3 ms·

You got a glib answer from another guy, but I like the question. It's kind of like you're saying: how much information can I store in a particle? And should the

by alecst 3y ago

You got a glib answer from another guy, but I like the question. It's kind of like you're saying: how much information can I store in a particle? And should there be a limit? (I'm assuming you're talking about in the classical case, since the article also also considers classical dynamics and the problems associated with it.) I'm actually gonna make a note to think about this later because this reminds me a lot of Charles Bennett's work on information and entropy, and I don't think it's a bad question at all. I'm considering the idea of representing the particle's position as x = .01010111001 and then idealizing a "machine" that lets it do work by erasing one bit of information. I have to work so I can't think about this right now but it's a cool thought. Edit: I did think about and you're right! You can extract infinite energy if you know a particle's position to perfect precision. Very interesting! Make the particle an ideal gas in a box at temperature T. At some instant in time, measure the position of the particle to N bits precision. Now place membranes around the particle to keep it to within the precision we measured it. We can kill one bit of precision by allowing the particle to isothermally expand the membranes into a volume with half the precision that we measure (so if we measure down to 1mm precision, we let it expand into 2mm.) The amount of work we can extract is: W = \int p dV = \int kT dV V = kT ln 2 So for N bits precision you can extract NkT ln2 units of energy. I'll leave it to someone else to comment on whether this makes a black hole or not but this is exactly in the spirit of the article!

alecst 3y ago
Alright: the kicker (and the reason why I don't think this will result in a black hole) is that in order to extract that energy from the particle, you have to continuously re-heat it and add more energy back each time you want kT \ln 2 units of work done. Remember that the work is done isothermally, so the particle's energy is actually constant throughout this process. What's really happening is that if we consider the positional information to be continuous, then the particle's positional entropy is basically infinite. We can reduce this entropy (locally, to the particle) with a measurement, and use that lowered entropy to extract as much isothermal work as we want. But its energy density is unaffected by the positional information.

by alecst 3y ago

alecst 3y ago

Alright: the kicker (and the reason why I don't think this will result in a black hole) is that in order to extract that energy from the particle, you have to continuously re-heat it and add more energy back each time you want kT \ln 2 units of work done. Remember that the work is done isothermally, so the particle's energy is actually constant throughout this process. What's really happening is that if we consider the positional information to be continuous, then the particle's positional entropy is basically infinite. We can reduce this entropy (locally, to the particle) with a measurement, and use that lowered entropy to extract as much isothermal work as we want. But its energy density is unaffected by the positional information.