Additions:

""""   [[SingularitiesRevisited Singularities Revisited]]
In classical general relativity, a ""singularity"" may be described as a point at which the known laws of physics necessarily break down. The singularities of interest to physics are the big bang (and the big crunch) and black holes. We may expect that known laws of physics break down not just at a singularity, but also close to it.

Additions:

""""   [[TeleconnectionIntro Introduction to the Teleconnection]]
=====[[CosmologicalImplications Cosmological Parameters and Empirical Evidence]] =====
Relational quantum gravity predicts that ""galaxy rotation curves"" are not flat, but appear flat because of an ""unmodelled component of spectral shifts due to cosmological expansion"". The [[http://sci.esa.int/science-e/www/area/index.cfm?fareaid=26 Gaia space telescope]] will carry out measurements accurate enough to show the truth of this prediction for individual stars. In the meantime, we have designed a ""statistical test on a population local stars with accurate measurements of distance and motion"". The test, summarised here, rejects the null hypothesis, that ""there is no systematic error in spectrographic measurement of radial velocity"", with 99.9993% confidence, and supports the prediction of relational quantum gravity, according to which stars in galaxies follow orbits determined by conventional matter under conventional Newtonian gravity, but [[http://www.classzone.com/books/earth_science/terc/content/visualizations/es2802/es2802page01.cfm spectral shifts]] due to cosmological expansion create the [[QuantumCoordinates illusion]] that rotation curves are flat.
In an ""analysis of solar motion relative to halo stars"", we found that the motion of the Sun with respect to halo stars within a cone with axis in the direction of Galactic rotation is significantly faster than its motion with respect to stars outside of that cone. This result can be explained by an [[QuantumCoordinates illusory component of radial velocity]] in accordance with the prediction of [[RelationalQuantumGravity relational quantum gravity]]. On account of the small population of halo stars this test does not demonstrate an illusory component of radial velocity at the 3σ level, or lead to a precise calculation of the orbital velocity of the Sun, but it does offer independent supporting evidence for the results of the regression test.
Our paper, ""Galactic Spiral Structure"", [[http://arxiv.org/abs/0901.3503 arXiv:0901.3503]], shows how galaxies naturally evolve to form grand-design two-arm spirals. Here we give a brief description of the workings of spiral arms.

Deletions:

""""   [[TeleconnectionIntro The Teleconnection in a Friedmann Cosmology]]
=====[[CosmologicalImplications Cosmological Implications and Empirical Evidence]] =====
Relational quantum gravity predicts that ""galaxy rotation curves"" are not flat, but appear flat because of an ""unmodelled component of spectral shifts due to cosmological expansion"". The [[http://sci.esa.int/science-e/www/area/index.cfm?fareaid=26 Gaia space telescope]] will carry out measurements accurate enough to show the truth of this prediction for individual stars. In the meantime, we have designed a ""statistical test on a population local stars with accurate measurements of distance and motion"". The test, summarised here, rejects the null hypothesis, that ""there is no systematic error in spectrographic measurement of radial velocity"", with 99.9993% confidence, and supports the prediction of relational quantum gravity, according to which stars in galaxies follow orbits determined by conventional matter under conventional Newtonian gravity, but [[http://www.classzone.com/books/earth_science/terc/content/visualizations/es2802/es2802page01.cfm spectral shifts]] due to cosmological expansion create the [[QuantumCoordinates illusion]] that rotation curves are flat.
In an ""analysis of solar motion relative to halo stars"", we found that the motion of the Sun with respect to halo stars within a cone with axis in the direction of Galactic rotation is significantly faster than its motion with respect to stars outside of that cone. This result can be explained by an [[QuantumCoordinates illusory component of radial velocity]] in accordance with the prediction of [[RelationalQuantumGravity relational quantum gravity]]. On account of the small population of halo stars this test does not demonstrate an illusory component of radial velocity at the 3σ level, or lead to a precise calculation of the orbital velocity of the Sun, but it does offer independent supporting evidence for the results of the regression test.
Our paper, ""Galactic Spiral Structure"", [[http://arxiv.org/abs/0901.3503 arXiv:0901.3503]], shows how galaxies naturally evolve to form grand-design two-arm spirals. Here we give a brief description of the workings of spiral arms.

