Vibe Physics: When Deriving an Answer Becomes Faster Than Checking It

An eleven-minute calculation changes expectations

A research calculation expected to take days came back in eleven minutes. The companion article to this conversation recounts Alex Lupsasca’s encounter with o3 as the point when AI became useful for his theoretical-physics research. The recording opens with a second experience: GPT-5 reportedly reproduced a result from one of the researcher’s best papers in about half an hour. The crucial details emerge later: an initial failure, an easier warm-up problem, and a successful retry.

The central research case goes further. Physicists had spent roughly a year seeking a compact formula for a family of particle interactions. They could represent the answer, but expanding it became unmanageable. AI helped identify a simplifying condition, conjecture a general expression, and prove it. Humans established that the amplitudes could be nonzero; AI helped find the compact answer.

What a scattering amplitude predicts

Quantum field theory accommodates relativity and quantum mechanics. Here, its practical task is to predict outcomes when particles interact. A scattering amplitude is a complex-valued function—a quantity with real and imaginary components—from which an outcome’s probability is calculated. Its inputs include the incoming and outgoing particles’ energies, momenta, and polarizations. Because particles can be created or destroyed, the incoming and outgoing counts need not match. Researchers want formulas for an arbitrary total number of participating particles.

Polarized sunglasses offer a familiar starting point: tilting your head changes how much reflected lake light passes through because the lenses selectively transmit a polarization direction. The discussion introduces helicity as the handedness of polarization as a particle propagates, distinguishing positive and negative helicity. Those signs organize the calculation for gluons, the particles that carry the strong force.

The paper Single Minus Gluon Tree Amplitudes Are Nonzero concerns tree amplitudes, the leading contributions in an expansion, before adding loop corrections. Three helicity configurations explain the title’s significance: - All plus: every gluon has positive helicity. General arguments give a vanishing tree amplitude. - Single minus: one gluon has negative helicity and the rest positive. Standard treatments appeared to rule these amplitudes out too. - Two minus: two gluons have negative helicity and the rest positive. These nonzero configurations are called MHV amplitudes, short for maximally helicity violating, reflecting what had been thought to be the largest helicity imbalance permitting a nonzero answer.

The two-minus case supplied the motivation. Calculations in the 1980s produced large sums whose terms canceled, leaving a formula short enough to fit on a line. That precedent gave researchers reason to expect a compact single-minus answer, though it could not guarantee one.

A nonzero answer under special conditions

The usual vanishing argument assumes generic particle directions. A collinear regime, where particles are aligned, opens a loophole—but alignment alone is insufficient. The work also changes the spacetime signature, the distinction between its space and time dimensions. The companion article makes this qualification explicit: the proposed nonzero case uses two space and two time dimensions, while the original vanishing statement remains valid in ordinary three-space, one-time-dimensional spacetime. The full mathematical conditions are not developed in the conversation.

Alfredo Guevara is credited with substantial hand calculation using complicated building blocks and a recursive formula. Expansion produced one term for three particles, two for four, eight for five, and 32 for six. Each of the 32 terms was a product of four factors containing further formulas. Six particles was reportedly the limit of the team’s explicit calculations.

Feynman diagrams organize the intermediate interactions. Fix which particles enter and leave, then sum contributions from the possible interactions connecting them. Each interaction vertex contributes a power of a coupling constant, which controls interaction strength. In the expansion described here, additional interactions contribute suppressed corrections, so researchers begin with the simplest diagrams. A loop can arise when a particle splits into two intermediate particles that later rejoin.

The direct representation’s term count grows factorially with particle count because of the combinations of possible interactions. The goal was therefore a compact formula for arbitrary particle count. Andrew Strominger proposed this unresolved problem for an OpenAI visit. Collaborators began experimenting with ChatGPT the week beforehand and reportedly solved it before he arrived.

Find the simplifying region, then conjecture and prove

Given the five-particle expression, ChatGPT identified an additional condition under which it simplified. Phase space here means the possible combinations of particle energies and momenta. In the relevant region, one particle’s frequency has the opposite sign from the others. An interviewer suggests thinking of one particle decaying into the others; the researcher accepts this as an approximate intuition, with the unusual spacetime setting still essential.

After substantial back-and-forth, the reported reductions within that region were: - Five particles: eight products of three factors collapsed into one product of three factors. - Six particles: a sum of 32 terms collapsed into one product of four factors. The researcher says the first simplification could be rederived once known, but the team had not previously recognized it.

