How does conservation of angular momentum not violate the time invariance of Newtonian mechanics?

Question

Richard Feynman states:

This follows from the fact that if we substitute −t for t in the original differential equation, nothing is changed, since only second derivatives with respect to t appear. This means that if we have a certain motion, then the exact opposite motion is also possible. In the complete confusion which comes if we wait long enough, it finds itself going one way sometimes, and it finds itself going the other way sometimes. There is nothing more beautiful about one of the motions than about the other. So it is impossible to design a machine which, in the long run, is more likely to be going one way than the other, if the machine is sufficiently complicated.

One might think up an example for which this is obviously untrue. If we take a wheel, for instance, and spin it in empty space, it will go the same way forever. So there are some conditions, like the conservation of angular momentum, which violate the above argument. This just requires that the argument be made with a little more care. Perhaps the walls take up the angular momentum, or something like that, so that we have no special conservation laws. Then, if the system is complicated enough, the argument is true. It is based on the fact that the laws of mechanics are reversible.

• Richard Feynman 46-3 paragraphs 2 & 3 (https://www.feynmanlectures.caltech.edu/I_46.html).

I am not convinced that, if angular momentum is conserved, that a wheel will eventually (on an enormous enough time span) reverse itself in the absence of other forces or temperature gradients.

If a wheel is spinning alone in empty space, it must conserve its angular momentum such that it can never reverse. Doesn't this violate Feynman's argument? I do not understand his refutation, how can we avoid having "special conservation laws?"

Answer 1

Feynman isn't saying that a wheel spinning in empty space will eventually reverse itself. As he says, that is an example for which the earlier claim is "obviously untrue," essentially because it is too simple a system.

His argument is that if we add complexity - perhaps we have $10^{23}$ wheels which may exchange angular momentum with each other or with the environment (e.g. the walls, some background radiation field, external particles) - then the fact that the total angular momentum in the universe is conserved is not sufficient to constrain the dynamics of the individual wheels in any meaningful way. When we restrict our focus only to the wheels and not to the surrounding environment with which they may exchange angular momentum, angular momentum is no longer a conserved quantity.