How much information is required to completely describe a given volume in spacetime?


closed as unclear what you're asking by John Rennie, M. Enns, Buzz, Jon Custer, Cosmas Zachos Jan 29 at 22:28

Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.

  • 2
    $\begingroup$ Depends on what's inside the volume. The limit is given by the Bekenstein bound. $\endgroup$ – psitae Jan 25 at 16:42

There exists a limit on the maximum amount of entropy (or information) that can be contained in a physical system with a given volume and total energy, which is termed as Bekenstein bound. Though the second law of thermodynamics proposes that the entropy of an isolated system grows to a maximum value, this limit fills that knowledge gap. One can view this as an extension of the second law, limiting the growth of entropy beyond a maximum.

If a system of total energy $E$, including rest masses, is enclosed in a sphere of radius $R$, then the entropy $S$ of the system is bounded by $$S \leq \lambda RE$$ where $λ > 0$ is a constant (the value $λ = 2π$ is often proposed).

Here is a rigorous derivation using the general mathematical framework concerning quantum information of infinite systems.

References: Comments on Berkenstein bound


Not the answer you're looking for? Browse other questions tagged or ask your own question.