Quantum reference frame: Difference between revisions

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Revision as of 17:12, 30 April 2016

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One final remark may be made on the existence of a quantum reference frame. After all, a reference frame, by definition, has a well-defined position and momentum, while quantum theory, namely [[uncertainty principle]], states that one cannot describe any quantum system with well-defined position and momentum simultaneously, so it seems there is some contradiction between the two. It turns out, an effective frame, in this case a classical one, is used as a reference frame, just as in Newtonian mechanics a nearly inertial frame is used, and physical laws are assumed to be valid in this effective frame. In other words, whether motion in the chosen reference frame is inertial or not is irrelevant.

The following treatment of a hydrogen atom motivated by Aharanov and Kaufherr can shed light on the matter.<ref>{{cite journal|doi=10.1103/PhysRevD.30.368|last=Aharonov |first=Y.|author2=T. Kaufherr |title=Quantum frames of reference| year=1984|journal=Phys. Rev. D|volume=30|issue=2|pages = 368368–385|bibcode = 1984PhRvD..30..368A }}</ref> Supposing a hydrogen atom is given in a well-defined state of motion, how can one describe the position of the electron? The answer is not to describe the electron's position relative to the same coordinates in which the atom is in motion, because doing so would violate uncertain principle, but to describe its position relative to the nucleus. As a result, more can be said about the general case from this: in general, it is permissible, even in quantum theory, to have a system with well-defined position in one reference frame and well-defined motion in some other reference frame.

==Further considerations of quantum reference frame==

===An example of treatment of reference frames in quantum theory===

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:::<math>n_{max} \simeq \epsilon j^2</math>

So the longevity and the size of the reference frame are of quadratic relation in this particular case.<ref>{{cite journal|last=Bartlett|first=Stephen D. |author2=Rudolph, Terry |author3=Spekkens, Robert W.|title=Reference frames, superselection rules, and quantum information|journal=ReviewReviews of Modern Physics|volume=79|issue=2|date=April–June 2007|pages=555–606|doi=10.1103/RevModPhys.79.555|bibcode=2007RvMP...79..555B|arxiv = quant-ph/0610030 }}</ref>

In this spin-<math>j</math> system, the degradation is due to the loss of purity of the reference frame state. On the other hand, degradation can also caused by misalignment of background reference. It has been shown, in such case, the longevity has a linear relation with the size of the reference frame.<ref>{{cite journal| doi = 10.1088/1367-2630/9/5/156| last = Poulin| first = D. |author2=J. Yard | title = Dynamics of a quantum reference frame|year=2007|journal=New J. Phys|volume = 9| issue = 5|pages=156|arxiv = quant-ph/0612126 |bibcode = 2007NJPh....9..156P }}</ref>