Here is a link to last week’s blog posting of the book club for From Eternity to Here by Sean Carroll:
Sean Carroll makes the following couple points in the blog posting:
Some people labor under the impression that the transition from classical mechanics to quantum mechanics ends up “quantizing” everything, and turning continuous parameters into discrete ones, perhaps even including time. It doesn’t work that way; the conventional formalism of quantum mechanics (such as the Schrödinger equation) implies that time should be a continuous parameter. Things could conceivably change when we eventually understand quantum gravity, but they just as conceivably might not.
I personally come down on the side that believes that there’s no fundamental irreversibility, only apparent irreversibility, in quantum mechanics.