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Notes
V. Fock,The Theory of Space Time and Gravitation, Pergamon Press, New York, 1959, p. XVIII.
S. Körner,Observation and Interpretation, Butterworths Scientific Publications, London, 1957, p. 41.
P. A. Schilpp,Albert Einstein: Philosopher-Scientist, Library of Living Philosophers, Inc., Evanston, Ill., 1949, p. 3.
E. Schrödinger,Brit. J. Phil Sci. 3 (1952), 109, 233.
M. Planck,Scientific Autobiography and Other Papers, Philosophical Library, New York, 1949.
L. De Broglie,Non-Linear Wave Mechanics, Elsevier Publishing Co., Amsterdam, 1960.
M. von Laue,Naturwissenschaften 38 (1951) 60.
S. Körner,Observation and Interpretation, Butterworths Scientific Publications, London. 1957, p. 33.
This non-relativistic and static mechanical theory may be extended to the special theory of relativity and to true motion in time for the rays by modifying Fermat's principle to read' “the ray will take that path which accomplishes the motion in the least proper time”.
The actual history of geometrical optics was quite different, since Hamilton's optical theory (embodied in eq. (1)) was formulated in the first half of the 19th century. However, the theorymight have been created before Young's discovery of the wave-like nature of light.
At this stage of our argument, the rays are not to be confused with photons which only exist in a quantized theory. Our rays do not have all the properties of mass particles, a point which we shall amplify later.
1/k plays the same role in optics as does Planck's constanth in the quantum theory.
The probability distribution of rays defined byϕ * ϕd 3 x arises from the conservation law of electromagnetic field energy. We have chosenϕ to be proportional to a single component of the electric field vector, so thatϕ * ϕd 3 x is proportional to the electromagnetic energy in the volume elementd 3 x. In the limit of geometrical optics, we relate the density of rays to the energy density of electromagnetic energy by arbitrarily assuming a certain number of rays to be associated with a given energy density of the beam. Hamilton's theory of geometrical optics which is embodied in eq. (1), also predicts an equation of continuity for rays. The conserved density of rays in the short wave length limit is roughlyϕ * ϕ. The law states that the number of rays is conserved, and this conservation law is again a consequence of the conservation of electromagnetic energy.
In relativistic phenomena, particles may be created and destroyed, but our present discussion is reserved for non-relativistic effects.
Aspects of this thesis are in agreement with the views of Schrödinger; see footnote 4.
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Schiller, R. Interpretations of the quantum theory. Synthese 14, 5–16 (1962). https://doi.org/10.1007/BF02274801
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DOI: https://doi.org/10.1007/BF02274801