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In physics, the observer effect is the disturbance of an observed system by the act of observation.^[1]^[2] This is often the result of utilising instruments that, by necessity, alter the state of what they measure in some manner. A common example is checking the pressure in an automobile tire, which causes some of the air to escape, thereby changing the amount of pressure one observes. Similarly, seeing non-luminous objects requires light hitting the object to cause it to reflect that light. While the effects of observation are often negligible, the object still experiences a change (leading to the Schrödinger's cat thought experiment). This effect can be found in many domains of physics, but can usually be reduced to insignificance by using different instruments or observation techniques.

A notable example of the observer effect occurs in quantum mechanics, as demonstrated by the double-slit experiment. Physicists have found that observation of quantum phenomena by a detector or an instrument can change the measured results of this experiment. Despite the "observer effect" in the double-slit experiment being caused by the presence of an electronic detector, the experiment's results have been interpreted by some to suggest that a conscious mind can directly affect reality.^[3] However, the need for the "observer" to be conscious is not supported by scientific research, and has been pointed out as a misconception rooted in a poor understanding of the quantum wave function $ψ$ and the quantum measurement process.^[4]^[5]^[6]

Particle physics

An electron is detected upon interaction with a photon; this interaction will inevitably alter the velocity and momentum of that electron. It is possible for other, less direct means of measurement to affect the electron. It is also necessary to distinguish clearly between the measured value of a quantity and the value resulting from the measurement process. In particular, a measurement of momentum is non-repeatable in short intervals of time. A formula (one-dimensional for simplicity) relating involved quantities, due to Niels Bohr (1928) is given by $|v'_{x}-v_{x}|\Delta p_{x}\approx \hbar /\Delta t,$ where

$Δ p x$ is uncertainty in measured value of momentum,
$Δ t$ is duration of measurement,
$v x$ is velocity of particle before measurement,
$v' x$ is velocity of particle after measurement,
$ħ$ is the reduced Planck constant.

The measured momentum of the electron is then related to $v x$ , whereas its momentum after the measurement is related to $v' x$ . This is a best-case scenario.^[7]

Electronics

In electronics, ammeters and voltmeters are usually wired in series or parallel to the circuit, and so by their very presence affect the current or the voltage they are measuring by way of presenting an additional real or complex load to the circuit, thus changing the transfer function and behavior of the circuit itself. Even a more passive device such as a current clamp, which measures the wire current without coming into physical contact with the wire, affects the current through the circuit being measured because the inductance is mutual.

Thermodynamics

In thermodynamics, a standard mercury-in-glass thermometer must absorb or give up some thermal energy to record a temperature, and therefore changes the temperature of the body which it is measuring.

Quantum mechanics

Some interpretations of quantum mechanics posit a central role for an observer of a quantum phenomenon.^[8] The quantum mechanical observer is tied to the issue of observer effect, where a measurement necessarily requires interacting with the physical object being measured, affecting its properties through the interaction. The term "observable" has gained a technical meaning, denoting a Hermitian operator that represents a measurement.^[9]^: 55

