Editing Uncertainty principle (section)

== Critical reactions ==
{{Main article|Bohr–Einstein debates}}

The Copenhagen interpretation of quantum mechanics and Heisenberg's uncertainty principle were, in fact, initially seen as twin targets by detractors. According to the [[Copenhagen interpretation]] of quantum mechanics, there is no fundamental reality that the [[quantum state]] describes, just a prescription for calculating experimental results. There is no way to say what the state of a system fundamentally is, only what the result of observations might be.

[[Albert Einstein]] believed that randomness is a reflection of our ignorance of some fundamental property of reality, while [[Niels Bohr]] believed that the probability distributions are fundamental and irreducible, and depend on which measurements we choose to perform. [[Bohr–Einstein debates|Einstein and Bohr debated]] the uncertainty principle for many years.

=== Ideal detached observer ===
Wolfgang Pauli called Einstein's fundamental objection to the uncertainty principle "the ideal of the detached observer" (phrase translated from the German):

{{Blockquote|"Like the moon has a definite position," Einstein said to me last winter, "whether or not we look at the moon, the same must also hold for the atomic objects, as there is no sharp distinction possible between these and macroscopic objects. Observation cannot ''create'' an element of reality like a position, there must be something contained in the complete description of physical reality which corresponds to the ''possibility'' of observing a position, already before the observation has been actually made." I hope, that I quoted Einstein correctly; it is always difficult to quote somebody out of memory with whom one does not agree. It is precisely this kind of postulate which I call the ideal of the detached observer.|Letter from Pauli to Niels Bohr, February 15, 1955<ref>{{cite book |last1=Enz |first1=Charles Paul |last2=von Meyenn |first2=Karl |title=Writings on Physics and Philosophy by Wolfgang Pauli |url=https://books.google.com/books?id=ueTd4g7pc5MC&pg=PA43 |publisher=Springer-Verlag |year=1994 |page=43 |translator=Robert Schlapp |isbn=3-540-56859-X |access-date=2018-02-10 |archive-date=2020-08-19 |archive-url=https://web.archive.org/web/20200819235529/https://books.google.com/books?id=ueTd4g7pc5MC&pg=PA43 |url-status=live }}</ref>}}

=== Einstein's slit ===
The first of Einstein's [[thought experiment]]s challenging the uncertainty principle went as follows:

{{quote|Consider a particle passing through a slit of width {{mvar|d}}. The slit introduces an uncertainty in momentum of approximately {{mvar|{{sfrac|h|d}}}} because the particle passes through the wall. But let us determine the momentum of the particle by measuring the recoil of the wall. In doing so, we find the momentum of the particle to arbitrary accuracy by conservation of momentum.}}

Bohr's response was that the wall is quantum mechanical as well, and that to measure the recoil to accuracy {{math|Δ''p''}}, the momentum of the wall must be known to this accuracy before the particle passes through. This introduces an uncertainty in the position of the wall and therefore the position of the slit equal to {{math|{{sfrac|''h''|Δ''p''}}}}, and if the wall's momentum is known precisely enough to measure the recoil, the slit's position is uncertain enough to disallow a position measurement.

A similar analysis with particles diffracting through multiple slits is given by [[Richard Feynman]].<ref>Feynman lectures on Physics, vol 3, 2–2</ref>

=== Einstein's box ===
Bohr was present when Einstein proposed the thought experiment which has become known as [[Einstein's box]]. Einstein argued that "Heisenberg's uncertainty equation implied that the uncertainty in time was related to the uncertainty in energy, the product of the two being related to the Planck constant."<ref name="Gamow">Gamow, G., ''The great physicists from Galileo to Einstein'', Courier Dover, 1988, p.260.</ref> Consider, he said, an ideal box, lined with mirrors so that it can contain light indefinitely. The box could be weighed before a clockwork mechanism opened an ideal shutter at a chosen instant to allow one single photon to escape. "We now know, explained Einstein, precisely the time at which the photon left the box."<ref>Kumar, M., ''Quantum: Einstein, Bohr and the Great Debate About the Nature of Reality'', Icon, 2009, p. 282.</ref> "Now, weigh the box again. The change of mass tells the energy of the emitted light. In this manner, said Einstein, one could measure the energy emitted and the time it was released with any desired precision, in contradiction to the uncertainty principle."<ref name="Gamow" />

Bohr spent a sleepless night considering this argument, and eventually realized that it was flawed. He pointed out that if the box were to be weighed, say by a spring and a pointer on a scale, "since the box must move vertically with a change in its weight, there will be uncertainty in its vertical velocity and therefore an uncertainty in its height above the table. ... Furthermore, the uncertainty about the elevation above the Earth's surface will result in an uncertainty in the rate of the clock",<ref>Gamow, G., ''The great physicists from Galileo to Einstein'', Courier Dover, 1988, pp. 260–261. {{ISBN?}}</ref> because of Einstein's own theory of [[Gravitational time dilation|gravity's effect on time]]. "Through this chain of uncertainties, Bohr showed that Einstein's light box experiment could not simultaneously measure exactly both the energy of the photon and the time of its escape."<ref>{{cite book |last=Kumar |first=M. |title=Quantum: Einstein, Bohr and the Great Debate About the Nature of Reality |publisher=Icon |year=2009 |page=287}}</ref>

