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Physical Principles

Philosophical Foundations

The Infinite and the Infinitesimal
Atoms and the Void
The Plenum
Relationism
Measurement
Reference Frames
The General Principle of Relativity
Relational Quantum Gravity

Quantum Weirdness

Wave Particle Duality
Young’s Slits
Electrons as Waves
The Delayed Choice Quantum Eraser
The Collapse of the Wave Function
The Measurement Problem
Schrödinger’s Cat
Wigner’s Friend
Relational Quantum Gravity
The Einstein Podolsky Rosen Paradox (EPR)
Bell’s Inequality
The Aspect Experiment
Locality and Causality
Emergence of Spacetime

Special Relativity

Structure of Spacetime
What is the Time?
Minkowski Coordinates
Maximal Speed of Information
Spacetime Diagrams
Time Dilation
Lorentz Contraction
4-Vectors
E = mc²

Basics of Curvature

The Development of Non-Euclidean Geometry
Intrinsic and Extrinsic Curvature
Curvature of Spacetime
Positive and Negative Curvature
Singularities
Tensor Curvature
Charts or Coordinate Systems
The Metric
Tangent Space
Parallel Displacement
Parallel Transport
Geodesic Motion

The Equivalence Principle

Newton’s Laws of Motion
Inertial Matter
Active and Inertial Forces
The Twin Paradox
The Equivalence Principle
The Pound-Rebka Experiment
Gravitational Red Shift
Mach’s Principle

Mathematical Methods

Miscellaneous Methods

Complex Numbers
e to the i
Sums and Integrals
Analysis
The Axiom of Infinity
The Relationship of Mathematics to Physics
Geometric Progression
The Dirac Delta Function
Representations of the Delta Function
Delta Function of a Function

Introduction to Vector Space

Scalars
Vector Space
Coordinates
The Dot Product
Ket Notation
Hilbert Space
Dirac’s Joke
The Cauchy-Schwarz Inequality
The Dot Product as an Inner Product
Orthonormal Bases
Contravariant and Covariant Vectors
Einstein Summation Convention
The Metric
3 Dimensions plus Time
The Light Cone
Coordinate Transformation
Lorentz Transformation
Spherical Coordinates

Functions, Operators, and Derivatives

Terminology
Functions and Graphs
Function Composition
Identity and Inverse
Functionals and Operators
Linear Operators
The Commutator and Anticommutator
Hermitian Conjugation
Hermitian Operators
Unitary Operators
The Differential Operator
Partial Derivatives

Introduction to Tensors

Tensor Space
The Tensor Product
Tensor Rank
Index Gymnastics
The Metric Tensor
Contraction
Symmetry and Antisymmetry
The Levi-Civita Tensor
Tensor Fields
The Principle of General Covariance
Electromagnetic Force

Gravity

Concepts of General Relativity

The Spacetime Manifold
Differentiability
Tangent Charts
Coordinate Time and Proper Time
The Spacetime Metric
Stationary Observers
The Levi-Civita Connection

Riemann Curvature

Christoffel Symbols
Parallel Displacement
The Covariant Derivative
Geodesics
The Riemann Curvature Tensor
Symmetries of the Curvature Tensor
The Bianchi Identity
Contracted Curvature Tensors

Einstein’s Law of Gravitation

The Weak Field Limit
Conservation of Mass-Energy
The Stress-Energy Tensor
Einstein’s Law of Gravitation
Stationary Matter
The Newtonian Approximation
The Schwarzschild Solution
Black Holes

Large Scale Structure of the Universe

The Cosmological Constant
Weyl’s Postulate
The Cosmic Fluid
The Cosmological Principle
Spaces of Constant Curvature
Cosmological Expansion
Cosmological Redshift
The Friedmann Equation
Friedmann Models
Timeline for Processes from the Big Bang

Relativistic Quantum Theory

Foundations of Quantum Theory

Quantum Logic
Truth Values
Sentences Describing Hypothetical Measurement Results
Integral Representation
Plane Wave States
The Resolution of Unity in Momentum Space

Observable Quantities

Probability Interpretation
Measurement
Quantum Measurement
Observable Operators
Classical Quantities
Quantisation
The Uncertainty Principle
Time-Energy Uncertainty

Evolution of Quantum States

Linearity of Time Evolution
Continuity of Time Evolution
Unitarity of Time Evolution
Stone’s Theorem
The Heisenberg Picture
The Wave Function
Newton’s First Law
Wave Mechanics

The Dirac Equation

The Klein-Gordon Equation
Spin
The Dirac Equation
Covariance of the Dirac Equation
Dirac Particles
Antiparticles
Conserved Current