References

^ Dirac, P.A.M. (1967). The Principles of Quantum Mechanics (4th ed.). Oxford University Press. p. 3.
^ Dent, Eric B. "The Observation, Inquiry, and Measurement Challenges Surfaced by Complexity Theory" (PDF). In Richardson, Kurt (ed.). Managing the Complex: Philosophy, Theory and Practice. Archived from the original (PDF) on 19 August 2019. Retrieved 23 April 2019.
^ Squires, Euan J. (1994). "Does wavefunction reduction require conscious observers?". The Mystery of the Quantum World. Taylor & Francis Group. p. 62. ISBN 9781420050509.
^ "Of course the introduction of the observer must not be misunderstood to imply that some kind of subjective features are to be brought into the description of nature. The observer has, rather, only the function of registering decisions, i.e., processes in space and time, and it does not matter whether the observer is an apparatus or a human being; but the registration, i.e., the transition from the "possible" to the "actual," is absolutely necessary here and cannot be omitted from the interpretation of quantum theory." - Werner Heisenberg, Physics and Philosophy, p. 137
^ "Was the wave function waiting to jump for thousands of millions of years until a single-celled living creature appeared? Or did it have to wait a little longer for some highly qualified measurer - with a PhD?" -John Stewart Bell, 1981, Quantum Mechanics for Cosmologists. In C.J. Isham, R. Penrose and D.W. Sciama (eds.), Quantum Gravity 2: A second Oxford Symposium. Oxford: Clarendon Press, p. 611.
^ According to standard quantum mechanics, it is a matter of complete indifference whether the experimenters stay around to watch their experiment, or instead leave the room and delegate observing to an inanimate apparatus which amplifies the microscopic events to macroscopic measurements and records them by a time-irreversible process (Bell, John (2004). Speakable and Unspeakable in Quantum Mechanics: Collected Papers on Quantum Philosophy. Cambridge University Press. p. 170. ISBN 9780521523387.). The measured state is not interfering with the states excluded by the measurement. As Richard Feynman put it: "Nature does not know what you are looking at, and she behaves the way she is going to behave whether you bother to take down the data or not." (Feynman, Richard (2015). The Feynman Lectures on Physics. Vol. III. Basic Books. Ch 3.2. ISBN 9780465040834.).
^ Landau, L.D.; Lifshitz, E. M. (1977). Quantum Mechanics: Non-Relativistic Theory. Vol. 3. Translated by Sykes, J. B.; Bell, J. S. (3rd ed.). Pergamon Press. §7, §44. ISBN 978-0-08-020940-1.
^ Schlosshauer, Maximilian; Kofler, Johannes; Zeilinger, Anton (1 August 2013). "A snapshot of foundational attitudes toward quantum mechanics". Studies in History and Philosophy of Science Part B. 44 (3): 222–230. arXiv:1301.1069. Bibcode:2013SHPMP..44..222S. doi:10.1016/j.shpsb.2013.04.004. S2CID 55537196.
^ Rieffel, Eleanor G.; Polak, Wolfgang H. (4 March 2011). Quantum Computing: A Gentle Introduction. MIT Press. ISBN 978-0-262-01506-6.

[1] Dirac, P.A.M. (1967). The Principles of Quantum Mechanics (4th ed.). Oxford University Press. p. 3.

[2] Dent, Eric B. "The Observation, Inquiry, and Measurement Challenges Surfaced by Complexity Theory" (PDF). In Richardson, Kurt (ed.). Managing the Complex: Philosophy, Theory and Practice. Archived from the original (PDF) on 19 August 2019. Retrieved 23 April 2019.

[3] Squires, Euan J. (1994). "Does wavefunction reduction require conscious observers?". The Mystery of the Quantum World. Taylor & Francis Group. p. 62. ISBN 9781420050509.

[4] "Of course the introduction of the observer must not be misunderstood to imply that some kind of subjective features are to be brought into the description of nature. The observer has, rather, only the function of registering decisions, i.e., processes in space and time, and it does not matter whether the observer is an apparatus or a human being; but the registration, i.e., the transition from the "possible" to the "actual," is absolutely necessary here and cannot be omitted from the interpretation of quantum theory." - Werner Heisenberg, Physics and Philosophy, p. 137

[5] "Was the wave function waiting to jump for thousands of millions of years until a single-celled living creature appeared? Or did it have to wait a little longer for some highly qualified measurer - with a PhD?" -John Stewart Bell, 1981, Quantum Mechanics for Cosmologists. In C.J. Isham, R. Penrose and D.W. Sciama (eds.), Quantum Gravity 2: A second Oxford Symposium. Oxford: Clarendon Press, p. 611.

[6] According to standard quantum mechanics, it is a matter of complete indifference whether the experimenters stay around to watch their experiment, or instead leave the room and delegate observing to an inanimate apparatus which amplifies the microscopic events to macroscopic measurements and records them by a time-irreversible process (Bell, John (2004). Speakable and Unspeakable in Quantum Mechanics: Collected Papers on Quantum Philosophy. Cambridge University Press. p. 170. ISBN 9780521523387.). The measured state is not interfering with the states excluded by the measurement. As Richard Feynman put it: "Nature does not know what you are looking at, and she behaves the way she is going to behave whether you bother to take down the data or not." (Feynman, Richard (2015). The Feynman Lectures on Physics. Vol. III. Basic Books. Ch 3.2. ISBN 9780465040834.).

