Nothing is at last sacred but the integrity of your own mind.
Ralph Waldo Emerson
The Classical Wave Theory of Matter
Robert A. Close
The work presented here is a book-in-progress. It is intended as an undergraduate-level introduction to modern physics. Constructive suggestions are welcome via email to firstname.lastname@example.org.
Figures The figures are presently stored in a separate file. I apologize for the inconvenience.
Chapter1 Review of Conventional Physics
A review of conventional physics (not yet available).
Chapter 2 Matter Waves and Special Relativity
Special Relativity is usually understood as a fundamental property of space-time. However, the property of Lorentz invariance which forms the mathematical basis for special relativity is not special at all. All wave equations are Lorentz invariant. Lorentz transformations between inertial reference frames are obtained whenever waves are used to measure both time and distance. Light is 'special' because matter waves propagate at the same speed. Matter appears to move slower only because the wave packets propagate in closed paths (e.g. circles), forming localized vibrations or soliton waves.
It should be noted that the speed of light is not directly measurable using matter. Rather, the numerical value of the speed of light is simply a conversion factor between the units of distance and the units of time (one meter is in fact defined as the distance light travels in 1/c seconds).
Much of the analysis in this chapter has been previously published on the internet under the title: “The Other Meaning of Special Relativity” by R. Close, at http://SolidUniverse.home.att.net (© 2001). The original paper is also available here.
Chapter 3 Classical Waves and Quantum Mechanics
A Dirac-like equation is derived by factoring the one-dimensional wave equation and then generalizing with rotations of velocity and polarization. The general vector wave equation can then be derived from the resulting 'bispinor' equation. The general solution of the one-dimensional wave equation is a superposition of forward- and backward-propagating waves. These two independent states are separated in space by a 180 degree rotation and therefore form a spin 1/2 system. Complex spinors (Dirac spinors or bispinors) are required in order to rotate the wave velocities in three dimensions. Waves can propagate along curved paths (e.g. spirals) with mass proportional to the velocity rotation rate.
See also R. A. Close, "Torsion Waves in Three Dimensions: Quantum Mechanics with a Twist," Foundations of Physics Letters, 15(1):71-83, Feb. 2002.
More work is needed to determine whether elastic solitons actually correspond to elementary particles. If not, how are they different?
Chapter 4 Wave Refraction and Gravity
If the vacuum behaves like an elastic solid, then gravity can be interpreted as compression of the solid. Rigid rotation of an elastic solid must be balanced by compressional forces within the solid. The solid always expands within the region of rotation, resulting in an excess density outside the region of rotation. Since waves refract toward regions of slower wave speed, the increased density in the vicinity of elastic wave packets could result in a mutual attraction between waves. In Einstein's general theory of relativity the speed of light differs in a gravitational potential relative to empty space, as measured in the empty space coordinates [see e.g. A. Einstein, The Meaning of Relativity, (Fifth Edition, Princeton University Press, Princeton, 1956), p. 93]. This difference in the speed of light is proportional to the gravitational potential. Therefore gravitational acceleration may be interpreted as refraction of waves in a non-uniform medium.
©Copyright 2001-2009 Robert A. Close. All Rights reserved.
Created: 27 February 2006; Last updated: 22 October 2008
Copyright © 2006-2010 Robert A. Close