Superposition without myths
Lesson 2 of 23 in the course “Quantum”. Free, with animations and a quiz.
The coin: a good start, but not the whole story
Superposition is often explained with a coin: while it spins in the air, it’s “both heads and tails”. As a first picture that’s fine. But a coin’s outcome is already decided: the throw and the air set its flight, we just don’t know the answer. A quantum particle has no answer at all before measurement. It has a set of amplitudes, more on them next. Sounds like wordplay, but you can test the difference with an experiment. Here’s how.
Amplitudes: chances with a sign
Every possible outcome has an amplitude. The chance of seeing that outcome is the amplitude squared. Example: amplitude 0.7, so the chance is 0.7 × 0.7 ≈ 0.5, which is 50%. The key difference from ordinary chances: an amplitude can be negative. Coin chances only add up: 25% and 25% will never make zero. But amplitudes of +0.5 and −0.5 cancel each other out to zero. This trick is called interference, and all the quantum magic rests on it.
Experiment: one half-silvered mirror
A half-silvered mirror lets half the light through and reflects the other half. Send photons at it strictly one at a time. Behind the mirror sit two detectors, A and B. A photon never splits in half: each time exactly one detector clicks, and you can’t predict which. After a thousand photons A and B have roughly equal counts, 50% each. So far it’s just like a fair coin. Remember this picture, because we’re about to break it.
A second mirror breaks the coin
Now bring both paths together on a second half-silvered mirror. Coin logic says: each mirror is 50/50 again, so A and B get 50% each. In the real experiment only A clicks, 100% of the time. B stays silent. Why: the two amplitudes reach B with opposite signs and cancel, while at A they add up. This was tested with single photons back in 1986 in France, in Alain Aspect’s group. A coin can’t do that.
You peeked: the magic is gone
Put a detector on one path that records whether the photon went that way. That’s it: 50/50 again, both A and B click. As soon as information about the photon’s path exists anywhere in the world, the amplitudes stop cancelling. Superposition survives only while the path is unknown to anyone and anything. That’s a key rule for qubits: any leak of information to the outside breaks the computation. That’s why they’re hidden from the world so carefully.
Electrons one at a time
1989, a Hitachi lab in Japan. Akira Tonomura fires electrons one at a time through a “double slit”. Each electron leaves one dot on the screen at a random spot. After a dozen dots the picture looks like chaos. After thousands, the dots build up stripes, as if waves from two slits were overlapping. But the electrons flew one by one. So each one interfered with itself. That video is still shown in lectures around the world.
Myth: “two clones at once”
You often read that a particle in superposition is in two places at once. It sounds cool but it’s misleading. Nobody has ever caught two copies: when measured, the particle is always in one place. More precisely: before measurement the particle has no definite place, and each possible place has its own amplitude. A quantum computer works with exactly these amplitudes: it arranges things so that wrong answers cancel each other out.
Check yourself
- What will the detectors show if you put a “spy” on one path?
Correct answer: About 50% at A and 50% at B. The detector creates information about the path. With it, the amplitudes no longer cancel, and the experiment turns into a fair coin. - Two amplitudes reach detector B: +0.5 and −0.5. What’s the chance B clicks?
Correct answer: 0%. First add the amplitudes: +0.5 + (−0.5) = 0. Then square: 0² = 0. Zero chance, B stays silent. - Which explanation of superposition is more accurate?
Correct answer: No place yet, each option has its own amplitude. Before measurement there’s no definite place. There are amplitudes that can add up or cancel. When you measure, you always get one place.