OK so this, like my baseball thing, is a puzzler that I’ve been chewing on for many years. (I am not high.)
In high school my physics teacher, in explaining entropy, pointed out that if you push a porcelain teacup off of a table and it smashes, that requires far less energy than making the teacup. And that’s entropy, as I was taught it - the universe wants things to be in a chaotic state, and it’s easier in terms of energy to get things into a chaotic state than to get them into an ordered state. Then there was some math business. Now, before anyone goes impugning my physics teacher, I should note that I failed this class, and indeed failed seven out of my eight semesters of science classes in high school. (A feat I matched in math, and I’m fairly sure I only passed both my second semester sophomore year because my dad died.) So there is every chance in the world that I misunderstood her.
But my question persists: I intuitively see the teacup as more ordered than the bunch of broken shards on the ground because I’m a human and I like to drink tea and so teacups are useful for me. But the universe isn’t a human and doesn’t care about drinking tea. So my question is, what makes the teacup more ordered than the shards, in a non anthropo-chauvinistic way? Like, we can imagine some alien race that finds the shards more ordered than the cup, right? That doesn’t sound too crazy to me for an alien intelligence; they’ll have massively different values and observations and perceptions of what ordered means. After all, it’s still the same material at the same mass. So what’s the non-human version of order that the non-smashed teacup satisfies better than the smashed one?
I feel like this is especially important because YouTube teaches me that entropy is the key to the arrow of time. Although perhaps “teaches” is not the best word.`
It's more that it took massive amounts of coordinate effort (hence energy) to make that teacup than the micro second it takes to break it. Once the energy to make the teacup is already expended, I don't think that the universe cares all that much whether it stays intact or breaks, except to the extent that protecting the teacup against breakage itself expends more energy than breaking it.
The simple answer is that it's "easy" to turn the whole tea-cup into a broken tea-cup, but "hard" to turn the broken tea-cup into a whole tea-cup.
That's not completely accurate, but it's close enough. The model of entropy you're using applies much better to fluids than it does to solid objects, like tea-cups. For example: what happens when you mix tea with water?