**The criticism of Hartle-Hawking by Turok et al. is demonstrably wrong**

In the Quanta Magazine, Natalie Wolchover published a new article

Physicists Debate Hawking’s Idea That the Universe Had No Beginningabout the controversies surrounding the Hartle-Hawking "wave function of the Universe" which quantifies the philosophical guess that "the Universe was born out of nothing". In the "story", there must be two opposing sides – that's how journalism likes to work. So the "other side" standing against the Hartle-Hawking school is Neil Turok and a few sycophants. If I am overlooking someone on his side who is more than just a sycophant of Turok's, please let me know.

Physics normally predicts "what an initial state evolves into". Given an initial state \(\ket\psi\) or \(\rho\) at time \(t_1\), assuming that we have already accepted quantum mechanics, we may calculate the probabilities of measuring \(L(t_2)=\lambda_j\) at a later time \(t_2\). In quantum mechanics, all this evolution is encoded in unitary evolution operators \(U\) – which is called \(S\) if we evolve from \(-\infty\) to \(+\infty\). So we explain why something occurred later – by reducing it (in the case of quantum mechanics, probabilistically) on the laws of evolution in physics combined with some knowledge about the state at an earlier time.

But we may keep on asking: Why was the state of the Universe at the earlier time what it was? Hartle and Hawking have designed a sketch of the answer: there is actually a preferred, calculable "initial state of the Universe" \(\ket{\psi_{HH}}\), the Hartle-Hawking wave function. The amplitudes defining this wave function are completely calculable from the same path integrals from which we normally calculate the unitary operators \(U\) or \(S\) responsible for the evolution. One just uses different boundary conditions – boundary conditions that only allow us to pick the final state, not the initial state.

If true, physics can not only predict how the initial state evolves into a later state. It may also calculate the initial state. So the explanatory chain really ends – and it ends with something that is calculable, although, once again, it's only the probabilities of various observations that may be calculated – because we're doing quantum mechanics.

The geometry of their "creation out of nothing" is simple. Imagine that our planet is the sketch of the whole history of the Universe but \(R\), the radial coordinate measuring the distance from the center of the Earth, is interpreted as the time (that's why I placed the picture of the Earth's core at the top). At a given time \(R\), the space is two-dimensional, corresponding to the sphere \(S^2\) of radius \(R\). A nice fact is that \(R\geq 0\): there are no regions with a negative value of the radial coordinate. So the time strictly starts at \(R=0\) and there is "nothing before that moment of creation". Yes, I have used this spherical analogy to explain "why there was nothing before the Big Bang" long before I knew Jim Hartle's surname. ;-)

Also, the spacetime around \(R=0\) – near the creation event – is completely smooth. Indeed, this earliest history of the Universe is captured by the vicinity of the center of the Earth, and that looks like a rather smooth or non-singular portion of the spacetime which doesn't really differ from other, later regions of the same spacetime much. You may imagine that there's a Euclidean path integral defined on top of the Euclidean spacetime analogous to the Earth in our example. You may attach the wave function on the sphere \(S^2\) at any radius, and calculate the path integral, and it will give you the Hartle-Hawking wave function of the Universe. In principle, this wave function is not only the "initial state" of the Universe. Because it obeys the Wheeler-DeWitt equation, it should be the right "state of the Universe" at all times. In practice, it is only used as a method to determine the very early conditions in the Universe – and the subsequent state is calculate via the evolution using the unitary evolution operators.

If our Cosmos obeyed the same laws near the beginning as my Earth metaphor, the Universe at its earliest moments would demonstrably and calculably look like slices of an iron-nickel liquid.

The rest of this project is composed of technicalities. Can we actually calculate what the wave function of the Universe is? Can we do the path integral over the initial portion of the spacetime that resembles the ball inside the Earth from our analogy? Can we do it in an approximate, effective field theory including gravity? And can we do it in the full consistent theory of quantum gravity, i.e. string/M-theory? And if we do the latter, should there be one Hartle-Hawking wave function for all of string/M-theory? Or should there be one for every "compactification" i.e. every superselection sector? Most of these questions remain open.

If we choose the first, milder goal, and discuss the approximate Hartle-Hawking wave function in effective field theories, we're led to some finite-dimensional approximations of path integrals, the minisuperspace approximation etc. Those still need to compute some integrals over a complex plane.

Two years ago, I discussed the Feldbrugge-Lehners-Turok criticism of the whole Hartle-Hawking program. So far, these three authors have written four papers together (they have 19-48 citations so far, many fewer than over 2,000 of Hartle-Hawking). Their work is composed of the potentially valuable part; and the garbage.

