A heuristic comparison is made of relativistic and non-relativistic quantum theory. To this end the Segal approach is described for the non-specialist. The significance of antimatter to the local and microcausal properties of the fields is laid bare. The fundamental difference between relativistic and non-relativistic (complex) fields is traced to the existence of two kinds of complex numbers in the relativistic case. Their relation to covariant and Newton-Wigner locality is formulated.

The Casimir force between two neutral metallic plates is often considered conclusive evidence for the reality of electromagnetic zero-point fluctuations in ‘empty space’. However, it is not well known that the Casimir force can be derived from many different points of view. The purpose of this note is to supply a conceptually oriented introduction to a representative set of these different interpretations. The different accounts suggest that the Casimir effect reveals nothing conclusive about the nature of the vacuum.

The Casimir force between two neutral metallic plates is often considered conclusive evidence for the reality of electromagnetic zero-point fluctuations in ‘empty space’. However, it is not well known that the Casimir force can be derived from many different points of view. The purpose of this note is to supply a conceptually oriented introduction to a representative set of these different interpretations. The different accounts suggest that the Casimir effect reveals nothing conclusive about the nature of the vacuum.