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[Overview] [Myths] [Fast Physics] [Underwater Relativity] [What is Matter?] [Classical Theory] |
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Science is the belief in the ignorance of experts.
Richard Feynman [The Physics Teacher, 7 September, 1969, 313-320] For educational videos, please visit: https://www.youtube.com/user/ClassicalMatter Recent developments: Plane Wave Solutions to a Proposed “Equation of Everything” by Robert A. Close (updated 14 October 2024). This paper presents the Dirac bispinor representation of spin density plane waves in an ideal elastic solid. Dirac operators for momentum, spin, kinetic energy, and potential energy are derived. The paper also explains the intrinsic momentum associated with the Belinfante-Rosenfeld stress-energy tensor. Simple Calculations of Classical Spin Angular Momentum by Robert A. Close (updated 16 October 2024) This paper explains spin angular momentum and demonstrates with simple examples how it is calculated. The relationships between spin angular momentum, velocity, and angular velocity are similar to the relationships between magnetostatic vector potential, magnetic field, and electric current. It is summarized in this lecture and slides. A Classical Model of Quasi-Static General Relativity, by Robert A. Close (updated 07 May 2024). This work utilizes an elastic solid model of the vacuum to explain how the presence of wave energy would modify a medium to produce the metric variations of general relativity in a quasi-static environment. This analysis reproduces many predictions of general relativity, including the difference in acceleration of light and non-relativistic massive objects. Dirac Equation for Spin Density in an Ideal Elastic Solid by Robert A. Close (updated 14 March 2024). Slides for APS 2024 April Meeting. This work attempts to model elementary particles as shear waves in an elastic solid. The resulting equation is similar to the well-known Dirac equation for an electron. Instead of a single “mass” term representing a particle’s rest energy, the elastic solid equation contains mathematical expressions for both kinetic energy (associated with motion) and potential energy (associated with stresses in the solid). Analogs of electric and magnetic fields can be used to describe interactions between waves. Dirac Operators for Potential and Kinetic Energy by Robert A. Close (updated 14 March 2024). Slides for APS 2024 April Meeting. Since its discovery in the 1920’s, spin angular momentum of elementary particles was long presumed to have no counterpart in classical physics. However, in this century it was discovered that waves in an elastic solid have spin angular momentum described by an equation similar to the one used by Paul Dirac to describe electrons in 1928. This paper analyzes simple waves in an elastic solid to identify mathematical expressions for kinetic energy (attributable to motion) and potential energy (attributable to stresses in the solid). It is found that the “mass” term in Dirac’s equation corresponds to twice the potential energy of waves in an elastic solid. The Different Meanings of “Spin” by Robert A. Close (updated 8 March 2024). This paper explains three meanings of the word “spin”: (1) kinetic spin meaning angular velocity, (2) geometric spin describing the pointwise symmetry of basis states under rotation, and (3) dynamic spin, which is what we normally describe as angular momentum. The Dirac equation of relativistic quantum mechanics has geometric spin of one-half, and describes waves whose polarization vector is the density of dynamic spin angular momentum. In both classical physics and relativistic quantum mechanics, the spin density is the vector field whose curl is equal to twice the intrinsic momentum density. Predictions and Validations of an Elastic Solid Aether Model by Robert A. Close (updated 20 July 2022). Lecture slides explain how several seminal physics experiments validate the hypothesis of an elastic solid aether filling space. These include the Michelson-Moreley experiment (special relativity), the Eddington expedition (general relativity), the Stern-Gerlach experiment (spin angular momentum), and Wu's beta-decay experiment (spatial reflection). Recorded lecture at https://drive.google.com/file/d/1s0xLRi9EWvnD_N2Nqe-WCX1GiNenhyJC/view?usp=sharing Classical Wave Mechanics (pdf) by Robert A. Close. Lecture slides explaining how classical wave mechanics explains many features of relativistic quantum mechanics (revised 3 September 2020). Introduction to Wave Mechanics: Dirac Equation by Robert A. Close (draft version: 9 September 2021) An explanation of the wave nature of matter based on a model of the vacuum as an elastic solid. The paper offers simple physical interpretations of spin angular momentum, special relativity, and the Dirac equation. Plane wave solutions demonstrate the relationship between the first-order Dirac equation and the second-order wave equation. Introduction to Wave Mechanics: Interactions by Robert A. Close (draft version: 21 November 2024) Interference of classical waves yields the Pauli exclusion principle, electromagnetic potentials, and magnetic flux quantization. The relationship between electric charge and magnetic flux is derived from a standing wave model. The classical Lagrangian corresponding to quantum electrodynamics is derived for a particle interacting with the electromagnetic field of another particle. Constructive feedback is welcome at robert.close@classicalmatter.org
ORAAPT 2021 Lecture Slides: Relativistic Wave Mechanics for Undergraduates (pdf) An argument for teaching undergraduates the Dirac equation prior to the Schödinger equation.
