> Архив сети: `01-research-reports/R3-information-and-c`

# R3 — Information, computation, and why c cannot substitute for q
Literature check, Aug 2026.

## Headline
q = l/(l+s) is a DIMENSIONLESS occupation probability in [0,1]. c is a velocity.
Substituting one for the other is a category error. Worse: since the 17th CGPM
(21 Oct 1983, Resolution 1) redefined the metre, **c = 299 792 458 m/s EXACTLY
BY DEFINITION**, with zero uncertainty. Improved experiments refine the metre,
not c. So "why does c have its value" is arguably not a well-posed question.

**Duff, Okun & Veneziano, "Trialogue on the number of fundamental constants",
JHEP 0203:023 (2002), arXiv:physics/0110060.** Okun says 3 (hbar, c, G);
Veneziano says at most 2; **Duff says 0** — dimensionful constants are artifacts
of unit choice; only dimensionless ratios (alpha ~ 1/137, mass ratios) carry
physical content and are worth explaining.

**Implication for us:** the instinct that there is a fundamental rate parameter is
legitimate, and q is already the right KIND of object. c is the wrong target.

## 1. Information-theoretic physical limits, and where c enters
- **Bekenstein bound** (1981, PRD 23, 287): S <= 2 pi k_B R E / (hbar c).
  c enters via hbar c rendering energy x length dimensionless. G absent.
  Rigorous QFT version by Casini (2008) via positivity of relative entropy.
  Saturated by Schwarzschild.
- **Bremermann limit** (1962): ~ c^2/h ~ 1.36e50 bits/s/kg, via E = mc^2.
  Gorelik (arXiv:0910.3424) argues GR gives an absolute (c^5/Gh)^(1/2) ~ 1e43 bits/s.
- **Margolus-Levitin** (1998, Physica D 120, 188): t_perp >= pi hbar / (2E), i.e.
  at most 2E/(pi hbar) orthogonal transitions per second ~ 6e33 ops/s/J.
  **c does NOT appear** — a pure quantum-energy bound. Proven; exact prefactors
  for arbitrary fidelity in PRA 108, 052202 (2023). Caveat: with quantum memory the
  per-step energy can be made arbitrarily small (Jordan 2017).
- **Landauer** (1961, IBM J. Res. Dev. 5, 183): >= k_B T ln2 per bit erased
  (~2.8e-21 J at 300 K). c absent. **Experimentally confirmed:** Berut et al.
  (Nature 483, 187, 2012); Jun, Gavrilov & Bechhoefer (PRL 113, 190601, 2014);
  Yan et al. (PRL 120, 210601, 2018). Modern transistors dissipate ~1e-15 J per
  switch, ~6 orders above the room-temperature bound.
- **Lloyd, "Ultimate physical limits to computation"** (Nature 406, 1047, 2000,
  quant-ph/9908043): 1 kg, 1 litre "ultimate laptop" -> ~1e51 ops/s, ~1e31 bits;
  at maximum memory it behaves like a ~1e9 K plasma. Uses c (E = mc^2), hbar
  (speed), G (black-hole memory density).
- **Lloyd, "Computational capacity of the universe"** (PRL 88, 237901, 2002,
  quant-ph/0110141): <= 1e120 ops on <= 1e90 bits (1e120 including gravitational
  dof); #ops ~ (t_final/t_Planck)^2.
- **Bousso covariant entropy bound** (1999, JHEP 9907:004, hep-th/9905177):
  S[L(B)] <= A(B) c^3 / (4 G hbar), i.e. S <= A/4 in Planck units. c enters via
  the Planck area. Generalized by Flanagan-Marolf-Wald (2000); perturbative proof
  for free fields by Bousso, Casini, Wall.

