←  Papers  ↑

Relational Quantum Gravity

Relational Quantum Gravity I: Conceptual and Mathematical Foundations

Context. The well known problems of interpretation of quantum mechanics mean that physical law lacks a physical basis.
Aims. To derive the formalism of quantum mechanics from assertions about the world with clear physical meaning.
Methods. Kets are defined as formal conditional clauses referring to measurements in a formal language and have a natural structure as a vector space. Addition is logical disjunction. The dual space consists of consequent clauses, such that the inner product is a set of statements in the subjunctive mood. The probability interpretation gives truth values for corresponding future tense statements when the initial state is prepared and the final state is to be measured.
Results. The mathematical structure of quantum mechanics is formulated in terms of discrete measurement results at finite level of accuracy and does not depend on an assumption of a background spacetime continuum. Discrete position functions are uniquely embedded into smooth wave functions such that differential operators are defined. Using finite dimensional Hilbert space, a continuum of states, for , is defined such that the inner product can be expressed either as a finite sum or as an integral. Operators do not in general have an integral form. The Schrödinger equation is shown from the requirements of the probability interpretation.

Relational Quantum Gravity II: Quantum Electrodynamics

Context. While causal perturbation theory and lattice regularisation allow rigorous treatment of the ultraviolet divergences in qed, they do not resolve the Landau pole, or address questions of physical interpretation. Relational Quantum Gravity I (RQG I) presented an interpretation of quantum mechanics as a theory of measurements of particles, and found a representation of finite dimensional Hilbert space using in smooth wave functions such that differential operators are defined and a form of covariance is obeyed.
Aims. To construct quantum electrodynamics from quantum mechanics as formulated in RQG I.
Methods. Quantum field operators are defined from creation and annihilation operators on Fock space, obeying quantum covariance and locality, and suitable for a description of particle interactions under the Feynman-Stückelberg interpretation.
Results. The construction is consistent and identical in the continuum limit to quantum electrodynamics with all loop divergences removed. The Landau pole can be avoided by introducing a physical cut-off in the form of a minimal proper time between discrete particle interactions. Maxwell’s equations and the Lorentz force law are derived in the classical correspondence, showing that bare mass and charge are equal to their physical values.

Relational Quantum Gravity III: Remote Initial and Final States

Context. Relational Quantum Gravity I (RQG I) formulates quantum mechanics in terms of discrete measurement results at finite level of accuracy and does not depend on an assumption of a substantive spacetime.
Aims. To introduce the physical metric from physical processes and to show that the resulting model gives general relativity in the classical correspondence.
Methods. A simple form of the metric for static coordinates is found, using coordinates such that the radial speed of light is constant. This is generalised to expanding cosmologies. It is observed that Hilbert space is defined at the position of measurement. The teleconnection defines the relationship between quantum states when the initial measurement is remote from the final measurement.
Results. The Levi-Civita connection is found in the limit of close initial and final measurements. Gravitational redshift is as in classical general relativity, but the prediction for cosmological redshift is modified. The small time delay between interactions introduced to regularise qed in RQG II has a physical import equivalent Einstein’s field equation.

Relational Quantum Gravity IV: Observational Evidence

Context. There are substantial observational and theoretical problems both for &Lambda-CDM models and for MOND.
Aims. To show that observations currently attributed to &Lambda-CDM and/or MOND can reasonably be accounted for by the cosmological redshift predictions of relational quantum gravity.
Methods. Cosmological parameters are calculated and compared to supernova redshift data. Treatments are given for gravitational bending of light, and for light from distant objects in uniform motion, and in galactic orbits. A test is applied to look for a signature of the spectral prediction in measurements of local stars. A separate test is applied for a population of halo stars.
Results. Good agreement is found between predictions and supernova redshifts for a closed Friedmann Cosmology with no cosmological constant and expanding at half the rate of the standard model. Previously unmodelled components of cosmological redshift account for the anomalous Pioneer blueshift and for the flattening of galaxy rotation curves. For orbiting bodies the unmodelled component simulates a MONDian law with a value for the critical MOND acceleration in agreement with observation. Distant lenses have a quarter of the mass required by standard general relativity. Missing mass can be accounted by a massive neutrino. Missing mass can be accounted by a massive neutrino. Neither dark energy nor CDM is required. Based on accurate kinematic data on local stars, we reject the null hypothesis, there is no systematic error in spectrographic determinations of heliocentric radial velocity, with up to 99.95% confidence.

Relational Quantum Gravity V: Paradox

Quantum theory is famous for a number of conceptual paradoxes which have lead many physicists to think that interpretation in terms of visualizable mechanistic processes is not possible. Relational quantum gravity challenges this viewpoint, by developing a model from first principles in which Hilbert space is seen to make statements concerning measurements in a model in which the fundamental objects are particles, and in which all measurements are relative, in the sense that they involve comparison between matter and matter and such that the quantification of a relationship between matter and a background spacetime is meaningless at the fundamental level of the theory. A consistent mathematical model incorporating qed and general relativity was constructed from this interpretation. I review conceptual aspects of the model, and discuss the resolution of the important conceptual paradoxes of quantum mechanics.

