Thanks to The Great Courses Plus for supporting PBS Digital Studios. Let's talk about the best evidence we have that the theories of quantum physics truly represent the underlying workings of reality. Quantum field theory is notoriously complicated, built from mind-bendingly abstract mathematics. But could it be that the underlying rules that govern reality are really so far from human intuition, or are physicists just showing off? For better or worse, the physicists are definitely on the right track. We know this because the predictions of quantum field theory stand up to experimental test time and time again. Quantum field theory describes a universe filled with different quantum fields, in which particles are excitations: quantized vibrations. We've talked about QFT many times before, starting with the very first quantum field theory -- quantum electrodynamics.
QED talks about electromagnetic field, whose excitations give us the photon. The calculations of QED describe how this field interacts with charged particles to give us the electromagnetic force, which binds electrons to atoms, atoms to molecules, and therefore, you know, allows you to exist. QED is a much deeper and more complicated description of electromagnetism than the simple "opposite charges attract, like charges repel" of classical electrodynamics. But how do we know it's right? Well, because it makes some predictions that clash with the classical theory, and those predictions are the most precisely tested and thoroughly verified in all of physics. Today we're gonna talk about the theory and experiments behind one of these tests -- measuring the g-factor. Or in simple English: measuring the anomalous magnetic dipole moment of the electron. Okay, first off, what on Earth did I just say? What is the anomalous magnetic dipole moment? Well, it's just like the regular magnetic dipole moment, but more anomalous. Okay, not helpful. Let's break down this magnetic dipole moment thing. Consider a bar magnet. It has a dipole magnetic field, basicly meaning it has
north and south pole -- dipole, two poles. If we put a bar magnet in a second
extrernal magnetic field, it'll feel a torque, a force causing it to rotate
to align with that field. The tendency of a dipole magnet to rotate in an external magnetic field is its magnetic dipole moment. Anything with a dipole magnetic field has a magnetic dipole moment.
It's basically a measure of how much it would interact
with an external magnetic field, if one existed. Let's talk about this dipole thing
a bit more. Magnetic fields are produced by moving electric charges. A perfect dipole field is produced by charges moving in circles. For example, of loop of wire with an electric current, or the planet Earth with its dynamo core. But in case of a bar magnet, the source of its magnetic field is a bit weirder. It mostly comes from the summed dipole magnetic fields of individual electrons in the outer shells of its atoms. And those electron dipole
fields are indeed very weird. As we'll see, their nature is predicted by quantum theory -- measure electron moments, and you verify your quantum picture of reality. Electron magnetic field seem intuitive, if you think of the most tiny
balls of rotating electric charge. Except electrons aren't balls, and they aren't really rotating. As far as we know,
electrons are point-like, they have no size. And it doesn't really make sense to think of an infinitesimal point as rotating. Nonetheless, electrons do have a sort of intrinsic angular momentum, a fundamental quantum spin, that is as intrinsic as mass and charge. Despite not being the same as classical
rotation, this quantum spin does grant electrons
a dipole magnetic field. So, electrons have a magnetic dipole moment, meaning
they feel magnetic fields, and act as little bar magnets. Electrons in atoms feel the magnetic fields produced by their own orbits around the atom. This results in a subtle torque on these electrons, changing their electric states, and resulting in the fine structure splitting of
electron energy levels. The fine structure constant
is named after this effect, and I talked about this
fundamental constant in an earlier episode. Thinking of electrons as little bar magnets, or as rotating balls of charge, is a nice starting point, but in the end it's misleading. It also gives you completely
the wrong answer, if you try to calculate the
electron's magnetic moment. So, that electron diagram you
did in middle school -- it's time to kill that idea, just like you killed your
Tamagotchi. In fact, weirdly, if you measure the magnetic
dipole moment of an electron, you get almost exactly twice the value you'd expect for a tiny classical sphere with the same charge and
