Eight sky maps taken by different detectors on the Planck telescope are like eight road atlases of the same city drawn by different cartographers. Each atlas is rotated by its own angle: one cartographer held the clipboard slightly tilted, another slightly turned. If you overlay the atlases, the streets won't align. But if you know how each atlas is rotated, you can align them perfectly. This is exactly the problem scientists face when searching for cosmic birefringence, a tiny rotation in the polarization of ancient light that could reveal new particles.

The problem is that the rotation from a cosmic effect is indistinguishable from an error in the detector setup. If all detectors are rotated by the same angle, the sky picture rotates as a whole, and this common rotation is indistinguishable from a genuine cosmic signal. The existing method uses the polarization of dust in our Galaxy to separate the two contributions. But that method relies on a dust model, and if the model is wrong, so is the calibration. The authors of the new work devised a test that doesn't use the dust model at all.

Their approach is like measuring distances between cities when you don't have a coordinate map. If you measure the distance from Moscow to St. Petersburg, from St. Petersburg to Kazan, and from Kazan to Moscow, you can compute the triangle's angles without knowing where the triangle sits on the globe. Similarly, the authors compare maps in pairs. For each pair, they construct two combinations of spectra: symmetric and antisymmetric. The ratio of these combinations gives the difference in angles between the detectors, while the common cosmic rotation cancels out completely. Then all pairwise differences are combined into a network where maps are nodes and angle differences are links. The network is solved by least squares, yielding a pattern of angles for all detectors.

The result from comparing 28 pairs of detectors is encouraging. The angles from the differential method and those from the Minami–Komatsu method agree: the chi-square statistic is 8.18 with seven degrees of freedom, corresponding to a probability of 0.32. All deviations are less than 1.8 sigma. This means that the calibration pattern given by the dust model is reproduced by a method that doesn't use that model. In other words, the dust model isn't fooling us: it gives the same angles as an independent approach based solely on the properties of the cosmic microwave background itself.

Let's return to the atlases. If all cartographers rotated their clipboards by the same angle, aligning the atlases with each other is easy, but we won't know where north actually points. For that, you need an external reference, like the North Star. For Planck, no such external reference exists yet. But the differential test shows that all atlases are consistent with each other, meaning that any error, if present, is common to all. And that is already a big step toward trusting the map.