Microstates - Why Position and Momentum?
Answers
Answer:- Microstate gives a complete detailed description of the system, macrostate is a more generalised description. The macrostate of a system can be known exactly if you know microstate of all the constituents, but not the converse in general, because there may be many possible distributions of microstates for a single macrostate.
Answer:
Luke's answer is great! For a different (yet the same if you think about it) perspective, just look at Newton's second law
F⃗ =ma⃗ =mx⃗ ¨
This is a second order differential equation. To solve this we need (well dont need, but typically this is how it is done) to specify initial conditions x⃗ (0)=x⃗ 0 and x⃗ ˙(0)=v⃗ 0. Therefore, if we know the initial position and velocity of a particle along with the forces that act on it, then classically we know exactly where it will be and the velocity it will have at any point in time. Of course, p⃗ =mv⃗ , so anything we say about the velocity can also be said about the momentum (with just the difference of the mass of the particle).
The focus on momentum rather than velocity, as has been pointed out by others in the comments and in Luke's answer, is because it is very useful in Hamiltonian mechanics. This is especially true when you make the jump to quantum mechanics. There we have a momentum operator, but you usually do not hear anything about actual velocities.
Also as pointed out by others, some systems are better defined using other quantities. For example, in looking at systems with rotational symmetry it is much more useful to look at angular momentum. It really depends on the system in question as well as what questions you are asking of this system