In real life, why is space of states or state-space defined only by position and velocity?

Question

My book defines state-space as "the collection of all possible states of the system." For example, the state-space of a coin is heads or tails. It also said that in our world, state-space is defined by $x,y,z,v_x,v_y,v_z$ - the position and velocity. But is acceleration or force part of the state-space?

My book also says that the formal meaning of the state is "Everything you need to know (with perfect accuracy) to predict its future, given the dynamical law." In this case, do we need to know the acceleration or force or is it already given by the dynamical law (in this case, it's $\vec F = m\vec a$)

Answer 1

First, physics does not deal with real life. Only models of real life. Real life is too complicated for physicists. We leave the hard stuff to chemists and biologists.

Think of the state as the initial conditions needed to predict the future given a set of dynamical laws (Newton). Newton's law is a second-order differential equation, so only two initial conditions are needed. The simplest are position and velocity.