Additions:

Deletions:

Additions:

=====[[PhysicalPrinciples Physical Principles]] =====
Quantum theory is famous for the paradoxical way in which it describes the universe. More strictly the paradoxes lie in the “standard” [[http://en.wikipedia.org/wiki/Copenhagen_interpretation Copenhagen interpretaion]] of quantum mechanics, not in its mathematical structure. Some physicists adopt [[http://en.wikipedia.org/wiki/Interpretations_of_quantum_mechanics other interpretations]], but these appear inadequate to properly describe properties of matter in a complete, coherent, and consistent manner. Many declare that interpretation is not the business of physics. This section contains a general description of quantum theory and of paradox in the Copenhagen interpretation, and describes how the paradoxes are addressed in relational quantum gravity.
Newton’s laws are restated after replacing Newtonian absolute space with spacetime, leading to Einstein’s [[http://en.wikipedia.org/wiki/Equivalence_principle equivalence principle]], that gravity is an [[http://en.wikipedia.org/wiki/Fictitious_force inertial force]], from which it follows that gravity is a manifestation of spacetime curvature.
In general relativity, Einstein put his physical ideas on the nature of time and space, into the mathematical language of [[IntroductionToTensors tensors]] and [[BasicsofCurvature Riemannian geometry]].
If index gymnastics were a physical sport, this page would be a training session for the fit and athletic. In it, the covariant derivative is established from local parallelism, the ""Riemann curvature tensor"" is found, properties are analysed, and the ""Einstein curvature tensor"" is found and shown to obey the ""contracted Bianchi identity"", which has importance in ""Einstein’s law of gravitation"". From a philosophical perspective, the important aspect is that manipulations in mathematics introduce no new physical principles, and merely express relationships which necessarily hold in a universe obeying the general principle of relativity and in which we can translate objects through small distances. If you are prepared to take that on faith, you can skip the calculations and move quickly on to the next section. That is quite reasonable. You may reflect that these calculations have been checked and rechecked by tens of thousands of mathematicians since their original formulation in the 19th century. Such is the requirement of reproducibility in a strict approach to science. If you take the strict approach, that nothing should be taken on faith, and require that logic, rather than authority, should be the final arbiter, there is no help for it; you have to do the training session. No sympathy can be afforded to those who decry authority and yet are too idle or unfit to do the training.
“Einstein’s biggest blunder”, the [[http://en.wikipedia.org/wiki/Cosmological_constant cosmological constant]], is introduced. Weyl’s postulate is described, which treats the motions of galaxies as a “cosmic fluid” and allows us to talk of “cosmic time” and the large scale structure of the universe. Spaces of constant curvature are treated and the meaning of cosmological expansion is described. The cosmological principle, which essentially states that the universe is everywhere the same at any cosmic time, is used to derive Friedmann’s equation for the expansion of the universe. The equation is solved and the Friedmann models are described.
Quantum logic is introduced as a natural language for discussing measurement results in a universe consisting of only particles and relationships between them, and in which spacetime is not fundamental but emerges from those relationships. Relativistic considerations impose severe constraints, leading to the necessity for spin and antimatter, and to a precise description of the electron.
Quantum theory is often thought to be conceptually incomprehensible as physical theory, but it is as much a theory of language as it is a theory of physics. Properties like wave function collapse apply to statements about what we know of a situation, not directly to physical reality. All that is required to understand it is a bit of mathematical trickery applied to a language describing general principles of measurement.
The underlying idea is simple. Formal clauses are combined using the tensor product to model logical conjunction, ""AND"". The resulting structure, [[http://en.wikipedia.org/wiki/Fock_space Fock space]], contains clauses about the hypothetical measurement of all the particles under consideration, and allows that particles of the same type are indistinguishable from each other.
Interactions are modelled as a perturbation to the motion of free particles, using quantum logical ""OR"" to write the statement that, at each instant, either a particle interacts with another particle, or it does not, in which case its wave function evolves as a free particle. Relativistic considerations are used to derive the locality condition, showing that particles must meet in order to interact and which gives meaning to the claim that particles are point-like. Conservation of 3-momentum is demonstrated, showing that classical Newtonian mechanics is a consequence of the relational principles described in relativity and quantum logic.
