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Wave–particle duality is the fact that every elementary particle or quantic entity exhibits the properties of not only particles, but also waves. It addresses the inability of the classical concepts "particle" or "wave" to fully describe the behavior of quantum-scale objects. As Einstein wrote: "''It seems as though we must use sometimes the one theory and sometimes the other, while at times we may use either. We are faced with a new kind of difficulty. We have two contradictory pictures of reality; separately neither of them fully explains the phenomena of light, but together they do''". Various opinions have arisen about this. Initiated by Louis de Broglie, before the discovery of quantum mechanics, and developed later as the de Broglie-Bohm theory, the pilot wave interpretation does not regard the duality as paradoxical, seeing both particle and wave aspects as always coexisting. According to Schrödinger the domain of the de Broglie waves is ordinary physical space-time.〔 This formal feature exhibits the pilot wave theory as non-local, which is considered by many physicists to be a grave defect in a theory.〔Bransden, B.H., Joachain, C.J. (1989/2000). ''Quantum Mechanics'', second edition, Pearson, Prentice Hall, Harlow UK, ISBN 978-0-582-35691-7, p. 760.〕 Still in the days of the old quantum theory, another pre-quantum-mechanical version of wave–particle duality was pioneered by William Duane,〔Duane, W. (1923). (The transfer in quanta of radiation momentum to matter, ''Proc. Natl. Acad. Sci.'' 9(5): 158–164 ).〕 and developed by others including Alfred Landé.〔Landé, A. (1951). (''Quantum Mechanics'' ), Sir Isaac Pitman and Sons, London, pp. 19–22.〕 Duane explained diffraction of x-rays by a crystal in terms solely of their particle aspect. The deflection of the trajectory of each diffracted photon was due to quantal translative momentum transfer from the spatially regular structure of the diffracting crystal.〔Heisenberg, W. (1930). (''The Physical Principles of the Quantum Theory'' ), translated by C. Eckart and F.C. Hoyt, University of Chicago Press, Chicago, pp. 77–78.〕 Fourier analysis reveals the wave–particle duality as a simply mathematical equivalence, always present, and universal for all quanta. The same reasoning applies for example to diffraction of electrons by a crystal. In the light of de Broglie's ideas, Erwin Schrödinger developed his wave mechanics by referring the universal wave aspect not to ordinary physical space-time, but rather to a profoundly different and more abstract 'space'. The domain of Schrödinger's wave function is configuration space.〔Schrödinger, E. (1928). Wave mechanics, pp. 185–206 of ''Électrons et Photons: Rapports et Discussions du Cinquième Conseil de Physique, tenu à Bruxelles du 24 au 29 Octobre 1927, sous les Auspices de l'Institut International de Physique Solvay'', Gauthier-Villars, Paris, pp. 185–186; translation at p. 447 of Bacciagaluppi, G., Valentini, A. (2009), ''Quantum Theory at the Crossroads: Reconsidering the 1927 Solvay Conference'', Cambridge University Press, Cambridge UK, ISBN 978-0-521-81421-8.〕 Ordinary physical space-time allows more or less direct visualization of cause and effect relations. In contrast, configuration space does not directly display cause and effect linkages. Sometimes, nevertheless, it seemed as if Schrödinger visualized his own waves as referring to ordinary space-time, and there was much debate about this.〔Heisenberg, W., (1967). Quantum theory and its interpretation, quoted on p. 56 by eds. J.A. Wheeler, W.H. Zurek, (1983), ''Quantum Theory and Measurement'', Princeton University Press, Princeton NJ, from ed. S. Rozental, ''Niels Bohr: his Life and Work as seen by his Friends and Colleagues'', North Holland, Amsterdam.〕 Niels Bohr regarded the "duality paradox" as a fundamental or metaphysical fact of nature. A given kind of quantum object, will exhibit sometimes wave, sometimes particle, character, in respectively different physical settings. He saw such duality as one aspect of the concept of complementarity. Bohr regarded renunciation of the cause-effect relation, or complementarily, of the space-time picture, as essential to the quantum mechanical account.〔Bohr, N. (1927/1928). The quantum postulate and the recent development of atomic theory, (''Nature'' Supplement April 14 1928, 121: 580–590 ).〕 Werner Heisenberg considered the question further. He saw the duality as present for all quantic entities, but not quite in the usual quantum mechanical account considered by Bohr. He saw it in what is called second quantization, which generates an entirely new concept of fields which exist in ordinary space-time, causality still being visualizable. Classical field values (e.g. the electric and magnetic field strengths of Maxwell) are replaced by an entirely new kind of field value, as considered in quantum field theory. Turning the reasoning around, ordinary quantum mechanics can be deduced as a specialized consequence of quantum field theory.〔Camilleri, K. (2009). ''Heisenberg and the Interpretation of Quantum Mechanics: the Physicist as Philosopher'', Cambridge University Press, Cambridge UK, ISBN 978-0-521-88484-6.〕〔Preparata, G. (2002). ''An Introduction to a Realistic Quantum Physics'', World Scientific, River Edge NJ, ISBN 978-981-238-176-7.〕 Because of the difference of views of Bohr and Heisenberg, the main sources of the so-called Copenhagen interpretation, the position of that interpretation on wave–particle duality is ill-defined. In a modern perspective, wave functions arise naturally in relativistic quantum field theory in the formulation of free quantum fields. They are necessary for the Lorentz invariance of the theory. Their form and the equations of motion they obey are dictated by under which representation of the Lorentz group they transform.〔 Chapter 5.〕 ==Origin of theory== The idea of duality originated in a debate over the nature of light and matter that dates back to the 17th century, when Christiaan Huygens and Isaac Newton proposed competing theories of light: light was thought either to consist of waves (Huygens) or of particles (Newton). Through the work of Max Planck, Albert Einstein, Louis de Broglie, Arthur Compton, Niels Bohr, and many others, current scientific theory holds that ''all'' particles ''also'' have a wave nature (and vice versa). This phenomenon has been verified not only for elementary particles, but also for compound particles like atoms and even molecules. For macroscopic particles, because of their extremely short wavelengths, wave properties usually cannot be detected. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Wave–particle duality」の詳細全文を読む スポンサード リンク
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