Abstract
We concluded the previous chapter with the hope that the field may provide the way out of the paradoxes of thermodynamics. We point out that various intuitive ideas underlying field theory, such as action by ‘contact’, the idea of ‘locality’ or a ‘chain of causes’, or the mechanical model provided by the field, are respectively unintelligible, illusory, and redundant. Consequently, there is nothing ‘spooky’ about action at a distance.
We are left only with the differential equations of field theory, which admit both retarded and advanced solutions. In the context, the advanced solutions cannot be rejected on grounds of ‘causality’, and we state some of the paradoxes of advanced action: the pond, grandfather, and Wheeler-Feynman paradoxes.
We point out the divergences, due to self-action, in field theory. The Abraham-Lorentz model of the extended electron failed, while the action-at-a-distance approach is equivalent to time-symmetric fields. Even with Dirac’s approach, using the equivalence of advanced and retarded representations, the electron preaccelerates. Thus, consideration of interactions propagating into the past seems forced, and, prima facie, the introduction of the field seems to create more problems than it solves.
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Notes and References
M. Hesse, Forces and Fields, Westport, CT, 1973.
Ref. 1, p 78.
Ref. 1, p 168.
H. Poincaré [19021, Science and Hypothesis (N.Y.: Dover,1952), p 160–61.
Max Born, Einstein’s Theory of Relativity, Tr. Broce, London, 1924, p 132.
Nyayavarttika, Tr. Ganganath Jha, 1919, Indian Thought, pp 238–48; In: K. H. Potter, Encyclopaedia of Indian Philosophy, Vol. II, Motilal Banarsidass, Delhi, pp 334–5, 1977. The first part of the quotation refers to the pßrva paksa or the opponent’s position, and is actually a translation of Sutra IV.2.24. See, The Nyaya Sutras of Gautam, Tr. Ganganath Jha, Vol. IV, Motilal Banarsidass, New Delhi, reprint 1984.
Ref. 1, p 160.
Ref. 1, p 168.
Ref. 4, p 169.
In quantum-field theory, with the associated renormalization procedure, the field is regarded as necessary; but this could well be a case of bad mathematics masquerading as good physics. Specifically, the renormalization procedure can be made rigorous, using the Hahn-Banach theorem, but the usual procedure does not quite ‘work’, since the non-uniqueness of the Hahn-Banach extension cannot be removed for a variety of otherwise plausible Lagrangians. See, e.g., C.K.Raju, J. Phys. A: Math. Gen., 16, 3739 (1983); Hadronic J. Suppl., 1, 352 (1986).
This does not mean that a uniformly accelerated charge does not radiate. This point has caused some confusion especially in the relativistic case, e.g., a freely falling charge need not radiate, while a particle at rest in a gravitational field should. See, e.g., H.D. Zeh, The Direction of Time, Springer, Berlin, 1989.
K. R. Popper, Nature, 171, 538 (1956); 178, 382 (1956); 179, 297 (1957); 181, 402 (1958); Brit. J. Phil. Sci., 8, 151 (1957); The Open Universe, Hutchinson, London, 1982.
J.L. Friedmann and M.S. Morris, Phys. Rev. Lett., 66(4), 1991; M.S. Morris and K.S. Thorne, Amer.J. Phys., 56, 395 (1988); M.S. Morris, K.S. Thorne, and U. Yurtserver, Phys. Rev., D 42, 1915 (1990), and references cited therein.
J.A. Wheeler and R.P. Feynman, Rev. Mod. Phys., 21, 425 (1949).
P.C.W. Davies, The Physics of Time Asymmetry, Surrey Univ. Press, London, 1974.
F. Rohrlich, Classical Charged Particles, Addison-Wesley, Reading, Mass., 1965.
G.N. Plass, Rev. Mod. Phys., 33, 37–62 (1961); or Ref. 15.
Ref. 16, p 135, p 140.
C.J. Eliezer, Rev. Mod. Phys., 19, 147 (1947).
cited in Ref. 17.
M. Dresden, H.A. Kramers: Between Tradition and Revolution, Springer, New York, 1987.
Ref. 15.
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Raju, C.K. (1994). The Electromagnetic Field. In: Time: Towards a Consistent Theory. Fundamental Theories of Physics, vol 65. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-8376-3_7
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