Question

According to Heisenberg's uncertainty principle, the more we know about a particle's momentum, the less we know about what?

Answer 1

The more we know about momentum, the less we can know about position.

Explanation:

The Heisenberg Uncertainty Principle asserts that certain combinations of dynamical variables are coupled together in such a way that decreasing the error in one of them will increase the minimum possible error we can have in the other. Position and momentum are the best known such pair.

It's tied into the fact that particles are also waves, and as waves they inherently possess some delocalization in position and some spread in momentum. You can manipulate the wave in a way that cuts down the spread in momentum, but that change in the wave also spreads it out more in position.

The precise relation that describes this uncertainty relation is

`"(Root mean square error in position)" xx "(Root mean square error in momentum)" \ge "(Planck's Constant, h)"/(4\pi)`

See https://en.wikipedia.org/wiki/Uncertainty_principle.