One of the best-known examples of the counterintuitive behavior seen in the quantum world is the double-slit experiment. Take a piece of material that blocks light and cut two small slits in it; hit the slits with a flood of photons, and they'll interfere with each other as they exit the far side, creating a pattern of peaks and valleys corresponding to where the wavelengths of the photons interfered constructively and destructively. Do the same thing, but send the photons at the slits one at a time, and you still see the same pattern. In effect, the photon flows through both slits as a probability wave, and these probabilities interfere with each other.

Stranger still, the same behavior can be observed with particles. In many circumstances, an electron will behave as a simple, easy-to-quantify particle. But it will also act as a probability wave when confronted with a double slit.

It's a great example, but it also raises a question that's obvious only after you've heard it asked: what happens if there's more than two slits? Is there a limit to how many probabilities a single particle can adopt as it flows through the quantum realm? A paper that will be released by Science today provides a pretty clear answer: two, just as quantum mechanics have suspected. That deceptively simple answer, however, has major implications for our attempts to combine quantum mechanics and gravity into a unified theory of everything.

And, in fact, the new paper explains this rather nicely in the first few sentences of the abstract:

Quantum mechanics and gravitation are two pillars of modern physics. Despite their success in describing the physical world around us, they seem to be incompatible theories. There are suggestions that one of these theories must be generalized to achieve unification.

Apparently, one of the options for generalizing quantum mechanics would be to allow violations of Born's Rule, an axiom that dictates that quantum interference can only occur between pairs of probabilities. Higher order interference could potentially allow a reformulation of quantum mechanics that is compatible with, or even incorporates, gravitation. The authors helpfully point out that actually testing Born's Rule could be rather helpful for theoreticians, given that, if it proves to be an actual rule, then the theoreticians would have one less option to worry about when it comes to describing the Universe.

So, the authors built a triple-slit system, set up so that they could open and close each of the slits. One of the three ended up not opening fully, which actually created a small source of error in the experiments. The fact that the photodetectors at the far end didn't have perfect performance added another source. In the end, however, the authors calculated that the total errors in the system allowed it to be accurate down to one percent, a fairly rigorous test of Born's Rule.

To get their photons, they used two different light sources: a laser with the power turned down so that it only emitted one photon at a time, and a source of quantum light called heralded single photons. With everything in place, they started firing photons off one at a time, until 30 million of them had hit the detector.

By closing off different slits before starting a measurement, they were able to measure the interference probabilities of each of the potential combinations, and then compare them to the pattern seen when all three slits were open. As Born's Rule predicts, the three-slit interference pattern was a complex mixture of the pairwise interference of different slits, but no higher-order interference was present that involved all three slits.

Quantum mechanics remains secure, at least to the one percent error of the experimental setup. With better hardware or alternate experimental setups, the authors suggest, we could narrow that down even further.

That may be bad news for the theoreticians, but it's good news for quantum mechanics, given that the authors ominously suggest that, should Born's Rule be violated, "then Schrödinger’s equation would likely have to be modified as well."

Science, 2010. DOI: 10.1126/science.1190545 (About DOIs).