Editing Copenhagen interpretation (section)

==Consequences==
The nature of the Copenhagen interpretation is exposed by considering a number of experiments and paradoxes.

=== Schrödinger's cat ===
{{main|Schrödinger's cat}}
This [[thought experiment]] highlights the implications that accepting uncertainty at the microscopic level has on macroscopic objects.  A cat is put in a sealed box, with its life or death made dependent on the state of a subatomic particle.<ref name="omnes" />{{Rp|page=91}} Thus a description of the cat during the course of the experiment—having been entangled with the state of a subatomic particle—becomes a "blur" of "living and dead cat."  But this cannot be accurate because it implies the cat is actually both dead and alive until the box is opened to check on it. But the cat, if it survives, will only remember being alive.  Schrödinger resists "so naively accepting as valid a 'blurred model' for representing reality."<ref>{{Cite journal|last=Trimmer|first=John D.|date=1980|title=The Present Situation in Quantum Mechanics: A Translation of Schrödinger's "Cat Paradox" Paper|journal=[[Proceedings of the American Philosophical Society]]|volume=124|issue=5|pages=323–338|issn=0003-049X}}</ref> ''How can the cat be both alive and dead?''

In Copenhagen-type views, the wave function reflects our knowledge of the system. The wave function <math>(|\text{dead}\rangle + |\text{alive}\rangle)/\sqrt 2</math> means that, once the cat is observed, there is a 50% chance it will be dead, and 50% chance it will be alive.<ref name=":2">{{cite book| first=Asher |last=Peres |author-link=Asher Peres |title=Quantum Theory: Concepts and Methods |title-link=Quantum Theory: Concepts and Methods |pages=373–374 |year=1993 |publisher=[[Kluwer]] |isbn=0-7923-2549-4 |oclc=28854083}}</ref> (Some versions of the Copenhagen interpretation reject the idea that a wave function can be assigned to a physical system that meets the everyday definition of "cat"; in this view, the correct quantum-mechanical description of the cat-and-particle system must include a [[superselection rule]].<ref name=":7" />{{Rp|page=51}})

=== Wigner's friend ===
{{main|Wigner's friend}}
"Wigner's friend" is a thought experiment intended to make that of Schrödinger's cat more striking by involving two conscious beings, traditionally known as Wigner and his friend.<ref name="omnes" />{{Rp|pages=91-92}} (In more recent literature, they may also be known as [[Alice and Bob]], per the convention of describing protocols in [[information theory]].<ref>{{Cite journal |last1=Fuchs |first1=Christopher A. |last2=Mermin |first2=N. David |author-link2=N. David Mermin |last3=Schack |first3=Rüdiger |date=August 2014 |title=An introduction to QBism with an application to the locality of quantum mechanics |url=http://aapt.scitation.org/doi/10.1119/1.4874855 |journal=[[American Journal of Physics]] |language=en |volume=82 |issue=8 |pages=749–754 |arxiv=1311.5253 |bibcode=2014AmJPh..82..749F |doi=10.1119/1.4874855 |s2cid=56387090 |issn=0002-9505}}</ref>) Wigner puts his friend in with the cat. The external observer believes the system is in state <math>(|\text{dead}\rangle + |\text{alive}\rangle)/\sqrt 2</math>. However, his friend is convinced that the cat is alive, i.e. for him, the cat is in the state <math>|\text{alive}\rangle</math>. ''How can Wigner and his friend see different wave functions?''

In a Heisenbergian view, the answer depends on the positioning of [[Heisenberg cut]], which can be placed arbitrarily (at least according to Heisenberg, though not to Bohr<ref name="camilleri2015" />). If Wigner's friend is positioned on the same side of the cut as the external observer, his measurements collapse the wave function for both observers. If he is positioned on the cat's side, his interaction with the cat is not considered a measurement.<ref name=":6">{{Cite journal |last1=Nurgalieva |first1=Nuriya |last2=Renner |first2=Renato |date=2020-07-02 |title=Testing quantum theory with thought experiments |url=https://www.tandfonline.com/doi/full/10.1080/00107514.2021.1880075 |journal=[[Contemporary Physics]] |language=en |volume=61 |issue=3 |pages=193–216 |arxiv=2106.05314 |bibcode=2020ConPh..61..193N |doi=10.1080/00107514.2021.1880075 |s2cid=232313237 |issn=0010-7514}}</ref> Different Copenhagen-type interpretations take different positions as to whether observers can be placed on the quantum side of the cut.<ref name=":6" />

=== Double-slit experiment ===
{{main|Double-slit experiment}}
In the basic version of this experiment, a light source, such as a [[laser]] beam, illuminates a plate pierced by two parallel slits, and the light passing through the slits is observed on a screen behind the plate. The wave nature of light causes the light waves passing through the two slits to [[interference (wave propagation)|interfere]], producing bright and dark bands on the screen – a result that would not be expected if light consisted of classical particles. However, the light is always found to be absorbed at the screen at discrete points, as individual particles (not waves); the interference pattern appears via the varying density of these particle hits on the screen. Furthermore, versions of the experiment that include detectors at the slits find that each detected [[photon]] passes through one slit (as would a classical particle), and not through both slits (as would a wave). Such experiments demonstrate that particles do not form the interference pattern if one detects which slit they pass through.<ref name="Plotnitsky2012">{{cite book |last= Plotnitsky |first= Arkady |title= Niels Bohr and Complementarity: An Introduction |publisher= Springer |year= 2012 |location= US |pages= 75–76 |url= https://books.google.com/books?id=dmdUp97S4AYC&pg=PA75 |isbn= 978-1461445173}}</ref>{{Rp|73–76}}

