The Crisis in Physics (Script) (Patreon)

According to quantum physics, the universe should have collapsed on itself in the instant after the Big Bang due to all particles being 100 million billion times heavier. But recent observations of the universe existing suggest that this may not have happened. Even more recent observations at the Large Hardron Collider have failed to find out why. In particular, why the Higgs boson is light enough to allow the universe to exist. This is part of something known as the hierarchy problem, and some consider it to be the most important unsolved problem in physics.

The Standard Model of particle physics is a pretty humble name for one of the pinnacle achievements of 20th century physics. It takes the mathematical formalism of quantum field theory and uses it to describe every known particle in the universe. But when first developed, the standard model had a pretty major issue. In its early form, none of the particles, not even the matter particles, had any mass. A particle without mass is obliged to travel at exactly the speed of light all the time and never slower. The Standard model predicted a universe in which all particles acted like radiation, which would imply no atoms or what we think of as matter. Maybe such a universe exists out there, but it’s not this one. Apparently.

The particles of matter—the electrons, quarks, etc. do have mass—so the builders of the standard model needed a mechanism to give it to them. And the best candidate for the job was a mechanism simultaneously developed by several people in the early 60s. That mechanism is driven by what we now call the Higgs field, after one of those several. With that field also came the inevitability of a new particle—the Higgs boson. Now, if we could just detect this particle we would verify this mass-granting mechanism and wrap up the standard model.

So the large hadron collider was built, fired up, and in 2012 the Higgs boson obediently appeared with the right mass to make sense of the masses of the other known particles. Nice work! Standard Model achieved! Of course, mysteries still remained—dark matter, dark energy, the matter-antimatter asymmetry, neutrino masses, how gravity fits into the picture. Quite a bit actually. But the discovery of the Higgs really did close out the Standard Model as a fully self-consistent theory.

There was one particular detail to sort out with regards to the Higgs. An i to dot, so to speak. If the Higgs gives mass to the particles of the standard model, what gives the Higgs its mass? And more importantly, why does it have the specific mass that it does? It turns out that, just as we needed the Higgs to explain the masses of the Standard Model particles, we needed a whole family of new particles to explain why the Higgs has the mass it does. In particular, to explain why it has a low mass, in the range of other standard model particles.

So the LHC kept powering up, physicists expected these new particles to pop out, and there was nothing. It’s now been well over a decade since the discovery of the Higgs Boson and it’s the only new elementary particle the LHC has found.

This seems like a relatively minor problem—nothing a little more theorizing can’t fix. But it’s considered such a serious issue by many that it’s been called the crisis in physics. Today I want to convey why some think of this as such a big deal.

It all comes down to one questions: why is the mass of the Higgs boson small? In particular, why is it so much smaller than the current version of the Standard Model predicts it to be?

This episode is a follow-on from our two recent ones on the quantum structure surrounding the electron and how that defines the electron’s mass. If I stop making sense at any point, maybe go check those out and come back. Or just absorb all the science words and hope for the best.

Let’s go step by step. First, the origin of mass. We covered how the Higgs field grants mass to the particles of matter a long time ago. For now it’s enough to know that due to the unusual nature of the Higgs field, it exists in a state of non-zero energy everywhere in the universe. Particles that interact with this field absorb some of that energy and this becomes their mass. Or at least part of it. Once a particle has mass from the Higgs field, it will also gain even more mass from the cloud of quantum fluctuations that surrounds the particle. We covered that in a lot of detail in the last episode in this series. The mass of the electron comes from both its so-called bare mass, as well as the mass of the swarm of matter-antimatter pairs flickering around it that lead to quantum corrections to that mass, resulting in what we call the dressed mass.

Those quantum corrections come from literally every quantum field the particle can interact with, and every energy scale that these interactions can happen at. If we just keep adding up those quantum corrections with no upper limit on the energy scale, we get that the particle has infinite mass. Particles don’t have infinite mass, so what’s up? So, it’s possible to cancel out some of these quantum corrections because some add positive energy and some add negative energy. If the quantum corrections are basically random, then the cancellation in general won’t be perfect except by extreme luck. So imagine that we discover a particle that has a tiny mass and we can only explain that tinyness as being due to many enormous quantum corrections cancelling out almost perfectly by pure chance. That would seem unnatural. The mass should really be around the scale of the largest corrections. We also call such an unnatural cancellation as “finely tuned” because it seems like someone went in and twiddled the knobs of these otherwise unrelated quantum corrections to make the cancellation work.

If we see that a particle’s mass looks unnaturally small or finely tuned, we typically assume that we’ve missed something. And we’re typically right. There are a few cases where we’ve found some sort of new physics that enables cancellation of those quantum corrections. This new physics typically works above a certain energy scale, suppressing quantum corrections above that scale. For a given particle, its mass will still receive contributions from random quantum corrections up to that scale. In general this means the measured mass of any particle will be at around the energy scale where that new physics gets started with its cancellation.

In the case of the electron we figured out that most of the mass cancellation comes from a particular virtual interaction involving the electron’s antimatter counterpart. This works all the way down to the low measured mass of the electron. See the previous episode for the deets. An important point is that this works for the electron because it’s a spin-½ fermion, which means it has an antimatter counterpart of assist in this cancellation. More formally, the electron has an extra symmetry—chiral symmetry—that want to pull the mass to zero, just as quantum fluctuations want to increase it.

So, new physics that appears at a particular energy can give us a way to avoid piling on virtual mass up to infinity.

