Quantum reference frame
It, like any reference frame, is an abstract coordinate system which defines physical quantities, such as time, position, momentum, spin, and so on.Because it is treated within the formalism of quantum theory, it has some interesting properties which do not exist in a normal classical reference frame.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?This notion of absolute space troubled a lot of physicists over the centuries, including Newton.It may appear an inertial frame can now be easily found given the Newton's laws as empirical tests are accessible.In fact, when a reference frame is classical, whether or not including it in the physical description of a system is irrelevant.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 degree of freedom.Two laboratories trying to establish a single shared reference frame will face important issues involving alignment.The study of this sort of communication and coordination is a major topic in quantum information theory.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.The following treatment of a hydrogen atom motivated by Aharanov and Kaufherr can shed light on the matter.[3] Supposing a hydrogen atom is given in a well-defined state of motion, how can one describe the position of the electron?Coulomb potential depends on the distance between the proton and electron only: With this symmetry, the problem is reduced to that of a particle in a central potential: Using separation of variables, the solutions of the equation can be written into radial and angular parts: whereNow consider the Schrödinger equation for the proton and the electron: A change of variables to relational and centre-of-mass coordinates yields whereHowever, if the change of variables done early is now to be reversed, centre-of-mass needs to be put back into the equation for: The importance of this result is that it shows the wavefunction for the compound system is entangled, contrary to what one would normally think in a classical standpoint.It was originally introduced to impose additional restriction to quantum theory beyond those of selection rules.This is a powerful statement because superselection rules have long been thought to have axiomatic nature, and now its fundamental standing and even its necessity are questioned.