According to Bohr's [[Complementarity (physics)|complementarity principle]], light is neither a wave nor a [[stream of particles]]. A particular experiment can demonstrate particle behavior (passing through a definite slit) or wave behavior (interference), but not both at the same time.<ref>{{Cite journal |last=Rosenfeld |first=L. |author-link=Léon Rosenfeld |date=1953 |title=Strife about Complementarity |url=https://www.jstor.org/stable/43414997 |journal=Science Progress (1933– ) |volume=41 |issue=163 |pages=393–410 |jstor=43414997 |issn=0036-8504}}</ref>

The same experiment has been performed for light, electrons, atoms, and molecules.<ref>{{cite journal |doi=10.1103/PhysRevLett.87.160401 |pmid=11690188 |title=Diffraction of Complex Molecules by Structures Made of Light |year=2001 |last1=Nairz |first1=Olaf |last2=Brezger |first2=Björn |last3=Arndt |first3=Markus |last4=Zeilinger |first4=Anton |author-link4=Anton Zeilinger |journal=[[Physical Review Letters]] |volume=87 |issue=16|pages=160401 |arxiv = quant-ph/0110012 |bibcode = 2001PhRvL..87p0401N |s2cid=21547361 }}</ref><ref>{{cite journal |doi=10.1103/PhysRevLett.88.100404 |title=Matter-Wave Interferometer for Large Molecules |year=2002 |last1=Brezger |first1=Björn |last2=Hackermüller |first2=Lucia |last3=Uttenthaler |first3=Stefan |last4=Petschinka |first4=Julia |last5=Arndt |first5=Markus |last6=Zeilinger |first6=Anton |author-link6=Anton Zeilinger |journal=[[Physical Review Letters]] |volume=88 |issue=10 |arxiv = quant-ph/0202158 |bibcode = 2002PhRvL..88j0404B |pmid=11909334 |pages=100404 |s2cid=19793304 }}</ref> The extremely small [[matter wave|de Broglie wavelength]] of objects with larger mass makes experiments increasingly difficult,<ref>{{Cite journal |last1=Arndt |first1=Markus |last2=Hornberger |first2=Klaus |date=April 2014 |title=Testing the limits of quantum mechanical superpositions |url=http://dx.doi.org/10.1038/nphys2863 |journal=Nature Physics |volume=10 |issue=4 |pages=271–277 |doi=10.1038/nphys2863 |arxiv=1410.0270 |bibcode=2014NatPh..10..271A |s2cid=56438353 |issn=1745-2473}}</ref> but in general quantum mechanics considers all matter as possessing both particle and wave behaviors.

=== Einstein–Podolsky–Rosen paradox ===
{{main|EPR paradox}}
This thought experiment involves a pair of particles prepared in what later authors would refer to as an [[Quantum entanglement|entangled state]]. In a 1935 paper, Einstein, [[Boris Podolsky]], and [[Nathan Rosen]] pointed out that, in this state, if the position of the first particle were measured, the result of measuring the position of the second particle could be predicted. If instead the momentum of the first particle were measured, then the result of measuring the momentum of the second particle could be predicted. They argued that no action taken on the first particle could instantaneously affect the other, since this would involve information being transmitted faster than light, which is forbidden by the [[theory of relativity]]. They invoked a principle, later known as the "Einstein–Podolsky–Rosen (EPR) criterion of reality", positing that, "If, without in any way disturbing a system, we can predict with certainty (i.e., with [[probability]] equal to unity) the value of a physical quantity, then there exists an element of reality corresponding to that quantity". From this, they inferred that the second particle must have a definite value of position and of momentum prior to either being measured.<ref name="EPR">{{cite journal | title = Can Quantum-Mechanical Description of Physical Reality be Considered Complete? | date = 1935-05-15 | first1 = A. | last1 = Einstein |first2=B. |last2=Podolsky |first3=N |last3=Rosen |author-link1=Albert Einstein |author-link2=Boris Podolsky |author-link3=Nathan Rosen | journal = [[Physical Review]] | volume = 47 | issue = 10 | pages = 777–780 | url=http://www.drchinese.com/David/EPR.pdf |archive-url=https://ghostarchive.org/archive/20221010/http://www.drchinese.com/David/EPR.pdf |archive-date=2022-10-10 |url-status=live |bibcode = 1935PhRv...47..777E |doi = 10.1103/PhysRev.47.777 | doi-access = free }}</ref>

Bohr's response to the EPR paper was published in the ''[[Physical Review]]'' later that same year.<ref name="Bohr1935"/> He argued that EPR had reasoned fallaciously. Because measurements of position and of momentum are [[Complementarity (physics)|complementary]], making the choice to measure one excludes the possibility of measuring the other. Consequently, a fact deduced regarding one arrangement of laboratory apparatus could not be combined with a fact deduced by means of the other, and so, the inference of predetermined position and momentum values for the second particle was not valid. Bohr concluded that EPR's "arguments do not justify their conclusion that the quantum description turns out to be essentially incomplete."<ref name='Bohr1935'>{{cite journal |title=Can Quantum-Mechanical Description of Physical Reality be Considered Complete? |date=1935-10-13 |first=N. |last=Bohr |journal=[[Physical Review]] |volume=48 |issue=8 |pages=696–702 |doi=10.1103/PhysRev.48.696|bibcode=1935PhRv...48..696B |url=https://cds.cern.ch/record/1060284/files/PhysRev.48.696.pdf |archive-url=https://ghostarchive.org/archive/20221010/https://cds.cern.ch/record/1060284/files/PhysRev.48.696.pdf |archive-date=2022-10-10 |url-status=live |doi-access=free }}</ref>