Tag Archives: PublicPerception

The Many Worlds of Condensed Matter

Physics is the science of the very big and the very small. We study the smallest scales, the fundamental particles that make up the universe, and the largest, stars on up to the universe as a whole.

We also study the world in between, though.

That’s the domain of condensed matter, the study of solids, liquids, and other medium-sized arrangements of stuff. And while it doesn’t make the news as often, it’s arguably the biggest field in physics today.

(In case you’d like some numbers, the American Physical Society has divisions dedicated to different sub-fields. Condensed Matter Physics is almost twice the size of the next biggest division, Particles & Fields. Add in other sub-fields that focus on medium-sized-stuff, like those who work on solid state physics, optics, or biophysics, and you get a majority of physicists focused on the middle of the distance scale.)

When I started grad school, I didn’t pay much attention to condensed matter and related fields. Beyond the courses in quantum field theory and string theory, my “breadth” courses were on astrophysics and particle physics. But over and over again, from people in every sub-field, I kept hearing the same recommendation:

“You should take Solid State Physics. It’s a really great course!”

At the time, I never understood why. It was only later, once I had some research under my belt, that I realized:

Condensed matter uses quantum field theory!

The same basic framework, describing the world in terms of rippling quantum fields, doesn’t just work for fundamental particles. It also works for materials. Rather than describing the material in terms of its fundamental parts, condensed matter physicists “zoom out” and talk about overall properties, like sound waves and electric currents, treating them as if they were the particles of quantum field theory.

This tends to confuse the heck out of journalists. Not used to covering condensed matter (and sometimes egged on by hype from the physicists), they mix up the metaphorical particles of these systems with the sort of particles made by the LHC, with predictably dumb results.

Once you get past the clumsy journalism, though, this kind of analogy has a lot of value.

Occasionally, you’ll see an article about string theory providing useful tools for condensed matter. This happens, but it’s less widespread than some of the articles make it out to be: condensed matter is a huge and varied field, and string theory applications tend to be of interest to only a small piece of it.

It doesn’t get talked about much, but the dominant trend is actually in the other direction: increasingly, string theorists need to have at least a basic background in condensed matter.

String theory’s curse/triumph is that it can give rise not just to one quantum field theory, but many: a vast array of different worlds obtained by twisting extra dimensions in different ways. Particle physicists tend to study a fairly small range of such theories, looking for worlds close enough to ours that they still fit the evidence.

Condensed matter, in contrast, creates its own worlds. Pick the right material, take the right slice, and you get quantum field theories of almost any sort you like. While you can’t go to higher dimensions than our usual four, you can certainly look at lower ones, at the behavior of currents on a sheet of metal or atoms arranged in a line. This has led some condensed matter theorists to examine a wide range of quantum field theories with one strange behavior or another, theories that wouldn’t have occurred to particle physicists but that, in many cases, are part of the cornucopia of theories you can get out of string theory.

So if you want to explore the many worlds of string theory, the many worlds of condensed matter offer a useful guide. Increasingly, tools from that community, like integrability and tensor networks, are migrating over to ours.

It’s gotten to the point where I genuinely regret ignoring condensed matter in grad school. Parts of it are ubiquitous enough, and useful enough, that some of it is an expected part of a string theorist’s background. The many worlds of condensed matter, as it turned out, were well worth a look.

Pop Goes the Universe and Other Cosmic Microwave Background Games

(With apologies to whoever came up with this “book”.)

Back in February, Ijjas, Steinhardt, and Loeb wrote an article for Scientific American titled “Pop Goes the Universe” criticizing cosmic inflation, the proposal that the universe underwent a period of rapid expansion early in its life, smoothing it out to achieve the (mostly) uniform universe we see today. Recently, Scientific American published a response by Guth, Kaiser, Linde, Nomura, and 29 co-signers. This was followed by a counterresponse, which is the usual number of steps for this sort of thing before it dissipates harmlessly into the blogosphere.

In general, string theory, supersymmetry, and inflation tend to be criticized in very similar ways. Each gets accused of being unverifiable, able to be tuned to match any possible experimental result. Each has been claimed to be unfairly dominant, its position as “default answer” more due to the bandwagon effect than the idea’s merits. All three tend to get discussed in association with the multiverse, and blamed for dooming physics as a result. And all are frequently defended with one refrain: “If you have a better idea, what is it?”

