Tag Archives: theoretical physics

Breakthrough Prize 2026

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Because of last week’s “bonus info” post, I’m only now getting around to commenting on this year’s Breakthrough Prizes in Fundamental Physics. While I don’t comment on them every year, I know enough about several of this year’s winners that I figured a post would be helpful.

For those who haven’t heard of it, the Breakthrough Prizes are a bit like the Nobel, if it was created by a 21st century rich person instead of a 19th century one. They give out more money, and instead of an organization like the Swedish Academy of Sciences they pick winners via a committee of past winners. They’re more flexible in structure than the Nobel, with extra prizes for early-career researchers and a tendency to reward accomplishments that are either entirely theoretical or solid experimental work that doesn’t show a new discovery, both of which are things the Nobel Prize is structured to avoid. They’ve also shown willingness to reward large collaborations, rather than following the Nobel’s informal rule to only give the award to three people at a time.

This last was on display this year in their main award in physics this year, for the muon g-2 collaborations. The award is going to collaborations of scientists and engineers at three different particle colliders, for work done over a span of over fifty years to measure the magnetic properties of the muon. These measurements have shown a tantalizing discrepancy with predictions that inspired many to conjecture new physics. However, in the last few years it’s looked more and more like the discrepancy was due to an imprecise prediction, and better methods seem to be converging to the experimental value. At this point, smart money is that there is no disagreement with the Standard Model here, but as always in science there’s a chance some mystery remains.

The Breakthrough Prize also offered a special, out-of-schedule prize to David Gross. Already a Nobel laureate, Gross had a crucial role in our understanding of the force of quantum chromodynamics that binds protons and neutrons together. He was also a major founding figure in string theory, and since the Breakthrough Prize is more comfortable recognizing theoretical contributions they get to mention this as well. Gross is also known in the community for his personality, which tends to fill up any room he’s in. I can only imagine the conversations that led to Breakthrough’s decision to add a special prize for him this year.

Breakthrough is also adding a new recurring prize, the Vera Rubin New Frontiers Prize, honoring women who make important contributions to physics within two years of their PhD. The prize is a bit smaller than the exiting early-career New Horizons in Physics Prizes, presumably because it goes to even younger researchers. This year’s winner is from my old field, scattering amplitudes. Carolina Figueiredo is part of the latest evolution of the research program behind the amplituhedron. The new framework of “surfaceology” seems like a promising geometry-flavored way to understand particle physics calculations in more realistic theories, and unlike its predecessors may have some practical value eventually as well. Congrats Carolina!

Finally, the New Horizons in Physics Prizes are for impressive early-career researchers. I don’t know much about the first recipient, Benjamin Safdi, who works on searches for axions and axion-like particles, today’s most trendy dark matter candidate. I know a bit more about the work done by Clay Córdova, Thomas Dumitrescu, Shu-Heng Shao, and Yifan Wang, having met several of them in my physics career. They work on what are called generalized symmetries, concepts which go beyond the usual idea of how symmetry is supposed to work by involving more complicated tensors. I saw these crop up a fair bit in talks, but they were distant enough from my area that I never had a particularly clear grasp of what people were doing with them. I know even less about the work of the last three, Dillon Brout, J. Colin Hill, Mathew Madhavacheril, Maria Vincenzi, Daniel Scolnic, and W. L. Kimmy Wu, on cosmological measurements, but I was friends with Mathew in grad school and am impressed that he’s now working on cosmology given how little cosmology research there was at Stony Brook at the time.

A Window on Absolutely Everything

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It’s often said that in quantum physics, everything that can happen will happen.

One way this comes up is in something called a path integral, used to calculate the probabilities of quantum events. If you want to find what happens to a particle traveling from point A to point B, you have to add up a contribution for every path, no matter how windy, that goes between A and B. These contributions mostly cancel out, and matter less the further they are from a straight line, so the straight-line path is, for the most part, a good description of what happens. But in principle, all of the other paths matter too.

The same thing happens in quantum field theory, in more elaborate form. Instead of a path from one place to another, the paths are from one configuration of quantum fields to another, via all the different ways fields can in principle interact. We are almost never able to take account of all these possibilities mathematically, so we have to approximate, organizing the interactions into more and more complicated pictures called Feynman diagrams, each with a smaller and smaller effect.

In principle, these diagrams need to contain every single combination of interactions that might result in the end-state we’re interested in. These combinations can have a Rube Goldberg flavor, with one field activating another, which activates another, only to all cancel out in the end. Because of this, any field that exists, any particle no matter how rare, can matter, if only a little.

And from that, physicists can learn something.

Because absolutely everything matters, physicists get to reason about absolutely everything that exists.

The best example involves something called an anomaly. These aren’t the anomalies of experimental physics, unexpected results that have a tendency to go away with better measurements. Instead of something unexpected, a theorist’s anomaly is something impossible.

Anomalies are combinations of particles that, if they were to show up together in a sum of Feynman diagrams, would break the rules that the theory was made with in the first place. If they show up, they’re a sign of an inconsistent theory, one that doesn’t obey its own rules and thus doesn’t make sense.

In order to have a theory without anomalies, different calculations involving different particles need to cancel. For example, it might be that the charge of different particles has to add up to zero. This means that if you’ve only discovered a few particles, and their charges don’t add up to zero, then you know you’re missing one. There is an extra particle there, which you haven’t observed, that together makes charge add up to zero.

This logic actually works! It was used to predict the top quark. Before the top quark was discovered, the list of quarks, electrons, and neutrinos had electric charges that didn’t add up to zero. One particle was missing, with the same charge as the up quark and charm quark. It was found in 1995, after being proposed almost 20 years earlier.

What AI Physicists Are Missing and What They Aren’t

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I’ve seen a couple more thoughtful takes on use of LLMs for physics lately. This blog post by Minas Karamis is particularly nice.

He points out something that I’ve said a version of: an AI that must be supervised like a student isn’t very useful, because the main point of student projects isn’t the paper at the end: it’s training the student. If students don’t struggle through all the mistakes of a project, they won’t get the expertise to one day do greater things.

