Data–Matter Equivalence

Data–Matter Equivalence is the count of bits one atom of matter is worth at the temperature of its universe: a particle's rest energy divided by the Landauer cost of a bit, N⚛ = m_H · 𝒞→² / (k_B · T · ln 2). Every bit set against a thermal bath costs k_B · T · ln 2 to erase (Landauer, 1961), and the book prices data energy this way (Chapter 1, k_B·ln(2^N)); a particle's rest energy m·𝒞→² divided by that cost is the number of bits its energy can hold. Today, with the cosmic background at 2.725 K, one hydrogen atom is worth about 5.7 × 10¹² bits; when the first atoms formed, at about 3,000 K, about 5 × 10⁹; in the core of the Sun, at 1.5 × 10⁷ K, about 10⁶. A particle is not a small thing in this reading but an enormous coherent swarm of data. Because the radiation cools as the universe expands, T ∝ 1/a, each particle is worth more data as the universe grows, N⚛ ∝ a, which is the Dilation Toward the Final Well (Part 3.10) seen from inside a universe. The same price, set once at the Physical Nova, gives Data Matter its mass (Part 3.13). The book writes N⚛ = m_H · 𝒞→² / (k_B · T · ln(2)), where N⚛ is the number of bits whose energy equals one hydrogen atom's rest energy [∅], m_H the hydrogen mass [𝕄], 𝒞→ light speed, one Pulse Length a Tempo [𝕃·𝕋⁻¹], k_B the Boltzmann constant [𝕄·𝕃²·𝕋⁻²·Θ⁻¹] and T the temperature of the universe's radiation, the bath every bit is set against [Θ]: [𝕄·𝕃²·𝕋⁻²] ÷ [𝕄·𝕃²·𝕋⁻²] = [∅]. It connects to Information-Energy Equivalence, Data Energy Mass Equivalence, BPT Mass-Energy Equivalence, Data Matter and Data Pressure.