Chaves and his colleagues Gabriela Lemos and Jacques Pienaar focused on Wheeler’s delayed choice experiment, fully expecting to fail at finding a model with a hidden process that both grants a photon intrinsic reality and also explains its behavior without having to invoke retro-causality. They thought they would prove that the delayed-choice experiment is “super counterintuitive, in the sense that there is no causal model that is able to explain it,” Chaves said.

But they were in for a surprise. The task proved relatively easy. They began by assuming that the photon, immediately after it has crossed the first beam splitter, has an intrinsic state denoted by a “hidden variable.” A hidden variable, in this context, is something that’s absent from standard quantum mechanics but that influences the photon’s behavior in some way. The experimenter then chooses to add or remove the second beam splitter. Causal modeling, which prohibits backward time travel, ensures that the experimenter’s choice cannot influence the past intrinsic state of the photon.

Gabriela Lemos, a physicist at the International Institute of Physics, showed how a “hidden variable” could be affecting the results of the experiment. Courtesy of Gabriela Barreto Lemos

Given the hidden variable, which implies realism, the team then showed that it’s possible to write down rules that use the variable’s value and the presence or absence of the second beam splitter to guide the photon to D1 or D2 in a manner that mimics the predictions of quantum mechanics. Here was a classical, causal, realistic explanation. They had found a new loophole.

This surprised some physicists, said Tim Byrnes, a theoretical quantum physicist at New York University, Shanghai. “What people didn’t really appreciate is that this kind of experiment is susceptible to a classical version that perfectly mimics the experimental results,” Byrnes said. “You could construct a hidden variable theory that didn’t involve quantum mechanics.”

“This was the step zero,” Chaves said. The next step was to figure out how to modify Wheeler’s experiment in such a way that it could distinguish between this classical hidden variable theory and quantum mechanics.

In their modified thought experiment, the full Mach-Zehnder interferometer is intact; the second beam splitter is always present. Instead, two “phase shifts”—one near the beginning of the experiment, one toward the end—serve the role of experimental dials that the researcher can adjust at will.

The net effect of the two phase shifts is to change the relative lengths of the paths. This changes the interference pattern, and with it, the presumed “wavelike” or “particle-like” behavior of the photon. For example, the value of the first phase shift could be such that the photon acts like a particle inside the interferometer, but the second phase shift could force it to act like a wave. The researchers require that the second phase shift is set after the first.

With this setup in place, Chaves’s team came up with a way to distinguish between a classical causal model and quantum mechanics. Say the first phase shift can take one of three values, and the second one of two values. That makes six possible experimental settings in total. They calculated what they expected to see for each of these six settings. Here, the predictions of a classical hidden variable model and standard quantum mechanics differ. They then constructed a formula. The formula takes as its input probabilities calculated from the number of times that photons land on particular detectors (based on the setting of the two phase shifts). If the formula equals zero, the classical causal model can explain the statistics. But if the equation spits out a number greater than zero, then, subject to some constraints on the hidden variable, there’s no classical explanation for the experiment’s outcome.