This phenomenon is seen for other particles too. There are a couple of cases involving mesons, which are combinations of a quark and an anti-quark. For example the Kaon, which is a strange quark combined with either an up or down quark. The masses of the kaon sub-types are very close to each other. However, when the kaon was first discovered we tried to calculate that mass difference and found that it should be much larger than measured—and that large predicted mass difference was due to large quantum quantum corrections. This felt unnatural, and so physicists guessed that there must be some unknown physics at a very particular, low-ish energy in order to keep the kaon masses in check. They figured that the energy to be a few giga-electron volts. Shortly afterwards the charm quark was discovered at 1.5 GeV, and adding the charm to the quantum correction calculations gave us the correct mass difference for the kaon. So, new physics appeared at right around the necessary energy to protect the kaon from being unnatural.

Something similar is true of the pion, another meson whose mass difference is protected by the rho meson, which has exactly the right energy to keep the pion in check.

OK, great, so if the particle mass is small then we expect to find new physics at an energy scale not too much greater than the particle’s mass in order to suppress large quantum corrections. Now back to the Higgs.

The Higgs boson is particularly vulnerable to having its mass blown up because of its unusual status as the only spin-0 particle in the Standard Model. It doesn’t have the natural protection that the electron and quarks have by virtue of their additional symmetries. The Higgs is its own antiparticle, so it does have the same self-canceling virtual interactions as the electron, for example. Based on the standard model as we currently know it, there is no mechanism to protect its low mass at any known energy. Now, we know that the standard model for sure fails at a certain very high energy—that’s the energy of the Planck scale—10^17 times more energetic than the Higgs boson. This is also the scale at which we think gravity and spacetime themselves become quantum. We don’t know what happens above this scale, but at the very least we expect fluctuations so energetic that they curve the fabric of spacetime. For sure there could be mechanisms above that scale to prevent the Higgs mass from becoming literally infinite, but before we get to those we expect there to be fluctuations that should drive the Higgs mass close to the Planck scale. So maybe these extreme quantum corrections get eliminated by chance cancellations. But the chance to randomly tune that cancelation to one part in 100 million billion is low, to say the least. It would be the biggest fine-tuning problem in physics.

Because of that, physicists expect that other non-random mechanisms are at work at lower energy scales to do the necessary cancellations. In the 1970’s, physicists came up with an elegant system to do just that called supersymmetry, or SUSY. SUSY postulates that every particle, both the fermions that constitute matter and the boson that transmit forces, has a supersymmetric counterpart. For every fermion there’s a supersymmetric boson, and for every boson a counterpart fermion. If these SUSY particles have the right energies, they cleanly cancel out the diverging quantum corrections of the Higgs.

And to do the job they’re needed for, the lightest of these SUSY particles would have had masses not too much larger than the Higgs itself. In which case, the LHC should have found them by now. Which it didn’t. So, what went wrong and what does it mean?

First up, let me say that supersymmetry might still be right. The LHC has probed up to a particular energy range, and that includes the range where the most parsimonious version of SUSY was expected to reveal its first particles. But there could still be SUSY particles at higher energies, and those could still serve to protect the Higgs mass. The problem is that even if LHC finds its first SUSY particle in the next year, its mass will be too high to completely avoid some fine-tuning of the Higgs mass. This has led to a lot of effort to come up with new theories that explain the low mass of the Higgs. I can’t go into them all now, so I’ll just mention a couple of prominent ones.

There are various models that describe the Higgs as a composite particle arising from a slightly more complicated quantum field than the usual Higgs field, but which does the same job of granting mass. This field is fermionic, which means its excitations have spin 1/2, and it behaves somewhat like the strong force in the way its particles bind via confinement in pairs to give the spin-zero composite Higgs. But the mass of this particle is "dynamical", meaning it arises from the interaction, not as a fundamental property of the individual particles. And those individual particles have their own mass protected in the same way as other fermions. That means this composite Higgs is safe from being blown up in the same way as an elementary Higgs would be. This family of theories are called "technicolor" as a play on the color charge of the strong force, although this would really be a different force and field altogether. The idea of a composite Higgs isn't new, and it predates the so-called crisis in physics. In fact, many technicolor models were ruled out by the discovery of the Higgs, and more have been ruled out since. However, there are still versions that could work and perhaps solve the hierarchy problem.

Maybe the most controversial solution is that it’s genuinely crazily unlikely to have such a small Higgs mass. Maybe those random cancellations really did happen to line up just by chance. Well, if this were the only universe then indeed this would be a stroke of good fortune. But what if there are many universes, each with slightly different physics and so that the Higgs mass takes on different values across the multiverse ? Most of these would have a Higgs particle without a ginormous mass—these would instantly recollapse. Only a few would last any time at all.

And there’d be fewer still with a Higgs mass and other standard model parameters that were amenable to the formation of stars, planets and life. And if that’s the case, well which universe do you think we’d find ourselves in ? One that can produce us, probably. This is the so

called the anthropic principle, and it’s a perfectly reasonable argument. It’s also strongly disliked by many physicists because it means that the whole idea of naturalness sort of dies as a tool for advancing physics. We’ve talked about the anthropic principle before, and will again—it’s a deep subject and often mischaracterized. And that’s why I won’t say any more about it now.

The Higgs hierarchy problem is actually just one facet of a more global hierarchy problem - related to other extreme differences in the scales of nature. The difference between the Higgs mass and the Planck scale, but also the difference between the strength of gravity and the strength the quantum forces, and the weakness of dark energy compared to the theoretical prediction from, again, the expected large quantum fluctuations approaching the Planck sale. In upcoming videos we'll talk more about the hierarchy problem, and why it's considered such a deep mystery, and why it may point the way to deeper physics. In the meantime let's just be grateful for the lightness of the Higgs boson, which, apparently, did not thwart the big bang and recollapse spacetime.