{
  "id": "oai:papers.qnfo.org:non-anthropocentric-natural-units-for-area-and-information-in-holographic-entrop",
  "slug": "non-anthropocentric-natural-units-for-area-and-information-in-holographic-entrop",
  "title": "Non-Anthropocentric Natural Units for Area and Information in Holographic Entropy Bounds",
  "authors": [
    "Rowan Brad Quni-Gudzinas"
  ],
  "abstract": "The holographic entropy bound is conventionally stated in bits, a unit that embeds two human conventions: integer counting of states and the choice of logarithm base 2. This paper asks whether the bound can be restated entirely in observer-independent quantities, and it situates the question in the current holographic literature. Working in Planck natural units (c=ℏ=G=k_B=1), area is a dimensionless number A in Planck areas and physical entropy is the natural-logarithm entropy S=A/4 (nats). We derive the base-free bound D≤ e^A/4 on the Hilbert-space dimension D, show that the bit appears only as the derived quantity b=S/ln 2, and prove that all base-b representations differ by fixed multiplicative constants, so they are empirically equivalent. A worked example with A=10⁶8 gives S=2.5×10⁶7 nats, b=3.6067376×10⁶7 bits, and D≤ 10¹.0857362×10⁶7. The only residual conventional element is the integer rounding of D: at A=4 (four Planck areas, S=1 nat) the relative deficit is 26.4\\%, while at A=10⁶8 it falls below 10^-10⁶7. The result is foundational: it separates the invariant content of holographic bounds (A, S, D) from methodological conventions, and it changes how capacity specifications for quantum-gravity experiments can be written.",
  "abstract_markdown": "The holographic entropy bound is conventionally stated in bits, a unit that embeds two human conventions: integer counting of states and the choice of logarithm base 2. This paper asks whether the bound can be restated entirely in observer-independent quantities, and it situates the question in the current holographic literature. Working in Planck natural units ($c=\\hbar=G=k_{B}=1$), area is a dimensionless number $A$ in Planck areas and physical entropy is the natural-logarithm entropy $S=A/4$ (nats). We derive the base-free bound $D\\le e^{A/4}$ on the Hilbert-space dimension $D$, show that the bit appears only as the derived quantity $b=S/\\ln 2$, and prove that all base-$b$ representations differ by fixed multiplicative constants, so they are empirically equivalent. A worked example with $A=10^{68}$ gives $S=2.5\\times10^{67}$ nats, $b=3.6067376\\times10^{67}$ bits, and $D\\le 10^{1.0857362\\times10^{67}}$. The only residual conventional element is the integer rounding of $D$: at $A=4$ (four Planck areas, $S=1$ nat) the relative deficit is $26.4\\%$, while at $A=10^{68}$ it falls below $10^{-10^{67}}$. The result is foundational: it separates the invariant content of holographic bounds ($A$, $S$, $D$) from methodological conventions, and it changes how capacity specifications for quantum-gravity experiments can be written.",
  "date": "2026-10-10",
  "first_published": "2026-10-10",
  "last_revised": "2026-10-27T04:21:12Z",
  "modified": "2026-10-27T04:21:12Z",
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  "url": "https://papers.qnfo.org/papers/non-anthropocentric-natural-units-for-area-and-information-in-holographic-entrop",
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        "name": "Rowan Brad Quni-Gudzinas",
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    "titles": [
      {
        "title": "Non-Anthropocentric Natural Units for Area and Information in Holographic Entropy Bounds"
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        "description": "The holographic entropy bound is conventionally stated in bits, a unit that embeds two human conventions: integer counting of states and the choice of logarithm base 2. This paper asks whether the bound can be restated entirely in observer-independent quantities, and it situates the question in the current holographic literature. Working in Planck natural units (c=ℏ=G=k_B=1), area is a dimensionless number A in Planck areas and physical entropy is the natural-logarithm entropy S=A/4 (nats). We derive the base-free bound D≤ e^A/4 on the Hilbert-space dimension D, show that the bit appears only as the derived quantity b=S/ln 2, and prove that all base-b representations differ by fixed multiplicative constants, so they are empirically equivalent. A worked example with A=10⁶8 gives S=2.5×10⁶7 nats, b=3.6067376×10⁶7 bits, and D≤ 10¹.0857362×10⁶7. The only residual conventional element is the integer rounding of D: at A=4 (four Planck areas, S=1 nat) the relative deficit is 26.4\\%, while at A=10⁶8 it falls below 10^-10⁶7. The result is foundational: it separates the invariant content of holographic bounds (A, S, D) from methodological conventions, and it changes how capacity specifications for quantum-gravity experiments can be written.",
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