, without measurement the state of another one is…
We prove six theorems concerning exponentially accurate semiclassical quantum mechanics. Two of these theorems are known results, but have new proofs. Under appropriate hypotheses, they conclude that the exact and approximate dynamics of an…
Closed-form, normalizable solutions of Dirac's equation propagating within a semi-infinite cylindrical waveguide are obtained in terms of ordinary and modified Bessel functions. These relativistic wave packets induce quantum backflow on a…
We study the causal structure of a class of weakly nonlocal gravitational theories (eventually coupled to matter) that are compatible with perturbative unitarity and finiteness at quantum level. In particular, we show that in nonlocal…
Measurable quantities that have positive values in classical dynamical systems need not to be positive in quantum theory. For example, consider a free quantum mechanical particle in one dimension. There are quantum states in which the…
Two related problems in relativistic quantum mechanics, the apparent superluminal propagation of initially localized particles and dependence of spatial localization on the motion of the observer, are analyzed in the context of Dirac's…
In quantum theory particles are represented as wave packets. Shock wave analysis of quantum equations of motion shows that wave function representation in general and wave packet description in particular contains discontinuities due to a…
The salient feature of both classical and quantum gravity is its universal and attractive character. However, less is known about the behaviour and build-up of quantum correlations when quantum systems interact via graviton exchange. In…
The causality issues concerning Hegerfeldt's paradox and the localization of relativistic quantum systems are addressed through a proper-time formalism of single-particle operators. The proposed description does not depend on classical…