Resources (in order of difficulty): What would a classical universe be like? A brief summary is given here.
Rationale for studying aether models of the universe.
Some common misconceptions about modern physics.
Brief explanations of physics concepts.
2016
Clark College Faculty Speaker Series lecture "Illuminating
the Theory of Relativity"
Circulating Wave Model of Special Relativity [pdf] Print this sheet on transparency paper and roll it into a cylinder to demonstrate relativistic frequency shift, time dilation, length contraction, and de Broglie wavelength for a particle-like wave packet. (See the video No-Nonsense Physics: Wave-Particle Duality)
Matter Waves and Relativity [pdf] A hands-on high school or college-level activity for learning about relativistic time dilation and length contraction.
Underwater Relativity [html5] Animations demonstrate how the wave nature of matter implies the laws of Special Relativity. (For an overview, watch the video No-Nonsense Physics: Special Relativity)
What is Matter? [pdf] This is a slide presentation explaining relativity and other wave properties of matter at a high school level.
A Time Traveler's History of Physics [pdf] Presentation at the APS April Meeting, Anaheim, CA on April 30, 2011.
The Other Meaning of Relativity [pdf] Einstein’s special theory of relativity postulates that the speed of light is a constant for all inertial observers. This postulate can be used to derive the Lorenz transformations relating length and time measurements by different observers. In this paper it is shown that the Lorentz transformations can be obtained for any type of wave simply by defining distance to be proportional to wave propagation time. The special nature of light is that length and time measured by light propagation correspond exactly with length and time measured by material rulers and clocks. This suggests that material objects consist of waves propagating at the speed of light. Taking this as an alternative postulate for special relativity implies constancy of the measured speed of light without any recourse to non-Euclidean geometry of physical space-time. This alternative postulate is consistent with de Broglie’s wave hypothesis, with the Dirac velocity operator of quantum mechanics, and with experimental observations of transformations between matter and light.
Exact Description of Rotational Waves in an Elastic Solid (Adv. Appl. Clifford Algebras 21:273-281, 2011) The dynamical behavior of an ideal elastic solid is arguably the most fundamental problem in theoretical physics, yet its mathematical description has eluded physicists – until now. Rotational (incompressible) waves in an elastic solid provide a physical interpretation of quantum mechanical operators and statistics.
Spin Angular Momentum and the Dirac Equation (EJTP 12, No. 33 (2015) 43–60) The usual definition of angular momentum, r×p, is clearly unphysical because it depends on the choice of origin for definition of the radius vector r. A better physical description defines spin angular momentum density as the field whose curl is equal to twice the momentum density: p=(1/2)∇×S This definition yields the usual classical results for total angular momentum and kinetic energy. When applied to elastic waves, it also yields the quantum mechanical operators for orbital and spin angular momentum.
The Classical Wave Theory of Matter (2011 .pdf format) This is a rough (and outdated) draft undergraduate level book which uses classical wave theory to explain many properties of matter including Special Relativity, gravity, spin 1/2 'particles', and other wave characteristics of matter.
Torsion Waves in Three Dimensions: Quantum Mechanics with a Twist (Foundations of Physics Letters, Vol 15, No. 1, February 2002) . Available from SpringerLink. A classical physics derivation of the Dirac equation.
Links: Free and open inquiry is the basis of progress. Please support freedom of expression, human rights, and education for all. http://www.amnesty.org Amnesty International http://hrw.org Human Rights Watch http://www.oxfam.org Oxfam International http://www.redcross.int International Red Cross and Red Crescent Movement http://www.unicef.org United Nations Children’s Fund Physics Links: http://www.aps.org American Physical Society http://www.iop.org Institute of Physics http://home.online.no/ ~ukarlsen B. U. Karlsen "The Great Puzzle," 2003 updated from "Sketch of a Matter Model in an Elastic Universe," 1998. This is a different attempt at a classical description of matter based on the elastic solid model. This is a good summary of doubts about modern physics and possible alternatives. http://math.ucr.edu/home/baez/relativity.html
Relativity
on the World Wide Web http://www.skeptic.com The Skeptics Society is a scientific and educational organization of scholars, scientists, historians, magicians, professors and teachers, and anyone curious about controversial ideas, extraordinary claims, revolutionary ideas, and the promotion of science. About the Author: Dr. Robert A. Close holds a BS in physics from the Massachusetts Institute of Technology and a PhD in physics from the University of California at Berkeley. |
Created: February 27, 2006; Last updated: April 22,2 024
Copyright © 2006-2024 Robert A. Close
