On Radar Time and the Twin `Paradox'

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 Turn-around' 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.Comment: 9 pages, 10 figures. Minor changes (includes minor corrections not in published version

State-Space Based Approach to Particle Creation in Spatially Uniform Electric Fields

Our formalism described recently in (Dolby et al, hep-th/0103228) 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' approaches 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. 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.Comment: 36 pages, 16 figure

New Approach to Quantum Field Theory for Arbitrary Observers in Electromagnetic Backgrounds

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 (Schr\"odinger picture) states of the system, described in terms of Slater determinants of Dirac states, and not on the field operator $\hat{\psi}(x)$ (which is superfluous in this approach). The vacuum state `at time $\tau$' is defined as the Slater determinant of a basis for the span of the negative spectrum of the `first quantized' Hamiltonian $\hat{H}(\tau)$, 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 S-matrix 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 {\it 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 Gibbons' approach.Comment: 36 pages, 3 figure