Someone might object that not all suffering is educational. In the 1700’s, Leonhard Euler calculated digit after digit of transcendental numbers by hand. Nobody asks students to do that anymore, and they still seem to turn out alright. Why would using an LLM for science be worse than using a computer for numerical calculations?

In a word: different skills. Programming numerics teaches you some of the same skills as calculating the numbers by hand: skills at being specific about what you mean, aware of the consequences of the details and their implications. Prompting an AI still requires those skills, to check whether the AI’s output is correct. But it’s much worse at teaching them: unlike programming or calculating, when prompting AI, the consequences of your actions aren’t predictable.

For some, though, there is another objection. Sure, using AI reliably might require those skills now. But when it gets better, surely being careful will stop mattering. Surely the AI will end up doing science on its own, and all that training will be as useful as if we trained the students to play football.

I’m skeptical, but not as strongly as some. I think we’re still living in a time when it makes sense to hire scientists, and train people to think, and invest in your retirement.

I don’t think I have any knock-down arguments for that, though. Just some suggestive ones.

One I’ve talked about before is that a lot of the most important parts of thinking aren’t written down. An AI physicist is going to have a hard time replicating the kinds of methods and approaches that people use behind the scenes, but rarely describe or spell out. It will be easier to suss this out over time, as more data accumulates of people working with LLMs and correcting them. But ultimately there isn’t going to be a lot of documentation of this kind of thing.

Another limitation is memory. A mature scientist can draw from experiences across their entire career. For an LLM, any problem it’s solved in the past is by default lost in each new session. People build structures around this, taking notes and reminding the AI when it “wakes up”, or making documents the AI can be prompted to check. But nothing in this vein so far seems to get nearly as wide-scope or powerful as human memory. A scientist career is still the best way we have to build durable, functional expertise.

Finally, there is a question of costs, and efficiency. Here I’m not an expert, and I get the impression the actual experts disagree. I don’t know whether we should expect scaling to hit a wall, but I wouldn’t be that surprised if it did.

There are other common reasons for skepticism that seem more dubious to me. I don’t think AI is inherently worse at creativity just because they’re trained on existing work, though some of the skills we associate with creativity aren’t very well-documented, and thus are hard to train for. I don’t think AI’s randomness or unreliability is a deal-breaker, because human intuition is also random and unreliable: we solve that with tools, and that’s something AI can in principle do as well. I don’t think humans are “more agentic” or something, except in the sense that most AIs are made by companies who need to make them behave in a customer-friendly way. But an agent is just a game-theoretic construct, a way to figure out can win or lose in situations with defined stakes, and anything you can train or engineer to try to win can be modeled by that construct.

Coming from a place of uncertainty, my main appeal to you is to not get hung up on the bad reasons, either yourself, or from the people you’re arguing with. Focus on the best arguments, and see where they take you.

About the OpenAI Amplitudes Paper, but Not as Much as You’d Like

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I’ve had a bit more time to dig in to the paper I mentioned last week, where OpenAI collaborated with amplitudes researchers, using one of their internal models to find and prove a simplified version of a particle physics formula. I figured I’d say a bit about my own impressions from reading the paper and OpenAI’s press release.

This won’t be a real “deep dive”, though it will be long nonetheless. As it turns out, most of the questions I’d like answers to aren’t answered in the paper or the press release. Getting them will involve actual journalistic work, i.e. blocking off time to interview people, and I haven’t done that yet. What I can do is talk about what I know so far, and what I’m still wondering.

Context:

Scattering amplitudes are formulas used by particle physicists to make predictions. For a while, people would just calculate these when they needed them, writing down pages of mess that you could plug in numbers to to get answers. However, forty years ago two physicists decided they wanted more, writing “we hope to obtain a simplified form for the answer, making our result not only an experimentalist’s, but a theorist’s delight.”

In their next paper, they managed to find that “theorist’s delight”: a simplified, intuitive-looking answer that worked for calculations involving any number of particles, summarizing many different calculations. Ten years later, a few people had started building on it, and ten years after that, the big shots started paying attention. A whole subfield, “amplitudeology”, grew from that seed, finding new forms of “theorists’s delight” in scattering amplitudes.

Each subfield has its own kind of “theory of victory”, its own concept for what kind of research is most likely to yield progress. In amplitudes, it’s these kinds of simplifications. When they work out well, they yield new, more efficient calculation techniques, yielding new messy results which can be simplified once more. To one extent or another, most of the field is chasing after those situations when simplification works out well.

That motivation shapes both the most ambitious projects of senior researchers, and the smallest student projects. Students often spend enormous amounts of time looking for a nice formula for something and figuring out how to generalize it, often on a question suggested by a senior researcher. These projects mostly serve as training, but occasionally manage to uncover something more impressive and useful, an idea others can build around.

I’m mentioning all of this, because as far as I can tell, what ChatGPT and the OpenAI internal model contributed here roughly lines up with the roles students have on amplitudes papers. In fact, it’s not that different from the role one of the authors, Alfredo Guevara, had when I helped mentor him during his Master’s.

Senior researchers noticed something unusual, suggested by prior literature. They decided to work out the implications, did some calculations, and got some messy results. It wasn’t immediately clear how to clean up the results, or generalize them. So they waited, and eventually were contacted by someone eager for a research project, who did the work to get the results into a nice, general form. Then everyone publishes together on a shared paper.

How impressed should you be?

I said, “as far as I can tell” above. What’s annoying is that this paper makes it hard to tell.

If you read through the paper, they mention AI briefly in the introduction, saying they used GPT-5.2 Pro to conjecture formula (39) in the paper, and an OpenAI internal model to prove it. The press release actually goes into more detail, saying that the humans found formulas (29)-(32), and GPT-5.2 Pro found a special case where it could simplify them to formulas (35)-(38), before conjecturing (39). You can get even more detail from an X thread by one of the authors, OpenAI Research Scientist Alex Lupsasca. Alex had done his PhD with another one of the authors, Andrew Strominger, and was excited to apply the tools he was developing at OpenAI to his old research field. So they looked for a problem, and tried out the one that ended up in the paper.

