Monday, July 13, 2020

The most accurate equations in all of physics

A beautiful and profound article, Superconductivity and the Quantization of Energy, by D.G. McDonald was published in Science in 1990.
Ideas about quantized energy levels originated in atomic physics, but research in superconductivity has led to unparalleled precision in the measurement of energy levels. A comparison of levels produced by two Josephson junctions shows that they differ by no more than 3 parts in 10^19 at an energy of 0.0003 electron volt. The fact that the myriad of interactions of 10^12 particles in a macroscopic body, a Josephson junction, can produce sharply defined energy levels suggests a dynamical state effectively divorced from the complexities of its environment. The existence of this state, the macroscopic quantum state of superconductors, is well established, but its isolation from intrinsic perturbations has recently been shown to be extraordinary. These new results, with an improved precision of about ten orders of magnitude, are discussed in the context of highly accurate results from quantum electrodynamics, atomic spectroscopy, and the standards of metrology.  
McDonald suggests that the equations associated with the AC Josephson effect are the ``most accurate equations in all of physics". The central equation is the relationship between the voltage V across a junction and the frequency, nu, of the radiation shone on the junction.
The proportionality constant is the Josephson constant,
where e is the electronic charge and h is Planck's constant. Thus, the Josephson effect provides a means to make a macroscopic measurement of fundamental constants that are normally associated with measurements of atomic systems.

The relative value of the Voltage V in two different Josephson junctions can be measured with great precision using a SQUID. One obtains the same value for a range of systems of different chemical composition and Josephson junctions of different design.

On a philosophical level, these results are a beautiful illustration that superconductivity is an emergent state of matter and that the Josephson effect is an emergent effect. An important characteristic of emergent phenomena are that they are independent of most of the chemical and structure details of the materials involved.

These observations had important implications for metrology (the scientific study of measurement and the associated units and standards). In 1990 an international agreement was made that the voltage standard based on Weston cells (a particular type of electrical battery) would be replaced by the Josephson voltage standard. This change was not just one of precision, but also portability, reproducibility, and flexibility. The old voltage standard involved a specific material and device and required duplication in order to have an accurate standard. In contrast, the Josephson standard is independent of the materials used and the details of the device.

All of the above illustrates how much Josephson matters.


  1. Impressive facts, and well explained, thanks!

  2. For outreach purposes, could you give some examples of practical uses and implications of the much higher precision and reproducibility of the Josephson voltage standard?

    1. I think the answer is simply that there aren't any practical uses for the better voltage standard. Some may say quantum computing, but that is not correct, they don't use the voltage standard as a voltage standard there.