Adam Brown

is given by the surface area, and yet I also gave you a way to make it scale like the volume.

So eventually, if I make the region big enough, the amount of information in that volume will be bigger than the bound that I just said.

Therefore, I've ruled out Hawking's and Bekenstein's bound.

What goes wrong with that thought experiment

is that eventually if I make a big enough pile of hard drives, the whole pile of hard drives will undergo gravitational collapse and form a black hole.

Yeah, you have to run that calculation.

But if you do run the calculation, it turns out that it's nowhere near.

It wasn't close.

Yeah, they don't just balance each other out.

If I take a...

you know, an online shopping website and I buy a bunch of Western Digital hard drives and I calculate the information storage capacity of those and compare it to the area of a black hole, you know, figure out when the pressure in the hard drive would be enough to stop it collapsing to form a black hole.

It is nowhere close.

It will make a black hole way, way, way before it comes close to violating Bekenstein or King Pound.

So that's the information storage in black holes.

The reason you know that that's also the information storage bound for anything, not just black holes, is that if you had something that wasn't a black hole that had more information than that in a given region, and you just added matter, eventually that thing itself would collapse to form a black hole.

And so it couldn't be the case, just logically, that it had more information than the black hole it'll tend to.

It's been extremely important for our understanding of quantum gravity.

It's perhaps the central fact that we know about quantum gravity is that the information scales with the area.

And that is a hint.

That fact that was known since the 70s was a big hint that became very influential later on.