What is missing, from the paper, press release, and X thread, is any real detail about how the AI tools were used. We don’t have the prompts, or the output, or any real way to assess how much input came from humans and how much from the AI.

(We have more for their follow-up paper, where Lupsasca posted a transcript of the chat.)

Contra some commentators, I don’t think the authors are being intentionally vague here. They’re following business as usual. In a theoretical physics paper, you don’t list who did what, or take detailed account of how you came to the results. You clean things up, and create a nice narrative. This goes double if you’re aiming for one of the most prestigious journals, which tend to have length limits.

This business-as-usual approach is ok, if frustrating, for the average physics paper. It is, however, entirely inappropriate for a paper showcasing emerging technologies. For a paper that was going to be highlighted this highly by OpenAI, the question of how they reached their conclusion is much more interesting than the results themselves. And while I wouldn’t ask them to go to the standards of an actual AI paper, with ablation analysis and all that jazz, they could at least have aimed for the level of detail of my final research paper, which gave samples of the AI input and output used in its genetic algorithm.

For the moment, then, I have to guess what input the AI had, and what it actually accomplished.

Let’s focus on the work done by the internal OpenAI model. The descriptions I’ve seen suggest that it started where GPT-5.2 Pro did, with formulas (29)-(32), but with a more specific prompt that guided what it was looking for. It then ran for 12 hours with no additional input, and both conjectured (39) and proved it was correct, providing essentially the proof that follows formula (39) in the paper.

Given that, how impressed should we be?

First, the model needs to decide to go to a specialized region, instead of trying to simplify the formula in full generality. I don’t know whether they prompted their internal model explicitly to do this. It’s not something I’d expect a student to do, because students don’t know what types of results are interesting enough to get published, so they wouldn’t be confident in computing only a limited version of a result without an advisor telling them it was ok. On the other hand, it is actually something I’d expect an LLM to be unusually likely to do, as a result of not managing to consistently stick to the original request! What I don’t know is whether the LLM proposed this for the right reason: that if you have the formula for one region, you can usually find it for other regions.

Second, the model needs to take formulas (29)-(32), write them in the specialized region, and simplify them to formulas (35)-(38). I’ve seen a few people saying you can do this pretty easily with Mathematica. That’s true, though not every senior researcher is comfortable doing that kind of thing, as you need to be a bit smarter than just using the Simplify[] command. Most of the people on this paper strike me as pen-and-paper types who wouldn’t necessarily know how to do that. It’s definitely the kind of thing I’d expect most students to figure out, perhaps after a couple of weeks of flailing around if it’s their first crack at it. The LLM likely would not have used Mathematica, but would have used SymPy, since these “AI scientist” setups usually can write and execute Python code. You shouldn’t think of this as the AI reasoning through the calculation itself, but it at least sounds like it was reasonably quick at coding it up.

Then, the model needs to conjecture formula (39). This gets highlighted in the intro, but as many have pointed out, it’s pretty easy to do. If any non-physicists are still reading at this point, take a look:

Could you guess (39) from (35)-(38)?

After that, the paper goes over the proof that formula (39) is correct. Most of this proof isn’t terribly difficult, but the way it begins is actually unusual in an interesting way. The proof uses ideas from time-ordered perturbation theory, an old-fashioned way to do particle physics calculations. Time-ordered perturbation theory isn’t something any of the authors are known for using with regularity, but it has recently seen a resurgence in another area of amplitudes research, showing up for example in papers by Matthew Schwartz, a colleague of Strominger at Harvard.

If a student of Strominger came up with an idea drawn from time-ordered perturbation theory, that would actually be pretty impressive. It would mean that, rather than just learning from their official mentor, this student was talking to other people in the department and broadening their horizons, showing a kind of initiative that theoretical physicists value a lot.

From an LLM, though, this is not impressive in the same way. The LLM was not trained by Strominger, it did not learn specifically from Strominger’s papers. Its context suggested it was working on an amplitudes paper, and it produced an idea which would be at home in an amplitudes paper, just a different one than the one it was working on.

While not impressive, that capability may be quite useful. Academic subfields can often get very specialized and siloed. A tool that suggests ideas from elsewhere in the field could help some people broaden their horizons.

Overall, it appears that that twelve-hour OpenAI internal model run reproduced roughly what an unusually bright student would be able to contribute over the course of a several-month project. Like most student projects, you could find a senior researcher who could do the project much faster, maybe even faster than the LLM. But it’s unclear whether any of the authors could have: different senior researchers have different skillsets.

A stab at implications:

If we take all this at face-value, it looks like OpenAI’s internal model was able to do a reasonably competent student project with no serious mistakes in twelve hours. If they started selling that capability, what would happen?

If it’s cheap enough, you might wonder if professors would choose to use the OpenAI model instead of hiring students. I don’t think this would happen, though: I think it misunderstands why these kinds of student projects exist in a theoretical field. Professors sometimes use students to get results they care about, but more often, the student’s interest is itself the motivation, with the professor wanting to educate someone, to empire-build, or just to take on their share of the department’s responsibilities. AI is only useful for this insofar as AI companies continue reaching out to these people to generate press releases: once this is routinely possible, the motivation goes away.

More dangerously, if it’s even cheaper, you could imagine students being tempted to use it. The whole point of a student project is to train and acculturate the student, to get them to the point where they have affection for the field and the capability to do more impressive things. You can’t skip that, but people are going to be tempted to.

And of course, there is the broader question of how much farther this technology can go. That’s the hardest to estimate here, since we don’t know the prompts used. So I don’t know if seeing this result tells us anything more about the bigger picture than we knew going in.

Remaining questions:

At the end of the day, there are a lot of things I still want to know. And if I do end up covering this professionally, they’re things I’ll ask.

