arXiv subjects

Charles Francis

Publications and source records attributed to Charles Francis.

30 records · Page 2Linked to original sources

arXiv2009

Calculation of the Local Standard of Rest from 20,574 Local Stars in the New Hipparcos Reduction with Known Radial Velocities

Context. An accurate estimate of the local standard of rest (LSR) is required to determine key parameters used in approximate galactic mass models and to understand Galactic structure and evolution. However, authors are often forced to base dynamical analyses on potentially unreliable figures because recent determinations of the LSR have failed to reach agreement, especially with regard to the direction, V, of Galactic rotation. Aims. To explain why the traditional method for calculating the LSR fails, and to find alternative means of calculating the LSR with realistic error margins. Methods. We assemble and investigate the kinematic properties of 20 574 stars within 300pc, with complete and accurate kinematic data. The traditional method of calculating the LSR assumes a well-mixed distribution. In fact, the velocity distribution is highly structured, invalidating calculations based on mean motions and asymmetric drift. We find other indicators in the distribution which we believe give a better estimate of circular motion. Results. We find good agreement between results and give as our best estimate of the LSR (U_0, V_0, W_0) = (7.5 +- 1.0, 13.5 +- 0.3, 6.8 +- 0.1) km/s. We calculate the slope of the circular speed curve at the solar radius, finding -9.3 +- 0.9 km/s/kpc.

astro-ph↗

arXiv2002

Discrete Quantum Mechanics I: Quantum Covariance

Classically general covariance is found from the idea that a vector is a physical quantity which exists independently of choice of coordinate system and is unchanged by a change of coordinate system. It is often assumed that there exists some form of absolute mathematical space or space-time, and that in a flat space approximation vectors can be imagined between defined points in this space-time, much as we can imagine an arrowed line drawn on a piece of paper. However, while classical vector quantities can be represented on paper, in the quantum domain physical quantities do not in general exist with precise values except in measurement; a change of apparatus, for example by rotating it, may affect the outcome of the measurement, so the condition for general covariance does not apply. The purpose of this paper is to re-examine covariance within the context of an orthodox, Dirac-Von Neumann interpretation of quantum mechanics, to replace it with a new condition, here called quantum covariance, and to show that quantum covariance is the required condition for the unification of general relativity with quantum mechanics for non-interacting particles.

gr-qc↗

arXiv2001

An Intuitive Approach to Special and General Relativity

The k-calculus was advanced by Hermann Bondi as a means of explaining special relativity using only simple algebra (Bondi H.: Relativity and Common Sense, London, Heinemann, 1964). As used by Bondi, k is Doppler shift. This paper extends the k-calculus to include gravitational red shift and to develop techniques for an introductory treatment of general relativity in which the emphasis is on mathematical deduction from physical measurement procedure. Using ideas of geometric optics, geodesic motion is understood from the refraction of the wave function due curvature. The k-calculus gives a very simple derivation of Schwarzschild, showing that the geometry is equivalent to the existence of a fundamental minimum time, proportional to rest mass, between the interactions of elementary particles. The Newtonian approximation is seen from direct application of red shift to the wave function. Finally differential geometry is introduced, showing that the k-calculus gives an equivalent treatment of general relativity up to and including the general form of Einstein's field equation.

physics.gen-ph↗

arXiv2001

Discrete Quantum Electrodynamics

The purpose of this paper is to construct a quantum field theory suitable for describing quantum electrodynamics and Yang-Mills theory in a form which satisfies the conditions of the Millennium prize offered by the Clay Mathematics Institute as described by Jaffe and Witten [12], by showing that it satisfies 'axioms at least as strong as those cited by' Wightman [18] and by Osterwalder and Schrader [14], and by observing that this form of field theory has no mass gap. The definitions provide a model for relativistic quantum mechanics which supports a form of relativistic quantum field theory, but which does not depend on the second quantisation of a 'matter wave'. Continuous laws of wave mechanics are found in model of discrete particle interactions which does not involve waves, or the quantisation of interacting fields. Newton's first law and conservation of momentum are established from the principle of homogeneity. Maxwell's equations are derived from the simple interaction in which a Dirac particle emits or absorbs a photon, showing that the renormalised mass and coupling constant are equal to their bare values. Feynman rules are calculated for the discrete theory and give the predictions of the standard renormalised theory. Quark confining interactions are described for qed and for an adaptation of Yang-Mills theory.

