Editing Double-slit experiment (section)

==Interpretations of the experiment==
Like the [[Schrödinger's cat]] [[thought experiment]], the double-slit experiment is often used to highlight the differences and similarities between the various [[interpretations of quantum mechanics]].

===Standard quantum physics===
The standard interpretation of the double slit experiment is that the pattern is a wave phenomenon, representing interference between two probability amplitudes, one for each slit. Low intensity experiments demonstrate that the pattern is filled in one particle detection at a time. Any change to the apparatus designed to detect a particle at a particular slit alters the probability amplitudes and the interference disappears.<ref name="Zeilinger1999" />{{rp|S298}} This interpretation is independent of any conscious observer.<ref>{{Cite journal |last=Mandel |first=L. |date=1999-03-01 |title=Quantum effects in one-photon and two-photon interference |url=https://link.aps.org/doi/10.1103/RevModPhys.71.S274 |journal=Reviews of Modern Physics |language=en |volume=71 |issue=2 |pages=S274–S282 |doi=10.1103/RevModPhys.71.S274 |bibcode=1999RvMPS..71..274M |issn=0034-6861}}</ref>{{rp|S281|q= 
The analysis of some interference experiments confronts us with fundamental questions of interpretation and brings out that the quantum state reflects not what we know about the system, but rather what is knowable in principle. This avoids any reference to consciousness in the interpretation of the state.}}

===Complementarity===
{{main|Complementarity (physics)}}
[[Niels Bohr]] interpreted quantum experiments like the double-slit experiment using the concept of complementarity.<ref name="Faye-Stanford">{{Cite book|last=Faye|first=Jan|title=[[Stanford Encyclopedia of Philosophy]]|publisher=Metaphysics Research Lab, Stanford University|year=2019|editor-last=Zalta|editor-first=Edward N.|chapter=Copenhagen Interpretation of Quantum Mechanics|author-link=Jan Faye|chapter-url=https://plato.stanford.edu/entries/qm-copenhagen/}}</ref> In Bohr's view quantum systems are not classical, but measurements can only give classical results. Certain pairs of classical properties will never be observed in a quantum system simultaneously: the interference pattern of waves in the double slit experiment will disappear if particles are detected at the slits. Modern quantitative versions of the concept allow for a continuous tradeoff between the visibility of the interference fringes and the probability of particle detection at a slit.<ref>{{Cite journal |last1=Wootters |first1=William K. |last2=Zurek |first2=Wojciech H. |date=1979-01-15 |title=Complementarity in the double-slit experiment: Quantum nonseparability and a quantitative statement of Bohr's principle |url=https://link.aps.org/doi/10.1103/PhysRevD.19.473 |journal=Physical Review D |language=en |volume=19 |issue=2 |pages=473–484 |doi=10.1103/PhysRevD.19.473 |bibcode=1979PhRvD..19..473W |issn=0556-2821}}</ref><ref>{{Cite journal |last=Bartell |first=L. S. |date=1980-03-15 |title=Complementarity in the double-slit experiment: On simple realizable systems for observing intermediate particle-wave behavior |url=https://link.aps.org/doi/10.1103/PhysRevD.21.1698 |journal=Physical Review D |language=en |volume=21 |issue=6 |pages=1698–1699 |doi=10.1103/PhysRevD.21.1698 |bibcode=1980PhRvD..21.1698B |issn=0556-2821}}</ref>

