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

Classic Maximum Entropy Recovery of the Average Joint Distribution of Apparent FRET Efficiency and Fluorescence Photons for Single-molecule Burst Measurements

We describe a method for analysis of single-molecule Förster resonance energy transfer (FRET) burst measurements using classic maximum entropy. Classic maximum entropy determines the Bayesian inference for the joint probability describing the total fluorescence photons and the apparent FRET efficiency. The method was tested with simulated data and then with DNA labeled with fluorescent dyes. The most probable joint distribution can be marginalized to obtain both the overall distribution of fluorescence photons and the apparent FRET efficiency distribution. This method proves to be ideal for determining the distance distribution of FRET-labeled biomolecules, and it successfully predicts the shape of the recovered distributions

Reconstruction of Calmodulin Single-Molecule FRET States, Dye-Interactions, and CaMKII Peptide Binding by MultiNest and Classic Maximum Entropy

We analyze single molecule FRET burst measurements using Bayesian nested sampling. The MultiNest algorithm produces accurate FRET efficiency distributions from single-molecule data. FRET efficiency distributions recovered by MultiNest and classic maximum entropy are compared for simulated data and for calmodulin labeled at residues 44 and 117. MultiNest compares favorably with maximum entropy analysis for simulated data, judged by the Bayesian evidence. FRET efficiency distributions recovered for calmodulin labeled with two different FRET dye pairs depended on the dye pair and changed upon Ca2+ binding. We also looked at the FRET efficiency distributions of calmodulin bound to the calcium/calmodulin dependent protein kinase II (CaMKII) binding domain. For both dye pairs, the FRET efficiency distribution collapsed to a single peak in the case of calmodulin bound to the CaMKII peptide. These measurements strongly suggest that consideration of dye-protein interactions is crucial in forming an accurate picture of protein conformations from FRET data

Comment on ``Consistency, amplitudes and probabilities in quantum theory'' by A. Caticha

A carefully written paper by A. Caticha [Phys. Rev. A57, 1572 (1998)] applies consistency arguments to derive the quantum mechanical rules for compounding probability amplitudes in much the same way as earlier work by the present author [J. Math. Phys. 29, 398 (1988) and Int. J. Theor. Phys. 27, 543 (1998)]. These works are examined together to find the minimal assumptions needed to obtain the most general results

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

The expansion asymmetry and age of the Cassiopeia A supernova remnant

HST images of the young supernova remnant Cas A are used to explore the expansion and spatial distribution of its highest velocity debris. ACS WFC images taken in 2004 March and December with Sloan F625W, F775W, and F850LP filters were used to identify 1825 high-velocity, outlying ejecta knots through measured proper motions of 0."35 - 0."90 yr(-1), corresponding to V-trans = 5500-14,500 km s(-1) assuming d = 3.4 kpc. The distribution of derived transverse expansion velocities for these ejecta knots shows a striking bipolar asymmetry with the highest velocity knots (V-trans >= 10,500 km s(-1)) confined to nearly opposing northeast and southwest "jets'' at P.A. = 45 degrees-70 degrees and 230 degrees-270 degrees, respectively. The jets have about the same maximum expansion velocity of similar or equal to 14,000 km s(-1) and appear kinematically and chemically distinct in that they are the remnant's only S-rich ejecta with expansion velocities above the 10,000-11,000 km s(-1) exhibited by outer nitrogen-rich ejecta, which otherwise represent the remnant's highest velocity debris. In addition, we find significant gaps in the spatial distribution of outlying ejecta in directions that are approximately perpendicular to the jets (P.A. = 145 degrees-200 degrees and 335 degrees-350 degrees). The remnant's central X-ray point source lies some 700 to the southeast of the estimated expansion center ( P.A. = 169 degrees +/- 8.degrees 4) indicating a projected motion toward the middle of the broad southern ejecta knot gap. Extrapolations of measured 9 month proper motions for all 1825 outer ejecta knots and a selected subsample of 72 bright and compact knots suggest explosion dates (assuming no knot deceleration) of 1662 +/- 27 and 1672 +/- 18, respectively. We find some evidence for nonuniform deceleration in different directions around the remnant and find 126 knots located along the northwestern limb among the least decelerated ejecta, suggesting a convergence date of 1681 +/- 19. A remnant age of around 325 yr would imply a +/- 350 km s(-1) transverse velocity for the central X-ray point source