  1. What was the prompt given to the internal model, and how much did it do based on that prompt?
  2. Was it really done in one shot, no retries or feedback?
  3. How much did running the internal model cost?
  4. Is this result likely to be useful? Are there things people want to calculate that this could make easier? Recursion relations it could seed? Is it useful for SCET somehow?
  5. How easy would it have been for the authors to do what the LLM did? What about other experts in the community?

Hypothesis: If AI Is Bad at Originality, It’s a Documentation Problem

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Recently, a few people have asked me about this paper.

A couple weeks back, OpenAI announced a collaboration with a group of amplitudes researchers, physicists who study the types of calculations people do to make predictions at particle colliders. The amplitudes folks had identified an interesting loophole, finding a calculation that many would have expected to be zero actually gave a nonzero answer. They did the calculation for different examples involving more and more particles, and got some fairly messy answers. They suspected, as amplitudes researchers always expect, that there was a simpler formula, one that worked for any number of particles. But they couldn’t find it.

Then a former amplitudes researcher at OpenAI suggested that they use AI to find it.

“Use AI” can mean a lot of different things, and most of them don’t look much like the way the average person talks to ChatGPT. This was closer than most. They were using “reasoning models”, loops that try to predict the next few phrases in a “chain of thought” again and again and again. Using that kind of tool, they were able to find that simpler formula, and mathematically prove that it was correct.

A few of you are hoping for an in-depth post about what they did, and its implications. This isn’t that. I’m still figuring out if I’ll be writing that for an actual news site, for money, rather than free, for you folks.

Instead, I want to talk about a specific idea I’ve seen crop up around the paper.

See, for some, the existence of a result like this isn’t all that surprising.

Mathematicians have been experimenting with reasoning models for a bit, now. Recently, a group published a systematic study, setting the AI loose on a database of minor open problems proposed by the famously amphetamine-fueled mathematician Paul Erdös. The AI managed to tackle a few of the problems, sometimes by identifying existing solutions that had not yet been linked to the problem database, but sometimes by proofs that appeared to be new.

The Erdös problems solved by the AI were not especially important. Neither was the problem solved by the amplitudes researchers, as far as I can tell at this point.

But I get the impression the amplitudes problem was a bit more interesting than the Erdös problems. The difference, so far, has mostly been attributed to human involvement. This amplitudes paper started because human amplitudes researchers found an interesting loophole, and only after that used the AI. Unlike the mathematicians, they weren’t just searching a database.

This lines up with a general point, one people tend to make much less carefully. It’s often said that, unlike humans, AI will never be truly creative. It can solve mechanical problems, do things people have done before, but it will never be good at having truly novel ideas.

To me, that line of thinking goes a bit too far. I suspect it’s right on one level, that it will be hard for any of these reasoning models to propose anything truly novel. But if so, I think it will be for a different reason.

The thing is, creativity is not as magical as we make it out to be. Our ideas, scientific or artistic, don’t just come from the gods. They recombine existing ideas, shuffling them in ways more akin to randomness than miracle. They’re then filtered through experience, deep heuristics honed over careers. Some people are good at ideas, and some are bad at them. Having ideas takes work, and there are things people do to improve their ideas. Nothing about creativity suggests it should be impossible to mechanize.

However, a machine trained on text won’t necessarily know how to do any of that.

That’s because in science, we don’t write down our inspirations. By the time a result gets into a scientific paper or textbook, it’s polished and refined into a pure argument, cutting out most of the twists and turns that were an essential part of the creative process. Mathematics is even worse, most math papers don’t even mention the motivation behind the work, let alone the path taken to the paper.

This lack of documentation makes it hard for students, making success much more a function of having the right mentors to model good practices, rather than being able to pick them up from literature everyone can access. I suspect it makes it even harder for language models. And if today’s language model-based reasoning tools are bad at that crucial, human-seeming step, of coming up with the right idea at the right time? I think that has more to do with this lack of documentation, than with the fact that they’re “statistical parrots”.

The Timeline for Replacing Theorists Is Not Technological

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Quanta Magazine recently published a reflection by Natalie Wolchover on the state of fundamental particle physics. The discussion covers a lot of ground, but one particular paragraph has gotten the lion’s share of the attention. Wolchover talked to Jared Kaplan, the ex-theoretical physicist turned co-founder of Anthropic, one of the foremost AI companies today.

Kaplan was one of Nima Arkani-Hamed’s PhD students, which adds an extra little punch.

There’s a lot to contest here. Is AI technology anywhere close to generating papers as good as the top physicists, or is that relegated to the sci-fi future? Does Kaplan really believe this, or is he just hyping up his company?

I don’t have any special insight into those questions, about the technology and Kaplan’s motivations. But I think that, even if we trusted him on the claim that AI could be generating Witten- or Nima-level papers in three years, that doesn’t mean it will replace theoretical physicists. That part of the argument isn’t a claim about the technology, but about society.

So let’s take the technological claims as given, and make them a bit more specific. Since we don’t have any objective way of judging the quality of scientific papers, let’s stick to the subjective. Today, there are a lot of people who get excited when Witten posts a new paper. They enjoy reading them, they find the insights inspiring, they love the clarity of the writing and their tendency to clear up murky ideas. They also find them reliable: the papers very rarely have mistakes, and don’t leave important questions unanswered.

Let’s use that as our baseline, then. Suppose that Anthropic had an AI workflow that could reliably write papers that were just as appealing to physicists as Witten’s papers are, for the same reasons. What happens to physicists?

Witten himself is retired, which for an academic means you do pretty much the same thing you were doing before, but now paid out of things like retirement savings and pension funds, not an institute budget. Nobody is going to fire Witten, there’s no salary to fire him from. And unless he finds these developments intensely depressing and demoralizing (possible, but very much depends on how this is presented), he’s not going to stop writing papers. Witten isn’t getting replaced.

More generally, though, I don’t think this directly results in anyone getting fired, or in universities trimming positions. The people making funding decisions aren’t just sitting on a pot of money, trying to maximize research output. They’ve got money to be spent on hires, and different pools of money to be spent on equipment, and the hires get distributed based on what current researchers at the institutes think is promising. Universities want to hire people who can get grants, to help fund the university, and absent rules about AI personhood, the AIs won’t be applying for grants.

