Neil Turok: A New Route to Quantum Gravity (Without Strings)

ELI5 / TLDR

For fifty years the dominant story about combining gravity and quantum mechanics has been: you need strings, you need ten dimensions, you need a mountain of extra machinery. Neil Turok — a serious cosmologist, former head of the Perimeter Institute — says he used to believe that and now thinks it’s wrong. There’s a much simpler old theory of gravity that was abandoned in the 1970s because it seemed to produce “negative probabilities,” which sound impossible. Turok and his student claim those negative quantities were never probabilities at all — they were a red herring — and once you stop panicking about them, the simple theory works fine. If they’re right, the universe doesn’t need strings or a multiverse; the lumps we see in the sky from the Big Bang may literally be quantum gravity caught in the act.

The Full Story

Why this is a big deal at all

Quantum gravity is the unfinished business of physics. We have two spectacularly successful theories — Einstein’s gravity for big things, quantum mechanics for tiny things — and they refuse to be friends. The standard hope for the past half-century has been string theory: rewrite everything as tiny vibrating strings, accept extra dimensions, and the contradictions melt away. Turok’s complaint is not that string theory is ugly. It’s that after fifty years it hasn’t answered the questions it was supposed to answer.

“What happened at the Big Bang, what goes on in black holes… these kind of questions have not been solved by these very complex frameworks for quantum gravity.”

And, he adds, it makes no testable predictions. A theory that can’t be checked against the real world has, in his view, lost the plot.

The simple theory everyone gave up on

Start with Einstein’s description of gravity. The key ingredient is curvature — the bending of spacetime. Think of it like the shape of a trampoline once you put a bowling ball on it. Einstein’s equations care about that curvature.

Now, in the 1970s a physicist named Kelly Stelle asked: what if we add a term that’s the curvature squared? This is not a wild move. Every other force in physics — electromagnetism, the strong nuclear force — is built exactly this way, with a “squared” term in its core equation. Gravity was the odd one out. Add the squared term and gravity suddenly looks like its better-behaved cousins. This is called quadratic gravity (quadratic = squared).

The payoff is enormous. Plain Einstein gravity, when you try to do quantum calculations with it, spits out infinities you can never tame — it’s “non-renormalizable,” a polite way of saying the math breaks. Quadratic gravity is renormalizable: the infinities can be swept into a finite set of knobs, and you’re left with a sensible theory. In the 1980s it was even shown to be “asymptotically free” — meaning at very short distances the theory goes quiet and simple, the same beautiful behaviour the strong nuclear force has.

So why did everyone walk away from the simplest possible quantum gravity? Two problems.

Problem one: the energy that falls forever

The first is the oldest no-go theorem in physics, from a man named Ostrogradsky in 1850s St. Petersburg. He asked what happens if your equations of motion involve more derivatives than the usual two (Newton’s F = ma has two — position, then how fast acceleration changes, etc.). Adding more derivatives is exactly what the curvature-squared term does.

Ostrogradsky found something alarming: such systems have energy that is unbounded below. Picture a ball that doesn’t roll into a valley and stop — it rolls down a slope with no bottom, forever, releasing infinite energy. Couple that to the real world and you’d have a perpetual-motion catastrophe. Nothing in nature behaves like that, so people declared the theory dead.

Turok’s reply is delightfully cheeky: gravity already does this, and we never minded.

“Gravity has negative energy… Observations show us that the universe is expanding exponentially now. It doesn’t sound like a very stable system… That sounds awfully like an instability.”

When they analysed the runaway in the squared-curvature theory carefully, it turned out to be nothing but ordinary gravitational expansion — the same exponential stretching we already observe and call normal. Reinterpreted as gravity rather than a generic mechanical system, the “instability” is just the universe doing what it visibly does. The first horn of the dilemma quietly evaporates.

Problem two: the ghosts and the negative probabilities that weren’t

The second problem is the harder one, and it’s where the new result lives.

In the quantum version of these higher-derivative theories, some of the possible states of the system have a strange property. To explain it, a detour. In quantum mechanics, every possible configuration is a kind of arrow (a “state vector”) living in an abstract space. Normally every arrow has positive length. In these theories, some arrows have negative length-squared. Physicists call states like that ghosts.

For decades the reasoning went: negative length means negative probability, negative probability is nonsense, therefore ghosts are forbidden, therefore the theory is dead. You will find this argument in textbooks.

Turok says the second step is simply a mistake.

“A state with negative norm corresponds to a negative probability. That’s just not true. You can’t observe the norm of a quantum state.”

