Sean Carroll

There's going to be a certain time after which the universe just returns to its pre-existing quantum state.

So this

Fact is unsurprisingly known as the quantum recurrence theorem, and people have written papers about it.

It's a well-known thing.

In finite dimensional Hilbert spaces, you start the quantum state wherever you want, you will eventually come back to where you began.

Now, the time it takes to come back to where you began, the recurrence time, is generally hilariously long.

It's very, very, very, very long.

The details depend on what you count as really recurring.

But to give you a very vague idea, the area of our cosmological horizon

in desider space.

So just to make sense of those words, we live in a universe with dark energy, which is accelerating.

That means there is a horizon around us, and once we get rid of all the matter and galaxies and things like that, and we're just in empty space, there's a well-known calculable size to the horizon that is around us.

The horizon just means there are points that are so far away that space is expanding too fast,

If you're at one of those points, you can never return to where we are.

That's the horizon that is around us.

You'd have to move faster than the speed of light.

Stephen Hawking and his friends have shown that the horizon in the sitter space, a universe with a positive cosmological constant,

has an entropy and a temperature just like the horizon of a black hole does.

And the entropy of our desider horizon in the real world is something like 10 to the 122, okay?

A pretty big number, 10 to the 122.