I'm still absorbing some basic ideas about quantum physics and now I think I have to reconsider the Uncertainty Principle.
Here is what I understand, in summary:
- a "configuration" specifies the position, momentum, spin, and type, of every particle in the universe
- there is a complex amplitude distribution over the full space of configurations
- each configuration evolves into all possible subsequent configurations, and the associated amplitude transforms in some way for each of these
- the amplitude for a future configuration is the sum of amplitudes over all inbound evolutions
- this is basically what the Shrödinger Equation represents
- the probability that we are in any particular configuration is the relative squared amplitude.
I think I get it.
But now I've started to think about the Uncertainty Principle all over again. Long before I understood the above points, I understood that there was no exact joint (position,momentum) value that could ever be measured.
If I go back over it all now, I get the impression that, within each configuration, the position and momentum is exactly defined and in fact the Uncertainty Principle comes from the fact that the amplitude distribution itself is fuzzy.
That is, if I make a measurement of momentum, I am projecting many configurations, encoding many velocities, onto a preferred basis. The information from the momentum measurement is "you are in one of these configurations, for which the corresponding position is one of these values".
Is this interpretation correct?
Follow-up question: does this imply that, if the amplitude distribution was pointlike, then uncertainty would be eliminated? (Not that this ever actually happens.)