physics.gen-ph↗

arXiv2001

A Metric Determined by Photon Exchange

The k-calculus was advanced by Hermann Bondi as a means of explaining special relativity using only simple algebra [1]. Bondi's argument was placed in the context of classical electrodynamics. In this paper it is placed in context of particle theoretic QED. The central derivations are reviewed, using proofs only slightly more elegant than those in Bondi's books. As used by Bondi, k is Doppler red shift. The relativistic measurement of position is placed in the context of an information theoretic interpretation of quantum mechanics as a theory of measurement results. The law of geodesic motion is seen as consequent on the refraction of the wave function due curvature, as in geometric optics. The k-calculus is extended to include gravitational red shift and to account for gravity by observing that, after allowing a small inherent delay in the reflection of a photon, the metric defined by the radar method obeys Einstein's field equation. A very simple derivation of Schwarzschild is given using the k-calculus and avoiding differential geometry and calculation of Christoffel symbols. The Newtonian approximation is seen from a direct application of red shift to the wave function.

physics.gen-ph↗

arXiv1999

Conceptual Foundations of Special and General Relativity

The k-calculus was advocated by Hermann Bondi as a means of explaining special relativity using only GCSE level mathematics and ideas. We review the central derivations, using proofs which are only a little more elegant than those in Bondi's books, and extend his development to include the scalar product and the mass shell condition. As used by Bondi, k is the Doppler red shift, and we extend the k calculus to include the gravitational red shift and give a derivation of Newton's law of gravity using only 'A' level calculus and basic quantum mechanics.

physics.gen-ph↗

arXiv1999

An Alternative Model of Quark Confinement

In "A Theory of Quantum Space-time" we constructed a form of field theory in which Feynman diagrams describe real particle interactions, not virtual ones. In this paper we outline a theory of discrete interactions based on hadron field operators which bind quark in co- ordinate space, but not momentum space, and offer explanations for the strong force, jets and Zweig's rule. As yet no calculations have been carried out on the predictions of the theory, but we indicate possibilities for testable predictions.

physics.gen-ph↗

arXiv1999

A Pre-Geometric Model Exhibiting Physical Law

We describe a substructure for matter in which metric relations are not assumed as properties of a physical manifold, and instead the metric of general relativity is found in configurations of particle interactions. The 'state' of a particle is the set of possible configurations of surrounding particles. States are thus non-local, while particles are local. Kets are not states, or descriptions of states, but merely names for states. Ket space is a naming system constructed by an individual observer from the available information in such a way that the principle of superposition and the probability interpretation are definitional truisms, not physical laws. In this paper the treatment is developed as far as showing that the solution to the discrete equations describing the structure should be embedded into covariant continuous equations, and we remark that this leads to a requirement for four dimensions and spin in the organisation of a structure consisting solely of particle interactions, although neither dimensionality nor spin are assumed properties of particles.

physics.gen-ph↗

arXiv1999

A Model of Classical and Quantum Measurement

We take the view that physical quantities are values generated by processes in measurement, not pre-existent objective quantities, and that a measurement result is strictly a product of the apparatus and the subject of the measurement. We habitually make an inaccurate statements when we speak of the measurement of a quantity by an apparatus. These statements can be formalised as a many valued logic with the structure of a vector space with a hermitian form in such a way as to generate probabilities in the results of measurement. The difference between this and classical probability theory is that we are not finding probabilities generated by unknown variables, but probabilities generated by unknown structure. We thus interpret quantum logic as the application of complex truth values to statements in an inaccurate language, and find that the properties of vector space hold for approximate measurement as well as for measurement of optimal accuracy, suggesting that Planck's constant governs the scale of the fundamental structures of matter.

physics.gen-ph↗

arXiv1999

The Fabric of Space-time II: Gravity by Photon Exchange

This is one of a number of papers in which the metric for space-time is defined on the subatomic level by means of the interchange of photons, and constrained to be consistent with radar. It is shown that the discrete nature of particle interactions necessitates a small inherent delay in the radar method, and hence that the resulting geometry is non- Euclidean. Thus the forces of gravity and electromagnetism can each be seen as an effect of the same interaction between elementary particles, and we can identify gravitational and inertial mass.

physics.gen-ph↗

arXiv1999

The Fabric of Space-time

The formulae of special relativity are developed through the k-calculus with no presumption of a manifold. The metric is determined empirically by the exchange of photons, and the treatment suggests that the exchange of photons seen in quantum electrodynamics is also responsible for the 'fabric' of Minkowsky space-time. This suggests that on quantum scales the point-like nature of elementary particles, should appear 'defocussed' or 'fuzzy'. Further work on the implications in the laws of physics is referred to

physics.gen-ph↗

arXiv1999

Point-like Particles in Fuzzy Space-time

This paper is withdrawn as I am no longer using the term "fuzzy space- time" to describe the uncertainty in co-ordinate systems implicit in quantum logic. Nor am I using the interpretation that quantum logic can be regarded as a special case of fuzzy logic. This is because there are sufficient differences between quantum logic and fuzzy logic that the explanation is confusing. I give an interpretation of quantum logic in "A Theory of Quantum Space-time"

physics.gen-ph↗