Bekenstein derived the formula for the maximum energy content of a given volume of space by considering forming a black hole from particles each containing one bit of information.

Actually what is meant is that the black hole is formed by patches of space, each patch with bit of information determining the existence of a particle in that bit of space.

So why does it only have a bit of info per particle, since particles can have different properties. Also there is the positional or relational information between bits of space.

So this assumption makes no sense to me, and yet it conforms with hawking theorem for BH thermodynamics.

What information am I missing here :)

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    $\begingroup$ Can you clarify where you got the impression that the derivation attributes only one bit to each particle? (I'm looking at Bekensteins original paper, "Universal upper bound on the entropy-to-energy ratio for bounded systems", link to pdf, and his more recent review "How does the entropy/information bound work?", link to arXiv.) $\endgroup$ – Chiral Anomaly Sep 13 at 14:53
  • $\begingroup$ OK thank you, second paper seems more consicise, i haven't seen the actual physics behind this, only a conceptual description $\endgroup$ – Ezio Sep 13 at 15:35
  • $\begingroup$ So how much information does it need per particle $\endgroup$ – Ezio Sep 13 at 15:36
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    $\begingroup$ Bekenstein's reasoning is based on quantum fields. If I remember right, it works using a quantum version of counting the modes of a field in a box of a given size with a given amount of available energy. Quantifying the information per particle would be an auxiliary exercise that I don't recall seeing in Bekenstein's papers, because it wasn't needed. (Disclaimer: it's been a while since I really studied the derivation, and today I only skimmed the paper looking for the words "particle" and "bit", so my memory might be imperfect. Maybe someone with a fresher memory can write a real answer.) $\endgroup$ – Chiral Anomaly Sep 13 at 15:40

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