[7] Landau, L.D.; Lifshitz, E. M. (1977). Quantum Mechanics: Non-Relativistic Theory. Vol. 3. Translated by Sykes, J. B.; Bell, J. S. (3rd ed.). Pergamon Press. §7, §44. ISBN 978-0-08-020940-1.

[Observer_(quantum_physics)_snapshot-8] Schlosshauer, Maximilian; Kofler, Johannes; Zeilinger, Anton (1 August 2013). "A snapshot of foundational attitudes toward quantum mechanics". Studies in History and Philosophy of Science Part B. 44 (3): 222–230. arXiv:1301.1069. Bibcode:2013SHPMP..44..222S. doi:10.1016/j.shpsb.2013.04.004. S2CID 55537196.

[9] Rieffel, Eleanor G.; Polak, Wolfgang H. (4 March 2011). Quantum Computing: A Gentle Introduction. MIT Press. ISBN 978-0-262-01506-6.

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@@ Line 3: / Line 3: @@
 {{Use dmy dates|date=September 2020}}
 {{Quantum mechanics}}
-In [[physics]], the '''observer effect''' is the disturbance of an observed system by the act of observation.<ref>{{cite book | title=[[The Principles of Quantum Mechanics]] 4th Edition | page=3 | author=Dirac, P.A.M.. | year=1967 | publisher=Oxford University Press}}</ref><ref>http://faculty.uncfsu.edu/edent/Observation.pdf</ref> This is often the result of instruments that, by necessity, alter the state of what they measure in some manner. A common example is checking the pressure in an automobile tire; this is difficult to do without letting out some of the air, thus changing the pressure. Similarly, it is not possible to see any object without light hitting the object, and causing it to reflect that light. While the effects of observation are often negligible, the object still experiences a change. This effect can be found in many domains of physics, but can usually be reduced to insignificance by using different instruments or observation techniques.
+In [[physics]], the '''observer effect''' is the disturbance of an observed system by the act of observation.<ref>{{cite book |title=[[The Principles of Quantum Mechanics]] |edition=4th |page=3 |author=Dirac, P.A.M. |year=1967 |publisher=Oxford University Press}}</ref><ref>{{Cite book |author=Dent, Eric B. |chapter-url=http://faculty.uncfsu.edu/edent/Observation.pdf |chapter=The Observation, Inquiry, and Measurement Challenges Surfaced by Complexity Theory |editor=Richardson, Kurt |title=Managing the Complex: Philosophy, Theory and Practice |access-date=23 April 2019 |archive-date=19 August 2019 |archive-url=https://web.archive.org/web/20190819065402/http://faculty.uncfsu.edu/edent/Observation.pdf |url-status=dead }}</ref> This is often the result of utilising instruments that, by necessity, alter the state of what they measure in some manner. A common example is checking the pressure in an automobile tire, which causes some of the air to escape, thereby changing the amount of pressure one observes. Similarly, seeing non-luminous objects requires light hitting the object to cause it to reflect that light. While the effects of observation are often negligible, the object still experiences a change (leading to the [[Schrödinger's cat]] thought experiment). This effect can be found in many domains of physics, but can usually be reduced to insignificance by using different instruments or observation techniques.
-An especially unusual version of the observer effect occurs in [[quantum mechanics]], as best demonstrated by the [[double-slit experiment]]. Physicists have found that observation of quantum phenomena can actually change the measured results of this experiment. Despite the "observer effect" in the double-slit experiment being caused by the presence of an electronic detector, the experiment's results have been misinterpreted by some to suggest that a conscious mind can directly affect reality.<ref>{{cite book | title=The Mystery of the Quantum World | author=Squires, Euan J. | year=1994 | publisher=Taylor & Francis Group | chapter-url=https://books.google.com/books?id=PinUwd99CV8C | chapter=4| isbn=9781420050509 }}</ref> The need for the "observer" to be conscious is not supported by scientific research, and has been pointed out as a misconception rooted in a poor understanding of the quantum wave function {{mvar|ψ}} and the quantum measurement process.