Awesome question! Let’s dive into how Feynman’s probability amplitude (his famous "arrow" framework) explains single-slit, double-slit, and Fresnel diffraction—since he only gave a quick nod to single-slit in his second QED lecture, we’ll fill in the gaps properly.

First, a quick recap of Feynman’s core rules for these "arrows":

• Every possible path a photon can take from the source to the detector gets its own arrow. The arrow’s length is fixed (represents the amplitude’s magnitude).
• The arrow’s direction depends on the path’s optical length: every time the path length increases by one wavelength λ, the arrow rotates a full 360° (2π radians).
• The final total arrow is the vector sum of all individual path arrows. The square of this total arrow’s length gives the probability the photon hits the detector (which corresponds to the light intensity we observe).

Feynman mentioned this briefly, but let’s unpack it fully:

• Imagine splitting the single slit into an infinite number of tiny "source points"—each point represents a possible intermediate step for the photon (source → slit point → detector).
• For any point P on the screen, the optical path from different slit points to P varies slightly. This means each corresponding arrow is rotated by a small angle relative to its neighbor.
• When you add all these arrows tip-to-tail, they form a circular arc (a good approximation when the slit width is much smaller than the distance to the screen).
  • At the central bright fringe: all arrows point in the same direction, so the total arrow is the full length of the arc (max intensity, highest probability).
  • At the first dark fringe: the total rotation across all arrows is 180° (π radians), so the arc closes into a half-circle— the total arrow’s length is zero (zero probability, no light).
• The mathematical result of this vector sum is the sinc function, which describes the intensity distribution:

  I(θ) = I₀ * [sin(πa sinθ/λ) / (πa sinθ/λ)]²
  

  where a is the slit width, θ is the diffraction angle, and λ is the photon’s wavelength.

This is the classic experiment, and Feynman’s arrow framework makes it far more intuitive than separating "interference" and "diffraction":

• First, treat each slit exactly like the single-slit case: sum all the arrows from that slit’s source points to get a single "big arrow" for the slit (this is the single-slit sinc amplitude we just derived).
• Now, we have two big arrows—one from each slit. The angle between these two arrows depends on the optical path difference between the two slits and point P: ΔL = d sinθ (where d is the slit spacing), so the phase difference is φ = 2πΔL/λ.
• Add these two big arrows vectorially: the total amplitude is the sum of the two slit amplitudes, adjusted for their phase difference.
• The resulting intensity is the product of the single-slit diffraction envelope and the double-slit interference pattern:

  I(θ) = I₀ * [sin(πa sinθ/λ) / (πa sinθ/λ)]² * [2cos(πd sinθ/λ)]²
  

• The key insight here: there’s no need to distinguish "diffraction" (single-slit effect) and "interference" (two-slit effect)—it’s all just vector sums of probability amplitudes from every possible path.

Feynman never covered this in his QED lectures, but the arrow framework works perfectly here too (unlike far-field Fraunhofer diffraction, Fresnel diffraction applies when the source or detector is close to the slit/obstacle):

• Instead of splitting the slit into tiny source points, we split the wavefront into Fresnel half-period zones. Each zone is a ring (or strip, for a slit) where the optical path difference from the zone to the detector is λ/2 relative to the adjacent zone.
• Each zone’s total arrow is roughly the same length, but adjacent zones have arrows pointing in opposite directions (since λ/2 path difference equals a 180° phase rotation).
• Adding these arrows tip-to-tail forms a tight spiral—each subsequent arrow is slightly shorter (since edge paths have lower amplitude) and rotated 180° relative to the last.
• For example, in Fresnel circular aperture diffraction:
  • If the aperture includes an odd number of zones, the total arrow is the sum of alternating directions, ending with a non-zero length (bright central spot).
  • If it includes an even number, the arrows almost cancel out (dark central spot).
• This is exactly how the famous Poisson spot forms: when a circular obstacle blocks the first N even zones, the remaining zones’ arrows sum to a non-zero total, creating a bright spot at the center of the shadow.

The beauty of Feynman’s arrow theory is that it unifies all these optical phenomena under one simple rule: every possible photon path contributes an amplitude arrow, and you just add them up. No need to rely on classical wave intuitions—this is the core of QED’s power.

内容的提问来源于stack exchange，提问作者Wrichik Basu