We’re trained to think that causes precede effects, energy flows like water. With the variational principles in physics, it doesn’t work that way. The solutions don’t violate causality — they just don’t use it. Causality is what we identify as the reality after we have the solution. When we re-parametrize the solution using time, impose macroscopic irreversibility, and forget all about the boundary conditions that got us the solution, then causality appears. We are habituated to the use of causal language to describe the non-causal mathematical solutions that we obtain.
The question, “How does a photon know the shortest path to the absorber?” makes no sense. A “photon” is the name we give to a successful connection between an emitter and an absorber. It turns out that the solution has this nice property. Fermat’s principle doesn’t accommodate any spacelike solutions that would violate causality. There are no “instantaneous” segments along the later-determined path; it’s just that the path isn’t narrated along sequential segments. Our brains evolved to escape from each potential carnivore attack along the way, not to conceptualize some grand strategy of avoiding carnivores. We like trial and error and learning step by step; it makes sense to us, global optimization not so much.
But the fact that one learns something after the fact doesn’t imply that it wasn’t a fact all along.
Leave a Reply