## From Forbes Magazine : “Recent Reports Of Overturned Scientific Theory Are Premature”

Apr 17, 2021

.On April 7, 2021, the world’s scientific community watched with rapt attention as scientists based at Fermi National Accelerator Laboratory (US) presented a research result that the science media reported heavily. A new measurement disagreed in a very significant way with predictions. This disagreement could have been strong evidence that scientists would have to rethink their theory. That’s an exciting prospect, if it’s true. However, a theoretical paper [*Leading hadronic contribution to the muon magnetic moment from lattice QCD*] was released the same day as the experimental result that puts the entire situation in turmoil.

The new experimental measurement involved the magnetic properties of subatomic particles called muons. Muons are essentially heavy cousins of the electron. Like the electron, the muon has both electric charge, and it spins. And any spinning electric charge creates a magnet. It is the strength of the magnet that researchers measured.

It is possible for scientists to calculate the relationship between the strength of the magnet and the quantity describing the amount of spin. Ignoring some constants, the ratio of magnetic strength to amount of spin is called “g.” Using the quantum theory of the 1930s, it is easy to show that for electrons (and muons) that g is exactly equal to two (g = 2).

**History**

Measurements in 1947 [*Physical Review Journals Archive*] found that this prediction wasn’t quite right. The measured value of g was closer to 2.00238, or about 0.1% higher. This discrepancy could have been simply a measurement error, but it turned out that the difference was real. Shortly after measurement, a physicist by the name of Julian Schwinger used a more advanced form of quantum mechanics and found that the earlier prediction was incomplete and the correct value for g was indeed 2.00238. Schwinger shared the 1965 Nobel Prize in physics with Richard Feynman and Sin-Itiro Tomonaga, for developing this more advanced form of quantum mechanics.

This more advanced form of quantum mechanics considered the effect of a charged particle on the space surrounding it. As one gets close to a charged particle, the electric field gets stronger and stronger. This strengthened field is accompanied by energy. According to Einstein’s theory of relativity, energy and mass are equivalent, so what happens is that the energy of the electric field can temporarily convert into a pair of particles, one matter and one antimatter. These two particles quickly convert back to energy, and the process repeats itself. In fact, there is so much energy involved in the electric field near, for example, an electron, that at any time there are many pairs of matter and antimatter particles at the same time.

Quantum Foam

A principle called the Heisenberg Uncertainty Principle applies here. This quantum principle says that pairs of matter and antimatter particles can appear, but only for a short time. Furthermore, the more massive the particles are, the harder it is for them to appear, and they live for a shorter amount of time.

Because the electron is the lightest of the charged subatomic particles, they appear most often (along with their antimatter counterpart, called the positron). Thus, surrounding every electron is a cloud of energy from the electric field, and a second cloud of electrons and positrons flickering in and out of existence.

Those clouds are the reason that the g factor for electrons or muons isn’t exactly 2. The electron or muon interacts with the cloud and this enhances the particle’s magnetic properties.

So that’s the big idea. In the following decades, scientists tried to measure the magnetic properties of both electrons and muons more accurately. Some researchers have focused on measuring the magnetic properties of muons. The first experiment attempting to do this was performed in 1959 at the European Organization for Nuclear Research (Organisation européenne pour la recherche nucléaire)(CH) [CERN] laboratory in Europe. Because researchers were more interested in the new quantum corrections than they were with the 1930’s prediction, they subtracted off the “2” from the 1930s, and only looked at the excess. Hence this form of experiment is now called the “g – 2” experiment.

The early experiment measuring the magnetic properties of the muon was not terribly precise, but the situation has improved over the years. In 2006, researchers at the DOE’s Brookhaven National Laboratory (US) , measured an extremely precise value for the magnetic properties of the muon.

They measured exactly 2.0023318418, with an uncertainty of 0.0000000012. This is an impressive measurement by any standards. (The measurement numbers can be found at this URL (page 715).)

The theoretical calculation for the magnetic properties of the muon is similarly impressive. A commonly accepted value for the calculation is 2.00233183620, with an uncertainty of 0.00000000086. The data and prediction agree, digit for digit for nine places.

Two measurements (red and blue) of the magnetic properties of the muon can be statistically combined into an experimental measurement (pink). This can be compared to a theoretical prediction (green), and prediction and measurement don’t agree. DOE’s Fermi National Accelerator Laboratory(US).