angular momentum as an electron. This difference between the quantum versus classical magnetic moments for the electron is called the g-factor. It's the number you need to
multiply the classical value by to get the right answer. So, apparently, g = 2. Experiments point to this, but so does the Dirac equation. This equation is the origin
of quantum electrodynamics, and the first to correctly capture
the notion of quantum spin. It describes electrons as weird four-component objects with quantum
spin magnitudes of half. That's a whole bunch of crazy
we talk about here. So, measurements say the
g-factor is around 2, and Dirac says it's exactly 2. Case closed, right? Wrong, oh, so very wrong. See, even though the Dirac equation tells us how a relativistic
electron would interact with an electromagnetic field, it still treats this EM-field classically. It doesn't consider the quantum
nature of the field. Only the fully developed quantum electrodynamics -- the first
true quantum field theory -- does this. And QED tells us that the
quantum electromagnetic field is a messy, messy place. It's seethes with a faint quantum buzz, infinite phantom oscillations that add infinite complication to any electromagnetic interaction. This messiness messes with interaction of the electron
and the magnetic field to shift the g-factor slightly, so it's not exactly 2, it's 2.0011614... etc. That little bit extra is the anomaly. And this is the
anomalous magnetic dipole moment. It's really incredible that we can even begin to calculate the effect of the messy, buzzying
electromagnetic field, but in fact we can calculate its
effect extremely precisely, and test this through
experiments, showing the underlying truth of
quantum theory. So, one way to think about this
quantum buzz is with virtual photons. Quantum field theory describes the
interactions between particles as the sum total of all possible interactions that can lead to the same result. In the case of electromagnetism,
those interactions are mediated by virtual photons, which is just a mathematical
way to describe quantum buzz. Every interaction with virtual photons that can happen, does. At lest in a sense. And the sum of the infinite possible interactions defines the strength of the one real interaction. And if that doesn't make your head hurt, try thinking about it again. So, yeah, quantum field theory
is a type of madness. An again, we've been down that rabbit hole. In particular, we've looked a bit at Feynman diagrams, which are our best tool for dealing with the absurd
complexity of quantum fields. They represent the possible
interactions of the quantum field by way of virtual photons. And they tell you which interactions
are the most important and which are insignificant. So, you know, you don't have to calculate infinity of them. A basic interaction of an electron with an EM-field is illustrated by this partial Feynman diagram. An electron encounters a real photon that could represent an external magnetic
field, and it's deflected in some way. But the
same encounter could look like this. The electron first emits a virtual photon, then gets deflected, then reabsorbs the virtual photon. Same particles in and
out, so it leads to the same overall result. But now
the electron undergoes an additional interaction with the buzzing quantum field. We need to include this
sort of secondary interaction when we calculate, say,
the overall strength of an electron's interaction
with a magnetic field, when we calculate the
electron's magnetic dipole moment, and its g-factor. If we consider only the first interaction I showed, along with similar "primary" ones, you calculate a g-factor of exactly 2. But if you include the secondary interaction, you get g = 2.0011614. This correction was
first calculated by American physicist Julian Schwinger in 1949. It was an amazing result for the time, but a lot of time has
passed since then, and physicists were not content to simply stop
at this first correction. See, there really are infinite ways the electron
can interact with the EM-field, with crazy networks of
virtual particles and virtual matter-antimatter loops between the real ingoing and outgoing particles. The more complicated the
interaction, the less it contributes to the overall effect. But contribute they do. Over time, physicists have included more and more corrections,
refining the prediction of the g-factor to increasing precision. For each new degree of precision the number of Feynman diagrams needed explodes. Schwinger did his 1949 calculation by hand. Since 2008 all calculations are done on large supercomputing clusters. However, the ultimate arbiter of any physical theory is experiment. To actually measure the
g-factor with the same high precision as these calculations requires some cunning.
