How Much Information is in the Universe?

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Matt O'Dowd (1:03)

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 is 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 going to 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. It's 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 into any region of space. We'll 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 surface 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 1.6 times 10 to the negative 35 meters. It's the smallest possible chunk of space, so let's say it can contain the smallest amount of information, one bit per Planck 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 Planck 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 Planck lengths. Four on three, 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 its volume is 10 to the power of 180 units. And that's because cosmologists tend to...