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If you would be a real seeker after truth, you must at least once in your life doubt, as far as possible, all things.

René DesCartes
Discours de la Méthode (1637)

Welcome to ClassicalMatter.org

Classical Matter is a project devoted to science education. It is intended as a resource for students, educators, and others who are curious about our universe. The general purpose is to de-mystify science, offer sensible explanations of natural phenomena, refute popular myths, and promote evidence-based reasoning. Special emphasis is on the use of classical physical models and methods to explain properties of matter which are elsewhere deemed to be 'non-classical' , or counterintuitive. Topics include special and general relativity, spin 1/2 wave functions, and parity violation. If you want to truly understand how modern physics relates to classical physics, then select  Contents  to see Resources and Links. 

For educational videos, please visit: https://www.youtube.com/user/ClassicalMatter

Recent developments:

Predictions and Validations of an Elastic Solid Aether Model by Robert A. Close (updated 20 July 2022). Lecture slides (ppt, pdf) 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 (pptx, 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: 22 August 2022)

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, ppt)

An argument for teaching undergraduates the Dirac equation prior to the Schödinger equation.

Selected Publications:

Relativity Model: A stationary particle is modeled as a wave propagating in a circle. The corresponding moving particle has rotated wave crests and propagates along helical paths. This model yields relativistic frequency shift (kinetic energy), time dilation, length contraction, and the deBoglie wavelenth. The model is designed to be printed on a transparency sheet, but can be printed on paper and illuminated with a light shining through the cylindrical tube.

Spin Angular Momentum and the Dirac Equation, [R. A. Close, Elect. J. Theor. Phys. 12, 43 (2015)]

Abstract: Quantum mechanical spin angular momentum density, unlike its orbital counterpart,is independent of the choice of origin. A similar classical local angular momentum density maybe defined as the field whose curl is equal to twice the momentum density. Integration by parts shows that this spin density yields the same total angular momentum and kinetic energy as obtained using classical orbital angular momentum. We apply the definition of spin density to a description of elastic waves. Using a simple wave interpretation of Dirac bispinors, we show that Dirac’s equation of evolution for spin density is a special case of our more general equation. Operators for elastic wave energy, momentum, and angular momentum are equivalent to those of relativistic quantum mechanics.

The Wave Basis of Special Relativity, by Robert A. Close (published by Verum Versa, 2014)

For additional publications, visit VerumVersa.com.

Is there an (a)ether?

...we will not be able to do without the aether in theoretical physics, that is, a continuum endowed with physical properties; for general relativity, to whose fundamental viewpoints physicists will always hold fast, rules out direct action at a distance.

Albert Einstein, Concerning the Aether (Über den Äther) 1924

If one examines the question in light of present-day knowledge, one finds that the aether is no longer ruled out by relativity, and good reasons can now be advanced for postulating an aether.

Paul Dirac, in Nature, 1951, vol. 168, pp. 906-907

The modern concept of the vacuum of space, confirmed by everyday experiment, is a relativistic ether. But we do not call it this because it is taboo.

Robert Laughlin, A Different Universe, p.120-121 (2005)

It has also been shown that rotational waves in an isotropic continuous elastic solid can be described within the formalism of the Dirac equation providing a classical interpretation of relativistic quantum mechanics.15

P. A. Deymier, K. Runge, N. Swinteck, and K. Muralidharan in J. Appl. Phys. 115, 163510 (2014)

15R. A. Close, Adv. Appl. Clifford Algebras 21, 273 (2011).

Classical Matter Logo: Did you know that Einstein's famous mass-energy formula  E=mc2 is actually a special case of the Pythagorean Theorem? The relativistic 'mass' is actually the rest mass m0 times a factor γ  (gamma) which represents the ratio between the hypotenuse and the third side of a right triangle. The hypotenuse is the speed of light (c), the second side is particle velocity (v), and the third side is c/γ =(c2-v2)1/2, which represents speed in directions perpendicular to the average velocity (i.e. wave circulation). The equation can also be written as: 

where p=γ m0v is the particle momentum and E is the energy. In terms of wave variables:

with angular frequency ω and wave number k representing wave propagation, and the mass term represents oscillation without propagation.

Contact Information

If you would like to add an educational resource or link, comment on existing resources or links, or sponsor this site, please contact Robert Close at robert.close@classicalmatter.org.

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Created: February 27, 2006;  Last updated: 08/01/20

Copyright © 2006-2023   Robert A. Close