Simulating Physics with Computers

Abstract: Feynman gave in 1982 a keynote speech \textit{Simulating Physics with Computers} (Int. J. Theor. Phys. {\bf 21}, 467 (1982)) in which he talked ...about the possibility...that the computer will do exactly the same as nature". The motivation was that:...the physical world is quantum mechanical, and therefore the proper problem is the simulation of quantum physics". Here I try after more than forty years to answer Feynman's question of whether it is possible to perform exact computer simulations. Many computer simulations are not exact, they contain mean field approximations that disobey the symmetry in the quantum dynamics with Newton's third law, e.g. almost all astrophysical simulations of galaxy systems. After a review of computer simulations and the problems of simulating real systems, I argue that Newton's discrete dynamics, which is used in almost all computer simulations and which is exact in the same sense as Newton's analytic dynamics, is the classical limit path of Feynman's quantum paths. However, the physical world is not known exactly and it is much more complex than any simulated systems, and so far no real systems have been simulated exactly. Hence, more than forty years later, and after hundreds of thousands of computer simulations of the physical system's dynamics the answer to Feynman's question is still negative. But although it is not possible to simulate the dynamics exactly for any real systems, the simulations have been and will be of great use in Natural Science.