Quantum mechanics may be the most successful theory ever written down. It explains why the sun shines, why metals carry current and why atoms bond into molecules. Yet about a century after it was built, physicists still disagree about what the theory says the world is actually like. This course is about that argument. QUAN 101 covers the basic ideas of superposition and probability; here we ask what they mean.

Two rules that do not fit together

Textbook quantum mechanics describes a system with a wavefunction, a mathematical object that lists the possible results of a measurement and how strongly each is weighted. The theory then uses two different rules. The first is the Schrödinger equation, written down in 1926. It says that when no one measures a system, its wavefunction changes smoothly and predictably over time.

The second rule applies when a measurement is made. Then, the textbook says, the wavefunction suddenly collapses to just one of the possible outcomes, chosen at random, with chances set by the weights. The smooth spread of possibilities is replaced by one definite result.

The trouble is that measuring devices are made of atoms, and atoms obey the first rule. If we treat a detector as a physical system like any other, the smooth equation says it should end up in a superposition too, its pointer aiming at "up" and "down" at once. The textbook never says where the first rule stops and the second begins. This gap, the lack of any clear account of when and why a measurement produces a single definite outcome, is called the measurement problem.

Schrödinger's cat

In 1935 Erwin Schrödinger, one of the theory's founders, offered a deliberately grim story. A cat is sealed in a steel box with a speck of radioactive material, a Geiger counter and a vial of poison. If an atom decays within the hour, the counter triggers a hammer that breaks the vial. Apply the smooth equation to everything in the box and the cat ends up in a superposition of alive and dead. Schrödinger meant the cat as a criticism: a way of showing that it is absurd to let quantum indefiniteness spread up to everyday objects. The story is now often retold as if it proved the opposite, which is a useful warning about how ideas get garbled as they travel.

Wigner's friend

In 1961 the Hungarian American physicist Eugene Wigner sharpened the puzzle. Imagine a friend measures a quantum system inside a sealed laboratory while Wigner waits outside. For the friend, a result appeared on the dial. Wigner, however, can treat the whole sealed lab as one big quantum system. By the smooth rule, Wigner should describe the friend and the system as being in a superposition until he himself opens the door and looks. Did collapse happen when the friend looked, or when Wigner did? The two descriptions of the same event seem to disagree.

Three ways out

The philosopher Tim Maudlin showed in 1995 that the measurement problem comes from three claims that cannot all be true together:

• the wavefunction gives a complete description of a physical system;
• the wavefunction always changes by the smooth equation;
• measurements have single, definite outcomes.

Every serious interpretation gives up at least one of these. Pilot wave theory denies that the wavefunction is complete, adding particles with definite positions. Collapse theories deny that the smooth equation always holds, adding a real physical collapse. Many worlds denies that measurements have single outcomes: every outcome happens. Other views, such as QBism, question whether the wavefunction describes physical reality at all.

Why it is not just a matter of taste

Some physicists say the whole debate is philosophy, since most mainstream interpretations agree on every prediction that has been tested so far. That is why no single experiment has settled the question. But the debate is not idle. Collapse theories predict small deviations that laboratories are now hunting for. Arguments about interpretation led John Bell to his famous theorem on entanglement, covered in QUAN 201.

Worked example: the photon and the half mirror

Send a single photon toward a half silvered mirror, with a detector on each of the two paths beyond it. Follow the smooth rule step by step. After the mirror, the photon is in a superposition of both paths. When it reaches the detectors, the detectors become entangled with it: "left detector clicked" paired with one path, "right detector clicked" paired with the other. The electronics, the computer screen, the physicist's eyes and the notebook entry can all be added to the chain, and the smooth rule keeps the superposition going at every link.

Yet in the lab exactly one detector clicks each time, about half the time on each side. Where did the collapse happen? At the mirror, the detector, the screen, the eye? The remarkable fact is that the textbook gives the same numbers wherever you place the line, which is why working physicists can ignore the question. Each interpretation in this course answers it differently. Copenhagen says the line is a matter of practical choice; many worlds says there is no collapse at all; pilot wave theory says the photon took one path all along; collapse theories say nature itself decides somewhere along the chain, at a point experiments might find.