Complementarity (physics)

In physics, complementarity is a fundamental princi-ple of quantum mechanics, closely associated with theCopenhagen interpretation. It holds that objects havecomplementary properties which cannot be measured ac-curately at the same time. The more accurately oneproperty is measured, the less accurately the complemen-tary property is measured, according to the Heisenberguncertainty principle. Further, a full description of a par-ticular type of phenomenon can only be achieved throughmeasurements made in each of the various possible bases— which are thus complementary. The complementarityprinciple was formulated byNiels Bohr, a leading founderof quantum mechanics.[1]Examples of complementary properties:

• Position and momentum

• Spin on different axis

• Wave and particle

• Value of a field and its change (at a certain position)

1 Concept

Bohr summarized the principle as follows:

...however far the [quantum physical] phe-nomena transcend the scope of classical physi-cal explanation, the account of all evidencemustbe expressed in classical terms. The argumentis simply that by the word “experiment” we re-fer to a situation where we can tell others whatwe have done and what we have learned andthat, therefore, the account of the experimen-tal arrangements and of the results of the ob-servations must be expressed in unambiguouslanguage with suitable application of the ter-minology of classical physics.

This crucial point...implies the impossibil-ity of any sharp separation between the be-haviour of atomic objects and the interactionwith the measuring instruments which serve todefine the conditions under which the phenom-ena appear.... Consequently, evidence ob-tained under different experimental conditionscannot be comprehended within a single pic-ture, but must be regarded as complementary in

the sense that only the totality of the phenom-ena exhausts the possible information about theobjects.[2]

For example, the particle and wave aspects of physicalobjects are such complementary phenomena. Both con-cepts are borrowed from classical mechanics, where it isimpossible to be a particle and wave at the same time.Therefore it is impossible to measure the full proper-ties of the wave and particle at a particular moment.[3]Moreover, Bohr implies that it is not possible to regardobjects governed by quantum mechanics as having in-trinsic properties independent of determination with ameasuring device. The type of measurement determineswhich property is shown. However the single and double-slit experiment and other experiments show that someeffects of wave and particle can be measured in onemeasurement.[4]

2 Nature

A profound aspect of complementarity is that it not onlyapplies to measurability or knowability of some propertyof a physical entity, but more importantly it applies tothe limitations of that physical entity’s very manifesta-tion of the property in the physical world. All propertiesof physical entities exist only in pairs, which Bohr de-scribed as complementary or conjugate pairs (which arealso Fourier transform pairs). Physical reality is deter-mined and defined by manifestations of properties whichare limited by trade-offs between these complementarypairs. For example, an electron can manifest a greaterand greater accuracy of its position only in even tradefor a complementary loss in accuracy of manifesting itsmomentum. This means that there is a limitation on theprecision with which an electron can possess (i.e., man-ifest) position, since an infinitely precise position woulddictate that its manifested momentum would be infinitelyimprecise, or undefined (i.e., non-manifest or not pos-sessed), which is not possible. The ultimate limitationsin precision of property manifestations are quantified bythe Heisenberg uncertainty principle and Planck units.Complementarity and Uncertainty dictate that thereforeall properties and actions in the physical world manifestthemselves as non-deterministic to some degree.Physicists F.A.M. Frescura and Basil Hiley have summa-rized the reasons for the introduction of the principle ofcomplementarity in physics as follows:[5]

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2 4 EXPERIMENTS

“In the traditional view, it is as-sumed that there exists a reality inspace-time and that this reality isa given thing, all of whose aspectscan be viewed or articulated at anygiven moment. Bohr was the firstto point out that quantum mechan-ics called this traditional outlookinto question. To him the ‘indivis-ibility of the quantum of action’,which was his way of describingthe uncertainty principle, impliedthat not all aspects of a system canbe viewed simultaneously. By us-ing one particular piece of appara-tus only certain features could bemade manifest at the expense ofothers, while with a different pieceof apparatus another complemen-tary aspect could be made manifestin such a way that the original setbecame non-manifest, that is, theoriginal attributes were no longerwell defined. For Bohr, this wasan indication that the principle ofcomplementarity, a principle thathe had previously known to appearextensively in other intellectual dis-ciplines but which did not appear inclassical physics, should be adoptedas a universal principle.”

The emergence of complementarity in a system occurswhen one considers the circumstances under which oneattempts to measure its properties; as Bohr noted, theprinciple of complementarity “implies the impossibilityof any sharp separation between the behaviour of atomicobjects and the interaction with the measuring instru-ments that serve to define the conditions under which thephenomena appear.”[6] It is important to distinguish, asdid Bohr in his original statements, the principle of com-plementarity from a statement of the uncertainty princi-ple. For a technical discussion of contemporary issuessurrounding complementarity in physics see, e.g., Bandy-opadhyay (2000),[7] from which parts of this discussionwere drawn.