<ref>"Of course the introduction of the observer must not be misunderstood to imply that some kind of subjective features are to be brought into the description of nature. The observer has, rather, only the function of registering decisions, i.e., processes in space and time, and ''it does not matter whether the observer is an apparatus or a human being''; but the registration, i.e., the transition from the "possible" to the "actual," is absolutely necessary here and cannot be omitted from the interpretation of quantum theory." - [[Werner Heisenberg]], ''Physics and Philosophy'', p. 137</ref><ref>"Was the wave function waiting to jump for thousands of millions of years until a single-celled living creature appeared? Or did it have to wait a little longer for some highly qualified measurer - with a PhD?" -[[John Stewart Bell]], 1981, ''Quantum Mechanics for Cosmologists''. In C.J. Isham, R. Penrose and D.W. Sciama (eds.),
-''Quantum Gravity 2: A second Oxford Symposium''. Oxford: Clarendon Press, p.&nbsp;611.</ref><ref>According to standard quantum mechanics, it is a matter of complete indifference whether the experimenters stay around to watch their experiment, or instead leave the room and delegate observing to an inanimate apparatus which amplifies the microscopic events to macroscopic measurements and records them by a time-irreversible process ({{Cite book|title = Speakable and Unspeakable in Quantum Mechanics: Collected Papers on Quantum Philosophy|last = Bell|first = John|publisher = Cambridge University Press|year = 2004|isbn = 9780521523387|pages = 170}}). The measured state is not interfering with the states excluded by the measurement. As [[Richard Feynman]] put it: "Nature does not know what you are looking at, and she behaves the way she is going to behave whether you bother to take down the data or not." ({{Cite book|title = The Feynman Lectures on Physics, Vol. III|last = Feynman|first = Richard|publisher = Basic Books|year = 2015|isbn = 9780465040834|location =Ch 3.2 }}).</ref>
+A notable example of the observer effect occurs in [[quantum mechanics]], as demonstrated by the [[double-slit experiment]]. Physicists have found that observation of quantum phenomena by a detector or an instrument can change the measured results of this experiment. Despite the "observer effect" in the double-slit experiment being caused by the presence of an electronic detector, the experiment's results have been interpreted by some to suggest that a conscious mind can directly affect reality.<ref>{{cite book | title=The Mystery of the Quantum World | author=Squires, Euan J. | year=1994 | publisher=Taylor & Francis Group | chapter-url=https://books.google.com/books?id=PinUwd99CV8C | chapter=Does wavefunction reduction require conscious observers? | page=62 | isbn=9781420050509 }}</ref> However, the need for the "observer" to be conscious is not supported by scientific research, and has been pointed out as a misconception rooted in a poor understanding of the quantum wave function {{mvar|ψ}} and the quantum measurement process.<ref>"Of course the introduction of the observer must not be misunderstood to imply that some kind of subjective features are to be brought into the description of nature. The observer has, rather, only the function of registering decisions, i.e., processes in space and time, and ''it does not matter whether the observer is an apparatus or a human being''; but the registration, i.e., the transition from the "possible" to the "actual," is absolutely necessary here and cannot be omitted from the interpretation of quantum theory." - [[Werner Heisenberg]], ''Physics and Philosophy'', p. 137</ref><ref>"Was the wave function waiting to jump for thousands of millions of years until a single-celled living creature appeared? Or did it have to wait a little longer for some highly qualified measurer - with a PhD?" -[[John Stewart Bell]], 1981, ''Quantum Mechanics for Cosmologists''. In C.J. Isham, R. Penrose and D.W. Sciama (eds.),