Funding cuts might be argued for based on AI, but that will happen long before AI is performing at the Witten level. We already see this happening in other industries or government agencies, where groups that already want to cut funding are getting think tanks and consultants to write estimates that justify cutting positions, without actually caring whether those estimates are performed carefully enough to justify their conclusions. That can happen now, and doesn’t depend on technological progress.

AI could also replace theoretical physicists in another sense: the physicists themselves might use AI to do most of their work. That’s more plausible, but here adoption still heavily depends on social factors. Will people feel like they are being assessed on whether they can produce these Witten-level papers, and that only those who make them get hired, or funded? Maybe. But it will propagate unevenly, from subfield to subfield. Some areas will make their own rules forbidding AI content, there will be battles and scandals and embarrassments aplenty. It won’t be a single switch, the technology alone setting the timeline.

Finally, AI could replace theoretical physicists in another way, by people outside of academia filling the field so much that theoretical physicists have nothing more that they want to do. Some non-physicists are very passionate about physics, and some of those people have a lot of money. I’ve done writing work for one such person, whose foundation is now attempting to build an AI Physicist. If these AI Physicists get to Witten-level quality, they might start writing compelling paper after compelling paper. Those papers, though, will due to their origins be specialized. Much as philanthropists mostly fund the subfields they’ve heard of, philanthropist-funded AI will mostly target topics the people running the AI have heard are important. Much like physicists themselves adopting the technology, there will be uneven progress from subfield to subfield, inch by socially-determined inch.

In a hard-to-quantify area like progress in science, that’s all you can hope for. I suspect Kaplan got a bit of a distorted picture of how progress and merit work in theoretical physics. He studied with Nima Arkani-Hamed, who is undeniably exceptionally brilliant but also undeniably exceptionally charismatic. It must feel to a student of Nima’s that academia simply hires the best people, that it does whatever it takes to accomplish the obviously best research. But the best research is not obvious.

I think some of these people imagine a more direct replacement process, not arranged by topic and tastes, but by goals. They picture AI sweeping in and doing what theoretical physics was always “meant to do”: solve quantum gravity, and proceed to shower us with teleporters and antigravity machines. I don’t think there’s any reason to expect that to happen. If you just asked a machine to come up with the most useful model of the universe for a near-term goal, then in all likelihood it wouldn’t consider theoretical high-energy physics at all. If you see your AI as a tool to navigate between utopia and dystopia, theoretical physics might matter at some point: when your AI has devoured the inner solar system, is about to spread beyond the few light-minutes when it can signal itself in real-time, and has to commit to a strategy. But as long as the inner solar system remains un-devoured, I don’t think you’ll see an obviously successful theory of fundamental physics.

On Theories of Everything and Cures for Cancer

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Some people are disappointed in physics. Shocking, I know!

Those people, when careful enough, clarify that they’re disappointed in fundamental physics: not the physics of materials or lasers or chemicals or earthquakes, or even the physics of planets and stars, but the physics that asks big fundamental questions, about the underlying laws of the universe and where they come from.

Some of these people are physicists themselves, or were once upon a time. These often have in mind other directions physicists should have gone. They think that, with attention and funding, their own ideas would have gotten us closer to our goals than the ideas that, in practice, got the attention and the funding.

Most of these people, though, aren’t physicists. They’re members of the general public.

It’s disappointment from the general public, I think, that feels the most unfair to physicists. The general public reads history books, and hears about a series of revolutions: Newton and Maxwell, relativity and quantum mechanics, and finally the Standard Model. They read science fiction books, and see physicists finding “theories of everything”, and making teleporters and antigravity engines. And they wonder what made the revolutions stop, and postponed the science fiction future.

Physicists point out, rightly, that this is an oversimplified picture of how the world works. Something happens between those revolutions, the kind of progress not simple enough to summarize for history class. People tinker away at puzzles, and make progress. And they’re still doing that, even for the big fundamental questions. Physicists know more about even faraway flashy topics like quantum gravity than they did ten years ago. And while physicists and ex-physicists can argue about whether that work is on the right path, it’s certainly farther along its own path than it was. We know things we didn’t know before, progress continues to be made. We aren’t at the “revolution” stage yet, or even all that close. But most progress isn’t revolutionary, and no-one can predict how often revolutions should take place. A revolution is never “due”, and thus can never be “overdue”.

Physicists, in turn, often don’t notice how normal this kind of reaction from the public is. They think people are being stirred up by grifters, or negatively polarized by excess hype, that fundamental physics is facing an unfair reaction only shared by political hot-button topics. But while there are grifters, and people turned off by the hype…this is also just how the public thinks about science.

Have you ever heard the phrase “a cure for cancer”?

Fiction is full of scientists working on a cure for cancer, or who discovered a cure for cancer, or were prevented from finding a cure for cancer. It’s practically a trope. It’s literally a trope.

It’s also a real thing people work on, in a sense. Many scientists work on better treatments for a variety of different cancers. They’re making real progress, even dramatic progress. As many whose loved ones have cancer know, it’s much more likely for someone with cancer to survive than it was, say, twenty years ago.

But those cures don’t meet the threshold for science fiction, or for the history books. They don’t move us, like the polio vaccine did, from a world where you know many people with a disease to a world where you know none. They don’t let doctors give you a magical pill, like in a story or a game, that instantly cures your cancer.

For the vast majority of medical researchers, that kind of goal isn’t realistic, and isn’t worth thinking about. The few that do pursue it work towards extreme long-term solutions, like periodically replacing everyone’s skin with a cloned copy.

So while you will run into plenty of media descriptions of scientists working on cures for cancer, you won’t see the kind of thing the public expects is an actual “cure for cancer”. And people are genuinely disappointed about this! “Where’s my cure for cancer?” is a complaint on the same level as “where’s my hovercar?” There are people who think that medical science has made no progress in fifty years, because after all those news articles, we still don’t have a cure for cancer.

