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The classic example of a non-relativistic spacetime is the spacetime of Galileo and Newton. It is the spacetime of everyday "common sense". [1] Galilean/Newtonian spacetime assumes that space is Euclidean (i.e. "flat"), and that time has a constant rate of passage that is independent of the state of motion of an observer, or indeed of anything external.
In theoretical physics, quantum field theory (QFT) is a theoretical framework that combines classical field theory, special relativity, and quantum mechanics. [1]: xi QFT is used in particle physics to construct physical models of subatomic particles and in condensed matter physics to construct models of quasiparticles.
Some equations of the non-metric theory of Belinfante and Swihart [26] [27] have already been discussed in the section on bimetric theories. A distinctively non-metric theory is given by gauge theory gravity, which replaces the metric in its field equations with a pair of gauge fields in flat spacetime. On the one hand, the theory is quite ...
A free particle with mass in non-relativistic quantum mechanics is described by the free Schrödinger equation: (,) = (,) where ψ is the wavefunction of the particle at position r and time t . The solution for a particle with momentum p or wave vector k , at angular frequency ω or energy E , is given by a complex plane wave :
Early attempts to develop a general formulation for the dynamics of these guiding waves in terms of a relativistic wave equation were unsuccessful until in 1926 Schrödinger developed his non-relativistic wave equation. He further suggested that since the equation described waves in configuration space, the particle model should be abandoned. [4]
It is the non-relativistic limit of the Dirac equation and can be used where particles are moving at speeds much less than the speed of light, so that relativistic effects can be neglected. It was formulated by Wolfgang Pauli in 1927. [1] In its linearized form it is known as Lévy-Leblond equation.
Observations suggest that there is more cold dark matter (non-relativistic) than hot dark matter (relativistic). The active neutrinos of the Standard Model, having very low mass (and therefore very high speeds) are therefore unlikely to account for all dark matter. [18]
As such, the equation cannot be applied to the description of atoms, since the electron is a spin 1 / 2 particle. In the non-relativistic limit the equation reduces to the Schrödinger equation for a spinless charged particle in an electromagnetic field: [18]