John Earman

This paper surveys the issue of relativistic causality within the framework of algebraic quantum field theory . In doing so, we distinguish various notions of causality formulated in the literature and study their relationships, and thereby we offer what we hope to be a useful taxonomy. We propose that the most direct expression of relativistic causality in AQFT is captured not by the spectrum condition but rather by the axiom of local primitive causality, in that it entails a form of local determinism for quantum fields which generalizes the constraint of no superluminal propagation of classical field theories to relativistic quantum field theory. We discuss the status of the axiom of micro-causality by locating its place within a large family of separability/independence/locality conditions developed for AQFT and also by relating it to so-called no-signalling theorems. And we also provide a critical survey of attempts to understand the implications for relativistic causality of the distant correlations endemic to the states in models of AQFT satisfying the standard axioms, and we provide an assessment of attempts to employ Reichenbach's common cause principle in AQFT to defuse worries that these distant correlations implicate direct causal connections between relatively spacelike events

Nearly all accounts of the genesis of special relativity unhesitatingly assume that the theory was worked out in a roughly five week period following the discovery of the relativity of simultaneity. Not only is there no direct evidence for this common presupposition, there are numerous considerations which militate against it. The evidence suggests it is far more reasonable that Einstein was already in possession of the Lorentz and field transformations, that he had applied these to the dynamics of the electron, and that portions of the 1905 paper had actually been drafted well before the epistemological analysis of time.

The purpose of this paper is twofold. First, I want to examine some rather curious arguments of Kant’s which purport to show that some alleged properties of space can be derived from some alleged facts about incongruous counterparts. Secondly, I want to give some preliminary answers to some important questions about the distinction between right and left and the nature of space and space-time which are raised by Kant’s argument. As a byproduct, I hope that the discussion will provide an example of how science can illuminate philosophical issues and of how philosophy can at least lead one into interesting scientific issues.

Like moths attracted to a bright light, philosophers are drawn to glitz. So in discussing the notions of ‘gauge’, ‘gauge freedom’, and ‘gauge theories’, they have tended to focus on examples such as Yang–Mills theories and on the mathematical apparatus of fibre bundles. But while Yang–Mills theories are crucial to modern elementary particle physics, they are only a special case of a much broader class of gauge theories. And while the fibre bundle apparatus turned out, in retrospect, to be the right formalism to illuminate the structure of Yang–Mills theories, the strength of this apparatus is also its weakness: the fibre bundle formalism is very flexible and general, and, as such, fibre bundles can be seen lurking under, over, and around every bush. What is needed is an explanation of what the relevant bundle structure is and how it arises, especially for theories that are not initially formulated in fibre bundle language. Here I will describe an approach that grows out of the conviction that, at least for theories that can be written in Lagrangian/Hamiltonian form, gauge freedom arises precisely when there are Lagrangian/Hamiltonian constraints of an appropriate character. This conviction is shared, if only tacitly, by that segment of the physics community that works on constrained Hamiltonian systems.

This paper represents an attempt to clarify a number of long-standing issues concerning the nature and status of the special and general principles of relativity in particular and symmetry or invariance principles in general. An analysis of the active and passive interpretations of symmetry operations is offered. This analysis yields an evaluation of the old covariance-invariance issue. It also demonstrates that the passive interpretation, insofar as it is not trivial, is parasitic on the active picture. Finally, the analysis shows that grave difficulties lie in the way of any attempt to generalize the special principle of relativity in a manner like the one Einstein originally proposed

A criterion is proposed to ensure that classical relativistic fields do not propagate superluminally. If this criterion does indeed serve as a sufficient condition for no superluminal propagation it follows that various other criteria found in the physics literature cannot serve as necessary conditions since they can fail although the proffered condition holds. The rejected criteria rely on energy conditions that are believed to hold for most classical fields used in actual applications. But these energy conditions are known to fail at small scales for quantum fields. It is argued that such a failure is not necessarily a cause for concern about superluminal propagation in the quantum regime since the proffered criterion of no superluminal propagation for classical fields has a natural analog for quantum fields and, further, this quantum analog condition provably holds for some quantum fields despite the violation of energy conditions. The apparatus developed here also offers a different approach to treating the Reichenbach-Salmon cases of "pseudo-causal processes" and helps to clarify the issue of whether relativity theory is consistent with superluminal propagation.