How big can something be and still be quantum?

Interference has been demonstrated with electrons, with neutrons, with atoms, with fullerenes, by 2019 with tailored molecules of up to two thousand atoms, and by 2026 with sodium clusters of more than seven thousand atoms and masses above 170,000 atomic units.

Each step needs slower particles, colder sources and better isolation from gas and radiation. The experiments get much harder as the mass grows, and no step has revealed a limit imposed by nature rather than by the apparatus.

Heavier things have been put in superposition over far smaller distances. In 2023 a vibration of a crystal, with an effective mass of sixteen micrograms or some 10¹⁷ atoms, was put in two states at once, spread over about two billionths of a nanometre. Which object holds the record depends on whether size means mass or the distance between the two possibilities.

Any object interacting with its surroundings, through stray gas, thermal radiation or light, leaks information about its position into the environment, and interference becomes unobservable almost immediately.

This is decoherence. It is quantitative, and it explains why the boundary looks like a boundary in ordinary conditions, though not, on its own, why a measurement has a single outcome.

Decoherence works inside ordinary quantum mechanics, which sets no upper limit on size. On that theory, a well enough isolated object of any mass should still interfere.

A class of models adds a physical process that destroys superpositions spontaneously, at a rate increasing with mass, so that a large object could not be in two places even in perfect isolation.

These models were invented to solve the measurement problem and they make predictions, which is what distinguishes them from interpretations. Experiments with massive objects, and searches for the faint heating and radiation such a process would cause, are steadily excluding their parameters.

So far the exclusions have gone against the models rather than for them, and the question is open.

One proposal, from Lajos Diósi and Roger Penrose, is that gravity itself is responsible. A mass in two places curves spacetime in two different ways, and Penrose argues that quantum theory and general relativity cannot both be satisfied by such a superposition, so it decays, faster for larger masses.

The simplest version, with no adjustable parameter, has already failed a test that needed no interference: the collapse should make matter emit faint radiation, and a germanium detector under the Gran Sasso mountain in Italy saw too little of it. Versions with an adjustable scale survive. Testing them by interference would need, on one estimate, masses around a billion atomic units, thousands of times the current record.