## 24 July, 2010

### The Science article that made me speechless

In his blog post Igor Ivanov dragged attention to the following paper, that recently appeared in Science magazine:

Sinha et al. "Ruling Out Multi-Order Interference in Quantum Mechanics"

In the abstract the authors refer to unification of quantum mechanics with gravitation and such kinds of things, that somehow don't seem to be very relevant. Here is what they do.

In an optical double slit experiment two different light paths interfere with each other. That means that the resulting intensity is not given by the sum of intensities from two "one-slit" experiments, but by the square of added electromagnetic amplitudes:

I = (A1 + A2)2 = A12 + A22 + 2A1A2 = I1 + I2 + I12

In this way, in addition to one-slit amplitudes, I1 and I2, we have the interference term I12 here.

If we have three slits, all three paths will interfere with each other, and the resulting intensity will be also given by the square of the resulting amplitude:

I = (A1 + A2 + A3)2 = A12 + A22 + A32 + 2A1A2 + 2A1A3 + 2A2A3 = I1 + I2 + I3 + I12 + I13 + I23

What the authors do is they measure diffraction of light in the three-slit experiment and prove that the equation above is correct, and there is no "three-slit term" there, such as A1A2A3.

Then they explicitly state that the absence of the three-slit term means that light paths interfere with each other only in pairs, and there is no interference of three paths.

This is not correct, all three paths interfere with each other: we still sum up three amplitudes and then square them. The absence of the A1A2A3 term means that intensity is calculated as square of the amplitudes, but not cube or any higher power. However, if the intensity wasn't given by a square of the amplitude, that would be already revealed in other (even more precise) experiments with light, electrons, and atoms.

This article was highlighted in Science perspectives and Nature News, but I'm still puzzled how it passed through into the Science magazine.