Can you fit all of the information in the universe into a region smaller than the universe let's find out There's quite a bit of stuff in the universe to put it mildly Hundreds of billions of galaxies each with hundreds of billions of stars each with rather a lot of particles in them and Then there's all the stuff that isn't stars the dark matter black holes planets and the particles and radiation in between the stars and galaxies Not to mention space itself with its fluctuating quantum fields dark energy blah blah stuff everywhere but it's the universe actually made of stuff an increasing number of physicists view the universe view reality as informational at its most fundamental level and its evolution through time can be thought of as a computation and then there's the simulation hypothesis in which that computation is engineered by who knows what or who How big a memory bank would you even need to compute a universe?

Seriously, let's figure it out.

How much information does it take to describe the entire observable universe?

After we're done with that, I'm gonna have an even cooler challenge question for you.

I Casually mentioned in the last episode that our 3d universe may just be a projection of information imprinted on its two dimensional boundary No biggie, that's the holographic principle, and we've talked a lot about some ideas leading up to it Don't worry The full holographic principle episode is still coming But our recent episode on black hole entropy and some of the lead ups to that might be helpful here You can also watch this video as a standalone and go back to those earlier ones later if you feel like it But the main point the really weird Surprising point is that the maximum amount of information that can fit in a volume of space is not proportional to that volume is proportional To the surface area of that region of space Jacob, bekenstein figured this out by realizing that the entropy of a black hole is proportional to the surface area of its event horizon But entropy is just a measure of hidden information So the bekenstein bound is equally a limit on how much information you can fit in any region of space Will come back to the bekenstein bound in a sec But for now, let's think about why this dependence on surface area is surprising.

Well common sense would suggest that the maximum information Content depends on volume not service area.

I mean a pile of thumb drives has a total storage capacity that depends on its volume But instead of storage capacity, let's think about the information needed to perfectly describe a patch of space You think that to fully describe say the universe you'd need to know what's going on in every tiniest possible 3d chunk That smallest element is roughly a cube one Planck length on a side Where the Planck length is the smallest meaningful measure of distance at around one point six times ten to the negative thirty five Meters is the smallest possible chunk of space.

So let's see it can contain the smallest amount of information one bit per Plank volume.

That's kind of like saying we can describe the universe completely if we go through all of its Quantum voxels and answer the yes/no question of whether it's full or empty This probably way Underestimates how much info you really need to describe the universe, but let's start with this anyway So how many Plank volumes are there in the universe?

well The radius of the universe is something like 47 billion light-years Which is a few times 10 to the power of 61 Plank lengths 4 & 3 PI R cubed so the universe contains 10 to the power of 183 Planck volumes You'll see estimates that the radius of the universe is a mere 10 to the 60 Planck lengths rather than 10 to the 61 and that it's volume is 10 to the power of 180 units and that's because Cosmologists tend to round down at every step and so you drop a bunch of orders of magnitude Astrophysicists are by comparison highly accurate We only drop factors of 2 But what's a few orders of magnitude between friends?

You might argue that more than one bit can fit at each grid point in the universe You might be right particles have more information than just that position It will be better to use the number of grid points in quantum phase space which includes position But also other degrees of freedom like momentum spin direction etcetera in other words We should count all possible quantum states in the universe Anyway, the real number is going to be way higher than our estimate of 10 to the 180 But as we'll see we're already way way higher than the actual information limit of the universe Okay, so ten to the power of 180 or so Bits is the minimum if you want to describe every 3d quantum voxel completely independently But the bekenstein bound tells us that the information content of any volume isn't the number of these Plank volumes But rather the number of Plank areas on the surface the observable universe has a surface area of 10 to the power of 120 to 10 to the power of 124 Planck areas, depending on whether you're rounding like a cosmologists or an astrophysicist So the storage capacity of the universe is around 10 to the 60 lower than the number of volume elements it contains So how do you encode a whole universe in a space far smaller than the universe itself?

There must be some amazing compression algorithm maybe middle-out in Fact in a sense.

The holographic principle is a compression algorithm See, you don't really need 1 bit per volume element of the universe They'll be like having separate completely independent memory elements for every empty pixel in an image file Most of space is indeed empty.

Let's say instead.

You only need a single bit of information for every element in phase space That's occupied In other words one bit per elementary particle the observable universe contains something like 10 to the power of 80 Protons each proton has 3 quarks and there are a similar number of electrons.

Most other particles are much rarer So we're still in the realm of 10 to the 82 10 to the 81 neutrinos and photons Formed in the Big Bang are probably a billion times more abundant than protons That's verified experimentally in the case of photons the Cosmic Microwave Background Has around 10 to the power of 89 photons across the observable universe so almost all of the information for that matter the entropy in particles because in neutrinos and in the Cosmic Microwave Background photons the situation with dark matter is unclear So let's just round up to tend to the power of ninety bits of information in particles in our universe That sounds like a lot but happily it's way less than the ten to the power of 120 ish limit of the bekenstein bound But there's one more source of information Black holes as I mentioned last time black holes contain most of the entropy in the universe The relationship between black hole entropy any information deserves of thought black hole entropy in terms of number of bits Tells you the information you'd need to describe all possible initial states That could have possibly formed the same black hole of which there are many Two to the power of the number of bits of entropy and for black holes that entropy is the bekenstein bound for number of Planck areas on its event horizon Because the information about the black hole's previous state is lost to fully describe it You need to fully describe its event horizon.

You need its full bekenstein bound in information.

How much information is that?

let's take a Supermassive black hole as an example Sagittarius a star in the center of the Milky Way Which has a mass of four million Suns its event horizon is around 12 billion meters Giving it a surface area of 10 to the power of 92 10 to the power of 91 Plank units so the Milky Way's black hole has as much entropy and hidden information as all of the matter and radiation in the entire rest of the universe and There are some hundreds of billions of galaxies in the universe each with its own supermassive black hole we're talking something like 10 to the power of 100 and one to ten to the power of 100 and two bits of entropy or Information black holes contained by far most of the entropy in the universe and require most information to fully describe But again, we're still below the bekenstein bound for the whole universe I know you're as relieved as I am.

We are nowhere near the universe's memory limit The universe can keep having particles and you can leave your horribly bloated email inbox alone But what would actually happen if the universe contains too much information?

Say in the form of too many particles What if we started to fill up those empty lung sized cubes of space throughout the universe until?

It contained more information than the bekenstein bound allowed Well, the answer is straightforward enough at the moment The universe reached its informational limit you would immediately become a black hole with an event horizon as big as the current cosmic horizon would be the end of Space-time the bekenstein bound does apply equally to engineered information storage as it does to black holes and universes it gives the limit of storage capacity within a given volume before the interior collapses into a black hole t