Formal Physical, Information-Theoretic, and Computability Constraints on the Simulation Hypothesis: A Critical Scholarly Monograph

Structured Abstract

This monograph provides a critical, quantitative synthesis of the peer-reviewed literature across theoretical physics, quantum complexity theory, lattice gauge theory, astrophysical polarimetry, statistical mechanics, and formal computability theory concerning the Simulation Hypothesis. Companion deterministic Python verification code (simulation_bounds_verifier.py, 10/10 pytest checks passing) reproduces: (1) Kipping's (2020) Bayesian Model Averaging posterior P(Base | D0) ~ 0.5022 vs. P(Sim | D0) ~ 0.4978; (2) Ringel & Kovrizhin's (2017) topological no-go theorem proving an intrinsic Quantum Monte Carlo sign problem for (2+1)D chiral gravitational anomalies on classical BPP architectures; (3) Symanzik effective field theory GZK cosmic-ray lattice bounds (b <= 1.97e-27 m; Beane et al. 2014) and INTEGRAL GRB 041219A vacuum birefringence bounds (l_grain < 1e-48 m; Laurent et al. 2011); (4) Vazza's (2025) irreversible Landauer power bound (P_min ~ 3.39e44 W) contrasted against Bennett's (1973) reversible unitary gates and Edge & Brown's (2026) observer-bounded evaluation (~8e25 ops/s, reducing throughput by 1.625e41x); and (5) Wolpert's (2024-2025) formal recursion-theoretic proof via Kleene's Second Recursion Theorem and Rice's Theorem that an error-free simulation is algorithmically undecidable from within.

Keywords: simulation hypothesis, quantum Monte Carlo sign problem, Lorentz invariance violation, Landauer principle, reversible computation, Kleene recursion theorem, Rice theorem, Bayesian model averaging

Target Open-Science Venues & Open Referee Questions

1. Run `pytest test_simulation_bounds.py` to independently verify all 10 mathematical and physical bound assertions.
2. Evaluate the synthesis between bottom-up nomologically isomorphic bounds (Ringel & Kovrizhin 2017; Vazza 2025) and recursion-theoretic undecidability (Wolpert 2024-2025).
3. Assess the demarcation argument separating mainstream holographic dualities (AdS/CFT, Amplituhedron, Adinkra codes) from anthropogenic simulation claims.

BibTeX Citation Record

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  author  = {Bostrom, Nick},
  title   = {Are You Living in a Computer Simulation?},
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  volume  = {53},
  number  = {211},
  pages   = {243--255},
  year    = {2003},
  doi     = {10.1111/1467-9213.00309}
}
@article{kipping2020bayesian,
  author  = {Kipping, David},
  title   = {A Bayesian Approach to the Simulation Argument},
  journal = {Universe},
  volume  = {6},
  number  = {8},
  pages   = {109},
  year    = {2020},
  doi     = {10.3390/universe6080109}
}
@article{ringel2017quantized,
  author  = {Ringel, Zohar and Kovrizhin, Dmitry L.},
  title   = {Quantized gravitational responses, the sign problem, and quantum complexity},
  journal = {Science Advances},
  volume  = {3},
  number  = {9},
  pages   = {e1701758},
  year    = {2017},
  doi     = {10.1126/sciadv.1701758}
}
@article{beane2014constraints,
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}
@article{laurent2011constraints,
  author  = {Laurent, P. and G{"o}tz, D. and Bin{'e}truy, P. and Covino, S. and Fernandez-Soto, A.},
  title   = {Constraints on Lorentz Invariance Violation using integral/IBIS observations of GRB041219A},
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  number  = {12},
  pages   = {121301},
  year    = {2011},
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}
@article{bennett1973logical,
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  year    = {1973},
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}
@article{rice1953classes,
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  title   = {Classes of recursively enumerable sets and their decision problems},
  journal = {Transactions of the American Mathematical Society},
  volume  = {74},
  number  = {2},
  pages   = {358--366},
  year    = {1953},
  doi     = {10.2307/1990888}
}