If light is made of photons, where do Young's fringes come from?
We now have a puzzle. Young's fringes say light is a wave. The photoelectric effect and photon counters say light is made of particles. Which is it?
Try the experiment that settles it: send light through Young's two slits one photon at a time, so dim that there is never more than one photon in the apparatus, and record where each one lands on the screen.
Each photon lands at one single point. After thousands of photons, what does the screen show? The fringes appear, built dot by dot. Each photon arrives as a particle, at one point, but where it is likely to land follows the wave pattern: few dots where the waves cancel, many where they reinforce.
This experiment has been done many times. In 1909 Geoffrey Taylor already saw fringes with extremely faint light. In 1986 Philippe Grangier, Gérard Roger and Alain Aspect went further with true single photons: at a beam splitter each photon went one way only, never both, yet the same photons still produced interference in an interferometer. Each photon is detected whole, at one place. The wave tells us how likely each place is.
So light is neither just a wave nor just a particle. It travels like a wave, spreading through both slits and interfering, and it is detected like a particle, one whole photon at a time. Quantum physics describes both with one idea: a probability amplitude that behaves like a wave, whose square gives the chance of finding the photon there.
This is the heart of everything a quantum computer does. In module 5 you will take a single photon through an interferometer in the lab and see it interfere with itself. Before that, module 3 builds the mathematical tools to describe it, and module 4 explains the instruments you will use.
The chance that a photon lands at a point x is proportional to the brightness of the wave pattern there: P(x) ∝ cos^2(π d x / (λ L)).
Each photon's landing point is random; the pattern only emerges from many photons. With N photons, the counts in a region fluctuate by about √N around their average: with 100 photons the fringes are noisy, with 10,000 they are sharp.
In module 3 you will meet the complex numbers that describe the probability amplitude; its square gives the probability. This is the Born rule.
One photon at a time, the fringes still build up: light travels like a wave of probability and is detected as whole particles.