# Unification That Does Something

I’ve got unification on the brain.

Recently, a commenter asked me what physicists mean when they say two forces unify. While typing up a response, I came across this passage, in a science fiction short story by Ted Chiang.

Physics admits of a lovely unification, not just at the level of fundamental forces, but when considering its extent and implications. Classifications like ‘optics’ or ‘thermodynamics’ are just straitjackets, preventing physicists from seeing countless intersections.

This passage sounds nice enough, but I feel like there’s a misunderstanding behind it. When physicists seek after unification, we’re talking about something quite specific. It’s not merely a matter of two topics intersecting, or describing them with the same math. We already plumb intersections between fields, including optics and thermodynamics. When we hope to find a unified theory, we do so because it does something. A real unified theory doesn’t just aid our calculations, it gives us new ways to alter the world.

There’s a nice series of posts on the old Quantum Diaries blog that explains electroweak unification in detail. I’ll be a bit vaguer here.

You might have heard of four fundamental forces: gravity, electromagnetism, the strong nuclear force, and the weak nuclear force. You might have also heard that two of these forces are unified: the electromagnetic force and the weak nuclear force form something called the electroweak force.

What does it mean that these forces are unified? How does it work?

Zoom in far enough, and you don’t see the electromagnetic force and the weak force anymore. Instead you see two different forces, I’ll call them “W” and “B”. You’ll also see the Higgs field. And crucially, you’ll see the “W” and “B” forces interact with the Higgs.

The Higgs field is special because it has what’s called a “vacuum” value. Even in otherwise empty space, there’s some amount of “Higgsness” in the background, like the color of a piece of construction paper. This background Higgs-ness is in some sense an accident, just one stable way the universe happens to sit. In particular, it picks out an arbitrary kind of direction: parts of the “W” and “B” forces happen to interact with it, and parts don’t.

Now let’s zoom back out. We could, if we wanted, keep our eyes on the “W” and “B” forces. But that gets increasingly silly. As we zoom out we won’t be able to see the Higgs field anymore. Instead, we’ll just see different parts of the “W” and “B” behaving in drastically different ways, depending on whether or not they interact with the Higgs. It will make more sense to talk about mixes of the “W” and “B” fields, to distinguish the parts that are “lined up” with the background Higgs and the parts that aren’t. It’s like using “aft” and “starboard” on a boat. You could use “north” and “south”, but that would get confusing pretty fast.

What are those “mixes” of the “W” and “B” forces? Why, they’re the weak nuclear force and the electromagnetic force!

This, broadly speaking, is the kind of unification physicists look for. It doesn’t have to be a “mix” of two different forces: most of the models physicists imagine start with a single force. But the basic ideas are the same: that if you “zoom in” enough you see a simpler model, but that model is interacting with something that “by accident” picks a particular direction, so that as we zoom out different parts of the model behave in different ways. In that way, you could get from a single force to all the different forces we observe.

That “by accident” is important here, because that accident can be changed. That’s why I said earlier that real unification lets us alter the world.

To be clear, we can’t change the background Higgs field with current technology. The biggest collider we have can just make a tiny, temporary fluctuation (that’s what the Higgs boson is). But one implication of electroweak unification is that, with enough technology, we could. Because those two forces are unified, and because that unification is physical, with a physical cause, it’s possible to alter that cause, to change the mix and change the balance. This is why this kind of unification is such a big deal, why it’s not the sort of thing you can just chalk up to “interpretation” and ignore: when two forces are unified in this way, it lets us do new things.

Mathematical unification is valuable. It’s great when we can look at different things and describe them in the same language, or use ideas from one to understand the other. But it’s not the same thing as physical unification. When two forces really unify, it’s an undeniable physical fact about the world. When two forces unify, it does something.

