Yet the microscopic laws of nature [Newton's equations or Schrodinger's equation] are time reversal invariant. There is no arrow of time in these equations. So, where does macroscopic irreversibility come from?

There is a nice analogy to spontaneously broken symmetry in phase transitions. Strictly speaking for a finite number of particles there is no broken symmetry as the system can tunnel backwards and forwards between different states. However, in reality for even a small macroscopic system the time scale for this is ridiculously long.

Deriving irreversibility from microscopic equations is a major theoretical challenge. The first substantial contribution was that of Boltzmann's H-theorem. There are many subtleties associated with why it is not the final answer, but my understanding is superficial...

This post was stimulated by some questions from students when I recently visited Vidyasagar University.

About reversibility. You say that "even at a thousand atoms..." Its nowhere near that for single, isolated molecules. "Significant" recurrences never occur even at 7 atoms, at modest energies.

ReplyDeleteIf you excite a C-H stretch in for example acetaldehyde the energy will move out in a about 100 psec, never to return (never ever because the energy will radiate away). You only need a few, say 10, coupled quantum states to see this! Its a pity that physicists almost never look at isolated, gas phase, molecules because they are such a rich set of similar systems.