I remember sitting there staring at the “linear operators”, trying to figure out what the hell they physically did to the eigenvectors—trying to visualize the actual events that were going on in the physical evolution—before it dawned on me that it was just a math trick to extract the average of the eigenvalues. Okay, but… can’t you just tell me that up front? Write it down somewhere?
Umm, linear operators rescale the eigenvectors, without changing their direction, seems pretty physical to me. Like those polarizers EY kept talking about, they leave some polarizations unchanged. Another standard example is the rotation matrix, it does not affect the axis of rotation.
Oh, I forgot, the math doesn’t mean anything, it just works.
In exactly the same way the Lagrangian and the least action principle “doesn’t mean anything, it just works” in classical mechanics.
Umm, linear operators rescale the eigenvectors, without changing their direction, seems pretty physical to me. Like those polarizers EY kept talking about, they leave some polarizations unchanged. Another standard example is the rotation matrix, it does not affect the axis of rotation.
In exactly the same way the Lagrangian and the least action principle “doesn’t mean anything, it just works” in classical mechanics.
I think he was being sarcastic in that last bit.