With the exception of special relativity, [[http://en.wikipedia.org/wiki/Quantum_electrodynamics Quantum electrodynamics]] is the most [[http://en.wikipedia.org/wiki/Precision_tests_of_QED empirically accurate]] theory known to science, but it is fraught with mathematical difficulties and divergence problems. I follow a straightforward approach, based heavily on the Dirac-Von Neumann interpretation. The focus is on showing that the general considerations of relativity and quantum mechanics lead to both quantum and classical electrodynamics.
I introduce qed by constructing the Dirac field operators, which are used to describe the interactions of Dirac particles, demonstrate that they obey locality and I define the current density observable.
The possibilities for interactions between Dirac particles and other matter are limited by covariance. The most straightforward interaction, known as the //minimal interaction//, is with a vector particle, the photon. I introduce its properties and extend quantum logic to describe the behaviour of a particle whose position cannot be determined directly because it is only created or annihilated in interaction.
In keeping with the idea that particles are the fundamental building blocks of matter, and have behaviour constrained by quantum theory and relativity, classical electromagnetism has not been assumed in this account. To see that classical electromagnetism is the consequence of particle interactions we need to show that """" is a conserved current, and that the Lorentz force law and Maxwell’s equations follow from the minimal interaction in which a photon is emitted from, or absorbed by, a Dirac particle.
The accepted wisdom is that Feynman diagrams should not be taken literally, but should merely be treated as aids to calculation. That is not how Feynman regarded them, as described in, for example, [[http://en.wikipedia.org/wiki/QED_%28book%29 QED: The Strange Theory of Light and Matter]]. In the interpretation of quantum mechanics used here, they are understood as statements in quantum logic. Since we cannot say what combination of particle interactions takes place between measurements, we must sum the possibilities using quantum logical ""OR"". In Feynman diagrams only lines and vertices have meaning. They represent structures of matter as configurations of particle interactions in the absence of background of space or spacetime.
A principle application of quantum theory, and of quantum electrodynamics in particular, is in the interpretation of the results of scattering experiments. I describe the scattering cross section, show how it may be calculated from Feynman rules. The prototypical scattering experiment, on which much research into the properties of elementary particles has been based, was the [[http://en.wikipedia.org/wiki/Geiger-Marsden_experiment Geiger-Marsden gold foil experiment]] carried out under the supervision of [[http://en.wikipedia.org/wiki/Ernest_Rutherford Ernest Rutherford]]. I obtain the Rutherford formula for non-relativistic Coulomb scattering, verified by the experiment, and from which we deduce the structure of the atom containing a dense charged nucleus.
Quantum electrodynamics has had considerable success experimentally, but is renowned for difficulties with infinite quantities. Certain methods used to remove divergences have been severely criticised, even by some of the founders of the field. I describe here how divergences can be legitimately avoided. When correct methods are followed there are no remaining issues in qed.
===[[RelationalQuantumGravity Relational Quantum Gravity]]===
The construction of qed as a model of particle interactions using finite dimensional Hilbert space is straightforward, but sweeps thorny issues under the carpet. The problems are deep enough that most physicists believe that this approach is fundamentally flawed. I move on from the description of standard theory from a relational viewpoint, and describe my own research into a resolution. [[QuantumCovariance Quantum Covariance]] deals with the issue that manifest covariance requires a continuum model. [[Teleconnection The Teleconnection]] shows how quantum theory can be consistently defined when classical spacetime is curved. I conclude that quantum field theory should be interpreted strictly as a theory of discrete [[ParticlesOrFields particles]]. A consequence is that the arguments which led to Minkowski metric in [[FoundationsOfSpecialRelativity special relativity]] must be adapted and lead to [[OriginOfCurvature Einstein’s Field Equation]] in the case for a single gravitating particle.
""""   [[QuantumCovariance Quantum Covariance]]
In order to analyse redshift effects between remote initial and final quantum states, we need to study the relationship between inertial reference frames defined locally with speed of light equal to unity and ""τ−ρ"" coordinates used in a Penrose diagram of the universe with a non-physical metric, """". The factors of two in the non-physical metric are equivalent to a two way stretch of the wave function, and yields surprising results in conjunction with local fluctuations in geometry. Gravitational lenses in deep space have four times greater effect for given mass. The interpretation of redshifts by standard formulae leads to an illusory component in the velocities of astronomical objects.
""""   [[TeleconnectionIntro The Teleconnection in a Friedmann Cosmology]]