3 Additional considerations

In his original lecture on the topic, Bohr pointed out thatjust as the finitude of the speed of light implies the im-possibility of a sharp separation between space and time(relativity), the finitude of the quantum of action impliesthe impossibility of a sharp separation between the be-havior of a system and its interaction with the measuringinstruments and leads to the well known difficulties withthe concept of 'state' in quantum theory; the notion of

complementarity is intended to symbolize this new situ-ation in epistemology created by quantum theory. Somepeople consider it a philosophical adjunct to quantumme-chanics, while others consider it to be a discovery thatis as important as the formal aspects of quantum the-ory. Examples of the latter include Leon Rosenfeld, whoclaimed that "[C]omplementarity is not a philosophicalsuperstructure invented by Bohr to be placed as a deco-ration on top of the quantal formalism, it is the bedrockof the quantal description.”,[8] and John Wheeler, whoopined that “Bohr’s principle of complementarity is themost revolutionary scientific concept of this century andthe heart of his fifty-year search for the full significanceof the quantum idea.”[9]

4 Experiments

The quintessential example of wave–particle complemen-tarity in the laboratory is the double slit. The crux ofthe complementary behavior is the question: “What in-formation exists – embedded in the constituents of theuniverse – that can reveal the history of the signal parti-cles as they pass through the double slit?" If informationexists (even if it is not measured by a conscious observer)that reveals “which slit” each particle traversed, then eachparticle will exhibit no wave interference with the otherslit. This is the particle-like behavior. But if no infor-mation exists about which slit – so that no conscious ob-server, no matter how well equipped, will ever be ableto determine which slit each particle traverses – then thesignal particles will interfere with themselves as if theytraveled through both slits at the same time, as a wave.This is the wave-like behavior. These behaviors are com-plementary, according to the Englert–Greenberger dual-ity relation, because when one behavior is observed theother is absent. Both behaviors can be observed at thesame time, but each only as lesser manifestations of theirfull behavior (as determined by the duality relation). Thissuperposition of complementary behaviors exists when-ever there is partial “which slit” information. While thereis some contention to the duality relation, and thus com-plementarity itself, the contrary position is not acceptedby mainstream physics.[10]:35–40

Various neutron interferometry experiments demonstratethe subtlety of the notions of duality and complementar-ity. By passing through the interferometer, the neutronappears to act as a wave. Yet upon passage, the neutronis subject to gravitation. As the neutron interferometer isrotated through Earth’s gravitational field a phase changebetween the two arms of the interferometer can be ob-served, accompanied by a change in the constructive anddestructive interference of the neutron waves on exit fromthe interferometer. Some interpretations claim that un-derstanding the interference effect requires one to con-cede that a single neutron takes both paths through theinterferometer at the same time; a single neutron would

3

“be in two places at once”, as it were. Since the two pathsthrough a neutron interferometer can be as far as 5 cmto 15 cm apart, the effect is hardly microscopic. This issimilar to traditional double-slit and mirror interferome-ter experiments where the slits (or mirrors) can be arbi-trarily far apart. So, in interference and diffraction ex-periments, neutrons behave the same way as photons (orelectrons) of corresponding wavelength.[11][12]:211–213

5 History

Niels Bohr apparently conceived of the principle of com-plementarity during a skiing vacation in Norway in Febru-ary and March 1927, during which he received a let-ter from Werner Heisenberg regarding the latter’s newlydiscovered (and not yet published) uncertainty princi-ple. Upon returning from his vacation, by which timeHeisenberg had already submitted his paper on the uncer-tainty principle for publication, he convinced Heisenbergthat the uncertainty principle was a manifestation of thedeeper concept of complementarity.[3] Heisenberg dulyappended a note to this effect to his paper on the uncer-tainty principle, before its publication, stating:

Bohr has brought to my attention [that] theuncertainty in our observation does not ariseexclusively from the occurrence of discontinu-ities, but is tied directly to the demand that weascribe equal validity to the quite different ex-periments which show up in the [particulate]theory on one hand, and in the wave theory onthe other hand.

