From the Universe to Subsystems

Abstract

Any fundamental physical theory is a theory of the universe as a whole. Its laws describe the evolution of the entire configuration of matter. Thus, in classical mechanics, where the forces range over all physical space, the motion of any particle at any given time depends, strictly speaking, on the positions of all the other particles and hence on the initial state of the entire universe. In quantum mechanics, as we will discuss in Chap. 13, the only fundamental quantum state is the one pertaining to the universe as a whole and represented by the universal wave function. However, this fundamental point of view is utterly impractical for everyday science, which seeks to apply these theories locally to small parts of the physical universe. Aside from our limited computational resources, there is simply no hope of knowing the exact state of the universe so that we could solve the equations of motion for it.