To introduce the idea of the teleconnection I will here describe it diagramatically for a Friedmann Cosmology. In this case the analysis is particularly simple. The result is that the cosmological redshift of light from a distant galaxy is proportional to the square of the expansion parameter, not linear with it as predicted by the ""Levi-Civita connection"". A more general, and more mathematical, treatment will be given on the [[Teleconnection next page]].
""""   [[Teleconnection The Teleconnection]]
A ""connection"" defines the notion of parallel in vector spaces defined at nearby points of a manifold. The teleconnection defines the parallel displacement of momentum in quantum mechanics from an initial state to a final state when the reference matter used to describe the initial state is remote from that used to describe the final state. When the initial and final states are determined with respect to nearby reference matter, the teleconnection is equivalent to the ""Levi-Civita connection"".
""""   [[QuantumCoordinates Illusory Velocity]]
In order to analyse redshift effects between remote initial and final quantum states, we need to study the relationship between inertial reference frames defined locally with speed of light equal to unity and ""τ−ρ"" coordinates used in a Penrose diagram of the universe with a non-physical metric, """". The factors of two in the non-physical metric are equivalent to a two way stretch of the wave function, and yields surprising results in conjunction with local fluctuations in geometry. Gravitational lenses in deep space have four times greater effect for given mass. The interpretation of redshifts by standard formulae leads to an illusory component in the velocities of astronomical objects.
""""   [[ParticlesOrFields Particles Or Fields?]]
Usually quantum electrodynamics is approached from the viewpoint that the underlying (meta)physical structures are fields. I do not think there is any justification for this beyond the undeniable mathematical similarity between relativistic quantum field theory and the treatment of quasi-particles in [[http://en.wikipedia.org/wiki/Condensed_matter_physics condensed matter physics]]. Field theorists argue that, in like manner, the fundamental particles of Nature are really quasi-particles. In my view, argument by analogy is not a valid scientific methodology; it is often the case that identical mathematics can be applied to quite distinct physical situations. We have no means to conclude from similar mathematics that the vacuum has a physical structure analogous to that of a [[http://en.wikipedia.org/wiki/Superfluid superfluid]]. Despite considerable effort over the years, field theory has not been able to resolve fundamental mathematical problems in qed. Meanwhile, particle qed has largely been neglected. This section describes the issues and summarises the steps taken in relational quantum gravity to address the problems with the particle view.
""""   [[OriginOfCurvature A Gravitating Particle]]
Relational quantum gravity modifies the standard, continuum, form of qed and introduces an effective minimal interval of proper time between interactions of an elementary particle. The result of this modification is that instead of Minkowski spacetime, we find a curved spacetime obeying Einstein’s field equation.
""""   [[SpacetimeStructure The Emergence of Spacetime Structure]]
In relational quantum gravity, the most fundamental description of matter is illustrated by [[FeynmanDiagrams Feynman diagrams]]. In Feynman diagrams, space, and hence curvature, have no meaning, and emerge only in the classical correspondence from the mean behaviour of large populations of particles.
===[[CosmologicalImplications Cosmological Implications and Empirical Evidence]] ===
The predicted redshift relation under the teleconnection, together with observational evidence from supernovae, lead to a closed Friedmann model with no [[LargeScaleStructure cosmological constant]] or [[http://en.wikipedia.org/wiki/Cold_dark_matter cold dark matter]], and to the resolution of other problems in astrophysics.
""""   [[Supernova Supernovae Redshifts and Cosmological Parameters]]
The Teleconnection predicts a different redshift relation from that of standard general relativity. The redshift relation has a number of testable implications. A revised relationship between redshift and age offers the prospect of a reconciliation between observation and galaxy evolution models. The magnitude-redshift relation has been analysed using the [[http://supernova.lbl.gov/Union/ Union compilation]] compilation of data from the [[http://supernova.lbl.gov/ Supernova Cosmology Project]]. The quality of the fits is such that any improvement of the teleconnection no-""Λ"" model over the standard [[http://en.wikipedia.org/wiki/Lambda-CDM_model concordance model]] is wholly insignificant.
""""   [[Pioneer Anomalous Pioneer Blueshift]]
[[http://en.wikipedia.org/wiki/Pioneer_10 Pioneer 10]] and [[http://en.wikipedia.org/wiki/Pioneer_11 Pioneer 11]] were the first spacecraft to investigate [[http://en.wikipedia.org/wiki/Jupiter_(planet) Jupiter]] and explore the ""outer solar system"". For some years they sent back Doppler information interpreted as an anomalous acceleration toward the Sun ([[http://arxiv.org/abs/gr-qc/0104064v5 Anderson et al.]]). This cannot be accounted for by classical physics, but is predicted in relational quantum gravity.
