How much information per unit volume can the various states of matter hold?

This is a difficult question, but I’ll offer my limited insight anyway; perhaps you will find it useful.

One thing that people forget (no accusations made in your direction) is that on the microscopic scale, matter is incredibly chaotic. Even at extremely low temperatures, when electrons start to slow down and settle in lower energy levels, atoms can be expected to experience lattice vibrations, and maybe other phenomena that I’m not aware of.

What this means practically is that it’s terribly hard to actually encode information on an atomic level (bad news for you, homeopaths). When you think about hard drives, or similar media the actual data is encoded on a more macroscopic level, on groups of atoms. Funfact: new generations of Intel processors use 32nm gates – that’s several hundreds of thousands of atoms long.

Armed with that knowledge, we fall back onto less confusing concepts. Solid states of matter experience less chaotic motion than liquids, etc. Therefore, it would be easier to control data on a solid than a liquid. In fact, I’m tempted to assume it would be almost impossible to control a liquid enough to effectively store data on it; so yes, it would be easier to store data on a solid.

I’m not even going to bother thinking about plasma or Bose-Einstein condensate; I don’t know anything about them and assume they’re not very stable.

Note: Thermodynamics is kind of an umbrella term, so yes, it applies here, too.

Note 2: Actually, due to hydrogen bonding you can kind of assume that water has a kind of crystalline structure as well; it fact it can form several different arrangements.

Perhaps I didn’t tell you anything new; but at least you’ll find this reassuring?

Information, as I’m sure you are aware, is regarded by physicists as more fundamental than mass-energy. In this sense, the maximum amount of information in a given volume is dictated by the Bekenstein Bound. Considering the states of the matter, a quark-gluon plasma would have the most information because it is the most dense.

Information in the sense of usable data is a different matter though. Information storage depends on the stability of the system and the difficulty required to extract and write data to and from the storage medium. In the distant future, we may be able to encode data in different matter states, but for now (to my knowledge) we can only encode data in solid objects. Given the ultimate technology for read/write functions and data stability though (as well as unlimited power to maintain a high enough temperature), a quark-gluon plasma may be the future of data storage.

Note: My funfact is not completely correct. Amorphous silicon isn’t used in processors, so to determine the number of atoms in the transistor one would have to use a bit of a different formula, since crystalline silicon forms a structure similar to diamonds.

Thanks, @gggritso and @FireMadeFlesh.

Is it correct to simply say that information (in the fundamental physics sense, not necessarily computer data sense) is proportional to density?

What confuses me is this: I’ve heard it said that if matter falls into a neutron star, it becomes the same as the neutron star. So its information is presumably lost. But neutron stars (like black holes) are very dense. Is there some limit to density where, after a certain point, information gets harder to maintain?

@Qingu Ok, well, now I’m in way over my head; however the first statement would be correct based on what @FireMadeFlesh said.

I’m not sure about the second statement, but I suppose the fact that it is being transformed into a different state is what’s destroying the information?

@Qingu Yes, information is proportional to density. As far as I understand it, information is what describes the wave/particle nature of what we consider to be fundamental particles, so the more matter (including photons, gluons etc.) you compress into a certain volume, the more information that volume holds.
There has been a lot of debate about what happens to information when matter enters a black hole, and I assume similar issues apply to neutron stars. Some interpretations of quantum mechanics combine the conservation laws into the Law of Conservation of Information, so we know information cannot be lost. When matter enters a black hole, it may be organised, and when it exits as Hawking Radiation it is apparently disorganised. Some people say the information enters a parallel universe, some say copies are made on the edge of the universe, and others say it is spat out of a white hole. They all sound like fudge factors to me.
In the case of a neutron star, the gravitational field isn’t quite strong enough to form an event horizon, so I imagine information in the data sense would just require a huge amount of energy to maintain. I like to think that the information is transposed from information about one environment to information about the neutron star, but I’m not sure how correct that is.
I’m going to send this to our resident physics expert now, its getting too complex for me.

Ha! I was tempted to post a note here last night on something @FireMadeFlesh posted. You are all in deep trouble if I’m indeed the “resident expert”! ;) :p

Seth Lloyd published a paper a few years ago that’s relevant that got mentioned in a lot of places (Wired and Edge(dot)org which I followed more closely than I do now back in the day) finding the theoretical limits on the performance of the ‘ultimate laptop’. Here is a summary of it.

What I thought about mentioning last night is that @FireMadeFlesh ‘s claim that “information, as I’m sure you are aware, is regarded by physicists as more fundamental than mass-energy” is, I believe rather strongly worded (or even wrong?). I think it’s safe to say an influential set of theoretical physicists (it seems, including Lloyd) have embraced the idea (which was championed by John Wheeler with his inevitable catchy motto: “It From Bit”), but the mainstream can be surprisingly conservative when it comes to ideas like this. But for all this talk of strings and branes and what not, I’m not hearing so much about attempts to underpin them using just qubits (like this, or maybe this too).

@hiphiphopflipflapflop Thanks for the correction. From a little poking around, it seems the idea isn’t that popular after all. New Scientist seems to reference it a lot though, which is probably where I got the idea.

http://www.mth.kcl.ac.uk/~streater/lostcauses.html#XXV

The ultimate limit of information storage is a black hole. Something like one bit per Planck area on the event horizon. See: Bekenstein’s Bound.