Einstein
Dimensional Traveler
What it really means is that you can only know a certain total quantity of information about a quantum particle. Momentum and position are just two quantum properties of the state a particle. There are more - mass, energy, spin, charge, angular velocity, angular momentum...
But it's the non-commutating properties that are inportant to uncertaity. I won't go into matrix algebra, but that is where it is explained. In short, the non-commutatig properties goes like this:
A x B = C
B x A =/ C
A and B are non-commutating. You can't arbitrarily switch the order in which A and B appear in the equation/inequality because the order determines the outcome.
A x B = C
B x A = C
A and B are commutating in the manner that we all learned when we were taught the basic rules of arithmetic.
A, B and C are individual matrices, columns and rows of numbers, representing the individual quantum states of the particles under consideration.
You know there is a physical phenomena that parallels this type of math. The Faraday riddle. A rotating conductor in a uniform magnetic field will generate a current perpendicular to the axis of rotation. Yet when the uniform magnetic field is rotated instead, no current is generated through the conductor.