This was a great read! But I wish the article would have mentioned how tiny the microscopic time-reversal effects are, compared to macroscopic time reversal. The microscopic effects are too small to explain why we have such a clear direction of time. Our direction of time is defined by the observation that entropy (or "chaoticness") always increases with time. If you mix orange juice with water, you will not see the…
> Therefore, a system transitioning from state to state is much more likely to be in one that looks chaotic, and very, very unlikely to ever go back to a state that is non-chaotic. This one thing I don't understand about the 2nd law of thermodynamics: given enough time won't the system go back to a more organized state simply by chance? And in that case, wouldn't the total entropy be reduced?
Or to give you a somewhat similar problem - consider a 32x32px 8bit image (a standard Windows icon since version 3.0). The image consists of 1024 pixels, each capable of representing a different color from the set of 256 colors. How many possible pictures like this are there? Or, as you'd ask in thermodynamics, in how many states such a system can be? It's 256 states per pixel raised to 1024th power (just like 6-digit binary number has 2^6 possible values). It's 256^1024. You know how much is it?
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Now ask yourself, how many of those pictures represent a letter "A". Quite a lot probably, but nowhere near that much. In all those 256^1024 pictures, you have every possible representable letter A, as well as any other possible Unicode character. In those images are all your most cherished private photos (or at least their thumbnails), and also the photos of all things that you'd wish happened but didn't. A thumbnail of every possible photo of the universe is there as well.
There's also something else. Something much more frequent than all other image I've just mentioned taken together. It's the noise. The things we don't recognize, the things we consider uninteresting. I ask you, use your intuition - if you were to create a random Windows icon every second, how soon would you expect to get one depicting a letter "A"?
And now realize we were talking about silly icons that are probably barely visible on your screen.
There are 6.02 x 10²³ atoms in 12 grams of carbon. I.e. in a tip of your pencil. 602000000000000000000000 atoms. Those are your pixels. And if you want to compute the number of states this pile of atoms can be in, that is the number that goes in your exponent. The base is some combination of possible positions, orientations and velocities, and then probably something else I'm forgetting right now. And almost all of those states are noise. That's how the Second Rule works.