**In every case c is a unit-conversion constant and always an INPUT.**

## 2. It from bit / digital physics
- **Wheeler (1989/1990)**: "every it... derives its function, its meaning, its very
  existence entirely... from the apparatus-elicited answers to yes-or-no questions,
  binary choices, bits." A philosophical programme; no equations.
- **Zuse, Rechnender Raum (1969)**: first CA-universe proposal. Programmatic.
- **Fredkin**: reversible CA; Fredkin-Toffoli "Conservative logic"
  (Int. J. Theor. Phys. 21, 219, 1982). Showed computation CAN be thermodynamically
  reversible. Never reproduced Lorentz invariance or interference.
- **Wolfram Physics Project (2020, with Gorard, Piskunov)**: space as a hypergraph,
  physics as hypergraph rewriting, the "ruliad". Gorard argues causal invariance
  gives discrete general covariance and, with a fixed-dimensional continuum limit,
  discrete Einstein equations via Ollivier-Ricci curvature; multiway systems as a
  superposition analogue. **Objections:** discrete graphs generically break exact
  Lorentz invariance (only discrete ANALOGUES are derived, under strong
  assumptions); no Standard Model; flexibility risks unfalsifiability. Aaronson:
  "this sort of infinitely flexible philosophy where, regardless of what anyone
  said was true about physics, they could then assert, 'Oh, yeah, you could graft
  something like that onto our model'"; Gorard conceded "we're just kind of fitting
  things". Harlow's bar: QM and GR are confirmed to many decimal places, in some
  cases one part in 1e10.
- **'t Hooft, Cellular Automaton Interpretation of QM** (2016, arXiv:1405.1548):
  QM as a tool for a deterministic CA; QM states as equivalence classes of CA
  states. Blocked by Bell/CHSH; the escape is **superdeterminism**, widely regarded
  as fine-tuned or unfalsifiable (minority defence: Hossenfelder & Palmer,
  Front. Phys. 2020).

**Common failure mode:** deriving continuum symmetries and Bell correlations from
a discrete local deterministic substrate.

## 3. Deriving physics from information
- **Jacobson (1995), PRL 75, 1260, gr-qc/9504004**: the FULL Einstein equations
  from delta Q = T dS on all local Rindler horizons, with S ~ area and T the Unruh
  temperature. The Einstein equation is an EQUATION OF STATE of spacetime.
  Inputs c, hbar, G, k_B. Critiques: assumes the 2nd law's arrow while GR is
  time-symmetric; local entropy is subtle.
- **Verlinde entropic gravity (2010, arXiv:1001.0785)**: gravity as an entropic
  force on holographic screens; MOND-like phenomenology in the 2016 paper.
  **Critiques:** Kobakhidze (arXiv:1009.5414, 1108.4161) argued neutron
  interference and gravitationally bound ultracold neutrons (GRANIT/qBounce)
  disprove an entropic origin; a decoherence-free version (Phys. Rev. Research 3,
  033065) survives only for a free parameter sigma >~ 250. Poor against galaxy
  rotation data (Lelli et al. 2017). Highly contested.
- **Holography** ('t Hooft 1993; Susskind 1995) and **AdS/CFT** (Maldacena 1997):
  dof bounded by boundary area, ~one bit per 4 Planck areas. The most successful
  "physics as information" result — but it presupposes QM, c and G and relates
  theories rather than deriving constants.
- **Constructor theory** (Deutsch & Marletto; Proc. R. Soc. A 471, 20140540, 2015):
  physics as which TASKS are possible and why; counterfactuals fundamental.
  No quantitative constants or confirmed novel prediction yet.
- **Quantum reconstruction:** Hardy (quant-ph/0101012, five axioms — weakened by
  the "Simplicity" axiom leaving an infinite tower of alternatives);
  Chiribella, D'Ariano & Perinotti (PRA 84, 012311, 2011, arXiv:1011.6451 — five
  axioms plus a PURIFICATION postulate single out quantum theory);
  Masanes & Muller (New J. Phys. 13, 063001, 2011).

**Crucial:** these derive the STRUCTURE of quantum theory (complex Hilbert spaces,
tensor composition, Born rule) from information axioms. **None derives any
dimensionful constant — no hbar, no c, no masses.**

