This 4.2 standard deviation discrepancy is suggesting that the Standard Model of Physics is Incomplete!

Recently, the Muon g-2 experiment being conducted at Fermilab has been in the news quite a lot, because the scientists there have found a result that might point to the existence of a fifth (unknown) fundamental force of nature. In this video, I wanted to discuss the basics of the experiment itself, as well as whether this fifth force of nature is a reasonable explanation for the experimental results seen.

The first thing to discuss is the fact that Fermilab scientists are studying Muons (small particles very similar to electrons, except with a larger mass) when placed in magnetic fields. As it turns out, the spin of the muon results in an interaction between the particle and the magnetic field. In other words, scientists can define a quantity known as the "spin magnetic dipole moment" of the muon. In classical physics, a magnetic dipole moment is a measure of the strength of a magnetic dipole, such as a bar magnet. And in quantum physics, we can define a similar quantity for a fundamental particle like the muon.

Now as it turns out, the spin of the muon is directly related to its magnetic dipole moment, with a sort of constant of proportionality in the equation known as the g-factor. The value of this g-factor for the muon, can be calculated to be exactly 2 using just the basic principles of quantum physics. But if we use all of the physics that we know, a.k.a. the "Standard Model", then the value of g is calculated to be slightly larger than 2. And this g-factor value can be calculated using theory to an extremely high level of precision.

The problem comes when we try and measure this value experimentally. The first experiment to attempt to do this was conducted in Brookhaven about 20 years ago. They found something rather strange - the g-factor measured experimentally was quite a bit higher than the calculated theoretical value. Therefore, another experiment was set up at Fermilab to either confirm this or refute it. And it seems like Fermilab is confirming Brookhaven's finding - the value of g for the muon is larger than expected based on our current most "complete" theory.

This is therefore alluding to the idea that the Standard Model is incomplete. Perhaps there's a fifth fundamental force of nature (we already know about 4 - gravity, electromagnetism, strong nuclear, and weak nuclear). Maybe we need to study a fifth one that nobody has known about until now. Maybe there's another solution entirely. Either way, the Fermilab announcement recently suggests to us that there is brand new physics to be discovered, and that is very exciting.

In this video, I also wanted to discuss exactly how far apart the experimentally measured and theoretically calculated values needed to be in order for scientists to consider modifying the theory. We discuss the idea that any measured quantity in science needs to have a +/- error associated with it. This gives a reasonable range within which the experimentally measured quantity can actually lie, and is known as the standard deviation of the measurement. The standard deviation is represented with the Greek letter "sigma".

The general convention used in science is that if the theoretical value and the experimentally measured value are 5 sigma apart, then we can say the experimental measurement is a brand new scientific discovery. This is because a deviation of 5 sigma means the experimental value could only be a fluke or coincidence in 1 out of every 3.5 million experiments. This is extremely unlikely.

Currently, the data from Brookhaven and Fermilab combined shows a discrepancy of 4.2 sigma between the theoretical and experimental values. This is close to 5 sigma, but not quite there yet. The way to push this scenario over the 5 sigma threshold is to either conduct other experiments measuring the same value, or to improve existing experiments so that the standard deviation decreases (and scientists become more sure of the range within which the experimental value really lies).

The bottom line is, we seem to be very close to discovering brand new physics... and perhaps this will be best explained by a fifth unknown fundamental force of nature.

Here's the actual scientific paper publishing these findings from Fermilab: [ Ссылка ]

0:00 - Exciting Developments, Muons, and Fundamental Forces
1:29 - Spin Magnetic Dipole Moment (and g-factor)
4:27 - How Far Do Experiment and Theory Need to Be?
7:57 - tl;dr - a Summary

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