Quantum reference frame: Difference between revisions

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Revision as of 11:46, 20 March 2016

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{{see also| Frame of reference}}

A '''quantum reference frame''' is a reference frame which is treated quantum theoretically. It, like any [[Frame of reference|reference frame]], is aan physicalabstract coordinate system which defines physical quantities, such as [[time]], position, [[momentum]], [[spin (physics)|spin]], and so on. Because it is treated within the formalism of [[Quantum mechanics|quantum theory]], it has some interesting properties which do not exist in a normal classical reference frame.

==Reference frame in classical mechanics and inertial frame==

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Consider a simple physics problem: a car is moving such that it covers a distance of 1 mile in every 2 minutes, what is its velocity in metres per second? With some conversion and calculation, one can come up with the answer "13.41m/s"; on the other hand, one can instead answer "0, relative to itself". The first answer is correct because it recognises a reference frame is implied implicitly in the problem. The second one, albeit pedantic, is also correct because it exploits the fact that there is not a particular reference frame specified by the problem. This simple problem illustrates the importance of a reference frame: a reference frame is quintessential in a clear description of a system, whether it is included implicitly or explicitly.

A reference frame is a physical system in which physical quantities are defined, such as position, momentum, spin, time, etc. Some obvious examples of reference frame are metre stick for distance and clock for time. While some standards are widely accepted and used like the [[Metric system|metric]] and [[imperial units|imperial]] system, there is no constraint on what physical system a reference frame has to be, so it is perfectly valid, though peculiar, to use Tom Cruise (who is 1.70m high) as a reference frame and to describe Katie Holmes as 1.029 Tom Cruise high. Regardless of what reference frame is used, it is always relational, not absolute.

When speaking of a car moving towards east, one is referring to a particular point on the surface of the Earth; moreover, as the Earth is rotating, the car is actually moving towards a changing direction, with respect to the Sun. In fact, this is the best one can do: describing a system in relation to some reference frame. Describing a system with respect to an absolute space does not make much sense because an absolute space, if it exists, is unobservable. Hence, it is impossible to describe the path of the car in the above example with respect to some absolute space. This notion of absolute space troubled a lot of physicists over the centuries, including Newton. Indeed, Newton was fully aware of this stated that all inertial frames are [[Observational equivalence|observationally equivalent]] to each other. Simply put, relative motions of a system of bodies do not depend on the inertial motion of the whole system.<ref name = "Dickson">{{cite journal|doi = 10.1016/j.shpsb.2003.12.003|last = Dickson|first = Michael|title = A view from nowhere: quantum reference frames and uncertainty| journal = Studies in History and Philosophy of Modern Physics | volume = 35|issue = 2 |year = 2004 |pages = 195–220}}</ref>