In this paper we apply the concept of radar time (popularised by Bondi in his work on k-calculus) to the well-known relativistic twin 'paradox'. Radar time is used to define hypersurfaces of simultaneity for a class of travelling twins, from the 'Immediate Turn-around' case, through the 'Gradual Turnaround' case, to the 'Uniformly Accelerating' case. We show that this definition of simultaneity is independent of choice of coordinates, and assigns a unique time to any event (with which the travelling twin can send and receive signals), resolving some common misconceptions.

A reformulation of fermionic QFT in electromagnetic backgrounds is presented which uses methods analogous to those of conventional multiparticle quantum mechanics. Emphasis is placed on the (Schrödinger picture) states of the system, described in terms of Slater determinants of Dirac states, and not on the field operatorψ(x) (which is superfluous in this approach). The vacuum state "at time τ " is defined as the Slater determinant of a basis for the span of the negative spectrum of the "first quantized" HamiltonianĤ (τ ), thus providing a concrete realisation of the Dirac Sea. The general S-matrix element of the theory is derived in terms of time-dependent Bogoliubov coefficients, demonstrating that the Smatrix follows directly from the definition of inner product between Slater determinants. The process of "Hermitian extension," inherited directly from conventional multiparticle quantum mechanics, allows second quantized operators to be defined without appealing to a complete set of orthonormal modes and provides an extremely straightforward derivation of the general expectation value of the theory. The concept of "radar time," advocated by Bondi in his work on k-calculus, is used to generalise the particle interpretation to an arbitrarily moving observer. A definition of particle results, which depends only on the observer's motion and the background present, not on any choice of coordinates or gauge, or of the particle detector. We relate this approach to conventional methods by comparing and contrasting various derivations. Our particle definition can be viewed as a generalisation to arbitrary observers of the approach of G. W. Gibbons (1975, Comm. Math. Phys. 44, 245). C 2001 Academic Press

Our formalism, described recently in (C. E. Dolby and S. F. Gull, Ann. Phys. 293 (2001), 189-214.) is applied to the study of particle creation in spatially uniform electric fields, concentrating on the cases of a time-invariant electric field and a so-called adiabatic electric field. Several problems are resolved by incorporating the Bogoliubov coefficient approach and the tunnelling approach into a single consistent, gauge invariant formulation. The value of a time-dependent particle interpretation is demonstrated by presenting a coherent account of the time-development of the particle creation process, in which the particles are created with small momentum (in the frame of the electric field) and are then accelerated by the electric field to make up the bulge of created particles predicted by asymptotic calculations [2,3]. An initial state comprising one particle is also considered, and its evolution is described as being the sum of two contributions: the sea of current produced by the evolved vacuum and the extra current arising from the initial particle state. C 2002 Elsevier Science (USA)

The history of the particle concept is briefly reviewed, with particular emphasis on the 'foliation dependence' of many particle creation models, and the possible connection between our notion of particle and our notion of simultaneity. It is argued that the concept of 'radar time' (originally introduced by Sir Hermann Bondi in his work on k-calculus) provides a satisfactory concept of 'simultaneity' for observers in curved spacetimes. This is used to propose an observer-dependent particle interpretation, applicable to an arbitrary observer, depending solely on that observers motion and not on a choice of coordinates or gauge. This definition is illustrated with application to non-inertial observers and simple cosmologies, demonstrating its generality and its consistency with known cases.

Abstract. A coordinate system is constructed for a general accelerating observer in 1+1 dimensions, and is used to determine the particle density of the massless Dirac vacuum for that observer. Equations are obtained for the spatial distribution and frequency distribution of massless fermions seen by this observer, in terms of the rapidity function of the observer's worldline. Examples that are considered include the uniformly accelerating observer as a limiting case, but do not involve particle horizons. Only the low frequency limit depends on the possible presence of particle horizons. The rest of the spectrum is 'almost thermal' whenever the observer's acceleration is 'almost uniform'.