this post was submitted on 10 Aug 2023
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Part 1 - Background.
Start with the classical representation. A compass points in the direction of North when taken out and laid down. What is happening is that the magnet in the compass is aligning with the external magnetic field of the planet Earth. That is the classical mechanic and there is a quantum analog, which is what this whole experiment deals with.
On the quantum level we express the magnetic moment using the Dirac equation for bodies that have no internal structure as µ = g(e/2m)S. The e is the elementary charge, the m is mass of the particle, and the S is the spin angular momentum of the particle. In quantum mechanics spin plays a major role in magnetic moments, so we must consider it here. That g is the g-factor that the experiment is dealing with. It is a dimensionless quantity that characterizes the magnetic moment and angular momentum. Basically it serves as the thing we tweak to ensure µ lines up with things we observe.
Take two electrons that strike each other. They have the same charge (negative) and thus, they should repel each other. But "HOW?", they aren't allowed to touch each so what pushed them away form each other? Like, really really does the pushing? Not that, oh well their charge fields touch each other. There's got to be "a something" that literally pushes them. And that is the exchange of a virtual particle. Getting into what a virtual particle is a deeper dive into the fields, but here's a quick run down.
The universe is a bunch of layers that we call fields all sandwiched together. So all the things that exist are just point in that field that are excited (that is they have energy to bring them to a level that we call existing). So an electron, that's actually just a point in the electron field that has enough energy that we call it actually existing. Now there could be a point in the field that has energy that's below that threshold of calling it actually existing. That's a virtual particle. Virtual particles participate in interactions, but can only do so if everything stays the same in the end and momentum is conserved. Like we can conjure a virtual electron and a positron (anti-electron) to exchange energy, but they must cancel each other out (by running into each an annihilating) in the end. There's way more, but that's outside what we need for this.
So picture two electrons hitting each other and then they bounce away. Something has to push them. That something is a virtual photon. As the electron on the left approaches the electron on the right, they fire off a virtual photon which reduces virtually the energy in the electron. However, this loss is virtual, the books must balance in the end. Which the photon on the right ALSO fires off a virtual photon, virtually reducing it's energy. The left electron absorbs the virtual photon from the right electron and vice versa for the right electron. Thus, the balance is maintained, the electrons return to their original energy. But! Momentum MUST be conserved. The photon from the left electron was moving right so now the right electron, having absorbed a photon moving right, must move rightward, the right electron was moving left towards the left electron, but now it is that motion MINUS the motion of the emitted virtual photon PLUS the motion of the right moving virtual photon. So this is what is actually pushing the electrons away form each other. This is what the repelling of two like charges actually is at a very deep level.
However, in the end the books just have to be balanced. So it's balanced in one virtual photon exchange, but there could be two virtual photon exchanges. As long as it's balanced, it's all the same. In fact, we could have five virtual photon exchanges. One of the virtual photons could summon up a virtual electron/positron that cancel each other out to make a virtual photon. There's no end to the number of exchanges that could happen, there's an infinite number of exchanges that could happen. Richard Feynman indicated that the more and more exchanges that could happen all impart smaller and smaller "corrections" to a calculated event. So basically, if there were 126,347,428 virtual exchanges between two electrons, the conserved values (that motion that we call repulsion) would change very, very, very, very, very, very little if there were 126,347,429 virtual exchanges. Basically after the tenth or so virtual exchange, the additional repelling that would be added by the eleventh virtual exchange would be insanely small, but not zero. And everything thereafter would just get smaller and smaller and smaller, but still measurable.
Part 2 - g-factor.
So back to our equation µ = g(e/2m)S. If the exchange between two electrons is just a single virtual photon, that g = 2. But if say the electron emits two virtual photons and then absorbs two virtual photons, that g now equals 2.0011614. We can find this value out with some fancy math. And this "correction" as it's called was first calculated by Julian Schwinger in 1949. But as we go, we can toss into that calculation three virtual photons. And then toss in three virtual photons plus one of them become a virtual electron/positron pair, that cancels each other out into a virtual photon. This moves that g a tiny bit up to 2.0023193.
