# The link between theory and experiment

Industrial standards are based on natural constants. On World Standards Day on 14 October 2021, Aldo Antognini from the Laboratory for Particle Physics at PSI explains why there would be no physics without these fundamental constants and what this has to do with the French Revolution.

**Mr. Antognini, why are natural constants so important in physics?**

**Aldo Antognini:** Every theory in physics needs these fundamental constants, for example in particle physics, which is what we deal with here at PSI. There is no theory that can predict a physical quantity by mathematics alone. For example, to calculate the energy level of an atom or the interaction of an atom with a laser, the charge of the electron must be known. The charge of the electron is a fundamental constant that has to be experimentally determined. This is done by fitting the theoretical predictions that depend on this fundamental constant to the corresponding measurements.

Knowledge of the constant provides the theory with predictive power: If the fundamental constant is precisely known, the theoretical prediction can also be precise. The game of physics is to compare theory and experiment. If both agree, from the comparison we can extract the fundamental constant more precisely. If they don't agree, and if there is no mistake involved in the experiment and the calculation, something is wrong or incomplete at the fundamental level, and the theory has to come up with something new. This is how theories evolve.

**In 2019, there was a major change in the international system of units. What has changed in the SI units?**

Previously, for example, the kilogram was derived from an arbitrary physical object, the “primordial” kilogram, which is kept in a climate-controlled safe in Paris with questionable long-term stability. And the kelvin was defined using the triple point of water, a material property that is not so well controllable or fundamental. That was unsatisfactory for us physicists. In the new SI system all seven SI units – second, meter, kilogram, ampere, kelvin, mole, and candela – are now based on fundamental constants (invariants of nature) that appear in various fields of physics, from special relativity to quantum physics and condensed matter. The kilogram, for example, is now defined by the Planck constant, and the ampere is now defined via the electron charge. These defining constants have been fixed to their value in 2019, and their uncertainty has been removed.

Other constants could have been chosen as defining constants of the new SI system, as they are all linked, but the decision made in 2019 is the one that leads to the “cleanest” connection to experimental procedures for the practical realisation of the units.

**So the SI units are fixed once and for all?**

There might still be small changes, for example a redefinition of the second, but I think that fundamental changes are unlikely. And very likely the philosophy of fixing the units to fundamental constants of nature that can be cleanly observed in experiment will not be changed at all.

**Which fundamental constant plays the biggest role in your research?**

There are many: the elementary charge, the speed of light, the Planck constant. A combination of these constants is the Rydberg constant. It plays a special role for us because it is strongly linked to the proton radius, which is what we measure in our experiments. In other words, from the measurement of the proton radius from our experiment, a very precise value for Rydberg constant can be extracted. Hence the proton radius through the Rydberg constant plays a crucial role in the adjustment of many other fundamental constants impacting even the definition of the new SI units. So there is a little bit of our research on the proton radius in the new SI system.

**What are you researching in these experiments?**

We are interested in the hydrogen atom, the smallest of all atoms and a touchstone for many theories in physics and in the structure of the proton, the simplest nucleus. Using our proton accelerator, we produce muons that form muonic hydrogen, a cousin of regular hydrogen, with a muon instead of an electron orbiting the proton. PSI is the only research site in the world that produces enough slow muons for such experiments. Muonic hydrogen is only one 200th as big as hydrogen, so the energy levels of this atom are strongly affected by the size of the proton. Thus a measurement of the energy levels in muonic hydrogen by means of laser spectroscopy can be used for a precise measurement of the proton radius. This radius is an important benchmark for theories aiming at the understanding of the complex proton structure arising from the quark interactions at low energy.

**What about the Rydberg constant?**

The Rydberg constant comes into play when our measurement is combined with measurement in regular hydrogen. A comparison of theory with experiment in hydrogen, with the proton radius known from muonic hydrogen, leads to a very precise determination of the Rydberg constant. It turns out that the Rydberg constant determined in this way is the most precisely measured fundamental constant.

**All constants are defined by long numbers with many decimal places. Couldn't one or the other constant be set to 1, for example the speed of light? **

If you do that, all the quantities with physical units will change. The maximal speed on the highway will be a different number with a different unit. The kilogram would no longer be the kilogram, so the number indicated when you weigh yourself would be totally different. What happens then could be seen in the French Revolution. At that time, the gram as the weight of 1 cubic centimeter of water was introduced. Because people didn't know it, it led to chaos. The new SI system that was redefined in 2019 did not cause any of these problems, because it was defined in continuity with the previous SI system so that, practically, it has no immediate noticeable effect. This continuity was obtained by fixing the defining fundamental constants at their 2019 value and by continuing to use the same units: m/s, watt, newton, and so on. Yet the better choice of the system of units reduces the uncertainty of the various constants needed in our theories, providing science with a finer framework to investigate more subtle effects and giving technology more precision.

**That would probably also have an impact on industry standards?**

Yes, industry standards such as power consumption expressed in watts, voltages expressed in volts and resistance expressed in ohms have also been affected by the new SI system. The practical realisation of the unit of resistance and the unit of voltage in the new SI system is being obtained and linked to the defining constants (electric charge and Planck constant) using two beautiful quantum mechanical effects: the Josephson effect in two superconductors separated by a thin barrier, and the fractional quantum Hall effect.

Because the proton radius was used to extract the Rydberg constant, and the Rydberg constant is used to consistently define the set of defining constants including the electron charge and the Planck constant, there is a little bit of our proton radius research in your electric bill and in the number when you weigh yourself.

**Some physicists believe that there could be other universes besides ours. Would the natural constants be the same there?**

First, we would at least have to find evidence of such universes. So far there is none. What would that mean for the fundamental constants? That's hard to say. But what physicists are currently looking at is the question of whether the fundamental constants change over time. For example, there are thoughts that there was a time in the early universe in which the natural constants might have been different. Perhaps they are still drifting minimally now. There are several experiments around the world that are trying to find out.

**What if these experiments found such a drift?**

That would have considerable consequences. Then physicists would have to act and adjust their theories. This is another reason why this research is so important.

*Interview: Bernd Müller*