I read according to 'Newtonian' Mechanics any set of physical activity of particles can be reversed ( I think) so a set of complicated dynamic systems of particles and matter can reverse their 'behaviour'. Yet a Star collapsing towards a 'Black Hole' will probably not 'stop' and reverse it's behaviour. So could Gravity be considered part of the 'Arrow of Time'? Since entropy is part of this 'Arrow' could entropy have 'qualities similar to the qualities of Gravity?
$\begingroup$
$\endgroup$
Add a comment
|
1 Answer
$\begingroup$
$\endgroup$
3
Newtonian mechanics isn't quite as predictable as it's made out to be, both in theory and in practice. In theory, it's an easy task to set up a Newtonian system of particles that will eventually violate the Lipschitz continuity condition. You can toss reversibility and predictability out the window when that happens. In practice, we can't know state perfectly, and that means the complicated dynamic systems you mentioned eventually become unknowable. They'll eventually entire a region of strong chaos, and there's no telling what happens after that.
With regard to entropy, consider an interstellar gas cloud. The Jeans instability can make a portion of the cloud collapse to form a protostar and a protoplanetary disk. You won't see a protostar and protoplanetary disk undo themselves and reform that gas cloud because of entropy.
That's yet another gravitational example, but there are plenty of non-gravitational examples. Consider a semi-rigid body with three distinct principle moments of inertia rotating in space. Eventually that body will end up spinning about the axis with the largest moment of inertia. This is an irreversible process, and it lies almost entirely within the realm of Newtonian mechanics. The only non-Newtonian aspect is that the body radiates heat generated by internal friction away into the universe.
answered Sep 7, 2014 at 5:25
-
$\begingroup$ Very good explanation! I think the OP may be unaware, that during gravitational collapse part of the mass caries angular momentum and energy away and that that mass is no longer gravitationally bound by the system, hence that gravity can not reverse the dynamics in the future? That this seems to violate the recurrence theorems is, of course trivial... Newtonian gravity lives in an infinite phase space (which breaks the necessary conditions for the theorems), which we probably don't emphasize sufficiently, when we teach classical mechanics. $\endgroup$ Commented Sep 7, 2014 at 21:50
-
$\begingroup$ Can gravity be considered part of the Arrow of Time? $\endgroup$ Commented Sep 8, 2014 at 4:17
-
$\begingroup$ Could Gravity that is describable by Einstein's Relativity equations ( and not Newtonian mechanics) be considered an arrow of Time? $\endgroup$ Commented Oct 20, 2014 at 6:26