The quantum world provides fertile material for thought experiments that seem so strange-but-true as to defy logic. One of the most notorious is “Wigner’s friend”, which has challenged physicists and philosophers ever since it was first conceived by the Hungarian-American physicist Eugene Wigner. He published the thought experiment in a 1961 book edited by the mathematician Irving Good entitled The Scientist Speculates: an Anthology of Partly-baked Ideas.

Wigner’s thought experiment is a more humane version of Schrödinger’s less complex but more famous thought experiment a quarter century before, which involved a cat inside a box whose fate hangs on a quantum event. Inside the box Schrödinger’s cat is dead or alive, whereas for someone outside, the cat remains dead-and-alive; it’s in a “superposition”. The bizarre situation only vanishes when the box lid opens.

The set-up of Wigner’s thought experiment is disarmingly simple. Wigner and his friend are interested in the outcome of a particular experiment, let’s say preparing a quantum bit (qubit) whose measurement outcome will be either 0 or 1. The friend goes into a lab and sets up the equipment, while Wigner remains outside. Each is fully versed in the quantum formalism.

Counterintuitively, their predictions differ. Wigner’s friend – the experimentalist – prepares the qubit with a superposition of states, and predicts the final state to be 0 with 50% probability, or 1 with 50% probability. Wigner, on the other hand, is isolated from his friend. Using a single quantum state in superposition to describe his friend plus the lab contents, Wigner predicts that the system will remain in superposition with 100% probability.

Wigner maintains this prediction even if he believes that his friend has finished the experiment. According to quantum mechanics, Wigner cannot separate the friend out from the rest of the lab contents. Wigner must therefore ask his friend in order to gain information about the friend’s quantum state. So who’s got the right answer: Wigner or his friend?

Both are right

The answer is that both probabilities are correct – from the standpoint of each individual. Their two correct uses of the mathematics give different predictions: Wigner predicts that the state is 100% in superposition, while the friend predicts that the measurement outcome of the qubit is either 1 or 0. Essentially, Wigner’s thought experiment says that what’s true depends on where you stand.

But if we assume that the probabilities describe the same “set of facts” – and that there’s something that’s true from everyone’s point of view – then these predictions are in conflict. Wigner himself, and many who followed, thought it paradoxical that the quantum formalism gives two differing predictions for the same state of affairs. They believed that objectivity requires that observers must characterize the facts in the same way regardless of their position.

What makes this scenario seem paradoxical, however, is its reliance on hidden classical assumptions. One assumption is that Wigner is right and his friend wrong (or vice-versa) because both are ultimately modelling the outcome of the friend’s qubit measurement. But suppose their differing predictions mean that the two are modelling different systems. Wigner is modelling the friend-qubit-lab environment, while his friend models just the qubit.

In a classical situation, Wigner and friend could have the same probabilities for predicting the outcome of a coin flip. Even if Wigner were, say, standing behind a curtain, he would not have to treat the friend flipping the coin as being in superposition. In the quantum situation, however, Wigner cannot single out and isolate the probabilities for just the coin. There may as well be no “coin” for Wigner – there’s not one thing among others in a room full of objects.

But back to Wigner’s thought experiment. What happens when the laboratory door opens and Wigner and friend can talk about their predictions? The two had disagreed but now it looks like they agree on the final state of the qubit. It seems that their previously inconsistent descriptions of a single state of affairs have converged into one.

That’s not what happens, though. Rather, Wigner’s new information does not repudiate his initial prediction. The quantum formalism indicates Wigner and friend had consistent descriptions for two different states of affairs. This feels paradoxical only if we give in to our intuition and assume that it was the same system for Wigner and friend all along.

The eagerly awaited moment when Wigner and his friend share their findings, then, is not the resolution to the paradox, but what happens after the paradoxical situation has already ended. Wigner had his correct formalism and the friend had theirs.

Wigner, and many of those who followed, were bothered by the fact that there could be two people using the same methods on the same experiment arriving at two correct descriptions depending on whether one was inside or outside the lab. Our classical intuition is that the system is the same for everyone. Quantum mechanics inclines us to think that we can have different systems without there being an inconsistency or be objective without needing to make all our descriptions identical.

The critical point

Quantum information theorists have turned Wigner’s friend into a powerful set of thought experiments for testing the plausibility of physical assumptions we make when we share information. These elaborated thought experiments involve multiple participants in multiple labs, entangled quantum states between friends and real-life entangled photon experiments to smoke out what our classical assumptions are.

Is there a fork in the road, classical or quantum? To stick with the classical interpretation that says Wigner’s friend involves two inconsistent descriptions of one state of affairs produces paradoxes. The quantum perspective implies there are descriptions of two different states of affairs. The first is intuitive but ends up in a contradiction, the other is less intuitive, but consistent. Quantum friendship means never having to say you’re sorry for your use of the formalism.

Robert P Crease is a professor (click link below for full bio), Jennifer Carter is a lecturer and Gino Elia is a PhD student, all in the Department of Philosophy, Stony Brook University, US.