Abstract
Schrödinger has often been reproached for having formulated (or reformulated) a wave-interpretation of quantum mechanics in the 1950’s, without even trying to ground it in some calculations. People usually regret that he limited himself to generalities or philosophical considerations. L. Wessels notices that “(...)unlike de Broglie, who at about that same time returned to the task of constructing a precise mathematical theory based on his own pilot wave interpretation, Schrödinger did not attempt to work out his new wave picture in detail. Where in 1925 such an idea had been the starting point the creation of a new physical theory, it now gave rise only to philosophical polemic”1. However, there is an obvious difference between de Broglie’s and Schrödinger’s positions, which should not have escaped the commentators. De Broglie was bound to formulate new mathematical laws, in order to rule the classical-like entities of the “sub-quantal” realm which were supposed by him to be incompletely (only statistically) described by quantum mechanics. By contrast, Schrödinger strongly rejected the idea that quantum mechanics is incomplete in the sense advocated by Einstein and de Broglie.
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References
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ibid. p. 18
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E. Schrödinger, July 1952 colloquium 1952, (E. Schrödinger, The interpretation of quantum mechanics (Dublin seminars 1949–1955 and other unpublished texts), op. cit. p. 20). See chapter 6 for more details about Bohr’s and Schrödinger’s views on “complementarity”.
ibid.
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Schrödinger explicitly rejected the project of “framing ontologically” the elements of our physical pictures, if “ontologically” is taken in the metaphysical sense, see e.g. “Might perhaps energy be a merely statistical concept”, in: Gesammelte abhandlungen, op. cit., vol. 1, p. 508
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ibid.
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Unexpectedly, Born was not very far from this position either. A few sentences in his Waynflete lectures of 1948 could almost have been written by Schrödinger: “I personally like to regard a probability wave, even in 3N-dimensional space, as a real thing, certainly as more than a tool for mathematical calculations. For it has the character of an invariant of observation; that means it predicts the results of counting experiments, and we expect to find the same average numbers, the same mean deviations, etc., if we actually perform the experiment many times under the same experimental condition. Quite generally, how could we rely on probability predictions if by this notion we do not refer to something real and objective?”. M. Born, Natural philosophy of cause and chance, Oxford University Press, 1949, chap. IX
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See e.g. E. Husserl (1913), Ideas (general introduction to pure phenomenology), Engl. Tr. G. Allen & Unwin, 1931, §136: “We have yet to note that the expression ‘fulfilment’ (Erfüllung) has still another ambiguity which lies in a quite other direction: at one time it is ‘fulfilment of intention’, as a character which the actual thesis takes on through the special mode of meaning; at another it is precisely the peculiarity of this mode itself or the peculiar property of the meaning in question, to conceal ‘rich resources’ which motivate in accordance with reason”. Sometimes ‘Erfüllung’ is also translated ‘filling-out’. See also chapter 5.
See P. Heelan, Quantum mechanics and objectivity, op. cit. p. 118.
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ibid.
ibid. p. 82
Or the “interpretation”, in the restricted sense Schrödinger ascribed to this word.
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About this equivalence see B. d’Espagnat, Conceptual foundations of quantum mechanics, op. cit. p. 30;
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ibid.
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ibid. p. 80
ibid. A similar remark was made recently by S. Y. Auyang, How is quantum field theory possible?, Oxford University Press, 1995, p. 115: “Consider Heisenberg’s suggestion that the wavefunction represents not a microscopic system but our knowledge of it. The proposition sounds both indisputable and absurd. (…) All sciences are our knowledge, but the content of the sciences are features of the objective world”.
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July 1952 colloquium, (E. Schrödinger, The interpretation of quantum mechanics (Dublin seminars 1949–1955 and other unpublished texts), op. cit.). In the two last cases, and as in the original 1927 paper, the idea that a quantum jump of energy Ekl=hνk-hνl happens in the receiver (possibly belonging to a measurement apparatus) in order to compensate for a quantum jump of equal energy in the emitter was replaced by a concept of resonance between two oscillators O and O’. The condition of resonance is: νk-vl=νl’-vk’.
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ibid. p. 25
ibid. p. 31
ibid. p. 41
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ibid. p. 68
ibid. p. 62
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Bitbol, M. (1996). Towards a New Ontology. In: Schrödinger’s Philosophy of Quantum Mechanics. Boston Studies in the Philosophy of Science, vol 188. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-1772-9_4
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