=== EPR paradox for entangled particles ===
{{Main|Einstein–Podolsky–Rosen paradox}}
In 1935, Einstein, [[Boris Podolsky]] and [[Nathan Rosen]] published an analysis of spatially separated [[Quantum entanglement|entangled]] particles (EPR paradox).<ref>{{Cite journal |last1=Einstein |first1=A. |last2=Podolsky |first2=B. |last3=Rosen |first3=N. |date=1935-05-15 |title=Can Quantum-Mechanical Description of Physical Reality Be Considered Complete? |journal=Physical Review |volume=47 |issue=10 |pages=777–780 |doi=10.1103/PhysRev.47.777|bibcode=1935PhRv...47..777E |doi-access=free }}</ref> According to EPR, one could measure the position of one of the entangled particles and the momentum of the second particle, and from those measurements deduce the position and momentum of both particles to any precision, violating the uncertainty principle. In order to avoid such possibility, the measurement of one particle must modify the probability distribution of the other particle instantaneously, possibly violating the [[principle of locality]].<ref>{{Cite book |last=Kumar |first=Manjit |title=Quantum: Einstein, Bohr and the great debate about the nature of reality |date=2011 |publisher=Norton |isbn=978-0-393-33988-8 |edition=1st paperback |location=New York}}</ref>

In 1964, [[John Stewart Bell]] showed that this assumption can be falsified, since it would imply a certain [[Bell's theorem|inequality]] between the probabilities of different experiments. [[Bell test|Experimental results]] confirm the predictions of quantum mechanics, ruling out EPR's basic assumption of [[Local hidden-variable theory|local hidden variables]].

=== Popper's criticism ===
{{Main article|Popper's experiment}}
Science philosopher [[Karl Popper]] approached the problem of indeterminacy as a logician and [[Philosophical realism|metaphysical realist]].<ref name="Popper1959">{{cite book | last1 = Popper | first1 = Karl | author-link1 = Karl Popper | title = The Logic of Scientific Discovery | publisher = Hutchinson & Co. | year = 1959| title-link = The Logic of Scientific Discovery }}</ref> He disagreed with the application of the uncertainty relations to individual particles rather than to [[Quantum ensemble|ensembles]] of identically prepared particles, referring to them as "statistical scatter relations".<ref name="Popper1959" /><ref name="Jarvie2006">{{cite book | last1 = Jarvie | first1 = Ian Charles | last2 = Milford | first2 = Karl | last3 = Miller | first3 = David W. | title = Karl Popper: a centenary assessment | volume = 3 | publisher = Ashgate | year = 2006 | isbn = 978-0-7546-5712-5}}</ref> In this statistical interpretation, a ''particular'' measurement may be made to arbitrary precision without invalidating the quantum theory.

In 1934, Popper published {{lang|de|italic=no|Zur Kritik der Ungenauigkeitsrelationen}} ("Critique of the Uncertainty Relations") in {{lang|de|[[Naturwissenschaften]]}},<ref name="Popper1934">{{cite journal | title = Zur Kritik der Ungenauigkeitsrelationen |language=de |trans-title=Critique of the Uncertainty Relations | journal = Naturwissenschaften | year = 1934 | first = Karl | last = Popper | author2 = Carl Friedrich von Weizsäcker | volume = 22 | issue = 48 | pages = 807–808 | doi=10.1007/BF01496543|bibcode = 1934NW.....22..807P | s2cid = 40843068}}</ref> and in the same year {{lang|de|[[The Logic of Scientific Discovery|Logik der Forschung]]}} (translated and updated by the author as ''The Logic of Scientific Discovery'' in 1959<ref name="Popper1959" />), outlining his arguments for the statistical interpretation. In 1982, he further developed his theory in ''Quantum theory and the schism in Physics'', writing:

{{quote|[Heisenberg's] formulae are, beyond all doubt, derivable ''statistical formulae'' of the quantum theory. But they have been ''habitually misinterpreted'' by those quantum theorists who said that these formulae can be interpreted as determining some upper limit to the ''precision of our measurements''. [original emphasis]<ref>{{cite book |last=Popper |first=K. |title=Quantum theory and the schism in Physics |publisher=Unwin Hyman |year=1982 |pages=53–54}}</ref>}}