The potentially valuable part is a new trick to exactly calculate certain integrals in the complex plane – the import of the mathematicians' Picard-Lefschetz theory into quantum cosmology. The garbage is largely independent from the valuable part and is mainly built on their prejudice concerning the "right" choice of the contour. Much like typical laymen, Feldbrugge, Lehners, and Turok are terrified of imaginary and complex numbers and require the key contour to be chosen along the real axis. In particular, they demand that a variable called the "lapse" must be real. To emphasize these claims, they say that the Lorentzian path integral is nicer and more well-defined than the Euclidean one.

As e.g. Hertog and Hartle point out, these claims are clearly junk. Complex numbers are totally natural and fundamental in physics – especially physics at the level of quantum field theory and its extensions (which includes string theory for these purposes) – and in many cases, the right contour simply doesn't go along the real axis. If you calculate path integrals encoded by the Feynman diagrams, the propagators contain \(1/(p^2-m^2+i\epsilon)\) which means that the real axis is deliberately avoided by \(i\epsilon\), sometimes in one direction, sometime in another. This infinitesimal, asymmetric detour around the real axis is really equivalent to the logical arrow of time. Note that \(m^2-i\epsilon\) is used instead of \(m^2\) which really means that the rest mass has a small negative imaginary piece, and that's the same sign as the piece of resonances that exponentially decay in time. The probability that a particle hasn't decayed yet never exponentially grows with the time, an aspect of the arrow of time. The presence of \(i\epsilon\) in the denominator means that a stable particle is a limit of slowly decaying particles – which would differ from the unphysical "slowly growing" ones.

On top of that, we use the Euclidean path integrals because those are actually more well-defined and unambiguous than the Lorentzian ones from the mathematical perspective. The main mathematical essence that underlies the previous sentence really is that \(\exp(-x^2)\) is a nicer function to integrate over the real axis than \(\exp(ix^2)\). The former is clearly convergent, and the integral over the real axis is \(\sqrt{\pi}\), while the latter is only well-defined and convergent if some appropriate choices are made concerning the order of the limits and other things.

At the end, we are mainly interested in the quantities in the Minkowski spacetime whose signature is \(({+}{-}{-}{-})\) but it's important that I wrote "at the end". The fact that the final predictions are applied to the Minkowski spacetime doesn't mean that all the intermediate calculations must always work on the Minkowski background. Intermediate calculations may do anything they want, whatever is optimum for the theory to be maximally internally consistent and maximally compatible with the observations. In practice, quantum field theory is ideally calculated in the Euclidean spacetime and then analytically continued to the Minkowski spacetime which just happens to be the most controllable path towards the right results, whether you like this result or not, and whether you expected it or not.

Only the final results are being compared to calculations so they must produce the right results. If you tried to enforce some "traits" on the intermediate calculations, it would clearly be unjustified by the evidence – you would be enforcing your unjustified prejudices.

This open-mindedness about the "intermediate calculations" is something that way too many people totally misunderstand. This misunderstanding has many forms. Anti-quantum zealots insist on having an "objective state of the system" even prior to the observation – which is also an intermediate state, but in a different sense – and ignore the fact that only the actual outcomes when the measurement is made have to be well-defined for physics to be complete. Some people misunderstand the value of the formalisms with gauge symmetries because they want to ban the usage of gauge-non-invariant quantities. But gauge symmetry is so powerful exactly because we may use gauge-non-invariant quantities in the middle of the calculation and the condition that only gauge-invariant quantities are physical is only enforced at the very end of the calculation!

And the haters of complex numbers – which include Turok et al. – want to prohibit the Euclidean spacetimes or at least any contours that deviate from the real axis.

All these constraints are completely wrong. In the case of the theories and contours, we must allow the most general choice of the theory with any intermediate calculations which have any contours, including those deeply in the complex plane, to compete for the title "correct theory of the Universe". Turok's thesis that some spacetimes, signatures, or contours should be eliminate

*a priori*as if they were blasphemies is scientifically indefensible and wrong. That's the end of the story. He claims that the contours "have to be" along the real axis and it's simply incorrect. Whoever picks his side is just endorsing a demonstrably logically invalid statement.

We're not guaranteed that the Hartle-Hawking paradigm works and will be extremely useful and predictive in physics – it has no real quantitative successes so far – but it is surely conceivable and when trying to decide whether this paradigm works, we must focus on the most viable versions of it, not the least viable ones! So the Hartle-Hawking paradigm must be interpreted as a scheme where you must search for the right calculable quantities in the most general set of

*a priori*possible or allowed contours. The Hartle-Hawking program may ultimately fail – especially if an alternative is established – but the Turok et al. papers simply don't contain a valid argument against the Hartle-Hawking program.

