Causality in Quantum Electrodynamics

Gregory C. Dente

G. Compagno, G. Massimo Palma, Roberto Passante +1 more

Henry Margenau

Quantum mechanics, even in its early and simple phases, has often been regarded as a non-causal discipline. The argument supporting this view cites the uncertainty principle as prohibiting the ascertainment of complete knowledge concerning physical states upon which causal prediction could be based. Recent developments in atomic physics have added new and puzzling features to the problem of causality insofar as they operate, not only with intrinsically unmeasurable states, but also with time reversals which have been interpreted to mean that the effect can be prior to the cause. Feynman's theory of quantum electrodynamics is particularly rich in unorthodox suggestions which tantalise philosophers. The purpose of the present paper is to exhibit them, appraise their methodological function and see in what manner they violate the rules of causal description. This purpose, it seems, is best achieved by a sequential discussion of three questions: What does causality mean in physics? What is the new method of quantum electrodynamics? Is this new method compatible with the causal doctrine in some satisfactory form?

M. I. Shirokov

Causality, in the sense of finiteness of the velocity of propagation of signals, is discussed for quantum electrodynamics. The paper proposes an appropriate quantum-mechanical criterion for causality. According to this criterion local observables like the field strengths E(x), H(x) and the current density j/sub ..mu../(x) behave causally. However, the theory contains quantities (like the electron number density) which exhibit macroscopic acausality. The reason for this result is discussed in a theory where the usual causality condition, i.e., local commutativity of the operators A/sub ..mu../ and psi, is satisfied. (AIP)

M. I. Shirokov

The fulfillment in quantum electrodynamics of the principle of relativistic causality—the signal velocity does not exceed the velocity of light—is discussed. In Sec. 1 it is argued that this principle is not guaranteed automatically merely by the local commutativity of the theory. Section 2 is a critical review of the signal transmission problems which have been formulated and solved in the literature. In Sec. 3, this problem is considered in the framework of a simple but fairly realistic model of quantum electrodynamics. The signal source is an external current localized in some region S. The arrival of a signal in a region D at a distance R is established by a change in the coordinate, momentum, or energy of a charged particle. It is shown that proof of relativistic causality of the theory requires one to take into account appropriately quantum-mechanical and, in particular, quantum-electrodynamical features of the problem. In the final fourth section, a general formulation and exact solution of the signal transmission problem are given. The treatment is of sufficient generality for one to be able to assert that in the framework of quantum electrodynamics none of the possible methods of signal transmission violate relativistic causality.

Jean G. Valatin