""""   [[GalaxyRotationCurves Galaxy Rotation Curves, CDM and MOND]]
[[http://en.wikipedia.org/wiki/Cold_dark_matter Cold dark matter]] (CDM) has been hypothesised to make sense of a number of observations in Cosmology, but the theory is not without problems. [[http://en.wikipedia.org/wiki/Modified_Newtonian_dynamics MOND]] has offered an alternative, but also does not work in all cases. The [[QuantumCoordinates teleconnection]] offers a no-CDM alternative in which illusory velocities account for the phenomenology of MOND without modifying Newtonian dynamics
""""   [[SlopeOfRotationCurve The Local Slope of the Rotation Curve]]
""CDM"" and ""MOND"" allow flat [[GalaxyRotationCurves galaxy rotation curves]], but it is observed that the local gradient of the rotation curve is not flat. It appears that CDM defies general relativity as well as elementary particle physics and earth based laboratory experiments, and MOND fails in its aim of replacing Newtonian gravity with a law predicting the slope of the rotation curve from visible matter.
""""   [[RadialVelocityTest Radial Velocity Test]]
Relational quantum gravity predicts that ""galaxy rotation curves"" are not flat, but appear flat because of an ""unmodelled component of spectral shifts due to cosmological expansion"". The [[http://sci.esa.int/science-e/www/area/index.cfm?fareaid=26 Gaia space telescope]] will carry out measurements accurate enough to show the truth of this prediction for individual stars. In the meantime, we have designed a ""statistical test on a population local stars with accurate measurements of distance and motion"". The test, summarised here, rejects the null hypothesis, that ""there is no systematic error in spectrographic measurement of radial velocity"", with 99.9993% confidence, and supports the prediction of relational quantum gravity, according to which stars in galaxies follow orbits determined by conventional matter under conventional Newtonian gravity, but [[http://www.classzone.com/books/earth_science/terc/content/visualizations/es2802/es2802page01.cfm spectral shifts]] due to cosmological expansion create the [[QuantumCoordinates illusion]] that rotation curves are flat.
""""   [[SolarMotion Solar Motion Relative to the Metal-poor Halo]]
In an ""analysis of solar motion relative to halo stars"", we found that the motion of the Sun with respect to halo stars within a cone with axis in the direction of Galactic rotation is significantly faster than its motion with respect to stars outside of that cone. This result can be explained by an [[QuantumCoordinates illusory component of radial velocity]] in accordance with the prediction of [[RelationalQuantumGravity relational quantum gravity]]. On account of the small population of halo stars this test does not demonstrate an illusory component of radial velocity at the 3σ level, or lead to a precise calculation of the orbital velocity of the Sun, but it does offer independent supporting evidence for the results of the regression test.
===[[SpiralArms Spiral Arms Unravelled]] ===
This section is entirely Newtonian, and has no bearing on relational quantum gravity. I studied the kinematics of local stars to look for evidence of the spectral shift prediction, but, once familiar with the structure of the local velocity distribution, I realised that it fitted a simple model of galactic spiral structure. Much to my surprise, it turned out that apparently no one had seen the model before, and that the field is usually studied using an analysis based on Ptolemy’s epicycles, and fraught with simple mathematical mistakes.
""""   [[SpiralStructure The Anatomy of Spiral Arms]]
Our paper, ""Galactic Spiral Structure"", [[http://arxiv.org/abs/0901.3503 arXiv:0901.3503]], shows how galaxies naturally evolve to form grand-design two-arm spirals. Here we give a brief description of the workings of spiral arms.
""""   [[VelocityDistribution The Velocity Distribution of Local Stars]]
Observation shows that the velocity distribution of local stars is highly structured. Our [[rqgravity.net/Papers#LSR analysis]] is based on a population of 20 574 local stars with accurate [[http://en.wikipedia.org/wiki/Hipparcos Hipparcos]] [[http://en.wikipedia.org/wiki/Parallax parallaxes]] and known radial velocities.
""""   [[MilkyWay The Milky Way Spiral]]
We matched the model of [[SpiralStructure Spiral Structure]] to the [[http://en.wikipedia.org/wiki/Milky_Way Milky Way]], using the observed distribution of interstellar hydrogen and the observed distribution of [[VelocityDistribution velocities of local stars]]. We found that the [[http://en.wikipedia.org/wiki/Milky_Way Milky Way]] is a two-armed spiral galaxy, not a four-armed spiral as has been thought.
""""   [[PtolemyIsDead ptolemyisdeadalreadysogetoveritokay.com]]
Astonishing as it may seem, the study of Galactic orbits in the 20th century has been dominated by a theory of epicycles adapted from that of Ptolemy, which had been abandoned after Newton explained Kepler’s discovery that planetary orbits are elliptical. More seriously, the [[http://en.wikipedia.org/wiki/Density_wave_theory density wave hypothesis]] is often treated as though it were established science, although it conflicts with Newtonian gravity, and can reasonably be described as a catalogue of simple mathematical and physical mistakes.

