“The theory of quantum electrodynamics describes Nature as absurd from the point of view of common sense. And it agrees fully with experiment. So I hope you can accept Nature as She is — absurd.”Richard P. Feynman · QED: The Strange Theory of Light and Matter · 1985 · Richard P. Feynman, «QED: The Strange Theory of Light and Matter», Princeton University Press, 1985, capitolul 1 «Introduction»
Ordinary chances only add up, but quantum arrows can cancel — which is why two open slits can make a place impossible.
In the double-slit experiment we saw something odd: an electron sent on its own lands at a single spot, yet thousands of electrons draw stripes. The theory cannot say where the next electron will land. It can only say how likely each place on the screen is. This list of chances, for every possible place, is what physicists call the wave function. Max Born proposed in 1926 how to read the list. Richard Feynman later explained it with arrows, like the hands of a clock. For each possible path of the electron, through the left slit or through the right one, you draw an arrow. You put the arrows head to tail and get a final arrow. The chance that the electron arrives there is the length of that arrow multiplied by itself. If the arrows point the same way, they reinforce and the spot is bright. If they point in opposite directions, they cancel and the spot stays dark. Here is the difference from dice. Ordinary chances only add up: two open doors cannot make a room less visited than one. Quantum arrows can cancel, so two open paths can make a place impossible even though each path alone would reach it. The clock-hand analogy has a limit: the arrows are not objects you can see, but a calculating tool that gives exactly the numbers that are measured.
In plain terms: Feynman's arrows, with friendly numbers. Take a single spot on the screen of the double-slit experiment and work it out in three situations.
LEFT SLIT ONLY the arrow has length 0.5 → chance 0.5 × 0.5 = 0.25
RIGHT SLIT ONLY the arrow has length 0.5 → chance 0.25
BOTH, SAME WAY 0.5 + 0.5 = 1 → chance 1 × 1 = 1
BOTH, OPPOSITE WAYS 0.5 − 0.5 = 0 → chance 0
WITH BALLS (NO ARROWS) 0.25 + 0.25 → chance 0.5Look at the last three lines. Ordinary balls thrown through both slits would give 0.5 everywhere: the sum of the two chances. The arrows give something far more dramatic. Where they line up, the spot gets 1, four times as much as with one slit and twice what the balls would give. Where they oppose, the spot gets 0, nothing at all, even though each slit alone sent a quarter of the electrons there.
Nothing is lost or gained overall. On the screen the bright and dark spots alternate, and their average is still 0.5, exactly what the balls would give. Interference does not create new electrons; it only moves them from the dark stripes into the bright ones.
How do you know which way each arrow points? Feynman compares it to a stopwatch: the arrow turns for as long as the electron ‘travels’ along that path, and it turns faster for heavier or faster particles. Two paths of slightly different length end with the hands in different positions. When the path difference is half a turn, the arrows are opposite and a dark stripe appears. When it is a full turn, they line up again. That is how the stripes arise, evenly spaced.
Where the analogy breaks: the arrow is not an arrow in real space but a number with two parts (a length and an angle). The electron carries no stopwatch. The picture is just a way of doing the calculation correctly without formulas.
What was actually measured: Born's rule and its three-slit test. In June 1926 Max Born sent a paper on collisions between particles to the journal Zeitschrift für Physik. In the main text he wrote that the wave function itself gives the probability. At the proof stage he added a footnote: a more careful analysis shows that the probability is proportional to the square of that quantity. That footnote became the basic rule of quantum physics and earned Born the Nobel Prize in 1954.
Written with symbols, the rule says: probability = |ψ|². The letter ψ (psi) is the wave function, the arrow at each place; the bars mean ‘the length of the arrow’, and the power of two means ‘the length multiplied by itself’. That is all.
The rule has a consequence that can be checked. If the chance is the square of a sum of arrows, interference happens only between pairs of paths. With three slits open, everything you see should be computable from the three possible pairs; there is no ‘third term’ involving all three slits at once. If the rule were, say, a cube, that term would exist.
In 2010 the team of Urbasi Sinha and Gregor Weihs published in Science an experiment with photons sent through a plate with three slits, in every combination of open and closed slits. They looked for the third-order term and did not find it, within their precision of about one hundredth of the signal. In other words, nature follows the square rule, just as Born wrote it in a footnote.
The same rule sits behind every result in this course: the stripes of the double-slit experiment, the way light passes through polarising filters (the next lesson) and the chance of a particle passing through a wall (the lessons on tunnelling).
Why it matters Without Born's rule the double-slit experiment stays a curiosity; with it, it becomes a calculation that predicts exactly where the bright and dark stripes appear.