As the new year approaches, people think about the future. Me, I’m thinking about the future of fundamental physics, about what might lie beyond the Standard Model. Physicists search for many different things, with many different motivations. Some are clear missing pieces, places where the Standard Model fails and we know we’ll need to modify it. Others are based on experience, with no guarantees but an expectation that, whatever we find, it will be surprising. Finally, some are cool possibilities, ideas that would explain something or fill in a missing piece but aren’t strictly necessary.

The Almost-Sure Things

Science isn’t math, so nothing here is really a sure thing. We might yet discover a flaw in important principles like quantum mechanics and special relativity, and it might be that an experimental result we trust turns out to be flawed. But if we chose to trust those principles, and our best experiments, then these are places we know the Standard Model is incomplete:

• Neutrino Masses: The original Standard Model’s neutrinos were massless. Eventually, physicists discovered this was wrong: neutrinos oscillate, switching between different types in a way they only could if they had different masses. This result is familiar enough that some think of it as already part of the Standard Model, not really beyond. But the masses of neutrinos involve unsolved mysteries: we don’t know what those masses are, but more, there are different ways neutrinos could have mass, and we don’t yet know which is present in nature. Neutrino masses also imply the existence of an undiscovered “sterile” neutrino, a particle that doesn’t interact with the strong, weak, or electromagnetic forces.
• Dark Matter Phenomena (and possibly Dark Energy Phenomena): Astronomers first suggested dark matter when they observed galaxies moving at speeds inconsistent with the mass of their stars. Now, they have observed evidence for it in a wide variety of situations, evidence which seems decisively incompatible with ordinary gravity and ordinary matter. Some solve this by introducing dark matter, others by modifying gravity, but this is more of a technical difference than it sounds: in order to modify gravity, one must introduce new quantum fields, much the same way one does when introducing dark matter. The only debate is how “matter-like” those fields need to be, but either approach goes beyond the Standard Model.
• Quantum Gravity: It isn’t as hard to unite quantum mechanics and gravity as you might think. Physicists have known for decades how to write down a naive theory of quantum gravity, one that follows the same steps one might use to derive the quantum theory of electricity and magnetism. The problem is, this theory is incomplete. It works at low energies, but as the energy increases it loses the ability to make predictions, eventually giving nonsensical answers like probabilities greater than one. We have candidate solutions to this problem, like string theory, but we might not know for a long time which solution is right.
• Landau Poles: Here’s a more obscure one. In particle physics we can zoom in and out in our theories, using similar theories at different scales. What changes are the coupling constants, numbers that determine the strength of the different forces. You can think of this in a loosely reductionist way, with the theories at smaller scales determining the constants for theories at larger scales. This gives workable theories most of the time, but it fails for at least one part of the Standard Model. In electricity and magnetism, the coupling constant increases as you zoom in. Eventually, it becomes infinite, and what’s more, does so at a finite energy scale. It’s still not clear how we should think about this, but luckily we won’t have to very soon: this energy scale is vastly vastly higher than even the scale of quantum gravity.
• Some Surprises Guarantee Others: The Standard Model is special in a way that gravity isn’t. Even if you dial up the energy, a Standard Model calculation will always “make sense”: you never get probabilities greater than one. This isn’t true for potential deviations from the Standard Model. If the Higgs boson turns out to interact differently than we expect, it wouldn’t just be a violation of the Standard Model on its own: it would guarantee mathematically that, at some higher energy, we’d have to find something new. That was precisely the kind of argument the LHC used to find the Higgs boson: without the Higgs, something new was guaranteed to happen within the energy range of the LHC to prevent impossible probability numbers.

The Argument from (Theoretical) Experience

Everything in this middle category rests on a particular sort of argument. It’s short of a guarantee, but stronger than a dream or a hunch. While the previous category was based on calculations in theories we already know how to write down, this category relies on our guesses about theories we don’t yet know how to write.

Suppose we had a deeper theory, one that could use fewer parameters to explain the many parameters of the Standard Model. For example, it might explain the Higgs mass, letting us predict it rather than just measuring it like we do now. We don’t have a theory like that yet, but what we do have are many toy model theories, theories that don’t describe the real world but do, in this case, have fewer parameters. We can observe how these theories work, and what kinds of discoveries scientists living in worlds described by them would make. By looking at this process, we can get a rough idea of what to expect, which things in our own world would be “explained” in other ways in these theories.