**Commenters**

But my title was referring to the commenters under Wolchover's articles. They basically ignore the work by Turok et al. completely. Turok is too complicated a name for them and the difference between real and complex numbers is too cryptic for most readers. Instead, almost all of the 24 commenters tell us how much they hate the "creation of the Universe out of nothing".

For example, the most upvoted comment is one by Tarik Al-Hoshan who wrote:

How convenient... The universe came out of nowhere and we should stop looking for an explanation. That is the ultimate rationality because prophet Hawking says so. I would like to ask anyone coming up with a clever mathematical model on the creation of the universe or the existence as a whole, what experimental setup they plan to put together to confirm that yeah, a universe can just pop up out of nowhere. You know what? Show me. I want to see that with my own eyes.It sounds like some emotional gibberish written by a commenter who has been indoctrinated by the Mullahs. A problem is that virtually everyone else in that thread is

*comparably*dense and irrational as Tarik Al-Hoshan.

Physics doesn't look for convenient or inconvenient theories. Physics looks for correct theories. The correct theories may be convenient or inconvenient. They may be convenient for someone and inconvenient for others. But these adjectives are totally irrelevant for the decisions which theories survive in science. Whoever doesn't respect this basic principle simply doesn't understand the meaning of science, not even in the broadest sense. Such a person is analogous to Al Gore who looks for things that are inconvenient for his enemies – in his case, for the mankind – and calls them "the truth" because it's convenient for him to use the word "truth" for his convenient as well as inconvenient lies.

But Hartle-Hawking would indeed be "convenient" in some sense if it worked – and there is absolutely nothing wrong about it.

It's completely wrong to say that Hartle-Hawking represents "the end of looking for the explanations". On the contrary, if true, the Hartle-Hawking wave function provides us with the

*complete explanation*why the Universe is (or started) the way it is (or started). It is a wave function that makes all probabilities calculable. If such a wave function succeeded, it would mean that an explanation for a huge number of facts of the Universe has been found.

Hawking's title of a "prophet" is cute but it is just another childish insult. In some real-world mundane sense, a person who is right about many things may be called a prophet. Hawking has been wrong about many big things during his life – including the existence of the Higgs boson and the black hole information loss – but he has also been right about many things and the Hartle-Hawking paradigm may be right or wrong, too. Everyone who thinks that some would-be insults such as "a prophet" can change the probability that the Hartle-Hawking program is right is an idiot.

Sadly, virtually all the commenters belong to this class – the class of morons writing demagogic and insulting streams of nonsense and pretending that this nonsense may be counted as evidence in physics.

Tarik also makes crazy demands – such as "I must see the Universe to be born out of nothing to believe". Did he see the nucleosynthesis or the birth of the first galaxies, the Solar System, life on Earth, eukaryotes, vertebrates, mammals, humans, or his parents with this eyes? No. Does it mean that those events haven't taken place? No. Claims such as "I won't believe a theory about the early Universe unless I see the Universe born in a certain way again" only shows that the speaker is totally incapable of any impartial, rational thought. A person speaking in this way is just a prejudiced, obnoxious, and dishonest troll trying to give a hard time to those who do honest research. Science doesn't have the "duty" to persuade such bigots although the seem to think otherwise – these bigots are totally worthless and irrelevant from the scientific viewpoint. Sadly, most of the other readers are comparably hopeless.

What I find incredible is how much they fail to understand that their opposition is utterly dumb.

Some of these people are the same Internet users who oppose the eternal inflation and the multiverse that results from it. But it is pretty much obvious that

*either*the multiverse from the eternal inflation;

*or*the Hartle-Hawking-like birth out of nothing must be true!

The explanations "why the earlier state was what it was" either continue indefinitely or they don't. If they continue indefinitely, one must always have some Big Bang-like expansions that started from a bubble (because the neverending static-like universes are unstable), and one must trace an infinite sequence of bubbles arising from each other in a giant multiverse which almost certainly allows some diversity in the low-energy effective laws of physics; or the explanatory chain started somewhere so there was nothing "before it", and the Universe was therefore created out of nothing and physics must be able to pick a preferred wave function.

So it is either the Hartle-Hawking wave function of the Universe; or the multiverse, perhaps with some anthropic-like selection criteria that become important. There is pretty much no other choice, except for some combinations of the two. Whoever violently rejects

*both*possibilities is a simpleton because at least one of the possibilities must be at least partially right!

But these people don't care because it has become fashionable to attack science, rational thinking, and the basic laws of logic – while it has become politically incorrect to point out that idiots are idiots.

And that's the memo.

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