"Do not expand the theory. Sharpen the blade."

This repository presents a calibrated model for the breakdown of quantum unitarity at macroscopic scales. We derive a fundamental mass threshold where quantum coherence spontaneously decays due to interaction with the cosmological acceleration horizon.

The critical mass derives from 8-dimensional phase space geometry:

$$M_c = m_P \cdot \left(\frac{a_0}{a_P}\right)^{1/8}$$

Where:

• m_P ≈ 2.17 × 10⁻⁸ kg — Planck mass
• a_0 ≈ 6.8 × 10⁻¹⁰ m/s² — Cosmological acceleration (c · H₀)
• a_P ≈ 5.56 × 10⁵¹ m/s² — Planck acceleration

The relativistic phase space of a particle is 8-dimensional:

$$\dim(\mathcal{M}_8) = \dim(x^\mu) + \dim(p_\mu) = 4 + 4 = 8$$

Projection from 8D volume to 1D mass parameter yields the eighth root.

Derived from gravitational self-energy (Penrose-like):

$$\tau_c = \frac{\hbar \cdot R_c}{G \cdot M_c^2} \approx 2.18 \text{ s}$$

For masses above threshold:

$$\tau(M) = \tau_c \cdot \left(\frac{M_c}{M}\right)^\alpha \quad \text{for } M > M_c$$

Four-panel visualization: (a) Coherence time vs mass, (b) Decoherence rate, (c) Visibility decay, (d) Parameter space regions

Comparison with experimental scenarios and competing collapse models (CSL, Diósi-Penrose)

Decoherence rate predictions: M_c vs CSL, GRW, and Diósi-Penrose across mass range

• Mass: 10⁻¹⁵ kg (≈ 2× M_c)
• Predicted coherence time: 0.61 seconds
• Time to 50% visibility: ~63 milliseconds
• Verdict: Stable interference for t > 1s falsifies the theory

The theory is falsified if:

limits/
├── README.md                        # This file
├── index.html                       # Web article (full paper)
├── ESTRATEGIA_MC_RESEARCH.md        # Strategic research roadmap
│
├── massa_critica/                   # Original hypothesis
│   ├── README.md                    # Full derivation (English)
│   └── hipotese_colapso_quantico/   # Portuguese version
│
├── simulations/                     # Python framework
│   ├── constants.py                 # Physical constants & M_c
│   ├── calibration.py               # Model calibration
│   ├── collapse_dynamics.py         # Temporal models
│   ├── decoherence_models.py        # CSL, GRW, DP, M_c
│   └── experimental_predictions.py  # Concrete predictions
│
└── ajustefino/                      # Background materials

# Print calibrated constants
python -c "from simulations.constants import print_constants; print_constants()"

# Run full calibration analysis
cd simulations && python calibration.py

# Generate experimental predictions
cd simulations && python experimental_predictions.py

============================================================
PHYSICAL CONSTANTS FOR M_c RESEARCH
============================================================

--- CRITICAL MASS (CENTRAL PREDICTION) ---
M_c = m_P × Xi^(1/8)     = 5.2926e-16 kg
M_c in Daltons           = 3.1873e+11 Da

--- CALIBRATED MODEL PARAMETERS ---
τ_c (coherence @ M_c)    = 2.1763e+00 s (2.18 seconds)
α (power law exponent)   = 2.0

--- EXPERIMENTAL SCALES ---
Silica sphere radius @ M_c = 385.8 nm
============================================================

1. Verlinde, E. (2011). On the Origin of Gravity and the Laws of Newton. JHEP 1104:029.
2. Verlinde, E. (2017). Emergent Gravity and the Dark Universe. SciPost Phys. 2, 016.
3. Penrose, R. (1996). On Gravity's role in Quantum State Reduction. Gen. Relativ. Gravit. 28, 581.
4. Diósi, L. (1987). A universal master equation for the gravitational violation of quantum mechanics. Phys. Lett. A 120, 377.
5. Bassi, A. et al. (2013). Models of wave-function collapse. Rev. Mod. Phys. 85, 471.
6. Romero-Isart, O. (2011). Quantum Superposition of Massive Objects. Phys. Rev. A 84, 052121.
7. Kaltenbaek, R. et al. (2016). MAQRO: 2015 Update. EPJ Quantum Technology 3, 5.

Douglas H. M. Fulber
Federal University of Rio de Janeiro
January 2026

Component	Status
Theoretical derivation
Model calibration
Numerical simulations
Experimental predictions
Paper 0 (derivation)
Experimental collaboration

The number M_c ~ 10⁻¹⁶ kg bites reality.
Explore where this number makes predictions.