## 3 thoughts on “Unification That Does Something”

1. ohwilleke

A lot is written about “beyond the Standard Model” physics (or beyond “Core Theory” physics). But, it would be nice to see more “behind the Standard Model” or “within the Standard Model” physics. There just has to be a deeper order and structure behind its two dozen experimentally determined fundamental constants along the lines of the electroweak unification model that would provide not just a way to more precisely determine those constants, but also deeper insight in the nature of Nature. A lot of that work being done towards that end gets dismissed as numerology or phenomenology without connection to a theoretical basis (and this isn’t always wrong), but it certainly seems as if we are so close . . . and yet, so far from grasping it. Perhaps we have been led astray pursuing approaches like Supersymmetry and Technicolor and some related concepts that haven’t panned out as hoped?

My gut tells me that we might be missing a trick or two in conventional QCD as well. It is the only part of Standard Model physics, where it isn’t uncommon for two theoretical predictions to be greatly at odds with each other to the point of not being consistent at two sigma, and for an experimental result to be seriously discrepant from the conventionally calculated QCD prediction, without raising much of a stir, because no one is proposing any real alternatives to it, or major improvements upon it. And there are a lot of uncharted waters, although seemingly not “fundamental”: not only have we not seen free glueballs we don’t really have good a priori predictions of how they should blend with conventional hadrons; there are still open questions about scalar mesons, axial vector mesons, tetraquark, pentaquark, hexaquark, meson molecule, etc. hadronic structures too. We’re getting to the point where we can post-dict the particle spectrum and make three and four significant digit estimates of hadron properties like mass that can be measured to six to ten significant digits. PDFs have been determinable from first principles in theory for half a century, but we’re just starting to be able to do even that.

Some of that is surely because the math is hard and despite your best efforts, amplitudologists have managed to progress only incrementally in cracking this nut.

But both in both the SM and its QCD subset, it also feels like we’ve got most of the rules but not quite all of them, like knowing the rules of chess, except castling and promoting a pawn. The lack feels like it is contributing to the roadblock that fundamental physics is in (the “nightmare scenario” or “the physics desert”) because I’m skeptical that simply throwing more brute force energy at the problem is going to reveal these missing rules. It also seems like too many people, however, have giving up looking in favor of pursuing agendas that seem to be dead ends and losing focus and direction. Am I wrong?

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1. 4gravitons Post author

So, part of the point I was trying to make here is that anything that actually explains why the SM constants are the way they are has to involve BSM physics. I was specifically talking about unification, but it really applies to any other explanation as well. If all you’re doing is characterizing patterns in the known constants, then that’s not really a scientific explanation: it doesn’t let you do anything out there in the world you couldn’t do before, and if someone else has a different interpretation you have no way of convincing them you’re right. That’s why, by itself, that sort of thing really is just numerology.

That’s not to say that looking for patterns isn’t useful. If you have no idea what you’re looking for (and I think it’s fair to say we have no idea what we’re looking for) then any pattern can be a viable starting-point. All I’m saying is that a pattern can’t be the endpoint: if you never find any BSM implications, then you haven’t really explained the SM constants in a scientific way. This isn’t a knock on the people looking for these patterns, who aren’t at that endpoint anyway…but I feel like you in particular like to imagine a world where the SM really is all there is, and I’m trying to say that you can’t both have that and a scientific explanation for the SM constants. That would be having your cake and eating it too.

There’s a different point, which is that some things that seem mysterious now may just be consequences of the SM once we understand it better. As you say, QCD in particular is ill-understood. Apart from just getting a deeper understanding of the theory, it’s certainly conceivable that some of what we expect to be due to BSM physics is really just due to ill-understood SM physics. I don’t really have examples in mind there, just that I wouldn’t rule it out.

If it’s that understanding you care about, then I think the community is less off-track than you think. In particular, it’s hidden in a corner you probably don’t look at that often: formal QFT. Here I don’t mean my kind of stuff, but even more formal, the topics that the string theory community mostly works on. If you peel back the supersymmetry and multiple dimensions and the like, a huge amount of what they’re doing boils down to trying to understand strongly-coupled field theories in as many ways as possible. These people aren’t usually talking about QCD specifically, but still I think that if there is some deep reimagining of QCD it’s more likely to come from them than the actual QCD community. The QCD community will refine and polish the theory in every way possible, but for the most part they aren’t going to turn it on its head.

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