TL;DR – The Poisson bracket tells how a quantity changes under a transformation generated by another. It also tells us the state count of a cell of phase space identified by the two variables. Another operator of particular importance in Hamiltonian mechanics is the Poisson bracket: $\{f,g\}=\frac{\partial f}{\partial x}\frac{\partial g}{\partial p} – \frac{\partial f}{\partial p} …
TL;DR – The Hamiltonian description of a direction in space is the classical version of the spin of a particle. Now we turn our attention to the classical version of another quantum concept: spin. What we show here is that Hamiltonian motion of a spatial direction is qualitatively the same as the evolution of spin …
TL;DR – Statistics applies to populations, not individuals. There is no such thing as the probability of one individual having some characteristic. I remember talking to a friend of mine a long time ago. “I wonder what will I do when I grow up?” “What are the chances that I become a doctor?” “What are …