It’s probably tempting (on both sides) to view this as just another example of that argument. In reality, though, string theory, supersymmetry, and inflation are all in very different situations. The details matter. And I worry that in this case both sides are too ready to assume the other is just making the “standard argument”, and ended up talking past each other.

When people say that string theory makes no predictions, they’re correct in a sense, but off topic: the majority of string theorists aren’t making the sort of claims that require successful predictions. When people say that inflation makes no predictions, if you assume they mean the same thing that people mean when they accuse string theory of making no predictions, then they’re flat-out wrong. Unlike string theorists, most people who work on inflation care a lot about experiment. They write papers filled with predictions, consequences for this or that model if this or that telescope sees something in the near future.

I don’t think Ijjas, Steinhardt, and Loeb were making that kind of argument.

When people say that supersymmetry makes no predictions, there’s some confusion of scope. (Low-energy) supersymmetry isn’t one specific proposal that needs defending on its own. It’s a class of different models, each with its own predictions. Given a specific proposal, one can see if it’s been ruled out by experiment, and predict what future experiments might say about it. Ruling out one model doesn’t rule out supersymmetry as a whole, but it doesn’t need to, because any given researcher isn’t arguing for supersymmetry as a whole: they’re arguing for their particular setup. The right “scope” is between specific supersymmetric models and specific non-supersymmetric models, not both as general principles.

Guth, Kaiser, Linde, and Nomura’s response follows similar lines in defending inflation. They point out that the wide variety of models are subject to being ruled out in the face of observation, and compare to the construction of the Standard Model in particle physics, with many possible parameters under the overall framework of Quantum Field Theory.

Ijjas, Steinhardt, and Loeb’s article certainly looked like it was making this sort of mistake. But as they clarify in the FAQ of their counter-response, they’ve got a more serious objection. They’re arguing that, unlike in the case of supersymmetry or the Standard Model, specific inflation models do not lead to specific predictions. They’re arguing that, because inflation typically leads to a multiverse, any specific model will in fact lead to a wide variety of possible observations. In effect, they’re arguing that the multitude of people busily making predictions based on inflationary models are missing a step in their calculations, underestimating their errors by a huge margin.

This is where I really regret that these arguments usually end after three steps (article, response, counter-response). Here Ijjas, Steinhardt, and Loeb are making what is essentially a technical claim, one that Guth, Kaiser, Linde, and Nomura could presumably respond to with a technical response, after which the rest of us would actually learn something. As-is, I certainly don’t have the background in inflation to know whether or not this point makes sense, and I’d love to hear from someone who does.

One aspect of this exchange that baffled me was the “accusation” that Ijjas, Steinhardt, and Loeb were just promoting their own work on bouncing cosmologies. (I put “accusation” in quotes because while Ijjas, Steinhardt, and Loeb seem to treat it as if it were an accusation, Guth, Kaiser, Linde, and Nomura don’t obviously mean it as one.)

“Bouncing cosmology” is Ijjas, Steinhardt, and Loeb’s answer to the standard “If you have a better idea, what is it?” response. It wasn’t the focus of their article, but while they seem to think this speaks well of them (hence their treatment of “promoting their own work” as if it were an accusation), I don’t. I read a lot of Scientific American growing up, and the best articles focused on explaining a positive vision: some cool new idea, mainstream or not, that could capture the public’s interest. That kind of article could still have included criticism of inflation, you’d want it in there to justify the use of a bouncing cosmology. But by going beyond that, it would have avoided falling into the standard back and forth that these arguments tend to, and maybe we would have actually learned from the exchange.

What Space Can Tell Us about Fundamental Physics

Back when LIGO announced its detection of gravitational waves, there was one question people kept asking me: “what does this say about quantum gravity?”

The answer, each time, was “nothing”. LIGO’s success told us nothing about quantum gravity, and very likely LIGO will never tell us anything about quantum gravity.

The sheer volume of questions made me think, though. Astronomy, astrophysics, and cosmology fascinate people. They capture the public’s imagination in a way that makes them expect breakthroughs about fundamental questions. Especially now, with the LHC so far seeing nothing new since the Higgs, people are turning to space for answers.

Is that a fair expectation? Well, yes and no.

Most astrophysicists aren’t concerned with finding new fundamental laws of nature. They’re interested in big systems like stars and galaxies, where we know most of the basic rules but can’t possibly calculate all their consequences. Like most physicists, they’re doing the vital work of “physics of decimals”.

