This blog contains thoughts and observations on a wide range of physics related topics that I find interesting and which I believe are worthwhile sharing. My goal is to create one new entry every month. You will find that I have strong opinions on some topics. I'm always happy to discuss them in more depth. Feel free to send me an email for further discussion: stefan.kehrein@theorie.physik.uni-goettingen.de

Yes, you have read correctly. Magnetic field lines are not always closed. If you are surprised about this then you fell prone to a common misconception that is perpetuated by many textbooks (Sommerfeld, Griffiths, and many more) and instructors. This includes me until recently a student asked about this and I actually had a closer look.

The first thing to realize is that closed magnetic field lines are a sufficient condition for the validity of Maxwell's equation div B=0. But closedness is not a necessary condition. A simple example for this observation is a pair of identical Helmholtz coils with a common axis and equal but opposite currents. The magnetic field at the symmetry point between the two coils vanishes. The magnetic field lines approaching this symmetry point along the axis from either of the coils therefore have to terminate at the symmetry point. On the other hand, there are magnetic field lines starting at the symmetry point and running perpendicular to the axis. The overall effect is that the flux through a small sphere around the symmetry point vanishes, consistent with a divergenceless magnetic field. A second more generic situation are magnetic field lines that continue forever without beginning or end, but also without being closed. Imagine the closed field lines around a single Helmholtz coil, which you then perturb by a current running through some wire nearby. For a weak perturbation the field lines still wrap around the Helmholtz coil, but in general they will do so in an incommensurate manner without being closed. As a matter of fact, closed magnetic field lines are a set of measure zero in the space of current geometries. However, many textbook examples consider specific simple geometries leading to closed lines, which one then believes to always be the case. Putting it otherwise: Simply solvable cases can really give you the wrong idea about what is generic.

All of this is perfectly well known since at least 1929 (textbook by I. Y. Tamm), but the wrong picture is prevalent. Just go around and ask your fellow students/colleagues, the reactions can be quite entertaining. For more information including lots of references and the two examples above (plus many other examples) I recommend the following two articles: The Misconception of Closed Magnetic Flux Lines and A taxonomy of magnetostatic field lines (from 2024!).

There is a remarkable connection between geophysics, namely so called Kelvin and Yanai waves, and topological materials. Kelvin and Yanai waves are regular and stable, always travel eastward around the equator and are important for weather phenomena like El Niño. In two papers Delplace et al. and Xu et al. show that the equator as the boundary between the northern and southern hemisphere plays the role of a boundary in a topological material: The Coriolis force acts like the magnetic field in a quantum Hall device and the equatorial waves are the topologically protected currents at the boundary. The stability of Kelvin and Yanai waves is therefore rooted in nontrivial topological winding numbers that can be defined in frequency-wavevector space, and have actually been experimentally confirmed after their theoretical prediction. Truly remarkable.

The Ranga Dias scandal is a disturbing tale of scientific misconduct. Starring prominently is Nature and its publishing policies. At the center of this scandal are experiments done in Ranga Dias' lab at the University of Rochester on high-temperature high pressure superconductivity. This is an established (experimentally very challenging) field with the ultimate goal of realising superconductivity at room temperature under high pressure. In 2020 the Dias group published a Nature article claiming room temperature superconductivity at 270 GPa in carbonaceous sulfur hydride (CSH). There were immediate concerns regarding the validity of the experimental data, and after significant back and forth the paper was retracted by Nature in 2022 against the express will of its authors. Against this background Dias et al. submitted another even more spectacular manuscript to Nature in 2022, claiming room temperature superconductivity at just 10kbar in doped lutetium hydride (LuH). Under the veil of "decisions should be made on the basis of the scientific quality, not who the authors are" (quote from Magdalena Skipper, Nature’s editor-in-chief, source) the manuscript was accepted and published in 2023 in spite of the fact that only one out of four referees said that there was solid proof of superconductivity (source). Again there was immediate concern in the community, which led to numerous rounds of investigations at the University of Rochester. The first three rounds found no misconduct, until the genius decision was made to also interview the students involved in the experiment in round four. Then the whole thing fell apart because the students could not connect the published data with their actual measurements. Eventually the LuH manuscript was retracted by Nature in 2023.

One can learn some important lessons from this story. Like: Spectacular claims need spectacular proofs. And: If in doubt ask the students. It remains to be seen to what extent these lessons have been learned when they next collide with commercial interests.

For more background reading I recommend Physik Journal 23 (2024), p. 22 [german] and the investigation reports by Nature from 2024: Superconductivity scandal: the inside story and Exclusive: official investigation reveals how superconductivity physicist faked blockbuster results.