Quantum mechanics has a concept called a "wave function." It's incredibly important because it holds all the measurable information about a particle (or group of particles) within it. In practice, the wave function describes a set of probabilities that change in time. When we make a measurement, we are really poking at the wave function, causing these probabilities to collapse and take on a definite value. The value that the wave function predicts is determined by the relative probabilities of all the possible measurement results.

But physically, the wave function is problematic. It is often possible to figure out the physical meaning of a symbol in an equation by looking at the physical units you would use to measure it. A quick examination of the wave function shows that the units of the wave function don't make a great deal of sense. To avoid a mental hernia, physicists tell each other that the wave function is a useful calculation tool, but only has physical relevance in terms of statistics, rather than having some concrete existence. In other words, it's not really "real."

Until now, we have taken comfort from the idea that, real or not, the results from the wave function would be the same. So no worries, right? Quite possibly wrong. In a paper posted on the arXiv, a trio of researchers has shown that you can't have it both ways; a purely statistical wave function will not always give the same results as a wave function with real physical significance.

Weird science

There's a long, long history of puzzled physicists showing that the wave function must be a bizarre object. Quantum entanglement is a direct result of the properties of the wave function, for instance, and entanglement envisions particles separated by a vast gulf of space being, apparently, in instantaneous contact with each other. According to the rules of quantum mechanics, if I measure the spin of one of a pair of entangled particles, then that measurement automatically and instantaneously sets the spin of the other... even if it's on the opposite side of the Universe.

Such findings were only theoretical in nature until the 1980s. Since then, we have confirmed that entanglement is possible and have attempted to measure the speed with which the wave function collapse travels between entangled particles. The answer is: it's fast. Much faster than the speed of light (or neutrinos). The conclusion seems to be that the bizarre consequences of the wave function are real.

But is the wave function itself "real" in any traditional sense?

The only way to figure this out is to create a situation where the wave-function-as-a-statistical-object produces a different experimental result than the wave-function-as-a-real-object. Until now, this has proved to be elusive. But, by considering the consequences of joint measurements on independently prepared objects, the researchers have shown that it's possible for the statistical and real versions of the wave function to produce different results.

Don't try this at home



Imagine you build a system that is designed to prepare a photon in a particular state, called "good." Every now and again, however, it gets it wrong and uses a slightly different method, preparing a photon in a different, but related state, called "bad." For any particular photon, we cannot tell which method was used, because any measurement we might make is compatible with both preparation methods. But there's always a chance that the system has prepared a bad photon.

Now, we extend our experiment to two machines that are replicas of each other. These each prepare single photons and send them to detectors for joint detection.

With two photons, there are four possible measurement results (good-good, good-bad, bad-good, and bad-bad). Our measurements work by determining which state the pair isn't in (some combination of not good-good, not good-bad, not bad-good, and not bad-bad). If the wave function is a real object, then one of those possibilities always has a zero probability, because the wave function is either representing the good state or the bad state, but not both. If, however, the wave function is statistical in nature, then both good and bad states are described equally well, and there is always a chance that the bad-bad detector will click even though one of the photon-preparing machines sent it a good photon.

I think of this as a sort of meta-superposition argument. Quantum mechanics may allow the wave function to represent a superposition of different states, with measurement results determined by probabilities. The statistical interpretation of the wave function implies that there can be a superposition of superposition states, which changes the relative probabilities of the measurement outcomes. In this case, the superposition was not unique. If the wave function is a real object, however, then the superposition itself has to be a unique object.

What does all this mean? It means that someone is going to have to do a very elegant and difficult experiment to test this. Any real experiment has noise, so clicks that shouldn't have happened due to noise have to be distinguished from clicks that shouldn't have happened (but did) because the wave function is statistical in nature.

As for the implications, well, certainly this means a lot to those working at the most fundamental level of quantum mechanics. Like earlier work, this may well work its way up the food chain to applications, just as entanglement has. For those of us working at a more "shut up and calculate" level, though, this will not change our results or our interpretation of those results.

arXiV preprint, 2011, 1111.3328v1