The current status of localization and related concepts, especially localized statevectors and position operators, within Lorentz-invariant Quantum Theory (LIQT) is ambiguous and controversial.1 Ever since the early work of Newton & Wigner (1949), and the subsequent extensions of their work, particularly by Hegerfeldt (1974, 1985), it has seemed impossible to identify localized statevectors or position operators in LIQT that were not counterintuitive—strange—in one way or another; the most striking strange property being the superluminal propagation of the localized states. The ambiguous (...) and controversial status of these concepts arises from the varied reactions that workers have to the strange properties. Some regard them, particularly the superluminal propagation, as utterly unacceptable, and conclude that no precise concepts of localized statevectors and position operators exist in LIQT (Wigner 1973, p. 325-327; 1983, pp. 310-313; Malament 1996). Others downplay the whole issue, on the grounds that current theoretical and experimental practice has no need of sharply formulated concepts of localization, localized states etc. (Birrell & Davies 1984, pp. 48-59; Haag 1992, p. 34). Still others, including ourselves, believe that the superluminal propagation does not lead to causal contradictions, and is not in conflict with available empirical data: so that it should not be ruled out. We also believe that the other strange properties are merely unfamiliar novelties of LIQT which we must simply learn to accept. (Like the superluminal propagation, they do not lead to causal contradictions, nor conflict with available data.) So in this paper, we aim to help remove the ambiguous and controversial status of localization concepts in LIQT. Overall, our strategy will be to assess a number of localization concepts, and thereby clarify the often complex relationships among them. (shrink)

Time is often said to play in quantum mechanics an essentially different role from position: whereas position is represented by a Hermitian operator, time is represented by a c-number. This discrepancy has been found puzzling and has given rise to a vast literature and many efforts at a solution. In this paper it is argued that the discrepancy is only apparent and that there is nothing in the formalism of quantum mechanics that forces us to treat position and time differently. (...) The apparent problem is caused by the dominant role point particles play in physics and can be traced back to classical mechanics. (shrink)