Editing Double-slit experiment (section)

===De Broglie–Bohm theory===
{{Main|de Broglie–Bohm theory}}
An alternative to the standard understanding of quantum mechanics, the [[De Broglie–Bohm theory]] states that particles also have precise locations at all times, and that their velocities are defined by the wave-function. So while a single particle will travel through one particular slit in the double-slit experiment, the so-called "pilot wave" that influences it will travel through both. The two slit de Broglie-Bohm trajectories were first calculated by Chris Dewdney while working with Chris Philippidis and Basil Hiley at Birkbeck College (London).<ref>{{Cite journal|last1=Philippidis|first1=C.|last2=Dewdney|first2=C.|last3=Hiley|first3=B. J.|date=1979|title=Quantum interference and the quantum potential|journal=Il Nuovo Cimento B|language=en|volume=52|issue=1|pages=15–28|doi=10.1007/bf02743566|issn=1826-9877|bibcode=1979NCimB..52...15P|s2cid=53575967}}</ref> The de Broglie-Bohm theory produces the same statistical results as standard quantum mechanics, but dispenses with many of its conceptual difficulties by adding complexity through an ''ad hoc'' quantum potential to guide the particles.<ref>{{Cite book | chapter-url=https://plato.stanford.edu/entries/qm-bohm/ | title=The Stanford Encyclopedia of Philosophy| chapter=Bohmian Mechanics| publisher=Metaphysics Research Lab, Stanford University| year=2017}}</ref>

While the model is in many ways similar to [[Schrödinger equation]], it is known to fail for relativistic cases<ref>{{Citation |last=Goldstein |first=Sheldon |title=Bohmian Mechanics |date=2021 |url=https://plato.stanford.edu/archives/fall2021/entries/qm-bohm/ |encyclopedia=The Stanford Encyclopedia of Philosophy |editor-last=Zalta |editor-first=Edward N. |access-date=2023-08-14 |edition=Fall 2021 |publisher=Metaphysics Research Lab, Stanford University}}</ref> and does not account for features such as particle creation or annihilation in [[quantum field theory]]. Many authors such as nobel laureates [[Werner Heisenberg]],<ref>{{Cite journal |last=Heisenberg |first=W. |date=1956 |editor-last=Pauli |editor-first=W |title=''Niels Bohr and the Development of Physics: Essays Dedicated to Niels Bohr on the Occasion of his Seventieth Birthday'' |journal=Physics Today |volume=9 |issue=8 |page=12 |doi=10.1063/1.3060063 |issn=0031-9228}}</ref> Sir [[Anthony James Leggett]]<ref>{{Cite journal |last=Leggett |first=A J |date=2002 |title=Testing the limits of quantum mechanics: motivation, state of play, prospects |url=https://iopscience.iop.org/article/10.1088/0953-8984/14/15/201 |journal=Journal of Physics: Condensed Matter |volume=14 |issue=15 |pages=R415–R451 |doi=10.1088/0953-8984/14/15/201 |s2cid=250911999 |issn=0953-8984}}</ref> and Sir [[Roger Penrose]]<ref>{{Cite book |last=Penrose |first=Roger |title=The Road to Reality: A Complete Guide to the Laws of the Universe |year=2004 |publisher=Cape |isbn=978-0-224-04447-9 |url=https://books.google.com/books?id=SkwiEAAAQBAJ |location=London}}</ref> have criticized it for not adding anything new.

More complex variants of this type of approach have appeared, for instance the ''three wave hypothesis''<ref>{{Cite journal |last=Horodecki |first=R. |date=1981 |title=De broglie wave and its dual wave |journal=Physics Letters A |volume=87 |issue=3 |pages=95–97 |doi=10.1016/0375-9601(81)90571-5 |bibcode=1981PhLA...87...95H |issn=0375-9601}}</ref><ref>{{Cite journal |last=Horodecki |first=R. |date=1983 |title=Superluminal singular dual wave |journal=Lettere al Nuovo Cimento |volume=36 |issue=15 |pages=509–511 |doi=10.1007/bf02817964 |s2cid=120784358 |issn=1827-613X}}</ref> of [[Ryszard Horodecki]] as well as other complicated combinations of de Broglie and Compton waves.<ref>{{Cite journal |last=Das |first=S.N. |date=1984 |title=De Broglie wave and Compton wave |journal=Physics Letters A |volume=102 |issue=8 |pages=338–339 |doi=10.1016/0375-9601(84)90291-3 |bibcode=1984PhLA..102..338D |issn=0375-9601}}</ref><ref>{{Cite journal |last=Mukhopadhyay |first=P. |date=1986 |title=A correlation between the compton wavelength and the de Broglie wavelength |journal=Physics Letters A |volume=114 |issue=4 |pages=179–182 |doi=10.1016/0375-9601(86)90200-8 |bibcode=1986PhLA..114..179M |issn=0375-9601}}</ref><ref>{{Cite journal |last=Elbaz |first=Claude |date=1985 |title=On de Broglie waves and Compton waves of massive particles |journal=Physics Letters A |volume=109 |issue=1–2 |pages=7–8 |doi=10.1016/0375-9601(85)90379-2 |bibcode=1985PhLA..109....7E |issn=0375-9601}}</ref> To date there is no evidence that these are useful.

{{Multiple image
| image1            = Doppelspalt.svg
| caption1          = Trajectories of particles in De Broglie–Bohm theory in the double-slit experiment.
| image2            = 100 trajectories guided by the wave function.png
| caption2          = 100 trajectories guided by the wave function. In De Broglie-Bohm's theory, a particle is represented, at any time, by a wave function ''and'' a position (center of mass). This is a kind of augmented reality compared to the standard interpretation.
| image3            = Interference electrons double-slit at 10cm.png
| caption3          = Numerical simulation of the double-slit experiment with electrons. Figure on the left: evolution (from left to right) of the intensity of the electron beam at the exit of the slits (left) up to the detection screen located 10&nbsp;cm after the slits (right). The higher the intensity, the more the color is light blue – Figure in the center: impacts of the electrons observed on the screen – Figure on the right: intensity of the electrons in the [[Fraunhofer diffraction|far field]] approximation (on the screen). Numerical data from Claus Jönsson's experiment (1961). Photons, atoms and molecules follow a similar evolution.
| header            = Bohmian trajectories
| align             = center
| total_width       = 900
}}