Susskind Lecture 1 - Classical Mechanics
Lecture 1 starts from the idea that classical mechanics is about states and rules for how states change. The key move is to stop thinking only in terms of “where is the particle?” and start thinking in terms of the full information needed to predict its future.
State and phase space
A phase space is the space of all possible states of a system. For one particle moving in one dimension, a state needs position and momentum:
state = (x, p)For three-dimensional motion, it needs three position components and three momentum components:
state = (x, y, z, p_x, p_y, p_z)The point is visceral: position alone is not enough. A ball at height 1 m could be moving up, moving down, or momentarily stopped. Momentum tells you which future you are on.
Determinism
A deterministic law gives exactly one next state for each current state. In a finite-state toy model with discrete time, every state must have one outgoing arrow. If two different previous states collapse into the same future state, then looking backwards becomes ambiguous.
Susskind uses this to motivate information conservation: in classical reversible mechanics, time evolution should not squash many distinct states into one indistinguishable state. The system can scramble information, but it should not erase it.
Link to later mechanics
This is the seed of Hamiltonian mechanics: instead of only tracking trajectories in ordinary space, track motion through phase space. Forces and energies become rules for flow through that space.