Jacob Barandes (Harvard) - Quantum Theory, Indivisible Stochastic Processes, and the Tsirelson Bound

The textbook axioms of quantum theory, as formally laid down by Dirac and von Neumann in the 1930s, feature two categorically different rules for time evolution. When an external observer carries out a measurement, the system probabilistically collapses to a specific outcome. By contrast, when the system is not being measured, it evolves according to a rule that does not feature probabilities or a specific outcome, whether the system is closed or open to its environment. Deciding which evolution rule to apply depends on undefined terms like "external observer" and "measurement." This manifest problem with the axioms is called the measurement problem, and it has become an increasingly pressing issue for a number of research programs, including quantum gravity. 

 

As Bohm realized in the early 1950s, decoherence by itself, without changes to the axioms, is not capable of solving the measurement problem, because decoherence alone does not produce probabilities or a specific measurement outcome. Most modern attempts to resolve the measurement problem (and other problems) rely on trying to extend the non-probabilistic form of time evolution to cover the entire theory, but these approaches run into several significant obstacles that I will describe in my talk, including rigorously accounting for Born's formula for the probabilities of measurement outcomes.

 

I will then lay out an alternative approach that extends the probabilistic evolution rule to cover the entire theory, down to the microscale, leading to a stochastic reformulation of quantum theory with a number of interesting features. Among these features are new ways to think about superposition, interference, entanglement, and causal influence, as well as a first-principles argument for the Tsirelson bound, which refers to the precise degree to which quantum theory violates the Bell inequality.