Gravitational and Cosmological Spectral Shift with Remote Quantum States

A class of coordinate systems is found for Friedmann Cosmologies with local gravity such that it is possible to formulate quantum theory over astronomical and cosmological distances. When light from distance objects is treated as a quantum motion, new predictions are found for cosmological redshift and lensing. Good agreement is found between predictions and supernova redshifts for a closed Friedmann Cosmology with no cosmological constant and expanding at half the rate of the standard model. A previously unmodelled component of cosmological redshift accounts for the anomalous Pioneer blueshift, and for the flattening of galaxy rotation curves simulating a MONDian law. Distant lenses have a quarter of the mass required by standard general relativity. Missing mass can be accounted by a massive neutrino. CDM is not required.

Indications of an Unmodelled Component in Spectrographic Measurements of Local Stars

Context: While CDM models and MOND give explanations for flat rotation curves of other galaxies, both present observational problems and the local gradient of the Milky Way’s rotation curve is not flat.
Aims: We consider whether flat rotation curves could be an artifact of an unmodelled component in spectral shift.
Methods: In the absence of astrometric determinations of radial velocity, we apply a statistical test on a population of 20 440 Hipparcos stars inside 300 pc with known radial velocities and with accurate parallaxes in the New Hipparcos Reduction.
Results: The test rejects the null hypothesis, there is no systematic error in spectrographic determinations of heliocentric radial velocity, with 99.95% confidence. In a separate test on metal-poor stars, we find tension between calculations of the orbital velocity of the Sun and three populations of halo stars inside and outside of a cone of 60° semi-angle from the direction of rotation. Tension cannot be removed with only systematic distance adjustments.
Conclusions: We conclude that the most probable explanation is an unmodelled element in spectrographic determinations of heliocentric radial velocity with a probable cosmological origin, and propose that this unmodelled component, rather than CDM or MOND, is responsible for the apparent flatness of galaxy rotation curves.

Astronomical Analyses

Galactic Spiral Structure

We describe the structure and composition of six major stellar streams in a population of 20 574 local stars in the New Hipparcos Reduction with known radial velocities. We find that, once fast moving stars are excluded, almost all stars belong to one of these streams. The results of our investigation have lead us to re-examine the hydrogen maps of the Milky Way, from which we identify the possibility of a symmetric two-armed spiral with half the conventionally accepted pitch angle. We describe a model of spiral arm motions which matches the observed velocities and composition of the six major streams, as well as the observed velocities of the Hyades and Praesepe clusters at the extreme of the Hyades stream. Stellar orbits are perturbed ellipses aligned at a focus in coordinates rotating at the rate of precession of pericentre. Stars join a spiral arm just before apocentre, follow the arm for more than half an orbit, and leave the arm soon after pericentre. Spiral pattern speed equals the mean rate of precession of pericentre. Spiral arms are shown to be stable configurations of stellar orbits, up to the formation of a bar and/or ring. Pitch angle is directly related to the distribution of orbital eccentricities in a given spiral galaxy. We show how spiral galaxies can evolve to form bars and rings. We show that orbits of gas clouds are stable only in bisymmetric spirals. We conclude that the evolution of spiral galaxies is toward grand design two-armed spirals. We infer from the velocity distributions that the Milky Way evolved into this form about 9 Gyrs ago.

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 300 pc, 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 (U₀, V₀, V₀) = (7.5 ± 1.0, 13.5 ± 0.3, 6.8 ± 0.1 ) km s^-1. We calculate the slope of the circular speed curve at the solar radius, finding -9.3 ± 0.9 km s^-1 kpc^-1.

Lindblad’s epicycles – valid method or bad science?

The study of Galactic orbits in the last eighty years has been dominated by statistical assumptions made because of the lack of empirical evidence available in the early 20th century. Using evidence from Hipparcos and recent radial velocity surveys, Francis and Anderson recently showed that spiral structure is primarily a consequence of gravitational alignments of stellar orbits. I review the mechanism which creates spiral structure, consider the validity of widely held assumptions in galactic dynamics and the implications to notions such as the asymmetric drift and disc heating. I identify a number of fundamental mathematical and physical errors in Lindblad’s epicycle theory and in density wave theory. Students should be made aware that these ideas can no longer be considered as science, and authors of textbooks should consider whether they merit anything more than a historical note.

Mathematical

A Smooth Representation of Finite Dimensional Hilbert Space

A representation of a finite dimensional Hilbert space using smooth wave functions is shown. A continuum of states, for , is defined such that the inner product can be expressed either as a finite sum or as an integral. The orthogonality condition can be expressed using either a Kronecker or Dirac delta, where the Dirac delta is a smooth function. Operators do not generally have an integral form. The representation has potential applications in quantum theory, particularly with regard to the treatment of divergences in quantum electrodynamics.

Site Contents ← Papers ↑