Assumptions of Physics

A research project led by Christine Aidala and Gabriele Carcassi at the University of Michigan

What do the basic laws of physics describe? Why is the state of a classical particle identified by position and momentum (i.e. a point on a cotangent bundle) while the state of a quantum system is identified by a wave function (i.e. a vector in a Hilbert space)? Could we have had different laws?

The project aims to identify a handful of physical principles from which the basic laws can be rigorously derived.

We believe this approach allows us to answer the above questions as it forces us to:

  • Clarify our assumptions. As we are forced to formalize and make explicit our starting points, we understand under which conditions each physical theory is valid. We also have a better idea of when and how they fail, possibly giving new insights that may lead to new physics.
  • Put physics back at the center of the discussion. By starting from physical ideas we put physics back at the center of the discussion, instead of relegating it to a mere after-the-fact interpretation as it is currently done in most modern scientific theories. Many results can be directly understood in terms of the assumptions, fostering a better intuition for the mathematical results.
  • Give science sturdier mathematical grounds. As each mathematical symbol is given a precise physical meaning, our formal framework maps one-to-one to our physical understanding. This means we automatically leave out any unphysical mathematical artifact.
  • Foster connections between different fields of knowledge. We have found recurring core concepts between different fields of science, math, philosophy and engineering. In retrospect, this is not surprising: nature is one and does not care about such divisions, and therefore truly fundamental concepts must span freely across different areas.
  • Provides a way to pose deep questions. Once we have formalized what we mean by scientific theory and identified what conditions are required to rederive the basic laws, we can try to understand whether those requirements are statements about the world around us or are statements about what is needed to do science.