**Implications**

Such good agreement should be applauded, but the interesting feature is in a slight remaining disagreement. Scientists strip off all of the numbers that agree and remake the comparison. In this case, the theoretical number is 362.0 ± 8.6 and the experimental number is 418 ± 12. The two disagree by 56 with an uncertainty of 14.8.

When one compares two independently generated numbers, one expects disagreement, but the agreement should be about the same size as the uncertainty. Here, the disagreement is 3.8 times the uncertainty. That’s weird and it could mean that a discovery has been made. Or it could mean that one of the two measurements is simply wrong. Which is it?

To test the experimental result, another measurement was made. In April of 2021, researchers at Fermilab, America’s flagship particle physics laboratory, repeated the Brookhaven measurement. They reported a number that agreed with the Brookhaven measurement. When they combine their data and the Brookhaven data, they find a result of 2.00233184122 ± 0.00000000082. Stripped of the numbers that agree between data and theory, the current state of the art is:

Theoretical prediction: 362.0 ± 8.6

Experimental measurement: 412.2 ± 8.2

This disagreement is substantial, and many have reported that this is good evidence that current theory will need to be revised to accommodate the measurement.

However, this conclusion might be premature. On the same day that the experimental result was released, another theoretical estimate was published that disagrees with the earlier one. Furthermore, the new theoretical estimate is in agreement with the experimental prediction.

Two theoretical calculations are compared to a measurement (pink). The old calculation disagrees with the measurement, but the new lattice QCD calculation agrees rather well. The difference between the two predictions means any claims for a discovery are premature. Adapted from *Science Magazine*.

**How the theory is done**

Theoretical particle physics calculations are difficult to do. In fact, scientists don’t have the mathematical tools required to solve many problems exactly. Instead, they replace the actual problem with an approximation and solve the approximation.

The way this is done for the magnetic properties of the muon is they look at the cloud of particles surrounding the muon and ask which of them is responsible for the largest effect. They calculate the contribution of those particles. Then they move to the next most important contributors and repeat the process. Some of the contributions are relatively easy, but some are not.

While the particles surrounding the muon are often electrons and their antimatter electrons, some of the particles in the cloud are quarks, which are particles normally found inside protons and neutrons. Quarks are heavier than electrons, and they also interact with the strong nuclear charge. This strong interaction means that the quarks not only interact with the muon, the quarks interact with other quarks in the cloud. This makes it difficult to calculate their effect on the magnetic properties of the muon.

So historically, scientists have used other data measurements to get an estimate of the quarks contribution to the muon’s magnetism. With this technique, they came up with the discrepancy between the prediction and measurement.

However, a new technique has been employed which predicts the contribution caused by quarks. This new technique is called “lattice QCD,” where QCD is the conventional theory of strong nuclear force interactions. Lattice QCD is an interesting technique, where scientists set up a three dimensional grid and calculate the effect of the strong force on that grid. Lattice QCD is a brute force method and it has been successful in the past. But this is the first full attempt to employ the technique for the magnetic properties of muons.

This new lattice QCD calculation differs from the earlier theoretical prediction. Indeed, it is much closer to the experimental result.

So where does this leave us? When the Fermilab results were released, it appeared that the measurement and prediction disagreed substantially, suggesting that perhaps we needed to modify our theory to make it agree with data. However, now we have the unsettling situation that perhaps the theory wasn’t right. Maybe the new lattice QCD calculation is correct. In that case, there is no discrepancy between data and prediction.

I think that the bottom line is that the entire situation is uncertain and it is too soon to draw any conclusion. The lattice QCD calculation is certainly interesting, but it’s new and also not all lattice QCD calculations agree. And the Fermilab version of the experiment measuring the magnetic properties of the muon is just getting started. They have reported a mere 6% of the total data they expect to eventually record and analyze.

Precision measurements of the magnetic properties of muons have the potential to rewrite physics. But that’s only true if the measurement and predictions are both accurate and precise, and we’re not really ready to conclude that either are complete. It appears that the experimental measurement is pretty solid, although researchers are constantly looking for overlooked flaws. And the theory side is still a bit murky, with a lot of work required to understand the details of the lattice QCD calculation.

I think it’s safe to say that we are still many years from resolving this question. This is, without a doubt, an unsatisfying state of affairs, but that’s science on the frontier of knowledge for you. We waited nearly two decades to get an improved measurement of the magnetic properties of muons. We can wait a few more years while scientists work hard to figure it all out.

See the full article here .

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