The researchers then asked for a formula valid at arbitrary particle count. GPT-5.2 Pro conjectured the general expression over several interactions, with thinking periods of roughly twenty minutes. Symbolic software could help reduce individual examples; inferring the general expression was the step the researcher did not know how to automate conventionally. Within the chosen region, formula size grew linearly instead of factorially—a change in representation size, not a measured runtime speedup.

The public model could not prove its conjecture. An internal OpenAI model received a sharply specified problem with the conjectured answer withheld. After twelve hours, it reportedly returned the same expression and a proof whose three-step structure became the paper’s argument. The fresh run retained the discovered region, so it benefited from the earlier exploration even without receiving the expected formula.

An interviewer distinguishes extrapolating already simplified cases—which can look natural even to a beginning graduate student—from independently recovering and deriving the expression. The researcher says withholding the answer was intended to increase confidence. The paper credited AI’s conjecture and proof in a separate paragraph and omitted AI from the abstract to foreground the physics. Its lasting importance, the researcher argues, will depend on the work it enables.

Gravity requires different mathematics

The follow-up, Single Minus Graviton Tree Amplitudes Are Nonzero, extended the result to gravity. A graviton is a proposed quantum of a gravitational wave, analogous to a photon as a quantum of light. Gravitons have not been directly measured, and the researcher qualifies this picture: their ultimate description depends on a still-unknown theory of quantum gravity.

The extension required more than substituting one particle name for another. Gravitons have spin two rather than gluons’ spin one, making their polarization structure more complicated. In the special region discussed, the gravity calculation uses two labels where the gluon calculation uses one. A crucial step applied the directed matrix tree theorem in a way that reportedly surprised Guevara and David Skinner. Reconstructing that step requires the theorem and its application, which the conversation does not explain.

This calculation used publicly available GPT-5.2 Pro. The researchers supplied the gluon paper, emphasized its appendix manipulations, and added roughly two paragraphs identifying changes needed for gravity. The model proposed successive calculations and checks; humans asked it to continue. The roughly 110-page exchange included checks of basic cases, lists of remaining work, and thinking periods of twenty minutes or more. Extending Single Minus Amplitudes to Gravitons shares a main prompt and chat; the companion also links the full interaction transcript.

Human direction extended beyond the initial prompt: - Explain the result’s significance. The collaborator referred to as Andy wrote the abstract and introduction, adding broader physics connections. The model’s introduction had been more generic. - Ask how the symmetries fit. Researchers added a section on how the amplitudes transform under physical symmetries, guiding the model in a separate chat. - Verify before publication. The answer reportedly arrived within three days. The paper appeared three weeks after the gluon work, with most intervening effort spent checking the answer and preparing the paper.

The symmetry analysis connected the calculation to celestial holography, described here as a program exploring quantum-gravity symmetries. Such symmetries can provide a foothold toward a new theory. The researcher reports that the model derived the mathematics and produced a draft close to the final paper from section three onward, with experts choosing questions and checking the work. Fast generation shifted most human effort toward verification.

Training and exploration when calculations become cheaper

Delegating calculations creates an unresolved training problem. Arduous work traditionally tests students’ understanding and builds confidence that they can solve problems independently. Advisors bridge the gap between coursework and research with tractable questions whose answers they expect to exist. The researcher believes models can probably solve many of these starter problems, making it difficult to imagine a student working for six months without consulting ChatGPT.

AI can also ease the transition into research by explaining unfamiliar material at different levels of detail. The researcher identifies two changes in daily work: - Resolve conceptual mismatches sooner. Ask how a calculation’s result fits another known fact. The model may identify an omitted consideration, mistaken interpretation, or relevant standard result. - Explore several routes concurrently. Send different chats down different approaches, then use their responses to decide where to invest scarce attention. Exploratory suggestions can be useful even when imperfect: they help locate promising steps, while the derivation still needs checking.

Mentoring offers a practical analogy: match the problem to the collaborator and supply the right amount of detail. Knowing which question to give a student or postdoc, and how much context to include, transfers to working with ChatGPT. Adapting research and training to these capabilities is a responsibility for researchers and professors as well as model builders.

Technical skill and scientific taste

An interviewer asks how a field should choose useful directions if AI proliferates interesting theoretical results while experimental guidance is limited. The response centers on questions close enough to the frontier to be tractable. Why space has three dimensions is fascinating, but the respondent knows no compelling route to an answer and therefore does not spend professional research time on it. Training involves learning where the edge of knowledge lies and which questions available methods can reach.