===Copenhagen interpretation===
{{Main|Copenhagen interpretation}}
The [[Copenhagen interpretation]] is a collection of views about the meaning of [[quantum mechanics]], stemming from the work of [[Niels Bohr]], [[Werner Heisenberg]], [[Max Born]], and others. The term "Copenhagen interpretation" was apparently coined by Heisenberg during the 1950s to refer to ideas developed in the 1925–1927 period, glossing over his disagreements with Bohr.<ref name="Faye-Stanford"/><ref name="camilleri2015">{{cite journal|first1=K. |last1=Camilleri |first2=M. |last2=Schlosshauer |title=Niels Bohr as Philosopher of Experiment: Does Decoherence Theory Challenge Bohr's Doctrine of Classical Concepts? |arxiv=1502.06547 |journal=[[Studies in History and Philosophy of Modern Physics]] |volume=49 |pages=73–83 |year=2015 |doi=10.1016/j.shpsb.2015.01.005|bibcode=2015SHPMP..49...73C |s2cid=27697360 }}</ref><ref>{{cite book |last=Scheibe |first=Erhard |title=The Logical Analysis of Quantum Mechanics |publisher=Pergamon Press |year=1973 |isbn=978-0-08-017158-6 |oclc=799397091 |quote=[T]here is no point in looking for ''the'' Copenhagen interpretation as a unified and consistent logical structure. Terms such as "Copenhagen interpretation" or "Copenhagen school" are based on the history of the development of quantum mechanics; they form a simplified and often convenient way of referring to the ideas of a number of physicists who played an important role in the establishment of quantum mechanics, and who were collaborators of Bohr's at his Institute or took part in the discussions during the crucial years. On closer inspection, one sees quite easily that these ideas are divergent in detail and that in particular the views of Bohr, the spiritual leader of the school, form a separate entity which can now be understood only by a thorough study of as many as possible of the relevant publications by Bohr himself. |author-link=Erhard Scheibe}}</ref><ref name="Mermin 2017">{{Cite book |last=Mermin |first=N. David |title=Quantum [Un]Speakables II |date=2017-01-01 |publisher=Springer International Publishing |isbn=978-3-319-38985-1 |editor-last=Bertlmann |editor-first=Reinhold |series=The Frontiers Collection |pages=83–93 |language=en |chapter=Why QBism Is Not the Copenhagen Interpretation and What John Bell Might Have Thought of It |doi=10.1007/978-3-319-38987-5_4 |editor2-last=Zeilinger |editor2-first=Anton |editor-link2=Anton Zeilinger |arxiv=1409.2454 |s2cid=118458259}}</ref> Consequently, there is no definitive historical statement of what the interpretation entails. Features common across versions of the Copenhagen interpretation include the idea that quantum mechanics is intrinsically [[Indeterminism|indeterministic]], with probabilities calculated using the [[Born rule]], and some form of [[Complementarity (physics)|complementarity]] principle.<ref name="omnes1999">{{cite book|last=Omnès |first=Roland |author-link=Roland Omnès |chapter=The Copenhagen Interpretation |title=Understanding Quantum Mechanics |publisher=Princeton University Press |year=1999 |doi=10.2307/j.ctv173f2pm.9 |s2cid=203390914 }}</ref>{{rp|41–54}} Moreover, the act of "observing" or "measuring" an object is irreversible, and no truth can be attributed to an object, [[counterfactual definiteness|except according to the results of its measurement]]. In the Copenhagen interpretation, complementarity means a particular experiment can demonstrate particle behavior (passing through a definite slit) or wave behavior (interference), but not both at the same time.<ref name="omnes1999"/>{{rp|49|q=We may speak of an electron by using the language of waves when it crosses two slits in an interfering device, and we speak of the same electron as a particle when it is detected, but we cannot use the two modes of speaking at the same time.}}<ref>{{Cite journal |last=Rosenfeld |first=L. |author-link=Léon Rosenfeld |date=1953 |title=Strife about Complementarity |journal=Science Progress (1933– ) |volume=41 |issue=163 |pages=393–410 |issn=0036-8504 |jstor=43414997}}</ref><ref name="peres">{{Cite book|last=Peres|first=Asher|title=[[Quantum Theory: Concepts and Methods]]|publisher=Kluwer Academic Publishers|year=1995|isbn=0-7923-2549-4|author-link=Asher Peres |pages=36–39}}</ref> In a Copenhagen-type view, the question of which slit a particle travels through has no meaning when there is no detector.<ref name="omnes">{{cite book|first=R. |last=Omnès |author-link=Roland Omnès |title=The Interpretation of Quantum Mechanics |publisher=Princeton University Press |year=1994 |isbn=978-0-691-03669-4 |oclc=439453957 |page=167}}</ref><ref>{{cite book |last1=Brukner |first1=Časlav |chapter=Quantum Physics as a Science of Information |date=2005 |title=Quo Vadis Quantum Mechanics? |pages=47–61 |editor-last=Elitzur |editor-first=Avshalom C. |place=Berlin, Heidelberg |publisher=Springer  |language=en |doi=10.1007/3-540-26669-0_3 |isbn=978-3-540-22188-3 |last2=Zeilinger |first2=Anton |author-link1=Časlav Brukner |author-link2=Anton Zeilinger |editor2-last=Dolev |editor2-first=Shahar |editor3-last=Kolenda |editor3-first=Nancy}}</ref>

