Interaction picture as any other operator. In particular, let and be the density matrices in the interaction picture and the Schrödinger picture respectively. If there is probability to be in the physical state |"ψ"〉, then Transforming the Schrödinger equation into the interaction picture gives which states that in the interaction picture, a quantum state is evolved by the interaction part of the Hamiltonian as expressed in the interaction picture. If the operator "A" is time-independent (i.e., does not have "explicit time dependence"; see above), then the corresponding time evolution for "A"("t") is given by In the interaction picture the operators evolve in
Digital physics The study found that space-time is not quantized at the scale being measured. One objection is that extant models of digital physics are incompatible with the existence of several continuous characters of physical symmetries, e.g., rotational symmetry, translational symmetry, Lorentz symmetry, and the Lie group gauge invariance of Yang-Mills theories, all central to current physical theory. Proponents of digital physics claim that such continuous symmetries are only convenient (and very good) approximations of a discrete reality. For example, the reasoning leading to systems of natural units and the conclusion that the Planck length is a minimum meaningful unit of distance