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Relativistic rocket means any spacecraft that travels close enough to light speed for relativistic effects to become significant. The meaning of "significant" is a matter of context, but often a threshold velocity of 30% to 50% of the speed of light (0.3 c to 0.5 c ) is used.
In theoretical physics, the Madelung equations, or the equations of quantum hydrodynamics, are Erwin Madelung's alternative formulation of the Schrödinger equation for a spinless non relativistic particle, written in terms of hydrodynamical variables, similar to the Navier–Stokes equations of fluid dynamics. [1]
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.
The equation of state for ordinary non-relativistic 'matter' (e.g. cold dust) is =, which means that its energy density decreases as =, where is a volume. In an expanding universe, the total energy of non-relativistic matter remains constant, with its density decreasing as the volume increases.
By 1984, problems 2 and 3 had been solved by introducing a Lagrangian . A relativistic version of this based on scalar–tensor theory was rejected because it allowed waves in the scalar field to propagate faster than light. The Lagrangian of the non-relativistic form is:
Newton–Cartan theory (or geometrized Newtonian gravitation) is a geometrical re-formulation, as well as a generalization, of Newtonian gravity first introduced by Élie Cartan in 1923 [1] [2] and Kurt Friedrichs [3] and later developed by G. Dautcourt, [4] W. G. Dixon, [5] P. Havas, [6] H. Künzle, [7] Andrzej Trautman, [8] and others. [9]
The Lorentz self-force derived for non-relativistic velocity approximation , is given in SI units by: = ˙ = ˙ = ˙ or in Gaussian units by = ˙. where is the force, ˙ is the derivative of acceleration, or the third derivative of displacement, also called jerk, μ 0 is the magnetic constant, ε 0 is the electric constant, c is the speed of light in free space, and q is the electric charge of ...
As it turns out, the only pairs of these properties that lead to self-consistent, nontrivial solutions are 2 & 3, and possibly 1 & 3 or 1 & 4. Accepting properties 1 & 2, along with a weaker condition that 3 be true only asymptotically in the limit ħ →0 (see Moyal bracket ), leads to deformation quantization , and some extraneous information ...