We respond to Comay’s criticism of the use of covariant definitions of the electromagnetic and mechanical energy–momenta in an analysis of the role of hidden momentum in the total energy–momentum four vector of a macroscopic body.
REFERENCES
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Comay cites in detail from the proof of this statement in L. D. Landau and E. M. Lifshitz, The Classical Theory of Fields (Pergamon, Oxford, 1975). There are several such proofs in the literature, the oldest going back some 80 years:
H. Weyl, Space-Time-Matter (Dover, New York, 1950), first American printing of the 4th edition of 1922, Sec. 33;
W. Pauli, Theory of Relativity (Pergamon, London, 1958), Sec. 21;
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C. W. Misner, K. S. Thorne, and J. A. Wheeler, Gravitation (Freeman, San Francisco, 1973), Sec. 5.8, case (c).
4.
Comay’s examples are systems of infinite extension, and also of infinite energy and, except in his second example, infinite momentum. While the use of such systems simplifies the requisite integrations, infinite systems are, strictly speaking, unphysical; moreover, the general theorem that guarantees that the total momentum of a stationary macroscopic system vanishes [see, e.g.,
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There is an English, modernized presentation of Poincaré’s 1906 paper on the electron by
H. M.
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J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1999), 3rd ed., Secs. 16.4–16.6.
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