+''Quantum Gravity 2: A second Oxford Symposium''. Oxford: Clarendon Press, p.&nbsp;611.</ref><ref>According to standard quantum mechanics, it is a matter of complete indifference whether the experimenters stay around to watch their experiment, or instead leave the room and delegate observing to an inanimate apparatus which amplifies the microscopic events to macroscopic measurements and records them by a time-irreversible process ({{Cite book|title = Speakable and Unspeakable in Quantum Mechanics: Collected Papers on Quantum Philosophy|last = Bell|first = John|publisher = Cambridge University Press|year = 2004|isbn = 9780521523387|pages = 170}}). The measured state is not interfering with the states excluded by the measurement. As [[Richard Feynman]] put it: "Nature does not know what you are looking at, and she behaves the way she is going to behave whether you bother to take down the data or not." ({{Cite book |title=The Feynman Lectures on Physics |volume=III |last=Feynman |first=Richard |publisher=Basic Books |year=2015 |isbn=9780465040834 |at=Ch 3.2 }}).</ref>
 ==Particle physics==
 An [[electron]] is detected upon interaction with a [[photon]]; this interaction will inevitably alter the velocity and momentum of that electron. It is possible for other, less direct means of measurement to affect the electron. It is also necessary to distinguish clearly between the measured value of a quantity and the value resulting from the measurement process. In particular, a measurement of momentum is non-repeatable in short intervals of time. A formula (one-dimensional for simplicity) relating involved quantities, due to [[Niels Bohr]] (1928) is given by
+<math display="block">|v'_x - v_x|\Delta p_x \approx \hbar/\Delta t,</math>
-:<math>|v'_x - v_x|\Delta p_x \approx \hbar/\Delta t,</math>
 where
-:Δ''p<sub>x</sub>'' is uncertainty in measured value of momentum,
+* {{math|Δ''p<sub>x</sub>''}} is uncertainty in measured value of momentum,
-:Δ''t'' is duration of measurement,
+* {{math|Δ''t''}} is duration of measurement,
-:''v<sub>x</sub>'' is velocity of particle ''before'' measurement,
+* {{math|''v<sub>x</sub>''}} is velocity of particle ''before'' measurement,
-:{{SubSup|''v''|''x''|'}} is velocity of particle ''after'' measurement,
+* {{math|''v''&prime;<sub>''x''</sub>}} is velocity of particle ''after'' measurement,
-: {{math|''ħ''}} is the reduced [[Planck constant]].
+* {{math|''ħ''}} is the reduced [[Planck constant]].
-The ''measured'' momentum of the electron is then related to {{math|''v''<sub>''x''</sub>}}, whereas its momentum ''after'' the measurement is related to {{math|''v''&prime;<sub>''x''</sub>}}. This is a best-case scenario.<ref>{{cite book|first1=L.D.|last1=Landau|author-link1=Lev Landau|first2=E. M.|last2=Lifshitz|author-link2=Evgeny Lifshitz|translator-last1=Sykes|translator-first1=J. B.|translator-last2=Bell|translator-first2=J. S.|translator-link2=John Stewart Bell|year=1977|title=Quantum Mechanics: Non-Relativistic Theory|edition=3rd|volume=Vol. 3|publisher=[[Pergamon Press]]|isbn=978-0-08-020940-1|at=§7, §44|url=https://archive.org/details/QuantumMechanics_104}}</ref>
+The ''measured'' momentum of the electron is then related to {{math|''v''<sub>''x''</sub>}}, whereas its momentum ''after'' the measurement is related to {{math|''v''&prime;<sub>''x''</sub>}}. This is a best-case scenario.<ref>{{cite book| first1=L.D.| last1=Landau| author-link1=Lev Landau| first2=E. M.| last2=Lifshitz| author-link2=Evgeny Lifshitz| translator-last1=Sykes| translator-first1=J. B.| translator-last2=Bell| translator-first2=J. S.| translator-link2=John Stewart Bell| year=1977| title=Quantum Mechanics: Non-Relativistic Theory| edition=3rd| volume=3| publisher=[[Pergamon Press]]| isbn=978-0-08-020940-1| at=§7, §44| url=https://archive.org/details/QuantumMechanics_104}}</ref>