• The Hierarchy Problem: This is also called the naturalness problem. Suppose we had a theory that explained the mass of the Higgs, one where it wasn’t just a free parameter. We don’t have such a theory for the real Higgs, but we do have many toy models with similar behavior, ones with a boson with its mass determined by something else. In these models, though, the mass of the boson is always close to the energy scale of other new particles, particles which have a role in determining its mass, or at least in postponing that determination. This was the core reason why people expected the LHC to find something besides the Higgs. Without such new particles, the large hierarchy between the mass of the Higgs and the mass of new particles becomes a mystery, one where it gets harder and harder to find a toy model with similar behavior that still predicts something like the Higgs mass.
• The Strong CP Problem: The weak nuclear force does what must seem like a very weird thing, by violating parity symmetry: the laws that govern it are not the same when you flip the world in a mirror. This is also true when you flip all the charges as well, a combination called CP (charge plus parity). But while it may seem strange that the weak force violates this symmetry, physicists find it stranger that the strong force seems to obey it. Much like in the hierarchy problem, it is very hard to construct a toy model that both predicts a strong force that maintains CP (or almost maintains it) and doesn’t have new particles. The new particle in question, called the axion, is something some people also think may explain dark matter.
• Matter-Antimatter Asymmetry: We don’t know the theory of quantum gravity. Even if we did, the candidate theories we have struggle to describe conditions close to the Big Bang. But while we can’t prove it, many physicists expect the quantum gravity conditions near the Big Bang to produce roughly equal amounts of matter and antimatter. Instead, matter dominates: we live in a world made almost entirely of matter, with no evidence of large antimatter areas even far out in space. This lingering mystery could be explained if some new physics was biased towards matter instead of antimatter.
• Various Problems in Cosmology: Many open questions in cosmology fall in this category. The small value of the cosmological constant is mysterious for the same reasons the small value of the Higgs mass is, but at a much larger and harder to fix scale. The early universe surprises many cosmologists by its flatness and uniformity, which has led them to propose new physics. This surprise is not because such flatness and uniformity is mathematically impossible, but because it is not the behavior they would expect out of a theory of quantum gravity.

The Cool Possibilities

Some ideas for physics beyond the standard model aren’t required, either from experience or cold hard mathematics. Instead, they’re cool, and would be convenient. These ideas would explain things that look strange, or make for a simpler deeper theory, but they aren’t the only way to do so.

• Grand Unified Theories: Not the same as a “theory of everything”, Grand Unified Theories unite the three “particle physics forces”: the strong nuclear force, the weak nuclear force, and electromagnetism. Under such a theory, the different parameters that determine the strengths of those forces could be predicted from one shared parameter, with the forces only seeming different at low energies. These theories often unite the different matter particles too, but they also introduce new particles and new forces. These forces would, among other things, make protons unstable, and so giant experiments have been constructed to try to detect a proton decaying into other particles. So far none has been seen.
• Low-Energy Supersymmetry: String theory requires supersymmetry, a relationship where matter and force particles share many properties. That supersymmetry has to be “broken”, which means that while the matter and force particles have the same charges, they can have wildly different masses, so that the partner particles are all still undiscovered. Those masses may be extremely high, all the way up at the scale of quantum gravity, but they could also be low enough to test at the LHC. Physicists hoped to detect such particles, as they could have been a good solution to the hierarchy problem. Now that the LHC hasn’t found these supersymmetric particles, it is much harder to solve the problem this way, though some people are still working on it.
• Large Extra Dimensions: String theory also involves extra dimensions, beyond our usual three space and one time. Those dimensions are by default very small, but some proposals have them substantially bigger, big enough that we could have seen evidence for them at the LHC. These proposals could explain why gravity is so much weaker than the other forces. Much like the previous members of this category though, no evidence for this has yet been found.

I think these categories are helpful, but experts may quibble about some of my choices. I also haven’t mentioned every possible thing that could be found beyond the Standard Model. If you’ve heard of something and want to know which category I’d put it in, let me know in the comments!