===Relational interpretation===
According to the [[Relational quantum mechanics|relational interpretation of quantum mechanics]], first proposed by [[Carlo Rovelli]],<ref>{{Cite journal|doi = 10.1007/BF02302261|last = Rovelli|first = Carlo|author-link = Carlo Rovelli|title = Relational Quantum Mechanics|journal = International Journal of Theoretical Physics|volume = 35|issue = 8|pages = 1637–1678|year = 1996|arxiv = quant-ph/9609002 |bibcode = 1996IJTP...35.1637R |s2cid = 16325959}}</ref> observations such as those in the double-slit experiment result specifically from the interaction between the [[Observer (quantum physics)|observer]] (measuring device) and the object being observed (physically interacted with), not any absolute property possessed by the object. In the case of an electron, if it is initially "observed" at a particular slit, then the observer–particle (photon–electron) interaction includes information about the electron's position. This partially constrains the particle's eventual location at the screen. If it is "observed" (measured with a photon) not at a particular slit but rather at the screen, then there is no "which path" information as part of the interaction, so the electron's "observed" position on the screen is determined strictly by its probability function. This makes the resulting pattern on the screen the same as if each individual electron had passed through both slits.{{citation needed|date=September 2023}}

===Many-worlds interpretation===
As with Copenhagen, there are multiple variants of the [[many-worlds interpretation]]. The unifying theme is that physical reality is identified with a wavefunction, and this wavefunction always evolves unitarily, i.e., following the Schrödinger equation with no collapses.<ref>{{Cite journal|last=Kent|first=Adrian|author-link=Adrian Kent|date=February 2015|title=Does it Make Sense to Speak of Self-Locating Uncertainty in the Universal Wave Function? Remarks on Sebens and Carroll |journal=Foundations of Physics |language=en |volume=45 |issue=2 |pages=211–217  |arxiv=1408.1944 |doi=10.1007/s10701-014-9862-5 |issn=0015-9018 |bibcode=2015FoPh...45..211K |s2cid=118471198}}</ref><ref name="vaidman_stanfordencyclopedia">{{cite SEP |last=Vaidman |first=Lev |author-link=Lev Vaidman |title=Many-Worlds Interpretation of Quantum Mechanics |url-id=qm-manyworlds |date=5 August 2021 }}</ref> Consequently, there are many parallel universes, which only interact with each other through interference. [[David Deutsch]] argues that the way to understand the double-slit experiment is that in each universe the particle travels through a specific slit, but its motion is affected by interference with particles in other universes, and this interference creates the observable fringes.<ref>{{Cite book |last=Deutsch |first=David |url=http://archive.org/details/fabricofreality0000deut |title=The Fabric of Reality |date=1998 |location=London |publisher=Penguin  |isbn=978-0-14-014690-5|pages=40–53}}</ref> David Wallace, another advocate of the many-worlds interpretation, writes that in the familiar setup of the double-slit experiment the two paths are not sufficiently separated for a description in terms of parallel universes to make sense.<ref>{{cite book|first=David |last=Wallace |title=The Emergent Multiverse |page=382 |publisher=Oxford University Press |location=Oxford |isbn=978-0-19-954696-1 |year=2012}}</ref>

===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
}}