 ==Electronics==
@@ Line 28: / Line 28: @@
 ==Quantum mechanics==
-{{main|Observer (quantum mechanics)}}
+{{excerpt|Observer (quantum mechanics)}}
-The theoretical foundation of the concept of [[measurement in quantum mechanics]] is a contentious issue deeply connected to the many [[interpretations of quantum mechanics]]. A key focus point is that of [[wave function collapse]], for which several popular interpretations assert that measurement causes a ''discontinuous change'' into an [[Eigenvalues and eigenvectors#Schr.C3.B6dinger equation|eigenstate]] of the operator associated with the quantity that was measured, a change which is not time-reversible.
-More explicitly, the [[quantum superposition|superposition]] principle ({{math|''ψ'' {{=}} Σ<sub>''n''</sub>''a<sub>n</sub>ψ<sub>n</sub>'')}} of quantum physics dictates that for a wave function {{mvar|ψ}}, a measurement will result in a state of the quantum system of one of the {{mvar|m}} possible eigenvalues {{math|''f<sub>n</sub> , n'' {{=}} 1, 2, ..., ''m''}}, of the operator {{math|{{overset|&and;|''F''}} }} which in the space of the eigenfunctions {{math|''ψ<sub>n</sub> , n'' {{=}} 1, 2, ..., ''m''}}.
-Once one has measured the system, one knows its current state; and this prevents it from being in one of its other states ⁠— it has apparently [[decoherence|decohered]] from them without prospects of future strong quantum interference.<ref name="Quantum Theory and Pictures of Reality">B.D'Espagnat, P.Eberhard, W.Schommers, [[Franco Selleri|F.Selleri]]. ''Quantum Theory and Pictures of Reality''. Springer-Verlag, 1989, {{ISBN|3-540-50152-5}}</ref><ref name=Schlosshauer>{{cite journal|last=Schlosshauer|first=Maximilian|title=Decoherence, the measurement problem, and interpretations of quantum mechanics|journal=Rev. Mod. Phys.|year=2005|volume=76|issue=4|pages=1267–1305|doi=10.1103/RevModPhys.76.1267|url=http://rmp.aps.org/abstract/RMP/v76/i4/p1267_1|access-date=28 February 2013|arxiv = quant-ph/0312059 |bibcode = 2004RvMP...76.1267S |s2cid=7295619}}</ref><ref name="Giacosa2014">{{cite journal
- | last = Giacosa
- | first = Francesco
- | title = On unitary evolution and collapse in quantum mechanics
- | journal = Quanta
- | volume = 3
- | issue = 1
- | pages = 156–170
- | year = 2014
- | doi = 10.12743/quanta.v3i1.26
- | url = http://quanta.ws/ojs/index.php/quanta/article/view/26
-| arxiv = 1406.2344
- | s2cid = 55705326
- }}</ref> This means that the type of measurement one performs on the system affects the end-state of the system.
-An experimentally studied situation related to this is the [[quantum Zeno effect]], in which a quantum state would decay if left alone, but does not decay because of its continuous observation. The dynamics of a quantum system under continuous observation are described by a quantum [[stochastic]] master equation known as the [[Belavkin equation]].<ref name=Belavkin89>{{cite journal
- | author = V. P. Belavkin
- | title = A new wave equation for a continuous non-demolition measurement
- | journal = Physics Letters A
- | volume = 140
- | issue = 7–8
- | pages = 355–358
- | year = 1989
- | doi = 10.1016/0375-9601(89)90066-2
- | arxiv = quant-ph/0512136|bibcode = 1989PhLA..140..355B | s2cid = 6083856
- }}</ref><ref name=Carmichael93>{{cite book
- | author = Howard J. Carmichael
- | title = An Open Systems Approach to Quantum Optics
- | publisher = Springer-Verlag
- | year = 1993
- | location = Berlin Heidelberg New-York}}</ref><ref name=Bauer2012>{{cite techreport
- |author1=Michel Bauer |author2=Denis Bernard |author3=Tristan Benoist | title = Iterated Stochastic Measurements
