|
[Overview]
[Myths] [Fast Physics] [Underwater Relativity]
[What is Matter?] [Classical Theory]
|
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
An “Equation of Everything”?
Spin density (s) is defined in both
classical and quantum physics by the equation:
where p
is the incompressible momentum density (uniquely defined by Helmholtz
decomposition).
A proposed “Equation of Everything” is:
where s
is spin density, u is velocity (p/ρ where ρ is inertial density), c is the speed of light, and Q
is the time integral of s. The right-hand side represents torque density.
Recent developments:
Plane Wave Solutions to a Proposed
“Equation of Everything” by
Robert A. Close
Foundations of Physics (2025) 55:27
https://doi.org/10.1007/s10701-025-00839-0
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.
ORAAPT 2021
Lecture Slides: Relativistic Wave
Mechanics for Undergraduates (pdf)
An argument for
teaching undergraduates the Dirac equation prior to the Schödinger
equation.
Constructive
feedback is welcome at robert.close@classicalmatter.org
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"
Part 1:
https://www.youtube.com/watch…
Part 2:
https://www.youtube.com/watch…
Part 3:
https://www.youtube.com/watch…
Part 4:
https://www.youtube.com/watch…
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
https://www.ucs.org Union of Concerned
Scientists
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
Original by Chris Hillman; maintained by John Baez
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.