The discussion was revolving around their 5-weeks-old preprint
OK, so Mr Director wasn't satisfied with giving nonsensical negative monologues about the inflationary cosmology and string theory. He has added the Hartle-Hawking paradigm, too. And Tetragraviton seems to be an obedient, 100% corrupt employee of Mr Neil Turok's so he presented his rant totally uncritically.
OK, Vilenkin proposed that the early Universe – when its radius or curvature radius was very small – could have been created from nothing via the "tunneling from nothing". Alternatively, Hartle and Hawking proposed the paradigm that an early Universe whose slice looks like a 3-sphere may be continuously continued through the Euclidean spacetime to a point and it is smooth around that point. By continuing some most natural smooth conditions of the path integral around that initial point, one may calculate the preferred, Hartle-Hawking wave function on any sphere, including the finite ones.
It sounds plausible to me that when these general paradigms are done properly in a complete theory of quantum gravity, they are equivalent. But I don't think that Turok and pals have presented evidence that both of these pictures, and especially Hartle-Hawking, are dysfunctional.
In this business, people have encountered puzzles concerning the signs of the growing or decreasing terms in the exponential defining the path integral. And the continuation from the Minkowski to the Euclidean space often requires one to choose a contour in the complex \(N\)-plane (where \(N\) is the lapse function, a time interval) and there's no known universal rule to do it right.
Let me point out that the Turok et al. paper has one followup at this point,
Well, they use different contours. Turok et al. use a half-infinite contour, Hartle et al. use an infinite contour going along the whole real axis. As a consequence, Hartle et al. may extract a wave function that actually solves the Hartle-DeWitt equation, while Turok et al. don't end up with a solution to this "simplified Schrödinger equation in quantum gravity". Instead, the reduced contour of Turok et al. produces a Green's function for that equation.
That's too bad – what the alternative proposal by Turok et al. gives you doesn't solve "what replaces the Schrödinger equation in quantum gravity" but something that violates the equation. So it is not really a good candidate and should be abandoned. The Turok et al. calculation unsurprisingly leads them to focus on different saddle points than those of Hartle et al. – in fact, the Turok et al. saddle points make it impossible to get cosmological predictions.
You may see the general misunderstanding of the "logic of the derivation" on the side of Turok et al. The logic of the path integral is that Hartle and Hawking found a clever way to find a new cosmologically relevant solution to the Wheeler-DeWitt equation. Any clever trick using any clever contour or continuation of the signs is OK as long as the result really solves the desired equation.
In the most schematic form, the Wheeler-DeWitt equation is simply\[
H \Psi = 0.
\] It is like the Schrödinger equation except that the term \(i\hbar \partial \Psi / \partial t\) is missing. It has to be missing because in general relativity-based gravity, you don't have any universally well-defined coordinate \(t\). So you cannot define the derivative, either. Instead, the time \(t\) within quantum gravity has to be extracted as a value of an observable, e.g. from the density of matter or the position of hands on a clock, and when you do so, the time derivative term becomes just one part of the Hamiltonian term.
OK, so Hartle and friends have a solution to the equation that seems to be a verifiable solution and has some other desired characteristics. Turok only have a wrong candidate for such a solution, derived from a badly chosen contour etc. But the fact that the Turok "solution" is wrong doesn't mean that all other solutions are wrong.
At this place, I can't resist to mention that Turok's criticism seems analogous to many creationists' criticisms of Darwin's evolution. These critics sometimes create their own "plausible" model how species could have evolved, and they find out that it was too slow or otherwise unsatisfactory. However, they seem to ignore the fact that their detailed scenario isn't necessarily correct and Nature could have taken – and may actually be argued to have taken – a different path that simply works. For example, the mutation rate could have temporarily increased because the animals that participated in this speedup had some advantages. Creationists are just closed-minded about the existence of all such "simply clever" tricks. Turok et al. are analogous to the creationists. Their first guess doesn't work well – so they conclude that the whole paradigm, discovered by someone else, is wrong. But it doesn't follow. In particular, everything that works and is valuable was invented by someone else, while everything that sucks was proposed by Turok. One must remember that these two groups of ideas are disjoint, not identical.
The Hartle-Hawking paradigm has only been semi-successfully applied to some truncated, semiclassical, minisuperspace approximations of quantum gravity. At the end, I believe that someone will figure out how to do analogous things in string/M-theory properly, and she may figure out the deepest questions about the initial state of the Universe and maybe even the choice of the right vacuum or vacua from the landscape.
By the way, if I had read the abstract of the paper by Turok et al. five weeks ago, I would probably get provoked by the statement
We argue that the Lorentzian path integral for quantum cosmology is meaningful and, with...Quite generally, the Lorentzian path integral is well-defined but it's well-defined only when we properly define it, and to do so, we generally have to use a Euclidean continuation. In other words, the Lorentzian path integral may be well-defined at the end but the Euclidean one is more "immediately" well-defined. The number of operations and correct assumptions you need in the Euclidean path integral is smaller. If you wish: the Wick rotation is almost universally a good idea. There are lots of examples in which the Euclideanized structures in the path integral allow you to quantify the terms more reliably. One example are the genus \(g\) Riemann surfaces representing the world sheets' history in string theory – we assume that they are Euclidean and the work with the Lorentzian surfaces would create lots of new problems and puzzles.
The sentence quoted above sounds like they are saying that the "Lorentzian path integral is more well-defined than the Euclidean one" which is just wrong. This general sentence is a preparation for the fact that they would be making wrong contour and sign choices that would lead to wrong results – not the correct ones that are most naturally obtained by a continuation to the Euclidean signature.
Fine. So I believe that Turok et al. are just wrong and I am worried by the suggestion that he is abusing his power. I am worried that the likes of Tetragraviton are licking the director's rectum because it might be a good idea for them personally. More generally, it's bad for an institute of this singular character to have a director who isn't quite a top physicist but who tries to fight against top physicists – and the most important paradigms in physics. It looks like a classic example of the abuse of power. The directors should either be top physicists themselves, or someone else who has a lot of respect for top physicists. Someone's efforts to increase his influence within science by mostly political means is wrong, wrong, wrong.