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| | If you are looking for a specific plugin, then you can just search for the name of the plugin. Online available for hiring are most qualified, well knowledgeable and talented Wordpress developer India from offshore Wordpress development services company. Change the site's theme and you have essentially changed the site's personality. After confirming the account, login with your username and password at Ad - Mob. It is found that most of the visitors only look for the results that are displayed on the first page of the search engines and so if you get the service from professional service providers then they strive for the first page ranking of your site and improve the online visibility. <br><br>The Internet is a vast open market where businesses and consumers congregate. Wordpress have every reason with it which promote wordpress development. This is the reason for the increased risk of Down Syndrome babies in women over age 35. Being able to help with your customers can make a change in how a great deal work, repeat online business, and referrals you'll be given. Akismet is really a sophisticated junk e-mail blocker and it's also very useful thinking about I recieve many junk e-mail comments day-to-day across my various web-sites. <br><br>If you have any kind of questions relating to where and how you can use [http://GET7.pw/wordpress_backup_164422 backup plugin], you can contact us at our web-site. The least difficult and very best way to do this is by acquiring a Word - Press site. s cutthroat competition prevailing in the online space won. all the necessary planning and steps of conversion is carried out in this phase, such as splitting, slicing, CSS code, adding images, header footer etc. Provide the best and updated information to the web searchers and make use of these wonderful free themes and create beautiful websites. Customization of web layout is easy due to the availability of huge selection of templates. <br><br>A built-in widget which allows you to embed quickly video from popular websites. This plugin allows a webmaster to create complex layouts without having to waste so much time with short codes. re creating a Word - Press design yourself, the good news is there are tons of Word - Press themes to choose from. If you are looking for Hire Wordpress Developer then just get in touch with him. If your blog employs the permalink function, This gives your SEO efforts a boost, and your visitors will know firsthand what's in the post when seeing the URL. <br><br>Many developers design websites and give them to the clients, but still the client faces problems to handle the website. If you operate a website that's been built on HTML then you might have to witness traffic losses because such a site isn't competent enough in grabbing the attention of potential consumers. The days of spending a lot of time and money to have a website built are long gone. Word - Press is an open source content management system which is easy to use and offers many user friendly features. As for performing online business, websites and blogs are the only medium that are available to interact with customers and Word - Press perform this work with the help of cross-blog communication tools, comments and full user registration plug-ins. |
| | refimprove=November 2008
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| | orphan=February 2009}}
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| {{see also| Frame of reference}}
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| A '''quantum reference frame''' is a reference frame which is treated quantum theoretically. It, like any [[Frame of reference|reference frame]], is a physical 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.
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| ==Reference frame in classical mechanics and inertial frame==
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| {{see also| Frame of reference | 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.
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| 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, just as in this [[TomKat]] example.
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| 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 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>
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| An [[inertial]] reference frame (or [[inertial frame]] in short) is a frame in which all the physical laws hold. For instance, in a rotating reference frame, Newton's laws have to be modified because there is an extra Coriolis force (such frame is an example of non-inertial frame). Here, "rotating" means "rotating with respect to some inertial frame". Therefore, although it is true that a reference frame can always be chosen to be any physical system for convenience, any system has to be eventually described by an inertial frame, directly or indirectly. Finally, one may ask how an inertial frame can be found, and the answer lies in the [[Newton's laws]], at least in [[Newtonian mechanics]]: the first law guarantees the existence of an inertial frame while the second and third law are used to examine whether a given reference frame is an inertial one or not.
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| It may appear an inertial frame can now be easily found given the Newton's laws as empirical tests are accessible. Quite the contrary; an absolutely inertial frame is not and will most likely never be known. Instead, inertial frame is approximated. As long as the error of the approximation is undetectable by measurements, the approximately inertial frame (or simply "effective frame") is reasonably close to an absolutely inertial frame. With the effective frame and assuming the physical laws are valid in such frame, descriptions of systems will ends up as good as if the absolutely inertial frame was used. As a digression, the effective frame [[Astronomers]] use is a system called "[[International Celestial Reference Frame]]" (ICRF), defined by 212 radio sources and with an accuracy of about <math>10^{-5}</math> radians. However, it is likely that a better one will be needed when a more accurate approximation is required.