I appreciate that there are real problems in what messages are being delivered to the public about physics, both from hypesters in the physics mainstream and grifters outside it. But put those problems aside, and a deeper issue remains. People understand the world as best they can, as a story. And the world is complicated and detailed, full of many people making incremental progress on many things. Compared to a story, the truth is always at a disadvantage.

Bonus Info For “Cosmic Paradox Reveals the Awful Consequence of an Observer-Free Universe”

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I had a piece in Quanta Magazine recently, about a tricky paradox that’s puzzling quantum gravity researchers and some early hints at its resolution.

The paradox comes from trying to describe “closed universes”, which are universes where it is impossible to reach the edge, even if you had infinite time to do it. This could be because the universe wraps around like a globe, or because the universe is expanding so fast no traveler could ever reach an edge. Recently, theoretical physicists have been trying to describe these closed universes, and have noticed a weird issue: each such universe appears to have only one possible quantum state. In general, quantum systems have more possible states the more complex they are, so for a whole universe to have only one possible state is a very strange thing, implying a bizarrely simple universe. Most worryingly, our universe may well be closed. Does that mean that secretly, the real world has only one possible state?

There is a possible solution that a few groups are playing around with. The argument that a closed universe has only one state depends on the fact that nothing inside a closed universe can reach the edge. But if nothing can reach the edge, then trying to observe the universe as a whole from outside would tell you nothing of use. Instead, any reasonable measurement would have to come from inside the universe. Such a measurement introduces a new kind of “edge of the universe”, this time not in the far distance, but close by: the edge between an observer and the rest of the world. And when you add that edge to the calculations, the universe stops being closed, and has all the many states it ought to.

This was an unusually tricky story for me to understand. I narrowly avoided several misconceptions, and I’m still not sure I managed to dodge all of them. Likewise, it was unusually tricky for the editors to understand, and I suspect it was especially tricky for Quanta’s social media team to understand.

It was also, quite clearly, tricky for the readers to understand. So I thought I would use this post to clear up a few misconceptions. I’ll say a bit more about what I learned investigating this piece, and try to clarify what the result does and does not mean.

Q: I’m confused about the math terms you’re using. Doesn’t a closed set contain its boundary?

A: Annoyingly, what physicists mean by a closed universe is a bit different from what mathematicians mean by a closed manifold, which is in turn more restrictive than what mathematicians mean by a closed set. One way to think about this that helped me is that in an open set you can take a limit that takes you out of the set, which is like being able to describe a (possibly infinite) path that takes you “out of the universe”. A closed set doesn’t have that, every path, no matter how long, still ends up in the same universe.

Q: So a bunch of string theorists did a calculation and got a result that doesn’t make sense, a one-state universe. What if they’re just wrong?

A: Two things:

First, the people I talked to emphasized that it’s pretty hard to wiggle out of the conclusion. It’s not just a matter of saying you don’t believe in string theory and that’s that. The argument is based in pretty fundamental principles, and it’s not easy to propose a way out that doesn’t mess up something even more important.

That’s not to say it’s impossible. One of the people I interviewed, Henry Maxfield, thinks that some of the recent arguments are misunderstanding how to use one of their core techniques, in a way that accidentally presupposes the one-state universe.

But even he thinks that the bigger point, that closed universes have only one state, is probably true.

And that’s largely due to a second reason: there are older arguments that back the conclusion up.

One of the oldest dates back to John Wheeler, a physicist famous for both deep musings about the nature of space and time and coining evocative terms like “wormhole”. In the 1960’s, Wheeler argued that, in a theory where space and time can be curved, one should think of a system’s state as including every configuration it can evolve into over time, since it can be tricky to specify a moment “right now”. In a closed universe, you could expect a quantum system to explore every possible configuration…meaning that such a universe should be described by only one state.

Later, physicists studying holography ran into a similar conclusion. They kept noticing systems in quantum gravity where you can describe everything that happens inside by what happens on the edges. If there are no edges, that seems to suggest that in some sense there is nothing inside. Apparently, Lenny Susskind had a slide at the end of talks in the 90’s where he kept bringing up this point.

So even if the modern arguments are wrong, and even if string theory is wrong…it still looks like the overall conclusion is right.

Q: If a closed universe has only one state, does that make it deterministic, and thus classical?

A: Oh boy…

So, on the one hand, there is an idea, which I think also goes back to Wheeler, that asks: “if the universe as a whole has a wavefunction, how does it collapse?” One possibility is that the universe has only one state, so that nobody is needed to collapse the wavefunction, it already is in a definite state.

On the other hand, a universe with only one state does not actually look much like a classical universe. Our universe looks classical largely due to a process called decoherence, where small quantum systems interact with big quantum systems with many states, diluting quantum effects until the world looks classical. If there is only one state, there are no big systems to interact with, and the world has large quantum fluctuations that make it look very different from a classical universe.

Q: How, exactly, are you defining “observer”?

A: A few commenters helpfully chimed in to talk about how physics models observers as “witness” systems, objects that preserve some record of what happens to them. A simple example is a ball sitting next to a bowl: if you find the ball in the bowl later, it means something moved it. This process, preserving what happens and making it more obvious, is in essence how physicists think about observers.

However, this isn’t the whole story in this case. Here, different research groups introducing observers are doing it in different ways. That’s, in part, why none of them are confident they have the right answer.

One of the approaches describes an observer in terms of its path through space and time, its worldline. Instead of a detailed witness system with specific properties, all they do is pick out a line and say “the observer is there”. Identifying that line, and declaring it different from its surroundings, seems to be enough to recover the complexity the universe ought to have.

The other approach treats the witness system in a bit more detail. We usually treat an observer in quantum mechanics as infinitely large compared to the quantum systems they measure. This approach instead gives the observer a finite size, and uses that to estimate how far their experience will be from classical physics.

