Bass–Serre theory: Difference between revisions

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{{Other uses|Observer effect (disambiguation){{!}}Observer effect}}
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{{Cleanup|date=May 2010}}
 
In [[science]], the term '''observer effect''' refers to changes that the act of observation will make on a [[phenomenon]] being observed. This is often the result of instruments that, by necessity, alter the state of what they measure in some manner.  A commonplace 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. This effect can be observed in many domains of physics.
 
The observer effect on a physical process can often be reduced to insignificance by using better instruments or observation techniques.
 
Historically, the observer effect has been confused with the [[uncertainty principle]].<ref name="FurutaAya1">{{Citation|last=Furuta|first=Aya|title=One Thing Is Certain: Heisenberg's Uncertainty Principle Is Not Dead|journal=Scientific American|year=2012|url=http://www.scientificamerican.com/article.cfm?id=heisenbergs-uncertainty-principle-is-not-dead}}</ref><ref name="Ozawa2003">{{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|year=2003|doi=10.1103/PhysRevA.67.042105|arxiv = quant-ph/0207121 |bibcode = 2003PhRvA..67d2105O|issue=4 }}</ref>
 
==Particle physics==
For an [[electron]] to become detectable, a [[photon]] must first interact with it, and this interaction will change the path of that electron. It is also possible for other, less direct means of measurement to affect the electron.
 
==Electronics==
In [[electronics]], [[ammeter]]s and [[voltmeter]]s 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 [[Electrical load|load]] to the circuit, thus changing the [[transfer function]] and behaviour 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 [[mutual inductance|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==
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 topic is that of [[wave function collapse]], for which some interpretations assert that measurement causes a discontinuous change into an eigenstate of the operator associated with the quantity that was measured. More explicitly, the [[quantum superposition|superposition]] principle (ψ = Σa<sub>n</sub>ψ<sub>n</sub>) of quantum physics says that for a wave function ψ, a measurement will give a state of the quantum system of one of the m possible eigenvalues f<sub>n</sub>, n=1,2...m, of the operator <math>\hat{F}</math> which is part of the eigenfunctions ψ<sub>n</sub>, n=1,2,...n. Once we have measured the system, we know its current state and this stops it from being in one of its other states.<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> This means that the type of measurement that we do 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 is described by a quantum [[stochastic]] master equation known as the [[Viacheslav Belavkin|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
| number = 7-8
| pages = 355–358
| year = 1989
| doi = 10.1016/0375-9601(89)90066-2
| arxiv = quant-ph/0512136|bibcode = 1989PhLA..140..355B }}</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
| author = Michel Bauer, Denis Bernard, Tristan Benoist
| title = Iterated Stochastic Measurements
| note = To be published in J. Phys. A
| arxiv = 1210.0425}}</ref>
 
An important aspect of the concept of [[measurement in quantum mechanics|measurement]] has been clarified in some QM experiments where a small, complex, and non-sentient sensor proved sufficient as an "observer"—there is no need for a conscious "observer".<ref name="sciencedaily">[http://www.sciencedaily.com/releases/1998/02/980227055013.htm Science Daily]</ref>
 
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 opposite particle.  Additional problems related to [[quantum decoherence#In interpretations of quantum mechanics|decoherence]] arise when the observer too is modeled as a quantum system.
 
The [[uncertainty principle]] has been frequently confused with the observer effect, evidently even by its originator, [[Werner Heisenberg]].<ref name="FurutaAya1"/> The uncertainty principle in its standard form actually describes how [[accuracy and precision|precisely]] we may measure the position and momentum of a particle at the same time &mdash; 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.</ref>
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|year=2003|doi=10.1103/PhysRevA.67.042105|arxiv = quant-ph/0207121 |bibcode = 2003PhRvA..67d2105O }}</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 | number = 3 | pages = 611–635 | year = 1992 | doi = 10.1007/BF02097018 | arxiv = math-ph/0512070|bibcode = 1992CMaPh.146..611B }}</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.
<!--Is all this commented out stuff actually helpful to anybody???
This is demonstrated in a common thought experiment using the double slit setup. Imagine a double slit experiment where quantum particles are fired towards the two slits. The quantum particles pass through the slits and hit a momentum sensor a distance of D behind the slits. The momentum sensor has the ability to be turned off and on via a pin that stops the movement of the sensor when it is hit by a quantum particle. When the pin is in place, no measurement of the momentum can take place. When the pin is removed, the sensor can recoil when struck by a quantum particle and by measuring the recoil determine from which slit the quantum particle came.  
If the pin is removed and we can detect from which slit the particle came, then the wave-like passage through both slits cannot occur and no interference pattern will develop. However if we put the pin in place, and can no longer determine from which slit the particle passes through, then an interference pattern can develop.<ref name="Intro to Quantum Mechanics">A.C.Phillips. ''Introduction to Quantum Mechanics''. Wiley, 2003, ISBN:0-470-85323-9</ref>  This can be taken a step further using the [[Wheeler%27s_delayed_choice_experiment|delayed choice experiment]].
 
This thought experiment was proved correct experimentally. The people conducting the experiment found that when the sensor was turned off, an interference pattern developed, but when it was turned on, the interference pattern was destroyed. It was even found that the level of detection could affect the result. <ref name="Which path detector">E.Buks, R.Schuster, M.Heiblum, D.Mahalu, V.Umansky (February 1998)."Dephasing in electron interference by a 'which-path' detector", ''Nature'', vol 391, pp 871–874. {{doi|10.1038/36057}}</ref>
 
The change of the wave function from ψ to ψ<sub>n</sub> is called the collapse of the wave function and occurs when the measurement takes place.<ref name="Intro to Quantum Mechanics" /> This collapse of the wave function is not explainable using the Copenhagen interpretation.<ref name="Quantum Theory and Pictures of Reality" /> Other explanations on why the wave function collapses have been developed such as the [[Hidden_variable_theory| hidden variable theory]].
 
The [[many-worlds interpretation]] posits the existence of multiple universes in which an observed system displays all possible states to all possible observers. In this model, observation of a system does not change the behavior of the system—it simply answers the question of which universe the observer is located in. In some universes, the observer would observe one result from one state of the system, and in others the observer would observe a different result from a different state of the system.<ref name="everettq2">[http://www.hedweb.com/manworld.htm#what Everett FAQ "What is many-worlds?"]</ref>-->
 
==References==
{{Reflist}}
{{Use dmy dates|date=September 2011}}
* The observer effect by Massimiliano Sassoli de Bianchi http://arxiv.org/abs/1109.3536
 
{{DEFAULTSORT:Observer Effect (Physics)}}
[[Category:Concepts in physics]]

Latest revision as of 19:54, 26 July 2014

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