**How many bits of information could you fit in the whole universe?**

Let's figure it out! For starters, let's say we mean the

*observable*universe. The universe may be infinite in size. But when we look back all the way to when the hot gas of the early universe first cooled down and became transparent, everything we see fits in a finite-sized ball centered at us. That ball has by now expanded to be much larger. This larger present-day ball is called the

**observable universe**.

Maybe it should be called the 'once-observed universe', since we can't see what distant galaxies are doing

*now*. But regardless of what it's called, this ball is about 9 × 10^26 meters in diameter.

*How much information could we fit in it?*

When you keep trying to stuff more information into some region, eventually you get a black hole. The information becomes inaccessible, so then it's

*unknown*information, also known as entropy. The amount of entropy is proportional to the surface area of the black hole. And this is just 4π times the black hole's radius squared.

(At least this is true if the black hole isn't rotating or charged... and it's sitting in otherwise flat space. Luckily, while the universe is expanding, space at any moment seems close to flat.)

So let's work out the

*surface area*of the observable universe, by taking 4π times its radius squared. We get 9.5 × 10^54 square meters.

How much information fits onto this area? It turns out that for a black hole, each nat of information takes an area of 4 times the Planck length squared. A

**nat**is a bit divided by the natural logarithm of 2. Computer scientists like base 2, but black holes seem to like base e.

4 times the Planck length squared is 10^-69 square meters. So, calculating a bit, we see the number of nats of information we can pack into the observable universe is roughly 10^124. I hope you check my work!

But I know you prefer bits, so let's divide by the natural logarithm of 2. We get:

**the most information we can fit into the observable universe is 1.4 × 10^124 bits.**

Of course, doing this would require turning the observable universe into a black hole! But if we did so, the black hole would have lots of quantum states. If the entropy of a system is N bits, its number of quantum states is 2^N. So, this black hole would have 2^(10^124) quantum states.

That's the biggest number I know that has any good physical meaning. It's big... but still tiny compared to plenty of numbers I can easily name, like Graham's number. And next I'll tell you about some some numbers that make

*Graham's number*look tiny.

By the way, don't take this picture very seriously! It's just cute. But it comes from a good page on black hole entropy:

http://www.scholarpedia.org/article/Bekenstein-Hawking_entropy

#bigness #astronomy

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- Well then, I'll bite: How much information
*is*observed to exist in the physical universe?Jan 28, 2013 - +Kazimierz Kurz - wrote: "But what I read about that, is different from what you are saying here. There is many people who wrote that "we know that!" or "it is strong indication that it is true"."

Yes. I'm more careful, or honest, or aware of the problems, than these other people.

One way people try to go from black hole thermodynamics to more general situations is to note that any small null hypersurface*could*, approximately, be part of an event horizon. For example, we could be falling through the event horizon of a huge black hole right now! There is no way to detect this*locally*. So, if we can attribute entropy to the event horizon of a black hole, 1/4 nat per Planck area, perhaps we can do this to any null hypersurface. The question then becomes: what does this entropy mean?

And this is why people start speculating about ideas like gravity being an 'entropic force'. As you may know, Erik Verlinde won a 2.5 million euro prize for his work on this idea:

http://en.wikipedia.org/wiki/Erik_Verlinde

http://en.wikipedia.org/wiki/Entropic_gravity

but other people think it's nonsense. As I said, everyone is desperately struggling to get ideas that work.Jan 28, 2013 - +Joe Marshall - this calculation will take some real work, unlike the ones I've been doing so far in these posts. And right now I need to prepare for class! But maybe I'll give it a try. Someone should already have done it, but if nobody has, it would be lots of fun to be the first!Jan 28, 2013
- Do people think Verlinde work is nonsense or is it just that doesn't tell us anything we didn't already know? To give an example, 2 of the authors I mentioned above had substantial work clearly and intentionally using that idea without expressly using that phrase. So his work added to the theme of these in making it clearer to others, it didn't come from great creativity or deep insight but is still nice and I thought was a good paper. I suppose the attention it got annoyed some as it was significantly greater than the paper's contribution to the field. But that is independent of the science, that's human.

Regarding this post, it is interesting your calculation is comparable to the earlier one's I mentioned, one of which used the critical density of the universe.Jan 28, 2013 - By "I thought is was a good paper", I mean I am glad it was written.Jan 28, 2013
- Some people think Verlinde's paper is nonsense, some think it was great... great enough to give him 2.5 million euros!... and some think it wasn't novel enough to deserve that. I haven't been paying much attention to this stuff, but Ted Jacobson's work seems a lot more profound, along with its many offshoots, like this: http://arxiv.org/abs/1205.5529.Jan 29, 2013

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