Popper proposed an experiment to [[Falsifiability|falsify]] the uncertainty relations, although he later withdrew his initial version after discussions with [[Carl Friedrich von Weizsäcker]], Heisenberg, and Einstein; Popper sent his paper to Einstein and  it may have influenced the formulation of the EPR paradox.<ref name="Mehra2001">{{cite book | last1 = Mehra | first1 = Jagdish | last2 = Rechenberg | first2 = Helmut | author-link1 = Jagdish Mehra | author-link2 = Helmut Rechenberg | title = The Historical Development of Quantum Theory | publisher = Springer | year = 2001 | isbn = 978-0-387-95086-0 | url-access = registration | url = https://archive.org/details/completionofquan0000mehr }}</ref>{{rp|720}}

=== Free will ===
Some scientists, including [[Arthur Compton]]<ref>{{Cite journal | doi = 10.1126/science.74.1911.172| title = The Uncertainty Principle and Free Will| journal = Science| volume = 74| issue = 1911| pages = 172| year = 1931| last1 = Compton | first1 = A. H. | pmid=17808216|bibcode = 1931Sci....74..172C | s2cid = 29126625}}</ref> and [[Martin Heisenberg]],<ref>{{Cite journal | doi = 10.1038/459164a| pmid = 19444190| title = Is free will an illusion?| journal = Nature| volume = 459| issue = 7244| pages = 164–165| year = 2009| last1 = Heisenberg | first1 = M. |bibcode = 2009Natur.459..164H | s2cid = 4420023| doi-access = free}}</ref> have suggested that the uncertainty principle, or at least the general probabilistic nature of quantum mechanics, could be evidence for the two-stage model of free will. One critique, however, is that apart from the basic role of quantum mechanics as a foundation for chemistry, [[Quantum biology|nontrivial biological mechanisms requiring quantum mechanics]] are unlikely, due to the rapid [[Quantum decoherence|decoherence]] time of quantum systems at room temperature.<ref name="ReferenceA">{{Cite journal | doi = 10.1016/j.biosystems.2004.07.001| pmid = 15555759| title = Does quantum mechanics play a non-trivial role in life?| journal = Biosystems| volume = 78| issue = 1–3| pages = 69–79| year = 2004| last1 = Davies | first1 = P. C. W. | bibcode = 2004BiSys..78...69D}}</ref> Proponents of this theory commonly say that this decoherence is overcome by both screening and decoherence-free subspaces found in biological cells.<ref name="ReferenceA"/>

=== Thermodynamics ===
There is reason to believe that violating the uncertainty principle also strongly implies the violation of the [[second law of thermodynamics]].<ref>{{Cite journal |arxiv = 1205.6894|doi = 10.1038/ncomms2665|title = A violation of the uncertainty principle implies a violation of the second law of thermodynamics|year = 2013|last1 = Hänggi|first1 = Esther|last2 = Wehner|first2 = Stephanie|journal = Nature Communications|volume = 4|pages = 1670|pmid = 23575674|bibcode = 2013NatCo...4.1670H|s2cid = 205316392}}</ref> See [[Gibbs paradox]].

=== Rejection of the principle ===
Uncertainty principles relate quantum particles – electrons for example – to classical concepts – position and momentum. This presumes quantum particles have position and momentum. [[Edwin C. Kemble]] pointed out<ref>{{cite book |last=Kemble |first=E. C. |year=1937 |title=The Fundamental Principles of Quantum Mechanics |location=New York |publisher=McGraw-Hill, reprinted by Dover |page=244}}</ref>{{clarify inline|reason=What printing/edition does this page number refer to? Use year for that, and orig-year for original publication date|date=December 2024}} in 1937 that such properties cannot be experimentally verified and assuming they exist gives rise to many contradictions; similarly [[Rudolf Haag]] notes that position in quantum mechanics is an attribute of an interaction, say between an electron and a detector, not an intrinsic property.<ref>{{cite book |last=Haag |first=R. |year=1996 |title=Local Quantum Physics: Fields, Particles, Algebras |location=Berlin |publisher=Springer}}{{page?|date=February 2024}}{{ISBN?}}</ref><ref>{{Cite journal |last1=Peres |first1=Asher |url=https://link.aps.org/doi/10.1103/RevModPhys.76.93 |title=Quantum information and relativity theory |last2=Terno |first2=Daniel R. |journal=Reviews of Modern Physics |date=2004-01-06 |volume=76 |issue=1 |pages=93–123 [111] |language=en |doi=10.1103/RevModPhys.76.93 |arxiv=quant-ph/0212023 |bibcode=2004RvMP...76...93P |s2cid=7481797 |issn=0034-6861 |access-date=2024-01-25 |archive-date=2024-02-23 |archive-url=https://web.archive.org/web/20240223160147/https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.76.93 |url-status=live }}</ref> From this point of view the uncertainty principle is not a fundamental quantum property but a concept "carried over from the language of our ancestors", as Kemble says.