We analyze the restrictions on distinguishability of quantum states imposed by special relativity. An explicit expression relating the error probability for distinguishing between two orthogonal single-photon states to the time interval T between the beginning of the measurement procedure and the moment when the measurement result is obtained by the observer. Many problems of non-relativistic q...

In a reasonably self-contained and explicit presentation we illustrate the efficiency of the Feynman–Kac formula for the rigorous derivation of three inequalities of interest in non-relativistic quantum mechanics.

We propose a generalization of the standard geometric formulation of quantum mechanics, based on the classical Nambu dynamics of free Euler tops. This extended quantum mechanics has in lieu of the standard exponential time evolution, a nonlinear temporal evolution given by Jacobi elliptic functions. In the limit where latter’s moduli parameters are set to zero, the usual geometric formulation o...

This report outlines steps in deriving the Bloch Equation, beginning by applying the principles of relativistic and non-relativistic quantum mechanics to simple physical models of the proton, and deriving the two-component Schrödinger Equation, which describes the interaction of a single proton with externally applied magnetic fields. The off-diagonal entries of the Bloch equation matrix are de...

We present a possible scheme to tamper with non-local quantum correlations in a way that is consistent with relativistic causality, but goes beyond quantum mechanics. A non-local “jamming” mechanism, operating within a certain space-time window, would not violate relativistic causality and would not lead to contradictory causal loops. The results presented in this Letter do not depend on any mo...

This paper is concerned with the question of the existence of composition laws in the sum-overhistories approach to relativistic quantum mechanics and quantum cosmology, and its connection with the existence a canonical formulation. In non-relativistic quantum mechanics, the propagator is represented by a sum over histories in which the paths move forwards in time. The composition law of the pr...

1 Quantum Mechanics in a gravitational field ◮ Quantum effects in the classical gravitational field are observed, e.g. in neutron interferometry [1, 2]. All of the effects observed until now had been previously predicted by using the non-relativistic Schrödinger equation in the Newtonian gravity potential [2, 3, 4], and are still described by this same non-relativistic approximation. ◮ However,...

We exhibit a purely quantum mechanical carrier of the imprints of gravitation by identifying for a relativistic charge a property which (i) is independent of its mass and (ii) expresses the Poincare invariance of spacetime in the absence of gravitation. This carrier is a Klein-Gordon-equation-determined vector eld given by the \Planckian power" and the \r.m.s. thermal uctuation" spectra. Does t...

We demonstrate how to construct a lorentz-invariant, hidden-variable interpretation of relativistic quantum mechanics based on particle trajectories. The covariant theory that we propose employs a multi-time formalism and a lorentz-invariant rule for the coordination of the space-time points on the individual particle trajectories. In this way we show that there is no contradiction between nonl...

We present some informal remarks on aspects of relativistic quantum computing. The continuing miniaturization of electronic circuitry has forced designers of computer chips to deal with all of the complications that are entailed in using Quantum Mechanics. Meanwhile, physicists have identified dramatic new possibilities for increases in computer performance by making use of such uniquely quantu...