The information in a wave
MATHEMATICAL PICTURE LANGUAGE
Roberto Longo - University of Rome Tor Vergata
Suppose that some information is transmitted by an undulatory signal.
In Classical Field Theory, the stress-energy tensor provides the energy-momentum
density of the wave packet at any time. But, how to measure the information, or
entropy, carried by the wavepacket in a certain region at given time?
Surprisingly, one can answer the above (entirely classical) question by means of
Operator Algebras and Quantum Field Theory. In fact, in second quantisation a
wave packet gives rise to a sector of the Klein-Gordon Quantum Field Theory on
the Rindler spacetimeW. The associated vacuum noncommutative entropy of the
global von Neumann algebras of W is the entropy of the wave packet in the
wedge region W of the Minkowski spacetime. One can then read this result in first
quantisation via a notion of entropy of a vectorof a Hilbert space with respect to a
real linear subspace.
I give a path to the above results by an overview of some of basic results in
Operator Algebras and Quantum Field Theory and of the relation with the
Quantum Null Energy Inequality.
via Zoom: https://harvard.zoom.us/j/779283357