At the same time, there’s a decent chunk of astrophysics and cosmology that does matter for fundamental physics. Just not all of it. Here are some of the key areas where space has something important to say about the fundamental rules that govern our world:

 

1. Dark Matter:

Galaxies rotate at different speeds than their stars would alone. Clusters of galaxies bend light that passes by, and do so more than their visible mass would suggest. And when scientists try to model the evolution of the universe, from early images to its current form, the models require an additional piece: extra matter that cannot interact with light. All of this suggests that there is some extra “dark” matter in the universe, not described by our standard model of particle physics.

If we want to understand this dark matter, we need to know more about its properties, and much of that can be learned from astronomy. If it turns out dark matter isn’t really matter after all, if it can be explained by a modification of gravity or better calculations of gravity’s effects, then it still will have important implications for fundamental physics, and astronomical evidence will still be key to finding those implications.

2. Dark Energy (/Cosmological Constant/Inflation/…):

The universe is expanding, and its expansion appears to be accelerating. It also seems more smooth and uniform than expected, suggesting that it had a period of much greater acceleration early on. Both of these suggest some extra quantity: a changing acceleration, a “dark energy”, the sort of thing that can often be explained by a new scalar field like the Higgs.

Again, the specifics: how (and perhaps if) the universe is expanding now, what kinds of early expansion (if any) the shape of the universe suggests, these will almost certainly have implications for fundamental physics.

3. Limits on stable stuff:

Let’s say you have a new proposal for particle physics. You’ve predicted a new particle, but it can’t interact with anything else, or interacts so weakly we’d never detect it. If your new particle is stable, then you can still say something about it, because its mass would have an effect on the early universe. Too many such particles and they would throw off cosmologists’ models, ruling them out.

Alternatively, you might predict something that could be detected, but hasn’t, like a magnetic monopole. Then cosmologists can tell you how many such particles would have been produced in the early universe, and thus how likely we would be to detect them today. If you predict too many particles and we don’t see them, then that becomes evidence against your proposal.

4. “Cosmological Collider Physics”:

A few years back, Nima Arkani-Hamed and Juan Maldacena suggested that the early universe could be viewed as an extremely high energy particle collider. While this collider performed only one experiment, the results from that experiment are spread across the sky, and observed patterns in the early universe should tell us something about the particles produced by the cosmic collider.

People are still teasing out the implications of this idea, but it looks promising, and could mean we have a lot more to learn from examining the structure of the universe.

5. Big Weird Space Stuff:

If you suspect we live in a multiverse, you might want to look for signs of other universes brushing up against our own. If your model of the early universe predicts vast cosmic strings, maybe a gravitational wave detector like LIGO will be able to see them.

6. Unexpected weirdness:

In all likelihood, nothing visibly “quantum” happens at the event horizons of astrophysical black holes. If you think there’s something to see though, the Event Horizon Telescope might be able to see it. There’s a grab bag of other predictions like this: situations where we probably won’t see anything, but where at least one person thinks there’s a question worth asking.

 

I’ve probably left something out here, but this should give you a general idea. There is a lot that fundamental physics can learn from astronomy, from the overall structure and origins of the universe to unexplained phenomena like dark matter. But not everything in astronomy has these sorts of implications: for the most part, astronomy is interesting not because it tells us something about the fundamental laws of nature, but because it tells us how the vast space above us actually happens to work.

Popularization as News, Popularization as Signpost

Lubos Motl has responded to my post from last week about the recent Caltech short, Quantum is Calling. His response is pretty much exactly what you’d expect, including the cameos by Salma Hayek and Kaley Cuoco.

The only surprise was his lack of concern for accuracy. Quantum is Calling got the conjecture it was trying to popularize almost precisely backwards. I was expecting that to bother him, at least a little.

Should it bother you?

That depends on what you think Quantum is Calling is trying to do.

Science popularization, even good science popularization, tends to get things wrong. Some of that is inevitable, a result of translating complex concepts to a wider audience.

Sometimes, though, you can’t really chalk it up to translation. Interstellar had some extremely accurate visualizations of black holes, but it also had an extremely silly love-powered tesseract. That wasn’t their attempt to convey some subtle scientific truth, it was just meant to sound cool.

And the thing is, that’s not a bad thing to do. For a certain kind of piece, sounding cool really is the point.

Imagine being an explorer. You travel out into the wilderness and find a beautiful waterfall.

south_falls_silver_falls_state_park

Example:

How do you tell people about it?

