# Do physical laws require 2nd derivatives [duplicate]

Is it a happy coincidence that second degree differential equations approximate reality or a necessity? They describe how a system will evolve from one state to the next, but surely the ultimate laws of nature will not depend on two prior initial conditions. Surely reality can compute its next state from the current state alone.

• Of course,such as the Newton's second law. – Jack Mar 14 '17 at 6:18
• But surely the ultimate laws of nature will not depend on two prior initial conditions. Why? What do you mean? – Qmechanic Mar 14 '17 at 6:28
• Why 2nd derivatives? 0th and 1st derivatives are common. 4th derivatives occur in elasticity theory. ... Reality does not compute anything. We do all the computations. – sammy gerbil Mar 14 '17 at 7:04
• Possible duplicates: physics.stackexchange.com/q/18588/2451 , physics.stackexchange.com/q/4102/2451 and links therein. – Qmechanic Mar 14 '17 at 13:33

Actually if you think of classical (and non-relativistic) physics, the canonical equations of motion of the Hamiltonian formalism $$\dot p=-\frac{\partial H}{\partial q}\, ,\qquad \dot q=\frac{\partial H}{\partial p}$$ are first order. In addition, the Hamilton-Jacobi equation $$H+\frac{\partial S}{\partial t}=0\, ,\qquad p=\frac{\partial S}{\partial q}$$ is also of first order.