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

**Neil Turok** (0:00)
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.

**Curt Jaimungal** (0:10)
You don't believe this, and you have some recent results.

**Neil Turok** (0:13)
I used to believe it, that quantizing gravity required extra dimensions, strings, membranes.

**Curt Jaimungal** (0:19)
What are the assumptions that go into this theory?

**Neil Turok** (0:21)
One of them is that the theory lives in a Hilbert space. We have an example of a theory, which doesn't require that assumption.

**Curt Jaimungal** (0:29)
For some background for the viewers, I was sent this paper last night. Professor Neil Turok is the inaugural Higgs Chair at Edinburgh, former Director of Perimeter and a 2026 Fellow of the Royal Society.

**Neil Turok** (0:43)
States of negative norm are called ghosts. 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. Provided the S-matrix or Hamiltonian of this theory has this symmetry, the answers you get are always positive and the probabilities always add up to one. 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.

**Curt Jaimungal** (1:14)
On this channel, I, Curt Jaimungal, interview researchers regarding their theories of reality with rigor and technical depth.

**Neil Turok** (1:22)
Sam says, I think I know how it works. And all it took is a slight tweak of the Born Rule.

**Curt Jaimungal** (1:28)
Today, ghosts, the Born Rule, why strings may not be forced in nature, and why simplicity still matters. Why is simplicity so important?

**Neil Turok** (1:37)
Simplicity leads to understanding.

**Curt Jaimungal** (1:41)
Quantum gravity in four dimensions is usually said to require strings or require some other extra structure. You have some new interesting results.

**Neil Turok** (1:50)
Right.

**Curt Jaimungal** (1:51)
Which we're premiering today. Okay.

**Neil Turok** (1:55)
I used to believe it, that quantizing gravity required this huge amount of extra paraphernalia, extra dimensions, strings, membranes. The whole story has become more and more complex as time progressed without actually solving any real problem.
What I mean by real problem is what happened at the Big Bang, what goes on in black holes, is there information loss? These questions have not been solved by these very complex frameworks for quantum gravity.
What we've recently realized is that there's rather a simple-minded approach to quantum gravity, which actually has been around since the 1970s, was begun by somebody called Kelly Stel, who unfortunately passed away recently. But he wrote a paper arguing that if you include terms in the gravitational action, so you generalize Einstein's action, Einstein's action involves the curvature of spacetime, and also a length scale, which is called a Planck mass or Planck length, or Newton's constant, it's all the same thing. So there's a scale in Einstein's theory of gravity. If you include terms in the action which are the square of the curvature.

**Curt Jaimungal** (3:25)
In addition to the regular?

**Neil Turok** (3:26)
In addition to the regular Einstein action and the cosmological constant, which is kind of has no derivatives, then you have Einstein's term which has two derivatives because it's a curvature, and then you can include curvature squared terms. That makes gravity much more like a gauge theory, because in a gauge theory the action is an integral of the field strength squared. Maxwell's theory, QCD, they all work the same way. In gravity, you can put the curvature squared into the action. Then there's almost a trivial argument that tells you that that theory, which includes Einstein but also these four derivative terms, is renormalizable.
Now, renormalizable means that when you do quantum field theory and you calculate things, it is possible to, although you get infinities in various calculations, you can absorb these into redefinitions of the coupling constants.
Basically, you're led to a sensible theory with what we call a continuum limit, namely, at short distances, the theory is completely under control.
There is a renormalizable theory of quantum gravity, which has been known since the 1970s. As I say, this is the simple minded approach. Now, there are reasons why people more or less abandoned it, though they keep coming back to it. It's called quadratic gravity because it's quadratic in the curvature. The action is quadratic in the curvature.
There is actually more and more interest in this possibility, which certainly is the simplest possible theory of quantum gravity. It's renormalizable, and then in the 1980s, Avramedian-Bawinski showed its asymptotically free. Just like QCD, the theory of the strong interactions, when you go to short distances, the coupling constant goes to zero, and it becomes a trivial theory of just waves which don't interact. You can imagine at very short distances, this theory is really extremely simple. What's wrong with the theory? All those statements I made about renormalizability, asymptotic freedom, they are the Euclidean theory. That is how we do computations of the strong interactions, QCD. You can put it on the lattice and study the theory, but the only way we really know how to study non-perturbative properties of an E field theory is to work in imaginary time.