On the Question of the Measurability of Electromagnetic Field Quantities [with Niels Bohr] [1933b]
The question of limitations on the measurability of electromagnetic field quantities, rooted in the quantum of action, has acquired particular interest in the course of the discussion of the still unsolved difficulties in relativistic atomic mechanics. On the basis of exploratory considerations, Heisenberg1attempted to demonstrate that the connection between the limitation on the measurability of field quantities and the quantum theory of fields is similar to the relationship between the complementary limitations on the measurability of kinematical and dynamical quantities expressed in the indeterminacy principle and the non-relativistic formalism of quantum mechanics. However, in the course of a critical investigation of the foundations of the relativistic generalization of this formalism, Landau and Peierls2came to the conclusion that the measurability of field quantities is subjected to further restrictions which go essentially beyond the presuppositions of quantum field theory, and which therefore deprive this theory of any physical basis.
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- 1.W. Heisenberg, The Physical Principles of the Quantum Theory, trans, by C. Eckart and F. Hoyt (Dover. New York, 1930), pp. 42 ff.Google Scholar
- 3.Cf. N. Bohr. ‘Atomic Stability and Conservation Laws’, Atti del Congresso di Fisica Nucleare(1932). Added in the proof: A separate publication to appear shortly will contain a discussion of the consequences for the problems discussed in the cited reference implied by the recent discovery of the occurrence, under special circumstances, of so-called ‘positive electrons’; and by the recognition of the connection of this discovery with Dirac’s relativistic electron theory.Google Scholar
- s Cf. P. Jordan and W. Pauli. Zs.f. Phys. 47(1928). 151 and also W. Heisenberg and W. Pauli, Zs.f. Phys. 56(1929), 33. Apart from an unessential difference in sign resulting from a difference in the choice of time direction in the Fourier decomposition of the field strengths, the formulae above are equivalent in content with those derived in the papers quoted. In particular, the notation used here, where all terms appear as retarded, is a purely formal change which aims at an interpretation of the measurement problems that is as intuitive as possible.Google Scholar
- 6.Cf. L. Rosenfeld and J. Solomon, J. de Physique 2(1931), 139 and also W. Pauli, Handbuch d. Physik. 2nd edition. Vol. 24/1 (1933). p. 255.Google Scholar
- 7.Cf. W. Heisenberg. Leipziger Berichte 83(1931), 1.Google Scholar
- 8.Cf. V. Fock and P. Jordan, Zs.f. Phys. 66(1930), 206, where reference is made to such restrictions on field measurements, which are unrelated to the quantum theory of fields. Cf. also J. Solomon, J. de Physique 4 (1933), 368.Google Scholar
- 9.Cf. W. Pauli, Handbuch d. Physik, 2nd edition. Vol. 24/1 (1933), p. 257.Google Scholar
- 10.See N. Bohr, Atomic Theory and the Description of Nature(Cambridge University Press, Cambridge, England. 1934). In the meantime, this question has been treated in more detail by the author in a guest lecture in Vienna, to appear shortly, in which in particular the paradoxes arising in the interpretation of the indeterminacy principle when account is taken of the requirements of relativity are further discussed.Google Scholar