The researcher separates two skills: - Technical competence: learning whatever mathematical or coding tool a problem requires. - Scientific taste: choosing the next fruitful question, regarded as the harder skill to develop. Current AI is compared to an exceptionally technically skilled graduate student: potentially stronger than humans at some computations, but less reliable at choosing the right research question.

Asked whether the model merely recombines known facts, the respondent says the work felt like collaboration with a creative partner because it produced unfamiliar, surprising results. A secondhand account of Terry Tao offers a different threshold: apparently surprising mathematical proofs he had seen were later traced to obscure references. Surprise to a collaborator and novelty across the literature are distinct judgments.

The warm-up behind the half-hour result

The conversation returns to the opening reproduction story and Why Is There No Love in Black Holes? Love numbers are coefficients encoding an object’s tidal response, named for Augustus Love. The work connects vanishing black-hole Love numbers in the setting studied to symmetries of a perturbation equation. Its symmetry generators are differential operators that map one solution of the equation to another. The full tidal-response regime is not specified here; the claim should not be generalized to all black-hole responses.

The reported test proceeded in three stages: 1. Ask the full question. Given the black-hole perturbation equation and asked for its symmetries, GPT spent about five minutes and incorrectly answered that there were none. 2. Solve an easier analogue. Given the corresponding problem in empty, flat spacetime, GPT-5 Pro reportedly found its three known symmetry generators correctly in about nine minutes. 3. Retry with the warm-up in context. In the same chat, the model reportedly solved the full black-hole problem in eighteen minutes. The under-thirty-minute result covers the successful warm-up and retry, after an earlier failed attempt. The easier problem was also the starting point the researcher had used.

The researcher treated this as reproduction of work unseen in training because the paper appeared in June, after the stated training cutoff and before GPT-5’s August release. That was the basis for the claim, rather than an independent check of training exposure. An interviewer proposes a stronger test: could a model trained before a discovery find the conceptual direction itself? The respondent says they have not personally performed that exact counterfactual experiment.

A narrower experiment was encouraging: given a page of the paper, ChatGPT proposed three follow-up questions matching the researcher’s own top three. This supports the researcher’s judgment about question selection for that paper, without resolving the broader question of autonomous scientific direction.

The prescription is to raise the standard for a worthwhile paper. The researcher estimates that careful steering might already permit a paper a day on relatively easy questions or familiar extensions; this is a conditional estimate, not measured publication throughput. Poorly framed questions and unchecked answers also produce erroneous submissions. The proposed response is to pursue harder questions opened by the amplitudes work, rather than generate many similar follow-ups. The researcher distinguishes the reported solution to a problem that stumped three experts for a year from a milestone they have not yet seen: AI solving a question that has stumped an entire physics community for decades. Reaching that milestone remains a hope for future progress.

Communicating understanding and verifying at scale

Asked which bottleneck to remove, the researcher first names writing papers. In graduate school, a terse four-page algebraic-geometry paper became understandable only after a mathematician explained it at a blackboard. The polished document omitted the intuition. AI adds a peculiar round trip: develop understanding through conversation, compress it into a paper, then have the next reader upload that paper to another model to expand it again.

An interactive paper with an attached chatbot could let readers move between the big picture and detailed explanations. This is a proposed future format, with an important benefit of writing preserved: condensing an argument forces its author to clarify it. In the graviton project, however, drafting was already fast enough that checking the answer dominated the work.

The researcher wants two improvements for scientific models: - Encourage larger conceptual leaps. Everyday tasks often reward conventional answers; research can benefit from unusual ideas. The researcher believes model training should encourage more of that exploration. - Identify uncertain steps. Explicitly marking where a model is guessing could help researchers target their checks. This remains a desired capability, not a demonstrated calibration result. Finishing a long calculation does not establish its correctness. Even work that looks complete can contain a consequential mistake.

Proof generation at scale makes automated verification more valuable. Stronger natural-language reasoning had initially made formalization seem less urgent to the researcher: humans routinely discuss proofs without translating them into a formal verification language such as Lean. But when models tackle thousands of questions concurrently and return proofs for a substantial, unspecified fraction, humans must check the resulting volume. Formalizing mathematics and automating those checks become more valuable as review becomes the bottleneck.

The conversation closes with optimism grounded in the researcher’s changing experience: o3 made useful research calculations possible, GPT-5 reproduced difficult work, and later models helped solve open theoretical-physics questions. Continued rapid progress is an expectation rather than an established trajectory. The immediate change is concrete: researchers can spend less effort obtaining an answer and more deciding whether it is correct, what it means, and which question deserves to come next.