There is always a “look of indignation” on students’ faces when they first learn about quantum superposition, says physicist Marcelo Gleiser. He has taught quantum mechanics, the theory governing the microcosmic world of atoms and particles, for decades, and his students’ consternation inevitably emerges right on cue: when he reaches the part about quantum objects apparently being in several places at once.

The trouble is that words like “apparently” crop up an awful lot around this topic. Indeed, in the century or so since the idea of superposition emerged, its true meaning has remained contested. The only thing physicists agree on is that it takes us to the heart of what it means for something to be “real”.

A good place to start is with the Schrödinger equation. Developed by Erwin Schrödinger in the 1920s, it is a foundation stone of quantum theory that tells us the probability of finding a particle in a given state when we measure it. The point is that quantum mechanics is concerned with predicting the outcome of a situation – it says nothing concrete about what a particle was doing before it was measured.

However, the Schrödinger equation works by describing all the possible places a particle could be before it is measured using a piece of maths known as the wave function. This gives us one mathematical definition of a superposition: it is a sum of different possible quantum states.

We certainly know particles can exist in a superposition. In the double-slit experiment, for example, a single photon, a particle of light, is fired towards a grating with two narrow gaps in front of a screen. If a detector is watching, the photon will “pick” one slit and hit a specific spot on the screen. But if there is no detector, an “interference pattern” will appear on the screen, suggesting the particle behaved like a wave and went through both slits at once, interacting with itself.

What we don’t know for sure is what “being in superposition” means. Broadly, there are two views. One says the wave function is a useful mathematical tool and no more. That is certainly where Gleiser, who is based at Dartmouth College, New Hampshire, comes down. “Nothing in the formalism of quantum mechanics tells us that the wave function needs to be part of physical reality,” he says. “The belief in mathematics as truth is becoming a bit like a cult.”

Gleiser supports an interpretation of quantum mechanics called quantum Bayesianism (or QBism), which says the theory doesn’t describe reality per se, but rather what we know about it. Ultimately, what changes when we measure a quantum state is our information about it, not reality itself.

But there is a camp that flatly refutes this view. Simon Saunders, a philosopher at the University of Oxford, believes the wave function is real. For him, a particle in a superposition is physically in more than one place simultaneously. “It is an extended object,” he says. “It is delocalised.” According to this perspective, we must accept that the world of particles doesn’t bear any resemblance to reality as we experience it. The electrons orbiting an atom, for instance, exist as a cloud of probability before we measure them.

Critics of this position often ask what happens to those other possibilities when a measurement snaps a particle into one place. Saunders is happy to embrace the radical answer that they all manifest themselves in their own branch of an infinite multiverse.

A resolution to this question isn’t going to come any time soon. In the meantime, researchers have gone far beyond placing single particles into superposition – it has been achieved for large molecules and even a 16-microgram crystal. If this tells us anything, it is that reality is far stranger than it seems.