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We address the two foundational questions left open in Tang (2026): the origin and
quantization of time. Building on the disentanglement rate field Γ(x) and dimensionless
potential φ = Γ/Γ0, we establish six results. (i) Origin: physical time originates
as the counting measure on irreducible disentanglement events; coordinate time t is a
gauge label, and the apparent circularity is dissolved by this standard general-relativistic
distinction. (ii) The Cosmological Identity: Γ0 · NHub = c/ℓP at every cosmic epoch,
endowing the Planck time tP with a relational meaning as the inverse of (cosmic disentanglement
rate)×(causal depth), and showing that the 60-order hierarchy between
Planck and Hubble scales reflects the causal depth of the observable universe rather than
a fine-tuning. (iii) Quantization: time is integer-valued by construction; continuous
proper time dτ = φ dt is derived exactly as the Riemann limit of event counting and is
not an independent postulate; the Lindblad master equation of open quantum systems,
dρ/dt = −(i/ℏ)[ ˆH , ρ] + Γ(x)L(ρ), emerges from the same discrete map, with Γ(x) as
the exact coefficient of the dissipator. (iv) Zeno’s paradox: the infinite divisibility of
time assumed by Zeno’s dichotomy is false below the chronon τP = tP ; any finite journey
consists of a finite integer number of steps, providing a physical resolution of the
paradox rather than merely a mathematical one. (v) Shot noise: the gravitational noise
floor is operationally defined as the beat note between two co-located independent clocks,
δν/ν
beat
≈ 3.3×10−22 (1 s, φ = 1), requiring no external time reference. (vi) EP departure:
gravity and acceleration are physically distinct in the Γ-framework — the former
is sourced by matter, the latter is kinematic — with the equivalence principle holding
only as a first-order classical approximation; the distinction is observable in the quantum
vacuum structure and is consistent with the Pikovski et al. (2015) measurement. Three
open problems are precisely formulated: UV proof of ΔS = ln 2 irreducibility, tensor
generalisation Γ → Γμν, and derivation of ℓP from dimensionless quantities.
Full paper link
quantization of time. Building on the disentanglement rate field Γ(x) and dimensionless
potential φ = Γ/Γ0, we establish six results. (i) Origin: physical time originates
as the counting measure on irreducible disentanglement events; coordinate time t is a
gauge label, and the apparent circularity is dissolved by this standard general-relativistic
distinction. (ii) The Cosmological Identity: Γ0 · NHub = c/ℓP at every cosmic epoch,
endowing the Planck time tP with a relational meaning as the inverse of (cosmic disentanglement
rate)×(causal depth), and showing that the 60-order hierarchy between
Planck and Hubble scales reflects the causal depth of the observable universe rather than
a fine-tuning. (iii) Quantization: time is integer-valued by construction; continuous
proper time dτ = φ dt is derived exactly as the Riemann limit of event counting and is
not an independent postulate; the Lindblad master equation of open quantum systems,
dρ/dt = −(i/ℏ)[ ˆH , ρ] + Γ(x)L(ρ), emerges from the same discrete map, with Γ(x) as
the exact coefficient of the dissipator. (iv) Zeno’s paradox: the infinite divisibility of
time assumed by Zeno’s dichotomy is false below the chronon τP = tP ; any finite journey
consists of a finite integer number of steps, providing a physical resolution of the
paradox rather than merely a mathematical one. (v) Shot noise: the gravitational noise
floor is operationally defined as the beat note between two co-located independent clocks,
δν/ν
beat
≈ 3.3×10−22 (1 s, φ = 1), requiring no external time reference. (vi) EP departure:
gravity and acceleration are physically distinct in the Γ-framework — the former
is sourced by matter, the latter is kinematic — with the equivalence principle holding
only as a first-order classical approximation; the distinction is observable in the quantum
vacuum structure and is consistent with the Pikovski et al. (2015) measurement. Three
open problems are precisely formulated: UV proof of ΔS = ln 2 irreducibility, tensor
generalisation Γ → Γμν, and derivation of ℓP from dimensionless quantities.
Full paper link