His point: the “length” of a quantum state isn’t something you ever measure. It’s just a label, like a name tag. What you actually measure are transition probabilities — the odds of going from one situation to another. The length of the arrow never appears in the lab. So having some arrows with negative length is no more paranormal than the fact that, in spacetime, some directions are “time-like” and some “space-like,” one counted positive and one negative. We live with that mixed-sign geometry every day — it’s called Minkowski space. The quantum version of that mixed-sign space already has a name from the math literature: a Krein space (the interviewer keeps reaching for “pseudo-Hilbert space,” which is exactly the right intuition).

The interviewer’s analogy lands it cleanly:

“You can have a red dancing unicorn in your theory and the equations. If it’s unobservable, it actually doesn’t matter.”

The actual fix: tweaking the Born rule

Here’s the technical heart, kept gentle. The recipe quantum mechanics uses to turn states into probabilities is called the Born rule: take the overlap between a starting state and an ending state, and square it. That squaring step secretly assumes you can “normalize” your states — set their length to one. With ghosts around, you can’t.

So Turok and his student Sam Bateman rewrote the recipe so it never needs to normalize anything. Instead of squaring an amplitude, you build the probability directly using projection operators — mathematical tools that pick off a piece of an arrow — and then trace (sum) over every state, ghosts included. You never throw the ghosts out, you never project onto a “physical subspace.” You just include everything and add it up.

The miracle is that, provided the theory has a particular tidy symmetry they call ghost parity (an operation that hands you +1 on a normal state and −1 on a ghost), the final probabilities always come out positive and always add up to one. Exactly what a sane theory requires. The whole thing took, in Turok’s words, “a slight tweak of the Born rule.”

This is a real generalization. Physicists already use ghost-filled spaces in standard calculations (the “Faddeev-Popov ghosts” of gauge theory), but they always end by projecting down to a clean subspace. Turok’s version skips the projection entirely and is, he argues, the only version that fully respects the symmetries of spacetime — which is why he thinks rival approaches by Bender and Mannheim, which fix the ghosts by hand-editing the inner product, will eventually break.

The honest caveat

Turok is careful not to oversell. The full theory of gravity has several moving parts — a graviton (the particle of gravitational waves), a vector mode, a ghost graviton, and a scalar mode (the local “size” of spacetime). So far the new construction only fully tames a limiting case where everything except the scalar mode switches off.

“We claim we understand quantum gravity in a certain limit… The trick we used to make sense of it may or may not apply to the full thing.”

It’s a toy model — no gravitons, no gravitational waves, not the real world. But it’s a toy model that is fully consistent, UV-complete (well-behaved at the smallest scales), and built from the simplest possible ingredients. The bet is that the same ghost-parity trick will extend to the full theory. Hence his line that they’re “halfway there.”

The payoff: simplicity all the way down

What makes Turok evangelical is that this connects to a larger project he’s been running (the “CPT-symmetric universe,” with Latham Boyle). The philosophy is brutal minimalism: take everything we actually observe — five numbers describe the large-scale universe, the standard model describes particles — and refuse to add anything you don’t need. No inflation, no extra fields, no multiverse.

Doing that, several puzzles fell out for free: dark matter, why the universe is smooth and flat. The one holdout was the fabric of tiny temperature ripples we see in the afterglow of the Big Bang — the seeds of all galaxies. When they asked what kind of quantum field would naturally produce ripples with that exact pattern (more power on large scales, “redder”), the answer was: a four-derivative field. The same higher-derivative structure that defines quadratic gravity.

“It tells us what we’re looking at in the sky is a signal of quantum gravity… we’re just seeing the birth of the universe and those are precisely the quantum fluctuations in quantum gravity.”

So the squared-curvature term wasn’t a mathematical convenience — it may be written across the sky.

The bigger sermon: question your assumptions

The interview’s back half widens into Turok’s worry about the health of physics. His core message: string theory and the multiverse became orthodoxies, and orthodoxies stop checking their own foundations.

“You make one false move in theoretical physics and you’re totally wrong… We should be examining very, very closely each one of our assumptions.”

The string story, he argues, rested on hidden assumptions — chiefly that any sane quantum theory must live in a Hilbert space (all arrows positive). His work shows that one assumption is droppable. Pull that thread and the claim that gravity forces you into strings, extra dimensions, and a multiverse loses its footing.

He’s blunt about the institutional rot: jobs, grants, and referee reports all reward working on the popular paradigm, even when those paradigms haven’t delivered. Math departments hired armies of string theorists who don’t care about predictions. Young people get steered toward formalism and away from the foundations — which is precisely where, he insists, the real discoveries hide.

The Bateman story is the human heart of it. A student given an “impossible” four-year problem, no published papers, funding gone — and then, the conviction that he’d never get a job apparently freeing him, he cracked it last September with the Born-rule tweak. He was offered a postdoc at the Simons Center with zero papers, on the strength of the idea alone.

“And all it took is a slight tweak of the Born rule… And financial insecurity.”