Eventually we hit a point where calculating this by hand gets hard to do, but we have super computers now that can do thousands upon thousands of theses corrections and we arrive at a g-factor of 2.0023193043552. However we measure by spinning, physically not the quantum spin, an electron in a particular direction and then setting that spinning electron in an external magnetic field how long it takes the electron to align with the external field. Much like the compass and Earth's magnetic field eventually align. Now the electron can never perfectly align because of the particle's quantum spin and so the electron has a precession (much like a top will precess around its axis) , we can also measure the g-factor of the electron from this precession called Larmor Precession. We measure the g-factor this way at 2.00231930436146. The difference between the g = 2 and the g-factor we measure or calculate is the anomalous magnetic moment of the electron. The difference between the calculate and the measured g-factor comes down to the fine structure constant, but they agree.
Now we move to the muon, which is like the electron but much more massive. Chances to exchange with virtual particles is the square of the mass of the particle, so a more massive particle the more likely it will exchange virtual particles. Since the muon is so much more massive (40,000 times massive) than the electron, the likelihood that there will be virtual gluon exchange or virtual Higgs exchange is much more likely. So we do our thing of plugging all of that into a super computer to get the calculate g-factor. We then do our experiment where we spin it like a top to get the g-factor that way. Then we look at the two values and take into consideration the fine structure constant. And that's this experiment. And what they found is that the two numbers are off, by a quite a bit. Enough to point out that our super computers aren't taking into consideration all the various virtual exchanges that COULD happen. AND THAT is what the big deal is.
Part 3 - What it means
The super computers have all the expected virtual exchanges programmed in, so if we're off enough to indicate that we don't have all the virtual exchanges programmed in, then we're missing a fifth kind of virtual exchange that needs to be programmed in, and that may mean there's a fifth force (since all virtual exchanges derive from an actual field).
However, this won't tell us WHAT it is. This is just one way of finding a path to go down. We'll need entirely different avenues to take that path down to discover the actual force. Basically, we're balancing our checkbook and the bank statement, but in the end the checkbook is off by a few dollars. So there has to be some bank transaction in the statement we forgot to write down. So this being off tells us that we're missing something, but doesn't tell us what we're missing.
Additionally, Fermilab confirmed with a sigma of 4.7, which is short of 5 sigma which is needed to claim a discovery. So spinning muons that decay in a few microseconds is pretty hard and with just random cosmic electrons and nuetrinos and what not flying through the air, there's a lot of "noise" on the wires that are measuring the spinning of those muons. So they have to keep working to get a cleaner and cleaner signal. Additionally, once they hit five sigma, they have to repeat it. And then, they have to submit their experiment so that someone else can independently do it as well and they have to hit five sigma. Because in the end, the very experiment they're doing might be what's tossing all the values off to begin with. That is their machine is just fundamentally flawed. That's that consistent but inaccurate that gets covered in high school science. Independent confirmation ensures that someone else builds a machine that aims for the exact same goal but in their own very special way.
So it's a very long road ahead, just so that it can be shown that there is indeed something missing from the calculations. But that's way better than where everyone is right now, not knowing where to look for more physics. If this all pans out, what it points to is there is a fifth force that is very, very weak and that means it'll be difficult to coax it to come out on display so that we can study it. Just the fact that on a muon were talking differences of just a few thousandths means this force is much weaker than the weak force. What role it plays? What does it mediate? No one knows, that'll have to be different experiments. In fact, just like it might not be a single transaction that throws your checkbook off from the statement, same diff, we may be talking about multiple forces, no one knows.
But like all things. This will CONFIRM we are missing some part from the standard model. And that is a big deal. Because right now, everyone thinks we're missing some critical parts, like dark matter and dark energy, but we've got equations that might be right that allows our universe to exist without dark matter and dark energy. But we don't know either way. THIS WILL CONFIRM WE'RE MISSING SOMETHING. That is hugely exciting. Not often you hear people getting excited over "WE DON'T KNOW EVERYTHING!!"