Deletions:

=====[[PhysicalPrinciples Physical Principles] =====
Newton’s laws are restated after replacing Newtonian absolute space with spacetime, leading to Einstein’s [[http://en.wikipedia.org/wiki/Equivalence_principle equivalence principle]], that gravity is an [[http://en.wikipedia.org/wiki/Fictitious_force inertial force]], from which it follows that gravity is a manifestation of spacetime curvature.
In general relativity, Einstein put his physical ideas on the nature of time and space, into the mathematical language of [[IntroductionToTensors tensors]] and [[BasicsofCurvature Riemannian geometry]].
The covariant derivative is established from local parallelism, the Riemann curvature tensor is found, properties are analysed, and the Einstein curvature tensor is found and shown to obey the "" “Einstein’s biggest blunder”, the [[http://en.wikipedia.org/wiki/Cosmological_constant cosmological constant]], is introduced. Weyl’s postulate is described, which treats the motions of galaxies as a “cosmic fluid” and allows us to talk of “cosmic time” and the large scale structure of the universe. Spaces of constant curvature are treated and the meaning of cosmological expansion is described. The cosmological principle, which essentially states that the universe is everywhere the same at any cosmic time, is used to derive Friedmann’s equation for the expansion of the universe. The equation is solved and the Friedman models are described.
Quantum electrodynamics is perhaps the most empirically accurate theory known to established science, but it is fraught with mathematical difficulties and divergence problems. The approach here is based heavily on the Dirac-Von Neumann interpretation and focusses on showing that the general considerations of relativy and quantum mechanics lead to quantum and classical electrodynamics. This approach gives a simpler view of underlying physics than is generally presented from quantum field theory. The resulting calculations and predictions using Feynman rules are, of course, the same. Attention will be drawn to mathematical issues raised by the approach. These will be addressed in Relational Quantum Gravity.
Quantum theory is as much a theory of language as it is a theory of physics. Properties like wave function collapse apply to statements about what we know of a situation, not to physical reality. All that is required is a bit of mathematical trickery applied to a language describing general principles of measurement.
The underlying idea is simple. Formal clauses are combined using the tensor product to model logical conjunction, ""AND"". The resulting structure, [[http://en.wikipedia.org/wiki/Fock_space Fock space]], contains clauses about the hypothetical measurement of all the particles under consideration, and allows that particles of the same type are indistinguishable from each other.
Interactions are modelled as a perturbation to the motion of free particles, using quantum logical ""OR"" to write the statement that, at each instant, either a particle interacts with another particle, or it does not, in which case its wave function evolves as a free particle. Relativistic considerations are used to derive the locality condition, showing that particles must meet in order to interact and which gives meaning to the claim that particles are point-like. Conservation of 3-momentum is demonstrated, showing that classical Newtonian mechanics is a consequence of the relational principles described in relativity and quantum logic.
With the exception of special relativity, [[http://en.wikipedia.org/wiki/Quantum_electrodynamics Quantum electrodynamics]] is the most [[http://en.wikipedia.org/wiki/Precision_tests_of_QED empirically accurate]] theory known to established science, but it is fraught with mathematical difficulties and divergence problems. I follow a straightforward approach, and draw attention to issues which this raises. I believe that this approach gives a much truer view of underlying physics than is generally presented from quantum field theory. It is shown that the simple interaction in which a Dirac particle emits or absorbs a photon explains the form of Maxwell’s equations of electromagnetism.
===[[RelationalQuantumGravity Relational Quantum Gravity]]===
""""   [[QuantumCovariance Quantum Covariance]]
""""   [[TeleconnectionIntro The Teleconnection in a Friedmann Cosmology]]
""""   [[Teleconnection The Teleconnection]]
""""   [[QuantumCoordinates Illusory Velocity]]
""""   [[ParticlesOrFields Particles Or Fields?]]
""""   [[OriginOfCurvature A Gravitating Particle]]
""""   [[SpacetimeStructure The Emergence of Spacetime Structure]]
===[[CosmologicalImplications Cosmological Implications and Empirical Evidence]] ===
""""   [[Supernova Supernovae Redshifts and Cosmological Parameters]]
""""   [[Pioneer Anomalous Pioneer Blueshift]]
""""   [[GalaxyRotationCurves Galaxy Rotation Curves, CDM and MOND]]
""""   [[SlopeOfRotationCurve The Local Slope of the Rotation Curve]]
""""   [[RadialVelocityTest Radial Velocity Test]]
""""   [[SolarMotion Solar Motion Relative to the Metal-poor Halo]]
===[[SpiralArms Spiral Arms Unravelled]] ===
""""   [[SpiralStructure The Anatomy of Spiral Arms]]
""""   [[VelocityDistribution The Velocity Distribution of Local Stars]]
""""   [[MilkyWay The Milky Way Spiral]]
""""   [[PtolemyIsDead ptolemyisdeadalreadysogetoveritokay.com]]

