Penrose’s Spin Geometry Theorem is extended further, from SU(2) and E(3) (Euclidean) to E(1, 3) (Poincaré) invariant elementary quantum mechanical systems. The Lorentzian spatial distance between any two non-parallel timelike straight lines of Minkowski space, considered to be the centre-of-mass world lines of E(1, 3)-invariant elementary classical mechanical systems with positive rest mass, is expressed in terms of E(1, 3)-invariant basic observables, viz. the 4-momentum and the angular momentum of the systems. An analogous expression for E(1, 3)-invariant elementary quantum mechanical (...) systems in terms of the basic quantum observables in an abstract, algebraic formulation of quantum mechanics is given, and it is shown that, in the classical limit, it reproduces the Lorentzian spatial distance between the timelike straight lines of Minkowski space with asymptotically vanishing uncertainty. Thus, the metric structure of Minkowski space can be recovered from quantum mechanics in the classical limit using only the observables of abstract quantum mechanical systems. (shrink)

I argue that philosophical issues concerning reductive explanations help constrain the construction of quantum theories with appropriate state spaces. I illustrate this general proposal with two examples of restricting attention to physical states in quantum theories: regular states and symmetry-invariant states. 1Introduction2Background2.1 Physical states2.2 Reductive explanations3The Proposed ‘Correspondence Principle’4Example: Regularity5Example: Symmetry-Invariance6Conclusion: Heuristics and Discovery.

A number of arguments purport to show that quantum field theory cannot be given an interpretation in terms of localizable particles. We show, in light of such arguments, that the classical ħ→0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbar \rightarrow 0$$\end{document} limit can aid our understanding of the particle content of quantum field theories. In particular, we demonstrate that for the massive Klein–Gordon field, the classical limits of number operators can be understood to encode local information about particles (...) in the corresponding classical field theory. (shrink)