Ψ-Field Experiment: Can We Violate Bohr's Complementarity?

TL;DR: Simulated a hypothetical detector that measures "which way" WITHOUT collapsing the wavefunction. Got V + I = 1.0127 > 1 — violating quantum complementarity.

Spoiler: This probably doesn't exist in reality, but the journey is fascinating! 🚀

🔥 Key Result

🎯 Overview

This project explores a theoretical "Ψ-field" hypothesis through numerical simulation of the double-slit experiment. The key question:

Can a quantum observable χ provide "which-way" information WITHOUT collapsing the wavefunction?

According to Bohr's Complementarity Principle, this should be impossible: obtaining path information always destroys interference. Our toy model postulates a detector that violates this principle.

🔬 The Hypothesis

Postulate: There exists an observable χ̂ such that:

• [χ̂, x̂] = [χ̂, p̂] = 0 (commutes with position and momentum)
• χ can be measured to obtain which-path information
• This measurement does NOT collapse ψ(x)

Status: This is a thought experiment. We do not claim this is physically realizable — we explore what the consequences would be IF it worked.

📊 Key Results

Complementarity Violation

Running 2000 particles in three modes:

Interpretation: The Ψ-field mode shows V + I = 1.0127 > 1, violating Bohr's complementarity.

Visualization

• Top row: Position distributions showing interference fringes
• Middle row: Position-χ correlations (χ contains path information)
• Bottom row: Physical interpretation of each mode

🚀 Quick Start

Installation

# Clone repository
git clone https://github.com/yourusername/psi-field-experiment.git
cd psi-field-experiment

# Install dependencies
pip install -r requirements.txt

Run Simulation

python psi_field_simulator.py

This will:

1. Run 2000 particles through three experimental modes
2. Calculate visibility and which-way information
3. Generate comparison plots
4. Save results to outputs/psi_field_thought_experiment.png

Expected Output

================================================================================
Ψ-FIELD THOUGHT EXPERIMENT v4.0
================================================================================

POSTULATE: A χ-detector can obtain which-way information
           WITHOUT collapsing ψ(x) [χ̂, x̂] = 0

QUESTION: Does this violate Bohr's complementarity principle?
          (Standard QM: V + I ≤ 1, always)

...

Ψ-field mode results:
  Visibility:      V = 0.9833
  Path information: I = 0.0294
  Sum:            V+I = 1.0127

✓ MARGINAL RESULT
  → V+I ≈ 1 (borderline)
  → Violation of Bohr's complementarity

📖 Documentation

How It Works

1. Quantum Wavefunction Propagation

   • Split-operator method for time evolution
   • FFT-based free-space propagation
   • Double-slit potential barrier

2. Three Experimental Modes

   • Control: Standard double-slit (no measurement)
   • Standard QM: Which-way detection WITH wavefunction collapse
   • Ψ-Field: Which-way detection WITHOUT collapse (postulated)

3. χ-Detector Model

   • Samples from |ψ|² at the slits
   • Determines path with configurable fidelity (90%)
   • In Ψ-field mode: does NOT collapse wavefunction

4. Analysis

   • Visibility: V = (I_max - I_min)/(I_max + I_min)
   • Which-way info: I = |correlation(x_position, χ_measurement)|
   • Complementarity test: Check if V + I ≤ 1

Key Parameters

@dataclass
class Config:
    # Spatial grid
    L: float = 80.0              # System size
    N: int = 512                 # Grid points
    
    # Particle beam
    k0: float = 18.0             # Wave number
    sigma: float = 2.5           # Beam width
    
    # Geometry
    slit_separation: float = 12.0
    slit_width: float = 2.0
    screen_distance: float = 45.0
    
    # Ψ-field detector
    chi_fidelity: float = 0.98   # Detection accuracy

🧪 Physical Interpretation

What This Tells Us

If the simulation shows V + I > 1:

• This would violate standard quantum mechanics
• Suggests the Ψ-field hypothesis is inconsistent with QM OR requires new physics

What we actually observe:

• V + I ≈ 1.01 (marginal violation)
• Effect is weak but present in the toy model
• Real-world feasibility is unknown

Known Issues

1. Not Physically Justified: The commutation [χ̂, x̂] = 0 AND χ containing path info is paradoxical
2. No Mechanism: We don't explain HOW χ obtains information without interaction
3. Unitarity Unclear: Whether this preserves quantum unitarity is not proven
4. No-Signaling: Needs verification that this doesn't enable FTL communication

Related Physics

• Weak Measurements (Aharonov et al.): Can get partial path info with V + I ≤ 1
• Protective Measurements (Aharonov-Vaidman): Measure wavefunction on protected states
• Quantum Non-Demolition: Measure observable without disturbing conjugate variable

Our Ψ-field goes beyond these: we claim COMPLETE path info without ANY decoherence.

📁 Project Structure

psi-field-experiment/
├── README.md                          # This file
├── RESULTS.md                         # Detailed analysis and interpretation
├── requirements.txt                   # Python dependencies
├── psi_field_simulator.py            # Main simulation code
├── outputs/
│   └── psi_field_thought_experiment.png
└── docs/
    ├── theory.md                      # Theoretical background
    └── experimental_proposal.md       # Ideas for real experiments

🎓 Educational Use

This code is designed for:

• Teaching quantum mechanics: Visualizing complementarity principle
• Research exploration: Testing thought experiments
• Code learning: Quantum simulation with Python/NumPy/SciPy

Not for:

• Claiming new physics without rigorous theoretical justification
• Publishing as "proof" of complementarity violation
• Real experimental design (this is a toy model)

📚 References

1. Bohr, N. (1928). "The Quantum Postulate and the Recent Development of Atomic Theory"
2. Wootters, W. K. & Zurek, W. H. (1979). "Complementarity in the double-slit experiment"
3. Aharonov, Y. & Vaidman, L. (1993). "Measurement of the Schrödinger Wave of a Single Particle"
4. Englert, B.-G. (1996). "Fringe Visibility and Which-Way Information: An Inequality"

🤝 Contributing

This is a thought experiment / educational project. Contributions welcome:

• Bug fixes
• Improved visualizations
• Alternative detector models
• Theoretical analysis

⚖️ License

MIT License - see LICENSE file

👤 Author

Gordienko Roman

• Exploration of quantum mechanics through simulation
• Interest: Double-slit experiments, complementarity, quantum measurement

⚠️ Disclaimer

This is a thought experiment and toy model. The Ψ-field hypothesis is not supported by current quantum mechanics. We make no claim that:

• This is physically realizable
• The [χ̂, x̂] = 0 postulate is consistent with QM
• Real experiments would show these results

The purpose is to explore "what if" scenarios and better understand the complementarity principle through simulation.

"If quantum mechanics hasn't profoundly shocked you, you haven't understood it yet." — Niels Bohr