Theoretically, if you keep shaking it, there is a chance that all those grains of sand will fall, with all the white sand on the bottom, and the red sand on top. It's not very big chance, but it *does* exist. So if you want a more up to date model, than Newton's, this must be taken into account.

Because, in a Universe that is basically a Chaotic system, encompassing a few ordered and quantifiable elements, every dynamic available must be taken into account in order to get the most accurate view. You can't just omit a possibility because it doesn't fit the 2nd Law of Thermodynamics. A truly empirical mind, will try to improve the Law of Thermodynamics, rather than to pretend the Universe is something less than it is.

Either way, we are never going to see the sand fall in those layers again.

But to categorically state that it is impossible, that it can *never* happen, is wrong. Because according to the Laws of Probability, it is a possibility. And this means that it not only *could* happen, but at some point, it *will* happen.

In theory, yes. But

*only* in theory. What I gave was a real world example, I might have better said "always (within the lifetime of the universe)" and "never (within the lifetime of the universe)".

Wolfram Alpha tells us that there are

52,700 grains of sand in a litre.

With some room to shake in a 1L bottle, say that's 20,000 red grains and 20,000 white grains.

The number of permutations is 40,000! for the entire bottle. Of those permutations 20,000!

^{2} are perfectly separated.

Using Wolfram Alpha again to divide those numbers tells us the odds of getting a perfectly separated result after shaking randomly is 1 in 6.320245 ? 10

^{12038}.

Now, because you seem to be in a nitpicking mood

I'll pre-empt your protest that perfect separation is also not a real world example either, so let's divide that number by, say,

the number of permutations for 1000 grains to be out of place, 2.474612 x 10

^{1722} :

(6.320245 ? 10^12038) / (20000 choose 1000) = 2.554035 x 10

^{10316}With, say, one second per shake that's 8.098790x10

^{10308} years. On average you'll need half of that.

Wikipedia on the future of the Universe tells us that--even though it may go on for an unknown amount of time after that--within 10

^{40} years all nucleons will have decayed. That also means there won't be a bottle nor someone to shake it.

Dividing those, tells us that even if you keep on shakin' until the end of the universe, you

*still* only have a chance of 1 in 4.049395x10

^{10268} of

*ever* getting that sand just somewhat sorted out again. (pay attention though, cause if you accidentally miss it, and shake it again out of habit, you can start all over again--just sayin')

As you see, this means that the chance that it happens

*never at all, ever* is absurdly close to one.

And even if you insist that we just

*might* happen to live, out of all possible universes, in that one-in-4.049395x10

^{10268} universe in which this single bottle of sand will indeed randomly sort itself out, then

*still* my initial argument, "if something is already random, it'll still be random after randomizing" holds for each and any other thing in that universe except that one bottle with a very similar staggeringly high probability.

If not, you might want to keep an eye out of Zaphod Beeblebrox and GTFO this planet because you know there'll be Vogons bound to show up any minute now.