Abstract
The Schrödinger and Klein-Gordon equations for free, structureless particles are derived classically from two different continuum approximations to a Boltzmann equation for the trace component of a mixture. The majority component is designated as the ether. Deviations from these continuum approximations (rarefied ether) yield deviations from the Schrödinger and Klein-Gordon equations which are shown explicitly.
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References
J. C. Maxwell,Phil. Mag. 19, 19 (1860);20, 21 (1860), reprinted inCollected Works (Dover, New York, 1965), Vol. 1, p. 377, and inKinetic Theory I, S. G. Brush, ed. (Pergamon, Oxford, 1965), p. 148.
J. C. Maxwell,Phil. Trans. R. Soc. London 157, 49 (1867);Phil. Mag. 32, 390 (1866), reprinted inCollected Works (Dover, New York, 1965), Vol. 2, p. 26, and inKinetic Theory II, S. G. Brush, ed. (Pergamon, Oxford, 1966), p. 23.
P. Langevin,Ann. Chim. Phys. 5, 245 (1905), translated in E. W. McDaniel,Collision Phenomena in Ionized Gases (Wiley, New York, 1964), Appendix II.
H. R. Hassé,Phil. Mag. 1, 139 (1926).
G. H. Wannier,Statistical Physics (Wiley, New York, 1966), p. 457.
L. de Broglie,Comp. Rend. 183, 447 (1926).
L. de Broglie,Compt. Rend. 184, 273 (1927).
L. de Broglie,J. Phys. Radium (6)8, 225 (1927).
L. de Broglie,Comp. Rend. 234, 265 (1952).
L. de Broglie,Comp. Rend. 235, 557, 1345, 1453 (1952).
D. Bohm,Phys. Rev. 85, 166, 180 (1952).
D. Bohm,Progr. Theor. Phys. 9, 273 (1953).
D. Bohm and J. P. Vigier,Phys. Rev. 96, 208 (1954).
N. Wiener and A. Siegel,Phys. Rev. 91, 1551 (1953).
N. Wiener and A. Siegel,Nuovo Cimento Suppl. 2(4), 982 (1955).
P. Braffort and C. Tzara,Compt. Rend. 239, 157 (1954).
A. Siegel,Synthese 14, 171 (1962).
J. M. Janch and C. Piron,Helv. Phys. Acta 36, 827 (1963).
P. Braffort, M. Surdin, and A. Taroni,Compt. Rend. 261, 4339 (1965).
T. Marshal,Proc. Cambr. Phil. Soc. 61, 537 (1965).
R. C. Bownet,Can. J. Phys. 43, 619 (1965).
J. S. Bell,Rev. Mod. Phys. 38, 447 (1966).
D. Bohm and J. Bub,Rev. Mod. Phys. 38, 453 (1966).
R. Furth,Z. Physik 81, 143 (1933).
I. Fényes,Z. Physik 132, 81 (1952).
W. Weizel,Z. Physik 134, 264 (1953);135, 270 (1953);136, 582 (1954).
D. Kershaw,Phys. Rev. 136, B1850 (1964).
G. G. Comisar,Phys. Rev. 138, B1332 (1965).
E. Nelson,Phys. Rev. 150, 1079 (1966).
E. Nelson,Dynamical Theories of Brownian Motion (Princeton Univ. Press, Princeton, New Jersey, 1967).
A. F. Kracklauer,Phys. Rev. D 10, 1358 (1974).
J. von Neumann,The Mathematical Foundations of Quantum Mechanics (Princeton Univ. Press, Princeton, New Jersey, 1955).
L. Boltzmann,Ber. Akad. Wiss. Vienna II 66, 275 (1872); translated in S. G. Brush,Kinetic Theory II (Pergamon, Oxford, 1966), p. 88.
J. H. Ferziger and H. G. Kaper,Mathematical Theory of Transport Processes in Gases (North Holland, Amsterdam, 1972).
D. Burnett,Proc. London Math. Soc. 39, 385 (1935).
C. S. Wang-Chang and G. E. Uhlenbeck, inStudies in Statistical Mechanics, J. de Boer and G. E. Uhlenbeck, eds. (North-Holland, Amsterdam, 1970), Vol. V.
T. Kihara,Rev. Mod. Phys. 25, 844 (1953).
E. A. Mason and H. W. Schamp,Ann. Phys. (N.Y.)4, 233 (1958).
H.-S. Hahn and E. A. Mason,Phys. Rev. A 7, 1407 (1973).
J. H. Whealton and E. A. Mason,Ann. Phys. (N.Y.)84, 8 (1974).
H. Grad, inHandbuch der Physik, S. Flügge, ed. (Springer-Verlag, Berlin, 1958), Vol. 12, p. 205 ff.
H. Grad,Phys. Fluids 6, 147 (1963).
H. Grad,Rarefied Gas Dynamics (Academic Press, New York, 1963), Vol. 1, p. 26.
F. B. Pidduck,Proc. London Math. Soc. 15, 89 (1915).
S. Chapman,Phil. Trans. R. Soc. 216, 279 (1916).
D. Enskog, Dissertation, Uppsala 1917, translated in S. G. Brush,Kinetic Theory III (Pergamon, Oxford, 1972), p. 125.
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Whealton, J.H. Illustrations of a dynamical theory of the ether. Found Phys 5, 543–553 (1975). https://doi.org/10.1007/BF00708895
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DOI: https://doi.org/10.1007/BF00708895