One way to do it is to watch the way electrons precess in the constant magnetic field of a cyclotron -- a type of particle
accelerator. Electrons' spin axes are always slightly
misaligned with an external magnetic field due to quantum uncertainty in the spin direction. As a result they feel a torque from that field and precess like a top. This is called Larmor precession. And the rate of this precession tells
us the electron g-factor. And the results are staggering. The measured g-factor agrees
with the calculated value to 10 decimal places. Now, I need to add a little subtlety here -- to get from the QED
calculations to a value for g, you also need to know the fine structure constant that I mentioned earlier. This is the fundamental constant governing the strength of the electromagnetic
interaction of charged particles. This requires an independent
experimental measurement. So, it's really the relationship
between the electron magnetic moment and the fine structure
constant that we are verifying. But that prediction is the most accurately verified prediction
in the history of physics. At its heart, physics is the study of the natural world. We make observations
of reality and then try to find theoretical frameworks that explain those observations. If those theories are good, they are able to predict
things beyond the observations on which the theory was built. The better these predictions, the more universal and presumably the
more correct the theory. The theory of quantum electrodynamics has been pushed to the experimental
limit and come out unscathed. That means that it and
the quantum mechanical principles on which it is founded are good representations of reality. We have to conclude that we're
getting closer and closer to the truth in our search for theories to explain the underlying mechanics of space time. Thanks to The Great Courses Plus for supporting PBS Digital Studios. The Great Courses Plus is a digital learning service that allows you to learn
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thegreatcoursesplus.com/spacetime. And now on to your comments
about getting close to the Sun with the very recently launched Parker Solar Probe. Emma Farnan asks about how satellites and service electronics could be protected given advanced knowledge of a
Carrington-like geomagnetic storm. So, advanced
warning definitely helps a lot. Power grids can be shut down to prevent major damage. That damage
occurs when powerful currents are induced in long range power cables. When those currents hit transformers at
power stations, those transformers can be fried. Just disconnecting the
tranformers is enough to save them. There are various ways to automatically dissipate excess current even without forewarning, but that
would take proper investment in infrastructure to update our
antiquated power grid to the order of tens of billions of dollars. Satellites are tougher. Their electronics can withstand smaller currents,
but a Carrington-size event, it's not clear. Presumably better Faraday cages and integrated surge protections are the answer. Again, it requires investment in long term stability. All of these measures produce benefits outside of the next quarterly report or election
cycle, and that's the real impediment. AndriarSmith asks whether the Sun's million Kelvin corona temperature
is caused by magnetic reconnection. The answer is possibly, even probably, at least in part. So, the mystery here is why the Sun's corona, the extremely diffuse layer of material surrounding the Sun, can be so hot compared to the 5800 Kelvin solar surface. It's pretty firmly established that energy must be pumped into the corona by
magnetic fields. Just radiating it from the solar surface would lead to temperatures below 5800 Kelvin. Magnetic fields can do the job in two ways. One is this magnetic reconnection thing. When magnetic loops,
extending from the surface, brake and reconnect into
different forms, they can dump huge amounts of energy
into the plasma of the corona. Another possible mechanism
is through turbulence in waves generated by the rapid motion of magnetic fields. Fracois Lacombe drops some knowledge on the 1859 Carrington event. In his words, the Carrington event was actually a pair of coronal mass ejections. A lesser one that reached the Earth on August 29th 1859 and caused widespread auroral activity, and the big one that occurred on the Sun on September 1st 1859 and reached the Earth 17.6 hours later. It's been speculated that the first coronal mass ejection cleared
the way to allow the second one to travel so quickly. CMEs usually take several days to cross the distance between Earth and the Sun. And making its effect even more powerful than if it'd happen alone. Well, thanks Francois, I didn't know that. Master Therion expressed his
enjoyment at being mentioned in the comments. Sebastian Elytron cautioned him to enjoy this one -- the second time it feels nowhere near as good, speaking from experience.
Well, Master Therion, this is your second. How much worse was this? And what about you Sebastian?
Was number 3 worse still? Let us know in the comments, and we'll
see how boring these shout-outs can get.
Love this series!
The great courses, the ones I’ve listened to anyway, are really good