One option is the press. The news can cover your travels, so people can stay up to date with the latest in waterfall discoveries. In general, you’d prefer this sort of thing to be fairly accurate: the goal here is to inform people, to give them a better idea of the world around them.

Alternatively, you can advertise. You put signposts up around town pointing toward the waterfall, complete with vivid pictures. Here, accuracy matters a lot less: you’re trying to get people excited, knowing that as they get closer they can get more detailed information.

In science popularization, the “news” here isn’t just news. It’s also blog posts, press releases, and public lectures. It’s the part of science popularization that’s supposed to keep people informed, and it’s one that we hope is mostly accurate, at least as far as possible.

The “signposts”, meanwhile, are things like Interstellar. Their audience is as wide as it can possibly be, and we don’t expect them to get things right. They’re meant to excite people, to get them interested in science. The expectation is that a few students will find the imagery interesting enough to go further, at which point they can learn the full story and clear up any remaining misconceptions.

Quantum is Calling is pretty clearly meant to be a signpost. The inaccuracy is one way to tell, but it should be clear just from the context. We’re talking about a piece with Hollywood stars here. The relative star-dom of Zoe Saldana and Keanu Reeves doesn’t matter, the presence of any mainstream film stars whatsoever means they’re going for the broadest possible audience.

(Of course, the fact that it’s set up to look like an official tie-in to the Star Trek films doesn’t hurt matters either.)

They’re also quite explicit about their goals. The piece’s predecessor has Keanu Reeves send a message back in time, with the goal of inspiring a generation of young scientists to build a future paradise. They’re not subtle about this.

Ok, so what’s the problem? Signposts are allowed to be inaccurate, so the inaccuracy shouldn’t matter. Eventually people will climb up to the waterfall and see it for themselves, right?

What if the waterfall isn’t there?

wonder_mountain_dry_backside_waterfall

Like so:

The evidence for ER=EPR (the conjecture that Quantum is Calling is popularizing) isn’t like seeing a waterfall. It’s more like finding it via surveying. By looking at the slope of nearby terrain and following the rivers, you can get fairly confident that there should be a waterfall there, even if you can’t yet see it over the next ridge. You can then start sending scouts, laying in supplies, and getting ready for a push to the waterfall. You can alert the news, telling journalists of the magnificent waterfall you expect to find, so the public can appreciate the majesty of your achievement.

What you probably shouldn’t do is put up a sign for tourists.

As I hope I made clear in my last post, ER=EPR has some decent evidence. It hasn’t shown that it can handle “foot traffic”, though. The number of researchers working on it is still small. (For a fun but not especially rigorous exercise, try typing “ER=EPR” and “AdS/CFT” into physics database INSPIRE.) Conjectures at this stage are frequently successful, but they often fail, and ER=EPR still has a decent chance of doing so. Tying your inspiring signpost to something that may well not be there risks sending tourists up to an empty waterfall. They won’t come down happy.

As such, I’m fine with “news-style” popularizations of ER=EPR. And I’m fine with “signposts” for conjectures that have shown they can handle some foot traffic. (A piece that sends Zoe Saldana to the holodeck to learn about holography could be fun, for example.) But making this sort of high-profile signpost for ER=EPR feels irresponsible and premature. There will be plenty of time for a Star Trek tie-in to ER=EPR once it’s clear the idea is here to stay.

What’s in a Conjecture? An ER=EPR Example

A few weeks back, Caltech’s Institute of Quantum Information and Matter released a short film titled Quantum is Calling. It’s the second in what looks like will become a series of pieces featuring Hollywood actors popularizing ideas in physics. The first used the game of Quantum Chess to talk about superposition and entanglement. This one, featuring Zoe Saldana, is about a conjecture by Juan Maldacena and Leonard Susskind called ER=EPR. The conjecture speculates that pairs of entangled particles (as investigated by Einstein, Podolsky, and Rosen) are in some sense secretly connected by wormholes (or Einstein-Rosen bridges).

The film is fun, but I’m not sure ER=EPR is established well enough to deserve this kind of treatment.

At this point, some of you are nodding your heads for the wrong reason. You’re thinking I’m saying this because ER=EPR is a conjecture.

I’m not saying that.

The fact of the matter is, conjectures play a very important role in theoretical physics, and “conjecture” covers a wide range. Some conjectures are supported by incredibly strong evidence, just short of mathematical proof. Others are wild speculations, “wouldn’t it be convenient if…” ER=EPR is, well…somewhere in the middle.

