Dartmouth Events

Abstract: Measure Theory, Probability Theory, Information Theory, and the Feynman and Born Rules for Quantum Amplitudes are all derivable from similar fundamental symmetries.  These symmetries, which are algebraic in nature, relate to the fact that things can be combined, or shuffled, in multiple ways with identical results.  The symmetries result in sum and product rules, which are thereby given firm foundation.  Together these derivations demonstrate that many aspects of physical laws originate from fundamental symmetries. They are not ad hoc, which is a very powerful result.  Moreover, it is clear that quantum mechanics does not derive from information theory or computability any more than measure theory or probability theory does.  Nor is quantum mechanics an exotic probability theory.  Instead, quantum mechanics is a means by which one consistently assigns quantities to situations involving fundamental interactions, so that probabilities can be consistently assigned and inferences can be reliably made.