Equations of motion when masses move according to Newton's law of gravity. In general relativity, rotational motion is described by the relativistic angular momentum tensor, including the spin tensor, which enter the equations of motion under covariant derivatives with respect to proper time. The Mathisson–Papapetrou–Dixon equations describe the motion of spinning objects moving in a gravitational field. Unlike the equations of motion for describing particle mechanics, which are systems of coupled ordinary differential equations, the analogous equations governing the dynamics of waves and fields are always partial differential equations, since the waves or fields are functions of space and time. For a particular
Lorentz invariance in loop quantum gravity has black holes and loop quantum gravity connecting early universes together. Loop quantum gravity can be pulled into black holes. In Fecund universes, each new universes, according to Lee Smolin, has slightly different laws of physics. Because these laws are only slightly different, each is assumed to be like a mutation of the early universes. Loop quantum gravity (LQG) is a quantization of a classical Lagrangian field theory. It is equivalent to the usual Einstein–Cartan theory in that it leads to the same equations of motion describing general relativity with torsion. As such, it can be argued that LQG respects