you would be a real seeker after truth, you must at least once in
your life doubt, as far as possible, all things.
la Méthode (1637)
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.
educational videos, please visit:
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
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).
to Wave Mechanics: Dirac Equation by
Robert A. Close (draft version: 9 September 2021)
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
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.
feedback is welcome at email@example.com
2021 Lecture Slides: Relativistic Wave Mechanics for Undergraduates
for teaching undergraduates the Dirac equation prior to the
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.
Angular Momentum and the Dirac Equation,
A. Close, Elect. J. Theor. Phys. 12, 43 (2015)]
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.
Wave Basis of Special Relativity,
Robert A. Close (published by Verum Versa, 2014)
explanation of WHY special relativity works, not just how it works.
additional publications, visit VerumVersa.com.
Is there an (a)ether?
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.
the Aether (Über
den Äther) 1924
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
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,
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
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
which represents speed in directions perpendicular to the average
velocity (i.e. wave circulation).
The equation can also be written as:
is the particle momentum and E
is the energy. In terms of wave variables:
wave propagation, and the mass term represents oscillation without
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
This site is hosted by
Created: February 27, 2006;
Last updated: 08/01/20
Robert A. Close