Temporal wave mechanics question and answer workshop

George Jaroszkiewicz

Lee's discretization Time is a continuous parameter in standard Schrödinger wave mechanics, and quantum wavefunctions are differentiable functions of that parameter. We shall refer to this as temporal differentiability . Temporal differentiability is assumed in Dirac's more abstract formulation of quantum mechanics, where state vectors in some abstract Hilbert space and Hermitian operators over that space depend on continuous time (CT) (Dirac, 1958). The same is assumed in relativistic quantum field theories, where quantum field operators in the Heisenberg picture are differentiable over time and space. Temporal differentiability is a necessary condition for the existence of the quantum wave equations and operator field equations found in such theories. Unfortunately, these differentiable equations are usually impossible to solve exactly, so various techniques such as perturbation theory and computer simulation are employed to make suitable approximations. Numerical techniques on their own, however, are insufficient to answer questions of principle, such as the meaning of quantized spacetime. A more principled approach to the solution of quantum differential equations, namely the path integral (PI), was developed, exploited and popularized principally by Feynman (Feynman and Hibbs, 1965). In some situations, such as quantum gravity, the PI was found to be virtually the only technology available to discuss the quantum physics. We discuss this approach in greater detail in Chapter 18.

pKenneth M Rauenp

A.L. Stanford, J.M. Tanner

Mario Bunge

A survey is made of the hitherto proposed answers to the following crucial questions arising in the physical interpretation of the mathematical formalism of wave mechanics: (I) What is the meaning of the dynamical variables and of their eigenvalues? (II) What is the meaning of the wave function? (III) What is the nature and origin of Heisenberg's uncertainty relations? (IV) What is the nature of the systems dealt with by wave mechanics? Taking into account the interpretations that have been proposed in the last few years, a surprisingly large number of answers is found. The present situation in quantum mechanics is compared with similar crises in the past history of physics. The mere multiplicity of consistent interpretations of quantum mechanics is regarded as a warning against the dogmatic adherence to any one of them, to the exclusion of new possibilities.

Louis Harris, Arthur L. Loeb, Peter B. Kahn

Gerard van der Ham

yet have definite shapes at any moment? Could it be that quanta have statistical definite properties, wave- and particle properties at the same time? These questions need an answer to reach some consensus in physics and to solve some of the most urgent problems in physics. These questions will be answered in this paper. Also the probabilities in Bell experiments, predicted by quantum mechanics, are made visible and their explanation is accounted for mathematically.