Why must allowable physical laws have reversibility?

I'm watching Susskind's video lectures and he says in the first lecture on classical mechanics that for a physical law to be allowable in classical mechanics it must be reversible, in the sense that for any given state $S\in \mathcal{M}$ where $\mathcal{M}$ is the configuration space there should be only one state $S_0\in \mathcal{M}$ such that $S_0\mapsto S$ in the evolution of the system.

Now, why is this? Why do we really need this reversibility? I can't understand what are the reasons for us to wish it from a physical law. What are the consequences of not having it?

• The sense you describe is not reversibility as usually meant in mechanics. Reversibility in mechanics is meant in this way: keep all the positions $\mathbf r_i$, reverse all velocities $\mathbf v_i$ and calculate the evolution of positions $\mathbf r_i(t)$ according to the equations of motion. The equations of motion (physical laws of motion) are reversible if the coordinates retrace their past values. Feb 5, 2014 at 21:04
• Damped motion described by the equation of motion $m\ddot x + m\gamma \dot x = 0$ evolves position $S_0$ to single position $S$, but is not reversible in mechanical sense, due to the term $m\gamma\dot x$. Feb 5, 2014 at 21:06