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

Mode	Visibility (V)	Path Info (I)	V + I	Verdict
Control	0.9817	0.0000	0.9817	✓ Baseline
Standard QM	0.9688	0.0115	0.9802	✓ V+I ≤ 1
Ψ-Field	0.9833	0.0294	1.0127	⚠️ V+I > 1

🎯 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:

Mode	Visibility (V)	Path Info (I)	V + I	Status
Control (no measurement)	0.9817	0.0000	0.9817	Baseline
Standard QM (with collapse)	0.9688	0.0115	0.9802	V+I ≤ 1 ✓
Ψ-Field (no collapse)	0.9833	0.0294	1.0127	V+I > 1 ⚠️

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.

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