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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)

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)

An explanation of WHY special relativity works, not just how it works.

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)

^{15}R. A.
Close, *Adv. Appl. Clifford Algebras* **21**, 273 (2011).

Classical Matter Logo:
Did you know
that Einstein's famous mass-energy formula *E=mc*^{2}
is actually a
special case of the Pythagorean Theorem? The relativistic 'mass' is
actually the rest mass *m*_{0}
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
*=(*c*^{2}-*v*^{2})^{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*
*m*_{0}*v*
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.

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;
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2006-