States of Many Particles

The Vacuum State
Many Particles
Independence of Particles in Measurement
Identical Particles
The Pauli Exclusion Principle
Creation and Annihilation Operators

Particle Interactions

The Interaction Hamiltonian
The Classical Correspondence
The Interaction Picture
The Hamiltonian Density
The Perturbation Expansion
Time Ordered Diagrams
The Locality Condition
Conservation of Momentum

Quantum Electrodynamics

The Dirac Field Operator

Quantum Field Operators
Normal Order
The Dirac Field Operator
Locality of Dirac Field Operators
The Current Density Observable

The Photon Field Operator

Photons
Plane Wave Photon States
Evolution of Photon States
The Photon Field Operator
The Locality Condition for Photons

Classical Electromagnetism

The Classical Field
Gauge Symmetry
Momentum in the Interacting Theory
The Interacting Dirac Equation
The Lorentz Force Law
Gauge Invariance
Maxwell’s Equations

Feynman Diagrams

The Time Ordered Vertex for QED
Wick’s Theorem
The S-matrix
The Feynman Propagator
Conservation of Energy and Momentum
Feynman Rules OK

Scattering

The Scattering Cross Section
Cross Section and Probability
Cross Section and the Matrix Element
Two Particle Scattering
Rutherford Scattering

Regularisation and Renormalisation

The Ultraviolet Divergence
Regularisation
Vacuum Fluctuations
Renormalisation
The Renormalisation Group
The Landau Pole

Relational Quantum Gravity

Quantum Covariance

Substantivalism v Relationism
Measurement
Discrete Coordinates
Coordinate Rotation
Discretisation
Momentum Space
Bounds
Quantum Covariance
Operators
Lorentz Transformation

Introduction to the Teleconnection

The Status Quo
Distant Parallelism
The Teleconnection in a Friedmann Cosmology
Energy Transfer
Classical Spacetime

The Teleconnection

Absolute Space and Time
Suppression of Expansion in a Neighbourhood
The Teleconnection in a Friedmann Cosmology
Cosmological Redshift
Energy Transfer
Geometries with Expansion
Gravitational Redshift
The Levi-Civita Connection

Illusory Velocity

Quantum Coordinates
Bending of Light
Pioneer Blueshift
Circular Orbits

Particles Or Fields?

The Plenum
Quantum Field Theory
Particle Theory

A Gravitating Particle

The k-Calculus
A Modification to Radar
A Particle in a Position Eigenstate
The Path of Light
Einstein’s Field Equation

The Emergence of Spacetime Structure

Primitive Structures of Matter
The Physical Content of Einstein’s Field Equation
The Cosmological Constant
Non-Quantisability of Einstein’s Field Equation
The Page-Geilker Experiment
The Eppley-Hannah Thought Experiment

Singularities Revisited

Inflation
Pre-expansion as an Ametric Phase
Black Holes

Cosmological Parameters and Empirical Evidence

Supernovae Redshifts and Cosmological Parameters

Hubble’s Law
Cosmological Parameters
Observations of the Early Universe
Supernova Redshift

Anomalous Pioneer Blueshift

The Anomalous Pioneer Blueshift

Galaxy Rotation Curves, CDM and MOND

Dark Matter
Baryonic Dark Matter
Neutrinos (Hot Dark matter)
Bulk Flows and Structure Formation
Galaxy Rotation Curves
Cold Dark Matter
MOND
Illusory Velocity
Lensing
Halo Profiles

The Local Slope of the Rotation Curve

The Galaxy Rotation Curve
The Gradient of the Rotation Curve
Conflict with CDM and MOND

Radial Velocity Test

Method
Test Results
Implications

Solar Motion Relative to the Metal-poor Halo

The Metal-poor Halo
Distance Adjustments
Distance and Velocity Adjustment

Spiral Arms Unravelled

The Anatomy of Spiral Arms

Simulation
Galactic Orbits
Orbital Alignment
Spiral Potential
Flocculent Spirals
Multi-armed Spirals
Star Formation
Bisymmetric Spirals

The Velocity Distribution of Local Stars

Stellar Streams
Stream Properties

The Milky Way Spiral

Fitting Spiral Structure to the Milky Way
The Local Standard Of Rest
The Eccentricity Distribution
The Neutral Hydrogen Distribution
Streams and Spiral Structure
The Age of the Milky Way Spiral

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Epicycles
Closed Orbits
Density Wave Theory
Summary

Outline ↑ Philosophical Foundations →

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