27.4.2018 13.15 - 14.00 XVII,
(Leibniz Universität Hannover)
Uncertainty relations for measurement
The well-known textbook uncertainty relation makes a statement about the impossibility to prepare states, which have sharp distributions for both position and momentum.
This is only one aspect of Heisenberg's original work, and completely leaves out the issue he discusses with his famous gamma-ray microscope: The disturbance of momentum by an approximate position measurement. I will discuss how to formulate this aspect in a quantitative way as the impossibility of realizing accurate joint measurements of position and momentum. Curiously, the resulting uncertainty relations are formally exactly the same as for preparation, but with a quite different interpretation of Delta P and Delta Q. It turns out that this is a coincidence due to the high symmetry of such Fourier-related pairs. The setup presented works for any pair (or n-tuple) of observables, and in this setting such equality generally fails, although there are some inequalities.