Crucially, both approaches aren’t a matter of defining a physical object, and looking for it in the theory. Given a collection of atoms, neither team can tell you what is an observer, and what isn’t. Instead, in each approach, the observer is arbitrary: a choice, made by us when we use quantum mechanics, of what to count as an observer and what to count as the rest of the world. That choice can be made in many different ways, and each approach tries to describe what happens when you change that choice.

This is part of what makes this approach uncomfortable to some more philosophically-minded physicists: it treats observers not as a predictable part of the physical world, but as a mathematical description used to make statements about the world.

Q: If these ideas come from AdS/CFT, which is an open universe, how do you use them to describe a closed universe?

A: While more examples emerged later, initially theorists were thinking about two types of closed universes:

First, think about a black hole. You may have heard that when you fall into a black hole, you watch the whole universe age away before your eyes, due to the dramatic differences in the passage of time caused by the extreme gravity. Once you’ve seen the outside universe fade away, you are essentially in a closed universe of your own. The outside world will never affect you again, and you are isolated, with no path to the outside. These black hole interiors are one of the examples theorists looked at.

The other example are so-called “baby universes”. When physicists use quantum mechanics to calculate the chance of something happening, they have to add up every possible series of events that could have happened in between. For quantum gravity, this includes every possible arrangement of space and time. This includes arrangements with different shapes, including ones with tiny extra “baby universes” which branch off from the main universe and return. Universes with these “baby universes” are another example that theorists considered to understand closed universes.

Q: So wait, are you actually saying the universe needs to be observed to exist? That’s ridiculous, didn’t the universe exist long before humans existed to observe it? Is this some sort of Copenhagen Interpretation thing, or that thing called QBism?

You’re starting to ask philosophical questions, and here’s the thing:

There are physicists who spend their time thinking about how to interpret quantum mechanics. They talk to philosophers, and try to figure out how to answer these kinds of questions in a consistent and systematic way, keeping track of all the potential pitfalls and implications. They’re part of a subfield called “quantum foundations”.

The physicists whose work I was talking about in that piece are not those people.

Of the people I interviewed, one of them, Rob Myers, probably has lunch with quantum foundations researchers on occasion. The others, based at places like MIT and the IAS, probably don’t even do that.

Instead, these are people trying to solve a technical problem, people whose first inclination is to put philosophy to the side, and “shut up and calculate”. These people did a calculation that ought to have worked, checking how many quantum states they could find in a closed universe, and found a weird and annoying answer: just one. Trying to solve the problem, they’ve done technical calculation work, introducing a path through the universe, or a boundary around an observer, and seeing what happens. While some of them may have their own philosophical leanings, they’re not writing works of philosophy. Their papers don’t talk through the philosophical implications of their ideas in all that much detail, and they may well have different thoughts as to what those implications are.

So while I suspect I know the answers they would give to some of these questions, I’m not sure.

Instead, how about I tell you what I think?

I’m not a philosopher, I can’t promise my views will be consistent, that they won’t suffer from some pitfall. But unlike other people’s views, I can tell you what my own views are.

To start off: yes, the universe existed before humans. No, there is nothing special about our minds, we don’t have psychic powers to create the universe with our thoughts or anything dumb like that.

What I think is that, if we want to describe the world, we ought to take lessons from science.

Science works. It works for many reasons, but two important ones stand out.

Science works because it leads to technology, and it leads to technology because it guides actions. It lets us ask, if I do this, what will happen? What will I experience?

And science works because it lets people reach agreement. It lets people reach agreement because it lets us ask, if I observe this, what do I expect you to observe? And if we agree, we can agree on the science.

Ultimately, if we want to describe the world with the virtues of science, our descriptions need to obey this rule: they need to let us ask “what if?” questions about observations.

That means that science cannot avoid an observer. It can often hide the observer, place them far away and give them an infinite mind to behold what they see, so that one observer is essentially the same as another. But we shouldn’t expect to always be able to do this. Sometimes, we can’t avoid saying something about the observer: about where they are, or how big they are, for example.

These observers, though, don’t have to actually exist. We should be able to ask “what if” questions about others, and that means we should be able to dream up fictional observers, and ask, if they existed, what would they see? We can imagine observers swimming in the quark-gluon plasma after the Big Bang, or sitting inside a black hole’s event horizon, or outside our visible universe. The existence of the observer isn’t a physical requirement, but a methodological one: a restriction on how we can make useful, scientific statements about the world. Our theory doesn’t have to explain where observers “come from”, and can’t and shouldn’t do that. The observers aren’t part of the physical world being described, they’re a precondition for us to describe that world.

Is this the Copenhagen Interpretation? I’m not a historian, but I don’t think so. The impression I get is that there was no real Copenhagen Interpretation, that Bohr and Heisenberg, while more deeply interested in philosophy than many physicists today, didn’t actually think things through in enough depth to have a perspective you can name and argue with.

Is this QBism? I don’t think so. It aligns with some things QBists say, but they say a lot of silly things as well. It’s probably some kind of instrumentalism, for what that’s worth.

Is it logical positivism? I’ve been told logical positivists would argue that the world outside the visible universe does not exist. If that’s true, I’m not a logical positivist.

Is it pragmatism? Maybe? What I’ve seen of pragmatism definitely appeals to me, but I’ve seen my share of negative characterizations as well.

In the end, it’s an idea about what’s useful and what’s not, about what moves science forward and what doesn’t. It tries to avoid being preoccupied with unanswerable questions, and as much as possible to cash things out in testable statements. If I do this, what happens? What if I did that instead?

The results I covered for Quanta, to me, show that the observer matters on a deep level. That isn’t a physical statement, it isn’t a mystical statement. It’s a methodological statement: if we want to be scientists, we can’t give up on the observer.

C. N. Yang, Dead at 103

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I don’t usually do obituaries here, but sometimes I have something worth saying.

Chen Ning Yang, a towering figure in particle physics, died last week.

Picture from 1957, when he received his Nobel

I never met him. By the time I started my PhD at Stony Brook, Yang was long-retired, and hadn’t visited the Yang Institute for Theoretical Physics in quite some time.