Most popularizers don’t spend much effort distinguishing things in this middle ground. I’d like to talk a bit about the different sorts of evidence conjectures can have, using ER=EPR as an example.

octopuswormhole_v1

Our friendly neighborhood space octopus

The first level of evidence is motivation.

At its weakest, motivation is the “wouldn’t it be convenient if…” line of reasoning. Some conjectures never get past this point. Hawking’s chronology protection conjecture, for instance, points out that physics (and to some extent logic) has a hard time dealing with time travel, and wouldn’t it be convenient if time travel was impossible?

For ER=EPR, this kind of motivation comes from the black hole firewall paradox. Without going into it in detail, arguments suggested that the event horizons of older black holes would resemble walls of fire, incinerating anything that fell in, in contrast with Einstein’s picture in which passing the horizon has no obvious effect at the time. ER=EPR provides one way to avoid this argument, making event horizons subtle and smooth once more.

Motivation isn’t just “wouldn’t it be convenient if…” though. It can also include stronger arguments: suggestive comparisons that, while they could be coincidental, when put together draw a stronger picture.

In ER=EPR, this comes from certain similarities between the type of wormhole Maldacena and Susskind were considering, and pairs of entangled particles. Both connect two different places, but both do so in an unusually limited way. The wormholes of ER=EPR are non-traversable: you cannot travel through them. Entangled particles can’t be traveled through (as you would expect), but more generally can’t be communicated through: there are theorems to prove it. This is the kind of suggestive similarity that can begin to motivate a conjecture.

(Amusingly, the plot of the film breaks this in both directions. Keanu Reeves can neither steal your cat through a wormhole, nor send you coded messages with entangled particles.)

rjxhfqj

Nor live forever as the portrait in his attic withers away

Motivation is a good reason to investigate something, but a bad reason to believe it. Luckily, conjectures can have stronger forms of evidence. Many of the strongest conjectures are correspondences, supported by a wealth of non-trivial examples.

In science, the gold standard has always been experimental evidence. There’s a reason for that: when you do an experiment, you’re taking a risk. Doing an experiment gives reality a chance to prove you wrong. In a good experiment (a non-trivial one) the result isn’t obvious from the beginning, so that success or failure tells you something new about the universe.

In theoretical physics, there are things we can’t test with experiments, either because they’re far beyond our capabilities or because the claims are mathematical. Despite this, the overall philosophy of experiments is still relevant, especially when we’re studying a correspondence.

“Correspondence” is a word we use to refer to situations where two different theories are unexpectedly computing the same thing. Often, these are very different theories, living in different dimensions with different sorts of particles. With the right “dictionary”, though, you can translate between them, doing a calculation in one theory that matches a calculation in the other one.

Even when we can’t do non-trivial experiments, then, we can still have non-trivial examples. When the result of a calculation isn’t obvious from the beginning, showing that it matches on both sides of a correspondence takes the same sort of risk as doing an experiment, and gives the same sort of evidence.

Some of the best-supported conjectures in theoretical physics have this form. AdS/CFT is technically a conjecture: a correspondence between string theory in a hyperbola-shaped space and my favorite theory, N=4 super Yang-Mills. Despite being a conjecture, the wealth of nontrivial examples is so strong that it would be extremely surprising if it turned out to be false.

ER=EPR is also a correspondence, between entangled particles on the one hand and wormholes on the other. Does it have nontrivial examples?

Some, but not enough. Originally, it was based on one core example, an entangled state that could be cleanly matched to the simplest wormhole. Now, new examples have been added, covering wormholes with electric fields and higher spins. The full “dictionary” is still unclear, with some pairs of entangled particles being harder to describe in terms of wormholes. So while this kind of evidence is being built, it isn’t as solid as our best conjectures yet.

I’m fine with people popularizing this kind of conjecture. It deserves blog posts and press articles, and it’s a fine idea to have fun with. I wouldn’t be uncomfortable with the Bohemian Gravity guy doing a piece on it, for example. But for the second installment of a star-studded series like the one Caltech is doing…it’s not really there yet, and putting it there gives people the wrong idea.

I hope I’ve given you a better idea of the different types of conjectures, from the most fuzzy to those just shy of certain. I’d like to do this kind of piece more often, though in future I’ll probably stick with topics in my sub-field (where I actually know what I’m talking about 😉 ). If there’s a particular conjecture you’re curious about, ask in the comments!

