Cancelled - the talk needs to be rescheduled for Fall 2022.

On the simultaneous measurement of the canonical Q and P

Perhaps the two most fundamental observables are the canonical coordinate and momentum or “Q and P” which satisfy the canonical commutation relation [Q,P]=i.  Since the Heisenberg uncertainty principle, it has been understood that two such observables cannot in one sense be measured simultaneously.  However in another, very practical sense these two observables can be and are measured simultaneously.  Specifically, the heterodyne measurement of electromagnetic waves is such a simultaneous measurement of Q and P, which in this case correspond to the magnetic and electric forces respectively.  Although it had been vaguely understood since the 60s that the heterodyne measurement mathematically corresponds to the “overcomplete basis” of coherent states, a correct mathematical model of the heterodyne measuring process didn’t occur until 1993.  Even since then, the ideas of theoretical measurement, most notably the instrument, continue to become better developed.

In this talk, I will try to keep things simple by walking through how to calculate the heterodyne instrument from first principles, by a method I like to call the Principle Instrument Program, a term inspired by the theory of principle bundles.  The heart of the Principle Instrument Program is the evolution of a Kraus-operator density function, an invention of mine which is equivalent to the instrument.  My favorite thing about the Kraus-operator density is how it makes clear that measuring instruments are inherently independent of quantization, quantization being more about the specific properties of the state being measured.  Evolution of the Kraus operator density requires some basic differential geometry on Lie groups, in this case a nonRiemannian one.  Something to look forward to is how the Planck distribution will appear as a consequence of the heterodyne instrument’s completeness relation.  Time permitting, I will talk about a second Q&P measurement which is more analogous to the work I’ve done for spin as well as talk about the relationship between heterodyne and Borel subgroups.

 http://physics.unm.edu/pandaweb/events/index.php?display=event&event_id=7601