Additions:

=====[[PhysicalPrinciples Physical Principles] =====
""""   [[Paradox Quantum Weirdness]]
=====[[MathematicalMethods Mathematical Methods]]=====
=====[[Gravity Gravity]]=====
=====[[RelativisticQuantumTheory Relativistic Quantum Theory]]=====
""""   [[Evolution Evolution of Quantum States]]
""""   [[Interactions Particle Interactions ]]
===[[QuantumElectrodynamics Quantum Electrodynamics]]===
""""   [[QED The Dirac Field Operator]]
""""   [[Photons The Photon Field Operator]]
""""   [[CEM Classical Electromagnetism]]
""""   [[FeynmanDiagrams Feynman Diagrams]]
""""   [[Scattering Scattering]]
""""   [[Regularisation Regularisation and Renormalisation]]
===[[RelationalQuantumGravity Relational Quantum Gravity]]===
""""   [[QuantumCovariance Quantum Covariance]]
""""   [[TeleconnectionIntro The Teleconnection in a Friedmann Cosmology]]
""""   [[Teleconnection The Teleconnection]]
""""   [[QuantumCoordinates Illusory Velocity]]
""""   [[ParticlesOrFields Particles Or Fields?]]
""""   [[OriginOfCurvature A Gravitating Particle]]
""""   [[SpacetimeStructure The Emergence of Spacetime Structure]]
===[[CosmologicalImplications Cosmological Implications and Empirical Evidence]] ===
""""   [[Supernova Supernovae Redshifts and Cosmological Parameters]]
""""   [[Pioneer Anomalous Pioneer Blueshift]]
""""   [[GalaxyRotationCurves Galaxy Rotation Curves, CDM and MOND]]
""""   [[SlopeOfRotationCurve The Local Slope of the Rotation Curve]]
""""   [[RadialVelocityTest Radial Velocity Test]]
""""   [[SolarMotion Solar Motion Relative to the Metal-poor Halo]]
===[[SpiralArms Spiral Arms Unravelled]] ===
""""   [[SpiralStructure The Anatomy of Spiral Arms]]
""""   [[VelocityDistribution The Velocity Distribution of Local Stars]]
""""   [[MilkyWay The Milky Way Spiral]]
""""   [[PtolemyIsDead ptolemyisdeadalreadysogetoveritokay.com]]

