 Uncertainty in quantum mechanics is not a fudge factor. Its internal structure yields complex patterns of high and low probability that would not arise from simple measurement error. Seen here are the probability distributions of an electron in an atom.

This is the last article in a series about quantum mechanics. Previously, I talked about how quantities can be multivalued yet restricted to whole numbers, like a light switch that is both on and off; how quantum processes can include acausal influences, like a time traveler who gets his time machine by going back and giving it to himself; and how so-called particle waves are neither waves nor particles. These are such dubious claims that I was tempted to crowd the exposition with descriptions of experiments, but instead of confusing the issue, I left the “how we know” for this article.

There are several objections one could make to my presentation. Though I said that a quantum light switch is both on and off, measurements will find it either on or off, not both. The time loops of quantum processes are similarly hidden behind a veil of indeterminacy. It might seem like all of these quantum effects are just speculations about what’s happening inside the noise of an uncertain measurement, but there’s more to it than that.

The key ingredient is an effect known as interference. The probability of finding a multivalued quantity as one value rather than another is the square of a more fundamental description called the wavefunction. Squaring a number hides information: 25 is the square of 5, but it is also the square of −5. Since we can only measure probabilities, we can’t determine the sign of a wavefunction, but if two wavefunctions overlap, or “interfere,” we can discover a difference in their signs. For example, if one has magnitude 5 and the other has magnitude 3, the square of 5 + 3 (or −5 + −3) is 64, but the square of −5 + 3 (or 5 + −3) is 4. When you introduce a second wavefunction, the resulting probability can sometimes decrease.

Probabilities, on the other hand, only increase when you combine them. My chances of winning the lottery would be almost doubled if I had twice as many tickets. Most experiments that distinguish quantum multivaluedness from mere uncertainty exploit this distinction. Wavefunctions describing a particle’s spread in position have alternating peaks and troughs of high and low probability, whereas measurement error in the same circumstances would yield a smeared-out blob.

Physicists were so uncomfortable with the idea of acausal influence that they considered countless alternatives to quantum mechanics, cleverly accounting for the apparent acausality with complicated mechanisms. In 1964, John Bell used an interference effect to pose a numerical test that distinguishes quantum mechanics from all causal mechanisms based on a few weak assumptions. This test was experimentally performed in 1981 by Aspect and Grangier and is repeated often under different circumstances with weaker sets of assumptions. The results have always favored the quantum explanation.

Studying quantum mechanics is like a conversation with an alien race. Our prior experience and even brain evolution have not prepared us for this conversation, but if we can stretch our minds around what the data are telling us, we’ll never see the world the same way again.

Jim Pivarski