About sufficiently wise

Why are the laws of physics as they are? What do they describe? Could we have different laws? Why is the state of a quantum system a vector in a Hilbert space while the state of a classical particle a point in a cotangent bundle? Why does the piece of toast always fall on the buttered side?

These are the fundamental questions that I have been working on for a long time now. In 2007 it occurred to me that I would never have had a satisfactory answer until I had been able to rederive the basic laws from simple physical assumptions. In other words, we have Newton’s laws, the thermodynamics law, the invariance of the speed of light for special relativity… what are the fundamental assumptions for Hamiltonian/Lagrangian classical/quantum mechanics?

In 2017 I came across an essay written by Richard Hamming in which he wrote:

Thus my first answer to the implied question about the unreasonable effectiveness of mathematics is that we approach the situations with an intellectual apparatus so that we can only find what we do in many cases. It is both that simple, and that awful. What we were taught about the basis of science being experiments in the real world is only partially true. Eddington went further than this; he claimed that a sufficiently wise mind could deduce all of physics. I am only suggesting that a surprising amount can be so deduced. Eddington gave a lovely parable to illustrate this point. He said, “Some men went fishing in the sea with a net, and upon examining what they caught they concluded that there was a minimum size to the fish in the sea.”

Whether I am sufficiently wise to deduce all of physics I have no idea… but I have made some progress, more than I thought I could. A surprising amount can indeed be deduced from very little. I do believe that, once we really understand the fundamental laws, we’ll just see ourselves staring back at us, as the laws can only describe what we are able to catch intellectually and experimentally, like the fishermen with their net.

In this blog I’ll be sharing the insights and connections I have been gathering. If you like it, tell it to your friends. If you don’t like it, mind your own business.