Deletions:

=====Physical Principles =====
===[[PhysicalPrinciples Physical Principles]]===
=====Mathematical Methods=====
=====Gravity=====
=====Relativistic Quantum Theory=====
""""   [[Evolution Time Evolution]]
""""   [[Interactions Interactions between Particles]]
""""   [[QED Quantum Electrodynamics]]
""""   [[FeynmanDiagrams Feynman Diagrams]] - (under construction)
""""   [[DealingWithParadox Dealing with Paradox]] - (to be written).
=====Relational Quantum Gravity=====
""""   [[QuantumCovariance Quantum Covariance]] - To be written
""""   [[Teleconnection The Teleconnection]] - To be written
""""   [[DiscreteQuantumElectrodynamics Discrete Quantum Electrodynamics]] - To be written
""""   [[OriginOfCurvature A Gravitating Particle]]
""""   [[SpacetimeStructure The Emergence of Spacetime Structure]] - under construction
""""   [[CosmologicalImplications Cosmological Implications]]- To be written
=====Empirical Evidence =====
""""   [[SupernovaRedshift Supernova Redshifts]] - To be written
""""   [[Lensing Lensing]] - To be written
""""   [[Pioneer Pioneer]] - To be written
""""   [[GalaxyRotationCurves Galaxy Rotation Curves]] - To be written
""""   [[RadialVelocityTest Radial Velocity Test]] - To be written
""""   [[SolarMotion Solar Motion]] - To be written
""""   [[SlopeOfRotationCurve The Slope of the Rotation Curve]] - To be written
=====Future Directions=====
""""   [[BlackHoles Black Holes]]- To be written
""""   [[TheVeryBeginning The Very Beginning]]- To be written
""""   [[QuantumChromodynamics Quantum Chromodynamics]]- To be written