(Though there was still an office door, tucked behind the institute’s admin staff, that bore his name.)

The Nobel Prize doesn’t always honor the most important theoretical physicists. In order to get a Nobel Prize, you need to discover something that gets confirmed by experiment. Generally, it has to be a very crisp, clear statement about reality. New calculation methods and broader new understandings are on shakier ground, and theorists who propose them tend to be left out, or at best combined together into lists of partial prizes long after the fact.

Yang was lucky. With T. D. Lee, he had made that crisp, clear statement. He claimed that the laws of physics, counter to everyone’s expectations, are not the same when reflected in a mirror. In 1956, Wu confirmed the prediction, and Lee and Yang got the prize the year after.

That’s a huge, fundamental discovery about the natural world. But as a theorist, I don’t think that was Yang’s greatest accomplishment.

Yang contributed to other fields. Practicing theorists have seen his name strewn across concepts, formalisms, and theorems. I didn’t have space to talk about him in my article on integrability for Quanta Magazine, but only just barely: another paragraph or two, and he would have been there.

But his most influential contribution is something even more fundamental. And long-time readers of this blog should already know what it is.

Yang, along with Robert Mills, proposed Yang-Mills Theory.

There isn’t a Nobel prize for Yang-Mills theory. In 1953, when Yang and Mills proposed the theory, it was obviously wrong, a theory that couldn’t explain anything in the natural world, mercilessly mocked by famous bullshit opponent Wolfgang Pauli. Not even an ambitious idea that seemed outlandish (like plate tectonics), it was a theory with such an obvious missing piece that, for someone who prioritized experiment like the Nobel committee does, it seemed pointless to consider.

All it had going for it was that it was a clear generalization, an obvious next step. If there are forces like electromagnetism, with one type of charge going from plus to minus, why not a theory with multiple, interacting types of charge?

Nothing about Yang-Mills theory was impossible, or contradictory. Mathematically, it was fine. It obeyed all the rules of quantum mechanics. It simply didn’t appear to match anything in the real world.

But, as theorists learn, nature doesn’t let a good idea go to waste.

Of the four fundamental forces of nature, as it would happen, half are Yang-Mills theories. Gravity is different, electromagnetism is simpler, and could be understood without Yang and Mills’ insights. But the weak nuclear force, that’s a Yang-Mills theory. It wasn’t obvious in 1953 because it wasn’t clear how the massless, photon-like particles in Yang-Mills theory could have mass, and it wouldn’t become clear until the work of Peter Higgs over a decade later. And the strong nuclear force, that’s also a Yang-Mills theory, missed because of the ability of such a strong force to “confine” charges, hiding them away.

So Yang got a Nobel, not for understanding half of nature’s forces before anyone else had, but from a quirky question of symmetry.

In practice, Yang was known for all of this, and more. He was enormously influential. I’ve heard it claimed that he personally kept China from investing in a new particle collider, the strength of his reputation the most powerful force on that side of the debate, as he argued that a developing country like China should be investing in science with more short-term industrial impact, like condensed matter and atomic physics. I wonder if the debate will shift with his death, and what commitments the next Chinese five-year plan will make.

Ultimately, Yang is an example of what a theorist can be, a mix of solid work, counterintuitive realizations, and the thought-through generalizations that nature always seems to make use of in the end. If you’re not clear on what a theoretical physicist is, or what one can do, let Yang’s story be your guide.

When Your Theory Is Already Dead

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Occasionally, people try to give “even-handed” accounts of crackpot physics, like people who claim to have invented anti-gravity devices. These accounts don’t go so far as to say that the crackpots are right, and will freely point out plausible doubts about the experiments. But at the end of the day, they’ll conclude that we still don’t really know the answer, and perhaps the next experiment will go differently. More tests are needed.

For someone used to engineering, or to sciences without much theory behind them, this might sound pretty reasonable. Sure, any one test can be critiqued. But you can’t prove a negative: you can’t rule out a future test that might finally see the effect.

That’s all well and good…if you have no idea what you’re doing. But these people, just like anyone else who grapples with physics, aren’t just proposing experiments. They’re proposing theories: models of the world.

And once you’ve got a theory, you don’t just have to care about future experiments. You have to care about past experiments too. Some theories…are already dead.

The "You're already dead" scene from the anime North Star
Warning: this is a link to TVTropes, enter only if you have lots of time on your hands

To get a little more specific, let’s talk about antigravity proposals that use scalar fields.

Scalar fields seem to have some sort of mysticism attached to them in the antigravity crackpot community, but for physicists they’re just the simplest possible type of field, the most obvious thing anyone would have proposed once they were comfortable enough with the idea of fields in the first place. We know of one, the Higgs field, which gives rise to the Higgs boson.

We also know that if there are any more, they’re pretty subtle…and as a result, pretty useless.

We know this because of a wide variety of what are called “fifth-force experiments“, tests and astronomical observations looking for an undiscovered force that, like gravity, reaches out to long distances. Many of these experiments are quite general, the sort of thing that would pick up a wide variety of scalar fields. And so far, none of them have seen anything.

That “so far” doesn’t mean “wait and see”, though. Each time physicists run a fifth-force experiment, they establish a limit. They say, “a fifth force cannot be like this“. It can’t be this strong, it can’t operate on these scales, it can’t obey this model. Each experiment doesn’t just say “no fifth force yet”, it says “no fifth force of this kind, at all”.

When you write down a theory, if you’re not careful, you might find it has already been ruled out by one of these experiments. This happens to physicists all the time. Physicists want to use scalar fields to understand the expansion of the universe, they use them to think about dark matter. And frequently, a model one physicist proposed will be ruled out, not by new experiments, but by someone doing the math and realizing that the model is already contradicted by a pre-existing fifth-force experiment.

So can you prove a negative? Sort of.

If you never commit to a model, if you never propose an explanation, then you can never be disproven, you can always wait for the experiment of your dreams to come true. But if you have any model, any idea, any explanation at all, then your explanation will have implications. Those implications may kill your theory in a future experiment. Or, they may have already killed it.