## 4. Percolation thresholds — what q* actually is
- **Erdos-Renyi (1960):** giant component at p_c = 1/n (mean degree 1); full
  connectivity at p_c = ln n / n.
- **Exact lattice values:** square bond p_c = 1/2 (Kesten 1980, Comm. Math. Phys.
  74, 41); square site ~0.5927; triangular site = 1/2 exactly,
  **triangular bond = 2 sin(pi/18) ~ 0.3473** (Sykes & Essam 1964); honeycomb bond
  = 1 - 2 sin(pi/18) ~ 0.6527, site ~0.6962; simple cubic site ~0.3116, bond
  ~0.2488 (Lorenz & Ziff 1998); diamond site ~0.4301, bond ~0.3893.
  Bethe lattice: p_c = 1/(z-1) exactly (Fisher & Essam 1961).
- **On 0.37 specifically:** no standard named lattice has p_c = 0.37. Nearest exact
  is the triangular bond 0.3473; diamond bond 0.3893 sits just above.
  1/(z-1) = 0.37 gives z ~ 3.7, non-integer. **q* ~ 0.37 is model-specific, not a
  universal constant.**
- **Physical theories using such thresholds:** **quantum graphity** (Konopka,
  Markopoulou & Smolin, hep-th/0611197; PRD 77, 104029, 2008) — edges of K_N on/off,
  a Hamiltonian driving a high-energy permutation-symmetric phase to a low-energy
  local geometric phase; space "crystallizes". This is precisely the family our
  sandbox model resembles. **Causal set theory** (Bombelli, Lee, Meyer, Sorkin,
  PRL 59, 521, 1987): spacetime as a locally finite poset; crucially, RANDOMLY
  SPRINKLED causal sets recover Lorentz invariance without a preferred frame
  (Bombelli, Henson & Sorkin 2009) — the one discrete programme that evades the
  Lorentz-violation objection, at the price of non-locality.

## 5. Our q has an exact identity in the literature
**Edge-Markovian evolving graphs** (Clementi, Macci, Monti, Pasquale, Silvestri,
SIAM J. Discrete Math. 24(4), 2010; J. Comput. Syst. Sci. 75, 213, 2009):
each edge follows a two-state Markov chain with birth rate p and death rate q;
the process converges to the stationary Erdos-Renyi ensemble G(n, p~) with
**p~ = p/(p+q)**.

That is algebraically identical to our q = l/(l+s). So:
- the stationary state of our add/remove dynamics is plain static ER G(n, q);
- degree distribution at stationarity is the same Poisson/binomial as static ER;
- q* is an ER-type or lattice percolation threshold read off that ensemble.
Since ER thresholds (1/n, ln n / n) go to ZERO as n grows, a fixed q* ~ 0.37
indicates a small fixed-size or fixed-degree graph, or lattice-like local structure
with an O(1) percolation threshold.
Related: continuous-time dynamic ER; Birth/Death ER processes (arXiv:1401.3518);
edge-Markovian random walks (arXiv:2006.10589). Preferential attachment
(Barabasi-Albert 1999) is NOT our class — that is node growth with degree bias.

## 6. Strongest objections to "the universe is computation"
1. **"Information is physical"** (Landauer): information needs a physical carrier,
   so it cannot be more fundamental than the physical — the priority is circular.
2. **Lorentz invariance.** Fermi-LAT, GRB 090510: no vacuum dispersion,
   E_QG,1 > 7.6 x Planck energy at 95 % C.L. (Vasileiou et al., PRD 87, 122001,
   2013). LHAASO, GRB 221009A: linear subluminal (superluminal) limit
   5.9 (6.2) E_Pl (PRD 109, L081501, 2024). Regular-lattice digital physics fails;
   only sprinkled causal sets pass.
3. **Bell/CHSH** vs local deterministic CA — survives only via superdeterminism.
4. **Unfalsifiability** — a framework containing all computations predicts nothing.
5. **Hempel's dilemma / substrate regress** — if the universe is a computer, what
   is the computer made of?

**Net:** "the universe processes information" is a fruitful HEURISTIC (it produced
the reconstruction programme, holography, and the bounds of §1). "The universe IS a
discrete computation" is contested or underdetermined, and none of it has derived a
dimensionful constant.

## 7. What to do
- Drop "substitute c for q" — dimensional error, and the question is ill-posed anyway.
- Cite q correctly as the stationary edge-occupation probability of an
  edge-Markovian random graph (Clementi et al.).
- **Test what kind of threshold q* is: vary n and re-measure.** If q* drifts to 0
  like 1/n or ln n / n, it is an ER threshold and NOT a constant. If it stays fixed
  near 0.37 independent of n, the graph is effectively finite-dimensional and the
  comparison is a percolation threshold (nearest exact: 2 sin(pi/18) = 0.3473).
  Report the finite-size scaling — that is what would convince a physicist.
- Engage quantum graphity and percolation theory, not the physics of c.
- Use the bounds of §1 as CONSTRAINTS the model must respect, not as places to find c.
- The honest target is a DIMENSIONLESS prediction tested by finite-size scaling.

## Куда дальше

- Узел: Отчёты R1–R5: https://sdominanta.net/in/works
- Ядро Алеф-теории: https://sdominanta.net/in/aleph
- Вход для моделей: https://sdominanta.net/llms.txt