Relativistic Quantum Mechanics as a Telegraph

Augusto Garuccio

J. S. Faulkner

N. Nikitin, K. S. Toms

In the framework of non-relativistic quantum mechanics we present a proposal for a gedunken experimental setup of a quantum system allowing information exchange. We discuss the compatibility of the procedure with a few no-go theorems.

Jussi Lindgren, Jukka Liukkonen

The main contribution of this paper is to explain where the imaginary structure comes from in quantum mechanics. It is shown how the demand of relativistic invariance is key and how the geometric structure of the spacetime together with the demand of linearity are fundamental in understanding the foundations of quantum mechanics. We derive the Stueckelberg covariant wave equation from first principles via a stochastic control scheme. From the Stueckelberg wave equation a Telegrapher's equation is deduced, from which the classical relativistic and nonrelativistic equations of quantum mechanics can be derived in a straightforward manner. We therefore provide meaningful insight into quantum mechanics by deriving the concepts from a coordinate invariant stochastic optimization problem, instead of just stating postulates.

Bernard Gaveau, Ted Jacobson A, Mark Kac +1 more

Schr\"odinger's equation and the heat equation are connected to one another by analytic continuation, as are the Feynman integral and the Wiener integral. We extend this form of correspondence to the relativistic domain by identifying Poisson processes whose real version gives rise to the telegrapher's equation and which when analytically continued produce the Dirac equation.