Why simplicity

Turok’s deepest commitment is that the universe is, astonishingly, simple — at the very small and the very large. Atoms are simple, black holes are simple (mass, spin, charge, done), the universe on large scales is simple. All the genuine complexity lives in the middle, at human scale. Using Hawking’s notion of gravitational entropy, he and collaborators showed that a smooth, flat universe with a tiny positive cosmological constant is simply the most likely state — the same reason gas spreads evenly through a room rather than huddling in one corner. You don’t need a mechanism to smooth the universe out. You just need to count states and pick the typical one. No starting conditions, no cosmic ignition, no one lighting the fuse.

Key Takeaways

Quadratic gravity = Einstein’s gravity plus a curvature-squared term. Unlike plain Einstein gravity, it’s renormalizable (the infinities are tameable) and has been known since Kelly Stelle’s 1977 work.
Adding a squared-curvature term makes gravity structurally resemble the other forces (electromagnetism, QCD), all of which have a “field-strength-squared” core.
Higher-derivative theories were abandoned for two reasons: the Ostrogradsky instability (energy unbounded below) and ghosts (quantum states of negative norm).
Turok’s first move: the Ostrogradsky runaway, reinterpreted within gravity, is just normal cosmic expansion — the exponential stretching we already observe — and is actually stable.
Turok’s second move: negative-norm states do not imply negative probabilities. The norm of a quantum state is not an observable. It’s a label, not a measurement.
The fix is a generalized Born rule: build probabilities from projection operators and trace over all states (ghosts included), never normalizing, never projecting out a physical subspace.
This works provided the theory has ghost parity symmetry (an operator giving +1 on positive-norm states, −1 on ghosts). Then probabilities are guaranteed positive and sum to one.
The natural home for ghost-laden quantum mechanics is a Krein space — a Hilbert space generalized to allow negative-norm directions, analogous to how Minkowski spacetime generalizes Euclidean space.
Physicists already work with ghosts (Faddeev-Popov) but normally project down to a clean subspace; Turok’s construction is more economical and, he claims, the only fully covariant (spacetime-symmetry-respecting) version.
The result so far only covers a scalar-only limit of quadratic gravity — no gravitons, no gravitational waves. A toy model, not the full theory. Hence “halfway there.”
The CMB temperature fluctuations have the spectral signature of a four-derivative field — suggesting the lumps we see from the Big Bang may be a direct fingerprint of quantum gravity, no inflation required.
Hidden assumption behind string theory: that quantum theories must live in a Hilbert space (all norms positive). Drop it, and the “gravity requires strings/extra dimensions/multiverse” chain loses its necessity.
Turok’s cosmology of counting states: a smooth, flat universe is simply the most probable one (most microstates), via Hawking’s gravitational entropy — like gas filling a room. No special initial conditions needed.
Institutional critique: jobs, grants, and referees reward orthodox paradigms; foundations work is undervalued precisely where breakthroughs are most likely.

Claude’s Take

This is a genuinely interesting claim made by a credible person, which is rarer than it should be in the quantum-gravity discourse. Turok isn’t a fringe figure — he ran the Perimeter Institute, worked with Hawking, holds the Higgs Chair at Edinburgh. When someone like that says “I used to believe you need strings and now I don’t,” it’s worth listening, even discounting for the fact that this is a premiere on a podcast rather than a settled result in the literature.

The core insight — that the norm of a quantum state isn’t observable, so negative norms aren’t automatically fatal — is the kind of thing that’s either a deep loophole or a subtle trap, and the honest answer is we don’t yet know. The construction (trace over everything, lean on a discrete symmetry to guarantee positivity) is plausible and elegant on its face, but “plausible and elegant” has buried many a quantum-gravity proposal. The crucial caveat, which Turok states clearly to his credit, is that the proof only covers a scalar toy model with no gravitons. That is a long way from “solved quantum gravity,” and the video’s title (chosen by the channel, not Turok) wildly oversells it. Turok himself says “halfway there,” and even that is optimistic by his own admission.

The CMB-as-four-derivative-field connection is the most exciting and the most fragile piece — it’s the part that, if it holds, turns an abstract math fix into a falsifiable claim about the sky. But there’s already a published paper (Klein and Heil) arguing they’ve made errors, which Turok dismisses partly on grounds that the critics don’t know about the new work. That’s a fair point chronologically, but “they’ll be convinced once they see it” is what every theorist says.

I’m scoring this an 8. The physics is real, the speaker is serious, the explanations are unusually clear, and the meta-argument about questioning hidden assumptions is genuinely valuable regardless of whether this specific theory survives. It loses points only because it’s an unverified, self-premiered result wrapped in a clickbait title, and because the listener has to supply a lot of charitable trust. As intellectual texture and a window into how a real revolution might (or might not) start, it’s excellent. As established science, treat it as a promissory note.