History of variational principles in physics involves integrals over an interval of time and (for fields) extended region of space. Moreover, in the usual formulation of classical action principles, the initial and final states of the system are fixed, e.g., In particular, the fixing of the "final" state appears to give the action principle a teleological character which has been controversial historically. This apparent teleology is eliminated in the quantum mechanical version of the action principle. History of variational principles in physics A variational principle in physics is an alternative method for determining the state or dynamics of a physical system, by identifying it as an
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