A Tale of Two Archives

When it comes to articles about theoretical physics, I have a pet peeve, one made all the more annoying by the fact that it appears even in pieces that are otherwise well written. It involves the following disclaimer:

“This article has not been peer-reviewed.”

Here’s the thing: if you’re dealing with experiments, peer review is very important. Plenty of experiments have subtle problems with their methods, enough that it’s important to have a group of experts who can check them. In experimental fields, you really shouldn’t trust things that haven’t been through a journal yet: there’s just a lot that can go wrong.

In theoretical physics, though, peer review is important for different reasons. Most papers are mathematically rigorous enough that they’re not going to be wrong per se, and most of the ways they could be wrong won’t be caught by peer review. While peer review sometimes does catch mistakes, much more often it’s about assessing the significance of a result. Peer review determines whether a result gets into a prestigious journal or a less prestigious one, which in turn matters for job and grant applications.

As such, it doesn’t really make sense for a journalist to point out that a theoretical physics paper hasn’t been peer reviewed yet. If you think it’s important enough to write an article about, then you’ve already decided it’s significant: peer review wasn’t going to tell you anything else.

We physicists post our papers to arXiv, a free-to-access paper repository, before submitting them to journals. While arXiv does have some moderation, it’s not much: pretty much anyone in the field can post whatever they want.

This leaves a lot of people confused. In that sort of system, how do we know which papers to trust?

Let’s compare to another archive: Archive of Our Own, or AO3 for short.

Unlike arXiv, AO3 hosts not physics, but fanfiction. However, like arXiv it’s quite lightly moderated and free to access. On arXiv you want papers you can trust, on AO3 you want stories you enjoy. In each case, if anyone can post, how do you find them?

The first step is filtering. AO3 and arXiv both have systems of tags and subject headings. The headings on arXiv are simpler and more heavily moderated than those on AO3, but they both serve the purpose of letting people filter out the subjects, whether scientific or fictional, that they find interesting. If you’re interested in astrophysics, try astro-ph on arXiv. If you want Harry Potter fanfiction, try the “Harry Potter – J.K. Rowling” tag on AO3.

Beyond that, it helps to pay attention to authors. When an author has written something you like, it’s worth it not only to keep up with other things they write, but to see which other authors they like and pay attention to them as well. That’s true whether the author is Juan Maldacena or your favorite source of Twilight fanfic.

Even if you follow all of this, you can’t trust every paper you find on arXiv. You also won’t enjoy everything you dig up on AO3. Either way, publication (in journals or books) won’t solve your problem: both are an additional filter, but not an infallible one. Judgement is still necessary.

This is all to say that “this article has not been peer-reviewed” can be a useful warning, but often isn’t. In theoretical physics, knowing who wrote an article and what it’s about will often tell you much more than whether or not it’s been peer-reviewed yet.

Have You Given Your Kids “The Talk”?

If you haven’t seen it yet, I recommend reading this delightful collaboration between Scott Aaronson (of Shtetl-Optimized) and Zach Weinersmith (of Saturday Morning Breakfast Cereal). As explanations of a concept beyond the standard popular accounts go, this one is pretty high quality, correcting some common misconceptions about quantum computing.

I especially liked the following exchange:

ontology

I’ve complained before about people trying to apply ontology to physics, and I think this gets at the root of one of my objections.

People tend to think that the world should be describable with words. From that perspective, mathematics is just a particular tool, a system we’ve created. If you look at the world in that way, mathematics looks unreasonably effective: it’s ability to describe the real world seems like a miraculous coincidence.

Mathematics isn’t just one tool though, or just one system. It’s all of them: not just numbers and equations, but knots and logic and everything else. Deep down, mathematics is just a collection of all the ways we’ve found to state things precisely.

Because of that, it shouldn’t surprise you that we “put complex numbers in our ontologies”. Complex numbers are just one way we’ve found to make precise statements about the world, one that comes in handy when talking about quantum mechanics. There doesn’t need to be a “correct” description in words: the math is already stating things as precisely as we know how.

That doesn’t mean that ontology is a useless project. It’s worthwhile to develop new ways of talking about things. I can understand the goal of building up a philosophical language powerful enough to describe the world in terms of words, and if such a language was successful it might well inspire us to ask new scientific questions.

But it’s crucial to remember that there’s real work to be done there. There’s no guarantee that the project will work, that words will end up sufficient. When you put aside our best tools to make precise statements, you’re handicapping yourself, making the problem harder than it needed to be. It’s your responsibility to make sure you’re getting something worthwhile out of it.