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A physical constant’s value shouldn’t depend on how you measure it


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Measurements in physics are funny things. You'd hope that attempts to quantify some of the fundamental properties of the Universe would follow a simple pattern: they'd start with large error bars, but, over time, measuring technology improves and the error bars shrink. Ideally, the value would then remain nicely within the previous error.


It almost never really works like that. In many cases, measurements cluster together for a while before a new set makes a leap to somewhere else, outside the error bounds. And, even as technology improves, some sets of error bars stubbornly refuse to overlap. A new paper out this week indicates that this is the case with the Fine Structure Constant, which describes the strength of the electromagnetic force. But instead of chalking it up to the vagaries of measurement, the researchers suggest that the difference could be real—and it tells us something about what physics might lie beyond the Standard Model.


Mighty fine

The Fine Structure Constant is a measure of electromagnetic force, and that force shows up in a large number of phenomena. This means there are plenty of ways to do measurements that tell us something about the value of the Fine Structure Constant. When it comes to high-precision measurements, researchers have come up with two different ways of doing it. The first relies on particle physics and direct measurements of the magnetic properties of the electron. The second has been to study how atoms interact with light.


Over time, we've come up with better ways of measuring both of these, and the error bars on our measurements have shrunk accordingly. And, while the values produced by them have gotten closer, the error bars are stubbornly refusing to overlap.


The data of the new paper is a report on a new measurement, this one using interactions between photons and atoms. The experiment itself is pretty amazing. Like the LIGO gravitational-wave detectors, it relies on the fact that interference between waves can register extremely subtle changes in location. Unlike LIGO, however, the waves aren't light; they're atoms. Taking advantage of the quantum nature of atoms, the researchers send bunches of them along different paths as waves and then get them to interfere with each other.


Lasers are used to steer the atoms along the paths, making the interference intensely sensitive to the interactions between the lasers' photons and the atoms. And the strength of those interactions, as we said, are influenced by the value of the Fine Structure Constant. The new measurements provide a three-fold reduction in the error compared to previous work, with the accuracy being within ±2 × 10-10.


But the big story here is the range of values covered by those error bars. The range of values is entirely contained within the error bars of a previous measurement made using an atom interferometer. And neither of these measurements overlaps at all with the highest-precision measurement done by directly measuring the electron. The difference between the two measurements has a significance of 2.4 sigma.


What if it’s real?

It wouldn't be unreasonable to expect that, with further measurements, this difference would shrink or even disappear entirely. But there are some reasons to think it might not. The relationship between the electron's behavior and the Fine Structure Constant is set by the Standard Model, and there have been a lot of ideas put forward about how the Standard Model might be improved. Some of these would change the electron's behavior, so the researchers decided to take the difference between the measurements seriously. In other words, they assumed both measurements were right and considered how changes to the Standard Model could produce the apparent difference between them.


One case where this matters is a hypothetical particle called a dark photon. Dark photons would produce a difference in the measurements of the Fine Structure Constant, but it would be in the opposite direction of the difference seen in these experiments. In other words, dark photons would make things worse. By contrast, another hypothetical particle, the dark axial vector boson, isn't ruled out by this new measurement.


That isn't to say that these experiments have definitively told us anything about these hypothetical extensions to the Standard Model. There's still the chance that the electron measurements are wrong, and there are a couple of projects in the works that will be able to say more about that possibility. But it definitely shows those projects are worth pursuing, since a continued difference over several independent measurements would start to look interesting.


And, on a completely unrelated side note, the researchers behind the new work note that it also provides a standardized means of measuring the absolute mass of the atoms, which could be used to provide a way to define the kilogram without relying on chunks of metal. Bonus!


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