Editing Pilot wave theory (section)

==History==
[[Louis de Broglie]]'s early results on the pilot wave theory were presented in his thesis (1924) in the context of atomic orbitals where the waves are stationary. Early attempts to develop a general formulation for the dynamics of these guiding waves in terms of a relativistic wave equation were unsuccessful until in 1926 [[Erwin Schrödinger|Schrödinger]] developed his [[Schrödinger equation|non-relativistic wave equation]]. He further suggested that since the equation described waves in configuration space, the particle model should be abandoned.<ref>{{Cite arXiv|last1=Valentini|first1=Antony|last2=Bacciagaluppi|first2=Guido|date=2006-09-24|title=Quantum Theory at the Crossroads: Reconsidering the 1927 Solvay Conference|eprint=quant-ph/0609184|language=en}}</ref> Shortly thereafter,<ref>{{cite journal |last=Born |first=M. |year=1926 |title=Quantenmechanik der Stoßvorgänge |journal=Zeitschrift für Physik |volume=38 |issue=11–12 |pages=803–827 |bibcode=1926ZPhy...38..803B |doi=10.1007/BF01397184|s2cid=126244962 }}</ref> [[Max Born]] suggested that the wave function of Schrödinger's wave equation represents the probability density of finding a particle. Following these results, de Broglie developed the dynamical equations for his pilot wave theory.<ref>{{cite journal |last=de Broglie |first=L. |year=1927 |title=La mécanique ondulatoire et la structure atomique de la matière et du rayonnement |journal=[[Journal de Physique et le Radium]] |volume=8 |issue=5 |pages=225–241 |bibcode= 1927JPhRa...8..225D
 |doi=10.1051/jphysrad:0192700805022500|url=https://hal.archives-ouvertes.fr/jpa-00205292/document}}</ref> Initially, de Broglie proposed a ''double solution'' approach, in which the quantum object consists of a physical wave (''u''-wave) in real space which has a spherical singular region that gives rise to particle-like behaviour; in this initial form of his theory he did not have to postulate the existence of a quantum particle.<ref name="dewdney-et-al-1992">{{cite journal |last1=Dewdney |first1=C. |last2=Horton |first2=G. |last3=Lam |first3=M. M. |last4=Malik |first4=Z. |last5=Schmidt |first5=M. |year=1992 |title=Wave–particle dualism and the interpretation of quantum mechanics |journal=[[Foundations of Physics]] |volume=22 |issue=10 |pages=1217–1265 |bibcode=1992FoPh...22.1217D |doi=10.1007/BF01889712|s2cid=122894371 }}</ref> He later formulated it as a theory in which a particle is accompanied by a pilot wave.

De Broglie presented the pilot wave theory at the 1927 [[Solvay Conference]].<ref>{{cite book |author=Institut International de Physique Solvay |year=1928 |title=Electrons et Photons: Rapports et Discussions du Cinquième Conseil de Physique tenu à Bruxelles du 24 au 29 Octobre 1927 |publisher=Gauthier-Villars
}}</ref> However, [[Wolfgang Pauli]] raised an objection to it at the conference, saying that it did not deal properly with the case of [[inelastic scattering]]. De Broglie was not able to find a response to this objection, and he abandoned the pilot-wave approach. Unlike [[David Bohm]] years later, de Broglie did not complete his theory to encompass the many-particle case.<ref name="dewdney-et-al-1992"/> The many-particle case shows mathematically that the energy dissipation in inelastic scattering could be distributed to the surrounding field structure by a yet-unknown mechanism of the theory of hidden variables.{{clarify|date=May 2017}}

In 1932, [[John von Neumann]] published a book,<ref>{{cite book |last1=von Neumann |first1=J. |year=1932 |title=Mathematische Grundlagen der Quantenmechanik |publisher=Springer}}</ref> part of which claimed to prove that all hidden variable theories were impossible. This result was found to be flawed by [[Grete Hermann]]<ref>{{Cite book |last=Seevinck |first=Michiel |url=https://doi.org/10.1007/978-94-024-0970-3_7 |title=Grete Hermann - Between Physics and Philosophy |date=2016 |publisher=Springer Netherlands |isbn=978-94-024-0970-3 |editor-last=Crull |editor-first=Elise |location=Dordrecht |pages=107–117 |language=en |doi=10.1007/978-94-024-0970-3_7 |editor-last2=Bacciagaluppi |editor-first2=Guido}}</ref><ref>Hermann, G.: Die naturphilosophischen Grundlagen der Quantenmechanik (Auszug). Abhandlungen
der Fries’schen Schule 6, 75–152 (1935). English translation: Chapter 15 of “Grete Hermann —
Between physics and philosophy”, Elise Crull and Guido Bacciagaluppi, eds., Springer, 2016, 239-
278. [Volume 42 of Studies in History and Philosophy of Science]</ref> three years later, though for a variety of reasons this went unnoticed by the physics community for over fifty years.

In 1952, [[David Bohm]], dissatisfied with the prevailing orthodoxy, rediscovered de Broglie's pilot wave theory. Bohm developed pilot wave theory into what is now called the [[de Broglie–Bohm theory]].<ref name=Bohm1952a>{{cite journal |last1=Bohm |first1=D. |year=1952 |title=A suggested Interpretation of the Quantum Theory in Terms of Hidden Variables, I |journal=[[Physical Review]] |volume=85 |issue=2 |pages=166–179 |bibcode=1952PhRv...85..166B |doi=10.1103/PhysRev.85.166
}}</ref><ref name=Bohm1952b>{{cite journal |last1=Bohm |first1=D. |year=1952 |title=A suggested Interpretation of the Quantum Theory in Terms of Hidden Variables, II |journal=[[Physical Review]] |volume=85 |issue=2 |pages=180–193 |bibcode=1952PhRv...85..180B |doi=10.1103/PhysRev.85.180}}</ref> The de Broglie–Bohm theory itself might have gone unnoticed by most physicists, if it had not been championed by [[John Stewart Bell|John Bell]], who also countered the objections to it. In 1987, John Bell rediscovered Grete Hermann's work,<ref>{{cite book |last1=Bell |first1=J. S. |year=1987 |title=Speakable and Unspeakable in Quantum Mechanics |publisher=Cambridge University Press |isbn=978-0521334952}}</ref> and thus showed the physics community that Pauli's and von Neumann's objections only showed that the pilot wave theory did not have [[Principle of locality|locality]].