- | arxiv = 1210.0425|bibcode=2012JPhA...45W4020B|doi=10.1088/1751-8113/45/49/494020}}</ref> Further studies have shown that even observing the results after the photon is produced leads to collapsing the wave function and loading a back-history as shown by [[delayed choice quantum eraser]].<ref name="DCQE">{{cite journal | author = Kim, Yoon-Ho |author2=R. Yu |author3=S.P. Kulik |author4=Y.H. Shih |author5=Marlan Scully | title = A Delayed "Choice" Quantum Eraser | journal = [[Physical Review Letters]] | volume = 84 |issue=1 | year = 2000 | pages = 1–5 | doi = 10.1103/PhysRevLett.84.1| arxiv=quant-ph/9903047 | bibcode=2000PhRvL..84....1K | pmid=11015820|s2cid=5099293 }}</ref>
-When discussing the wave function {{mvar|ψ}} which describes the state of a system in quantum mechanics, one should be cautious of a common misconception that assumes that the wave function {{mvar|ψ}} amounts to the same thing as the physical object it describes. This flawed concept must then require existence of an external mechanism, such as a measuring instrument, that lies outside the principles governing the time evolution of the wave function {{mvar|ψ}}, in order to account for the so-called "collapse of the wave function" after a measurement has been performed. But the wave function {{mvar|ψ}} is ''not a physical object'' like, for example, an atom, which has an observable mass, charge and spin, as well as internal degrees of freedom. Instead, {{mvar|ψ}} is an ''abstract mathematical function'' that contains all the ''statistical'' information that an observer can obtain from measurements of a given system. In this case, there is no real mystery in that this mathematical form of the wave function {{mvar|ψ}} must change abruptly after a measurement has been performed.
-A consequence of [[Bell's theorem]] is that measurement on one of two [[quantum entanglement|entangled]] particles can appear to have a nonlocal effect on the other particle. Additional problems related to [[quantum decoherence#In interpretations of quantum mechanics|decoherence]] arise when the observer is modeled as a quantum system, as well.
-{{see also|Quantum decoherence|Delayed choice quantum eraser}}
+==See also==
-The [[uncertainty principle]] has been frequently confused with the observer effect, evidently even by its originator, [[Werner Heisenberg]].<ref>{{Cite news|url=https://www.scientificamerican.com/article/heisenbergs-uncertainty-principle-is-not-dead/|title=One Thing Is Certain: Heisenberg's Uncertainty Principle Is Not Dead|last=Furuta|first=Aya|work=Scientific American|access-date=2018-09-23|language=en}}</ref> The uncertainty principle in its standard form describes how [[accuracy and precision|precisely]] we may measure the position and momentum of a particle at the same time&nbsp;– if we increase the precision in measuring one quantity, we are forced to lose precision in measuring the other.<ref name="heisenberg">[[Werner Heisenberg|Heisenberg, W.]] (1930), ''Physikalische Prinzipien der Quantentheorie'', Leipzig: Hirzel English translation ''The Physical Principles of Quantum Theory''. Chicago: University of Chicago Press, 1930. reprinted Dover 1949</ref>
+*[[Observer (special relativity)]]
-An alternative version of the uncertainty principle,<ref>{{Citation|last=Ozawa|first=Masanao|title=Universally valid reformulation of the Heisenberg uncertainty principle on noise and disturbance in measurement|journal=Physical Review A|volume=67|issue=4|pages=042105|year=2003|doi=10.1103/PhysRevA.67.042105|arxiv = quant-ph/0207121 |bibcode = 2003PhRvA..67d2105O |s2cid=42012188}}</ref> more in the spirit of an observer effect,<ref name=Belavkin92>{{cite journal | author = V. P. Belavkin | title = Quantum continual measurements and a posteriori collapse on CCR | journal = Communications in Mathematical Physics | volume = 146 | issue = 3 | pages = 611–635 | year = 1992 | doi = 10.1007/BF02097018 | arxiv = math-ph/0512070|bibcode = 1992CMaPh.146..611B | s2cid = 17016809 }}</ref> fully accounts for the disturbance the observer has on a system and the error incurred, although this is not how the term "uncertainty principle" is most commonly used in practice.
 ==References==