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| Reconsidering the problem at the very beginning, one can certainly find a flaw of ambiguity in it, but it is generally understood that a standard reference frame is implicitly used in the problem. In fact, when a reference frame is classical, whether or not including it in the physical description of a system is irrelevant. One will get the same prediction by treating the reference frame internally or externally.
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| To illustrate the point further, a simple system with a ball bouncing off a wall is used. In this system, the wall can be treated either as an external [[Potential energy|potential]] or as a [[dynamical system]] interacting with the ball. The former involves putting the external potential in the equations of motions of the ball while the latter treats the position of the wall as a dynamical [[degrees of freedom (physics and chemistry)|degree of freedom]]. Both treatments provide the same prediction, and neither is particularly preferred over the other. However, as it will be discussed below, such freedom of choice cease to exist when the system is quantum mechanical.
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| ==Quantum reference frame==
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| A reference frame can be treated in the formalism of quantum theory, and, in this case, such is referred as a quantum reference frame. Despite different name and treatment, a quantum reference frame still share much of the notions with a reference frame in [[classical mechanics]]. It is still defined with the same definition. It is still always associated to some physical system. And it is still always relational.
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| For example, if a [[spin-1/2]] particle is said to be in the state <math>|\uparrow z \rangle</math>, reference frame is implicitly implied, and it can be understood to be some reference frame with respect to an apparatus in a lab. It is obvious that the description of the particle does not place it in an absolute space, and doing so would make no sense at all because, as mentioned above, absolute space is empirical unobservable. On the other hand, if a magnetic field along y-axis is said to be given, behaviour of the particle in such field can then be described. In this sense, y and z are just relative directions. They do not and need not have absolute meaning.
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| One can observe that a z direction used in a laboratory in Berlin is totally different from a z direction used in a laboratory in Melbourn. Issues like aligning and sharing reference frames arise when a communication between two laboratories are tried to be set up. It is absolutely correct, and the study of communications like this has been the main agenda in [[quantum information theory]].
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| Just as in this [[spin-1/2]] particle example, a quantum reference frames are almost always treated implicitly in the definition of quantum states, and the process of including the reference frame in a quantum state is called quantisation/internalisation of reference frame while the process of excluding the reference frame from a quantum state is called dequantisation/externalisation of reference frame. Unlike the classical case, in which treating a reference internally or externally is purely an aesthetic choice, internalising and externalising a reference frame does make a difference in quantum theory.<ref>{{cite journal|last=Barlett|first=Stephen D.|coauthors=Rudolph, Terry and Spekkens, Robert W.|title=Dialogue concerning two views on quantum coherences: factist and fictionist|journal=Int. J. Of Quant. Info|volume=4:17|year=2006}}</ref>
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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.
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| 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.|coauthors = T. Kaufherr|title=Quantum frames of reference| year=1984|journal=Phys. Rev. D|volume=30|issue=2|pages = 368|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.
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| ==Further considerations of quantum reference frame==
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| ===An example of treatment of reference frames in quantum theory===
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| Consider the a hydrogen atom. [[Coulomb potential]] depends on the distance between the proton and electron only:
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| :::<math>V(r) = \frac{-Ze^2}{r}</math>
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| With this symmetry, the problem is reduced to that of a particle in a central potential:
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| :::<math> -\frac{1}{2m}\nabla^2 \psi(\vec{r}) + \frac{-Ze^2}{r} \psi(\vec{r}) = E\psi(\vec{r})</math>
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| Using [[separation of variables]], the solutions of the equation can be written into radial and angular parts:
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| :::<math>\Phi(r,\theta,\phi) = R_{nl}(r) Y_{lm}(\theta, \phi)</math>
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| where <math>l,</math> <math> m</math>, and <math>n</math> are the orbital angular momentum, magnetic, and energy quantum numbers, respectively.
