Coherence Paradigm – Double Slit Simulation

This repository explores the double slit experiment through the lens of a new Coherence Paradigm, where coherence is treated as the fundamental driver of physical phenomena.

Instead of framing the double slit as a paradox of "wave vs particle," we treat visibility of the interference fringes as a direct measure of system coherence.
This reframes the double slit not as a mystery, but as the acid test of coherence as a physical principle.

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🌌 Key Ideas

• Fringe contrast = coherence.
  Visibility of the interference pattern depends on the degree of coherence between the two paths.

• Unification of photons & electrons.
  The same coherence-based visibility law applies to both photons and electrons, with wavelength given by
  $$[ \lambda = \frac{h}{p} ]$$

• Environment as decoherence channel.
  Which-path probes, thermal noise, or finite source size reduce fringe contrast exactly as predicted by a coherence parameter $$( \gamma_{12} )$$.

• Paradigm shift.
  Matter is not sometimes “wave” and sometimes “particle” — instead, it always carries a coherence state, and visibility follows directly from that.

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📂 Repository Structure

├── sim/ │ ├── sim_double_slit.py # Core simulation functions │ ├── interactive_double_slit.ipynb # Jupyter notebook with sliders ├── results/ │ └── example_plots.png # Sample output plots ├── README.md # This file

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🚀 Quickstart

1. Clone the repo:

   git clone https://github.com/your-username/coherence-double-slit.git
   cd coherence-double-slit

2. Install requirements:

   pip install -r requirements.txt

3. Run a quick simulation:

   python sim/sim_double_slit.py

This will generate a sample double slit interference plot with given parameters.

📊 Interactive Notebook

To explore the experiment dynamically:

1. Launch Jupyter:

   jupyter lab

2. Open

   sim/interactive_double_slit.ipynb

3. Use sliders to vary

• Electron energy ((eV))
• Slit separation ((d))
• Slit width ((a))
• Coherence length ((L_c))

📖 Theory

The intensity at the screen is modeled as:

$$ I(\theta) \propto |A_1(\theta)|^2 + |A_2(\theta)|^2 + 2 , \text{Re} { \gamma_{12} A_1(\theta) A_2^*(\theta) } $$

where:

• $$(A_1, A_2)$$ are the amplitudes from slit 1 and slit 2.
• $$(\gamma_{12})$$ is the coherence factor $$((|\gamma| \le 1))$$.

Special cases:

• If $$(\gamma_{12} = 1)$$ → perfect coherence, full interference pattern.
• If $$(\gamma_{12} = 0)$$ → full decoherence, no fringes.

This is the core visibility law — independent of whether the experiment uses photons or electrons. 🔭 Future Directions

Extend to multi-slit (N-slit interference with coherence matrix formalism).

Add decoherence models (thermal coupling, weak measurements).

Compare to experimental datasets.

Explore implications for coherence as a fundamental physical force.

✨ License

MIT License — free to use, adapt, and extend.

📬 Contributions

Pull requests, issues, and discussions are welcome. This is an open-ended research project — feel free to build on it.