Can every physically sound differential equation, that is covariant, deterministic etc. be derived by extremising a suitable action using a suitable lagrangian, that may be arbitary. Is this a mathematical theorem?

  • $\begingroup$ Possible duplicates: physics.stackexchange.com/q/20298/2451 , physics.stackexchange.com/q/20188/2451 and links therein. $\endgroup$ – Qmechanic Oct 20 '14 at 18:35
  • $\begingroup$ Short answer, yes, almost all physical equations (even Shrodiger and Dirac euqations) can be fomrulated as action extremum principles. Several textbooks actualy provide the action form of the equations a swell. Mathematicaly, it is relatively easy to transform any set of equations into a functional integral (or functional equation) similar to action principle $\endgroup$ – Nikos M. Oct 20 '14 at 19:22
  • $\begingroup$ Just because an equation derives from an action or a Lagrangian does not make it "physically sound". Most physicists actually believe that there is only one physical equation (TOE) and that all other equations are merely approximations for special cases. $\endgroup$ – CuriousOne Oct 20 '14 at 20:09