How a Photon "Knows" Where to Land in the Double-Slit Experiment

This is one of the most fascinating questions in quantum mechanics! The key to understanding how a photon "knows" where to land on the screen in the double-slit experiment lies in the wavefunction, probability distributions, and quantum mechanics principles—not in classical memory or communication between photons.

Key Explanations:

1. The Photon Doesn’t "Know"—It Follows a Probability Distribution

Each photon behaves independently, and it doesn’t "remember" where previous photons have landed. Instead, its landing position is dictated by the wavefunction of the system, which describes a probability distribution.

• The wavefunction (Ψ) describes all the possible paths the photon can take.
• When it reaches the screen, it doesn’t "choose" a random spot—it lands according to the probability distribution determined by constructive and destructive interference.

💡 Analogy: Imagine rain hitting a roof with grooves. Each raindrop lands independently, but over time, a pattern forms in the drainage system due to the underlying structure.

2. The Interference Pattern Emerges Over Time

Even though photons arrive one at a time, their probabilities follow the same interference pattern as if they were waves.

• If we fire a single photon, we don’t see an interference pattern.
• If we fire many photons without observing which slit they go through, an interference pattern gradually emerges.
• This suggests the photon follows wave-like probability rules rather than relying on past photons.

→ Quantum Rule: Each photon interferes with itself, as if it travels through both slits simultaneously in a superposition of paths.

3. Superposition and Wavefunction Collapse

• Before the photon reaches the screen, its wavefunction is spread out, meaning it exists in all possible paths simultaneously.
• When it is measured (e.g., detected on the screen), the wavefunction collapses to a single point.
• The next photon is completely independent, but its probability distribution is still governed by the same wave equation.

💡 Key Insight: The pattern emerges not because photons "remember" previous ones, but because all photons obey the same quantum rules.

4. The Role of the Observer and the Measurement Problem

• If we place a detector at the slits to measure "which slit" the photon goes through, the wavefunction collapses before reaching the screen, and the interference pattern disappears.
• This is because measuring the path destroys the superposition, forcing the photon to behave like a particle instead of a wave.
• When not measured, the photon behaves as if it goes through both slits at once, creating an interference pattern over time.

💡 Quantum Weirdness: The fact that "observation" changes the outcome suggests that wave-particle duality is deeply tied to how measurement affects quantum systems.

5. Quantum Field Theory Perspective: The Photon is an Excitation of a Field

• A photon is not a classical "billiard ball" moving through space.
• It is an excitation in the electromagnetic field.
• This field behaves like a wave, and the photon's landing spot is governed by this underlying field.

💡 Richard Feynman’s Sum Over Histories Approach:
– A photon takes all possible paths simultaneously.
– It interferes with itself.
– The final result is determined by probability amplitudes summing over all paths.

Summary: Why Does the Photon "Know" Where to Land?

• It doesn't "know"—it follows the wavefunction's probability rules.
• It behaves as a wave until it is measured, when it collapses into a particle-like spot.
• Each photon is independent, but they all obey the same quantum mechanics rules.
• The pattern emerges statistically over many photons due to wave interference.

→ Final Thought: The double-slit experiment isn't about photons communicating or remembering—it's about how nature follows quantum rules, where probability, not classical causality, determines the outcome.

🚀 Would you like to explore this with visual simulations or mathematical formulations?

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