Physics Colloquium - Reverse Physics: From Laws to Physical Assumptions

When the math is derived from the right physical assumptions, the physical assumptions can be derived from the math. This insight lies at the core of Reverse Physics, an approach to the foundations of physics that aims to dissect the mathematical structures of all physical theories to find exactly why they are needed and what they represent physically. We will present the general methodology and a series of results in classical mechanics, quantum mechanics, and statistical mechanics, showing how these share a lot more foundational aspects than typically realized. As a few highlights, we will see how placing a lower bound on the entropy imposes an uncertainty principle in classical mechanics, that the geometric structures of both classical and quantum
mechanics are equivalent to the definitions of their respective entropies, that classical mechanics is the high-entropy limit of quantum mechanics, and conversely, that quantization means putting an entropic lower bound on a classical theory.