Bohr publicly introduced the principle of complementar-ity in a lecture he delivered on 16 September 1927 atthe International Physics Congress held in Como, Italy,attended by most of the leading physicists of the era,with the notable exceptions of Einstein, Schrödinger,and Dirac. However, these three were in attendanceone month later when Bohr again presented the princi-ple at the Fifth Solvay Congress in Brussels, Belgium.The lecture was published in the proceedings of bothof these conferences, and was republished the followingyear in Naturwissenschaften (in German) and in Nature(in English).[13]

An article written by Bohr in 1949 titled “Discussionswith Einstein on Epistemological Problems in AtomicPhysics”[2] is considered by many to be a definitive de-scription of the notion of complementarity.[14]

6 See also• Afshar experiment

• Bohr–Einstein debates

• Copenhagen interpretation

• Englert–Greenberger duality relation

• Ehrenfest’s theorem

• Interpretation of quantum mechanics

• Quantum entanglement

• Quantum indeterminacy

• Transactional interpretation

• Wheeler–Feynman absorber theory

7 References

[1] Walker, Evan Harris (2000). The Physics of Conscious-ness. Cambridge, Massachusetts: Perseus. p. 271. ISBN0-7382-0436-6. "...the founders of quantummechanics --Heisenberg, Schrodinger and Bohr...”

[2] Niels Bohr (1949). “Discussions with Einstein on Epis-temological Problems in Atomic Physics”. In P. Schilpp.Albert Einstein: Philosopher-Scientist. Open Court.

[3] Jim Baggott (2011). The Quantum Story: A History in.Oxford University Press. p. 97.

[4] Boscá Díaz-Pintado, María C. (29–31 March 2007).“Updating the wave-particle duality”. “15th UK and Eu-ropean Meeting on the Foundations of Physics”. Leeds,UK. Retrieved 2008-06-21.

[5] F. A. M. Frescura, B. J. Hiley: Algebras, quantum the-ory and pre-space, published in Revista Brasileira deFisica, Volume Especial, Julho 1984, Os 70 anos deMarioSchonberg, pp. 49–86, p. 2

[6] Jørgen Kalckar, Niels Bohr, Léon Rosenfeld, ErikRüdinger, Finn Aaserud (1996). Foundations of QuantumPhysics II (1933-1958). Elsevier. p. 210. ISBN 978-0-444-89892-0. Retrieved 2011-10-24.

[7] Bandyopadhyay, Supriyo (2000). “Welcher Weg Experi-ments and the Orthodox Bohr’s Complementarity Princi-ple”. Physics Letters A 276 (5–6): 233–239. arXiv:quant-ph/0003073. Bibcode:2000PhLA..276..233B.doi:10.1016/S0375-9601(00)00670-8.

[8] Niels Bohr; fwd. Léon Rosenfeld; ed. Kalckar; et al.(1996). “Complementarity: Bedrock of the Quantal De-scription”. Foundations of Quantum Physics II (1933–1958). Niels Bohr CollectedWorks 7. Elsevier. pp. 284–285. ISBN 978-0-444-89892-0.

[9] John Wheeler, Physics Today, January 1963, p. 30.

[10] Haroche, Serge; Raimond, Jean-Michel (2006). Explor-ing the Quantum: Atoms, Cavities, and Photons (1st ed.).Oxford University Press. ISBN 978-0198509141.

4 9 EXTERNAL LINKS

[11] Colella, R.; Overhauser, A. W.; Werner, S. A.(1975). “Observation of gravitationally inducedquantum interference”. Phys. Rev. Lett. 34(23): 1472–1474. Bibcode:1975PhRvL..34.1472C.doi:10.1103/physrevlett.34.1472.

[12] Helmut Rauch; Samuel A. Werner (2000). Neutron Inter-ferometry: Lessons in Experimental Quantum Mechanics.Oxford University Press. ISBN 978-0-19-850027-8.

[13] Bohr N (1928). “The Quantum Postulate and the RecentDevelopment of Atomic Theory”. Nature 121: 580–590.Bibcode:1928Natur.121..580B. doi:10.1038/121580a0.Available in the collection of Bohr’s early writings, AtomicTheory and the Description of Nature (1934).

[14] Saunders S (2005). “Complementarity and Sci-entific Rationality”. Foundations of Physics35 (3): 417–447. arXiv:quant-ph/0412195.Bibcode:2005FoPh...35..417S. doi:10.1007/s10701-004-1982-x.

8 Further reading• Berthold-Georg Englert, Marlan O. Scully &Herbert Walther, Quantum Optical Tests of Com-plementarity, Nature, Vol 351, pp 111–116 (9 May1991) and (same authors) The Duality in Matter andLight Scientific American, pg 56–61, (December1994). Demonstrates that complementarity is en-forced, and quantum interference effects destroyed,by decoherence (irreversible object-apparatus cor-relations), and not, as was previously popularly be-lieved, by Heisenberg’s uncertainty principle itself.

• Niels Bohr, Causality and Complementarity: Sup-plementary papers edited by Jan Faye and Henry J.Folse. The PhilosophicalWritings of Niels Bohr, Vol-ume IV. Ox Bow Press. 1998.

9 External links• Discussions with Einstein on Epistemological Prob-lems in Atomic Physics

• Einstein’s Reply to Criticisms

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