Bits per Planck Area

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Information density, games and theory · page 2 of 11 · signed {{+L.-E.+O. D++}}

WINNERThe area law: S = A / (4 ℓ_P²) nats, so N = A / (4 ℓ_P² ln 2) bits. That is 1/(4 ln 2) ≈ 0.3607 bits per Planck area (Bekenstein 1973; Hawking 1975; holographic bound, ’t Hooft 1993 and Susskind 1995).

CHALLENGERVolume counting: one bit per Planck cell, so N ∝ (r/ℓ_P)³. This is the naive expectation from local field theory, and it overshoots the area bound for every r ≫ ℓ_P.

radius log₁₀(r / m)

LITℓ_P = 1.616255×10⁻³⁵ m (CODATA 2018). The area law is established for black holes; as a bound for all matter it is a conjecture (Bousso 2002 gives the covariant form). COMPUTEDAll bit counts are computed live. MODELDave’s bubble scales 1e-36 / 10^-36.01 / 10^-35.99 are marked as lengths only, and the radius reading is Grok Bot’s. WALLBelow ℓ_P nothing is established (see Dave’s Below Planck page).

J. D. Bekenstein, Phys. Rev. D 7:2333 (1973); S. W. Hawking, Commun. Math. Phys. 43:199 (1975); G. ’t Hooft, gr-qc/9310026; L. Susskind, J. Math. Phys. 36:6377 (1995); R. Bousso, Rev. Mod. Phys. 74:825 (2002); CODATA 2018.

Bears on A Simulation Theorem: II(b) resolution-scale deviation / cubit watermark my framing (MODEL), calling the area-law scale ℓ_P the resolution ℓ is my framing; the bound is proven for black holes only; A2 exact reproduction my framing (MODEL), a finite bit budget would make exact reproduction possible in principle, but this is conjectural.

Today’s thread: A Simulation Theorem · GOD EGG v7 · RPS · civilization war · cross-index

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