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| Now consider the Schrödinger equation for the proton and the electron:
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| :::<math>\frac{\partial}{\partial t}\Psi(x_1,y_1,z_1,x_2,y_2,z_2,t)=iH\Psi(x_1,y_1,z_1,x_2,y_2,z_2,t)</math>
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| A change of variables to relational and centre-of-mass coordinates yields
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| :::<math>\frac{\partial \Psi(x,y,z,X,Y,Z)}{\partial t} = i[\frac{1}{2M}\nabla_{c.o.m.}^2 +\frac{1}{2\mu}\nabla_{rel}^2 +V(x,y,z)]\Psi</math>
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| where <math>M</math> is the total mass and <math>\mu</math> is the reduced mass. A final change to spherical coordinates followed by a separation of variables will yield the equation for <math>\Phi(r,\theta,\phi)</math> from above.
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| However, if the change of variables done early is now to be reversed, centre-of-mass needs to be put back into the equation for <math>\Phi(r,\theta,\phi)</math>:
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| :::<math>r = \sqrt{(x_1-x_2)^2 +(y_1-y_2)^2+ (z_1-z_2)^2}</math>
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| :::<math>\theta = \tan^{-1}\left(\frac{\sqrt{(x_1-x_2)^2 +(y_1-y_2)^2}}{z_1-z_2} \right)</math>
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| :::<math>\phi=\tan^{-1}\left( \frac{y_1-y_2}{x_1-x_2}\right)</math>
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| :::<math>X=\frac{m_1x_1+m_2x_2}{m_1+m_2}</math>
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| :::<math>Y=\frac{m_1y_1+m_2y_2}{m_1+m_2}</math>
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| :::<math>Z=\frac{m_1z_1+m_2z_2}{m_1+m_2}</math>
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| The importance of this result is that it shows the wavefunction for the compound system is [[entangled]], contrary to one would normally think in a classical stand point. More importantly, it shows the energy of the hydrogen atom is not associated with the electron but also associated with the proton, and the corresponding states is not decomposable into states for electron and proton separately.<ref name = "Dickson" />
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| ===Superselection rules===
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| Superselection rules, in short, are postulated rules forbidding the preparation of quantum states that exhibit coherence between eigenstates of certain observables. It was originally introduced to impose additional restriction to quantum theory beyond those of [[selection rules]]. As an example, superselection rules for electric charges disallow the preparation of a coherent superposition of different charge eigenstates.
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| As it turns out, the lack of a reference frame is mathematically equivalent to superselection rules. This is a powerful statement because superselection rules have long been thought to have axiomatic nature, and now its fundamental stand and even its necessity are questioned. Nevertheless, it has been shown that it is, in principle, always possible though not always easy to lift all superselection rules on a quantum system.
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| ===Degradation===
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| During a measurement, whenever the relations between the system and the reference frame used is inquired, there is inevitably a disturbance to both of them, which is known as so-called measurement back reaction. As this process is repeated over time during a measurement, it negatively affects the accuracy of the measurement outcomes, and the gradual reduction of the usability of a reference frame is referred as the degradation. A way to gauge the degradation of a reference frame is to quantify the longevity, namely, the number of measurements that can be made against the reference frame until certain error tolerance is exceed.
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| For example, for a spin-<math>j</math> system, the maximum number of measurements that can be made before the error tolerance, <math>\epsilon</math>, is exceed is given by
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| :::<math>n_{max} \simeq \epsilon j^2</math>
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| 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.|coauthors=Rudolph, Terry and Spekkens, Robert W.|title=Reference frames, superselection rules, and quantum information|journal=Review of Modern Physics|volume=79|issue=2|month=April–June|pages=555–606|year=2007|doi=10.1103/RevModPhys.79.555|bibcode=2007RvMP...79..555B|arxiv = quant-ph/0610030 }}</ref>
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| 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. |coauthors=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>
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| ==References==
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| {{reflist}}
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| ==See also==
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| *[[Frame of reference]]
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| *[[Information theory]]
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| *[[Quantum information]]
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| [[Category:Quantum mechanics]]
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