## Sunday, May 13, 2012 ... /////

### Quantum gravity: replies to "top ten"

Backreaction highlights what Sabine Hossenfelder considers ten "most interesting and pressing open problems" in theoretical physics related to quantum gravity. The amount of ignorance – a type of ignorance that is unfortunately widespread – and the depth of the misunderstandings that are visibly contained in the very questions seems very high to me.

Let me try to clarify some of these basic misconceptions that are often apparent in the very way how she phrases the questions.

The original problems are blockquoted in the blue blocks.

1. How can the apparent disagreement between general relativity and quantum gravity be resolved? Does it require to quantize gravity?
(Still 1. Haven't changed my mind about that.)
The reconciliation of general relativity and quantum gravity is unique and is known as string/M-theory.

The people who claim that they professionally work on quantum gravity but they're not really doing any string theory – or they haven't even learned the first chapters of the "textbooks" on the subject – are pure fraudsters, charlatans, and crackpots in the same sense as professionals who study even prime integers greater than 56. There aren't any.

It's kind of amazing that there exists a whole industry that tries to hide this simple fact. There are so many crooks doing these things that many people are literally afraid to loudly say that those people are crooks even though everyone in the field knows that.

But even if I ignore the fact that Ms Hossenfelder is completely ignorant about the basic knowledge about the field that she pretends to be her own, namely string theory, the remaining misunderstanding is still profound. In particular, the question "does it require to quantize gravity?" makes no sense.

The only two known conceptual frameworks that may describe physical phenomena are classical physics and quantum mechanics. There is no third way, at least not a major one.

In particular, one can't consistently couple a classical system to a quantum one. A uranium nucleus may influence Schrödinger's cat as well as its gravitational field; it follows that the gravitational field has to evolve into the same kind of superpositions of states that are observed for the nuclei. The observables linked to gravity may only be predicted probabilistically, much like everything in quantum mechanics, and they have to be represented by Hermitian linear operators.

The answers to all questions of the type "does Nature require observables to obey the postulates of quantum mechanics" are obviously Yes. But the ignorance concentrated in Hossenfelder's questions doesn't end with that.

Another problem is that she asks about the need to "quantize gravity" rather than the need for "gravity to obey the postulates of quantum mechanics". But this phrase of hers hides another incorrect preconception. Hossenfelder talks about "quantization of gravity" which is a procedure to obtain a quantum theory out of its classical limit. We may obtain some theories – especially those in the "textbooks" of quantum mechanics – in this way. But it is in no way guaranteed that all quantum theories are "quantizations of something".

This point is especially important in quantum gravity. We know that the correct theory of quantum gravity is not a quantization of any classical limit. It's wrong to assume that one may always start from a classical theory. More generally, it's wrong to imagine that classical theories are central or primary players. The arrow of the relationship goes exactly in the opposite direction. The full quantum theory is the exact set of rules that makes sense and that is connected with the Universe, either the real one or a conceptually similar but thought one. The classical theory is just a limit of the quantum theory if it exists. In some cases, it doesn't exist. For example, the six-dimensional (2,0) superconformal field theory doesn't have any classical limit in the superconformal phase.

Similarly, quantum gravity in 11 dimensions, M-theory, isn't just a quantization of a classical theory (e.g. classical supergravity).

So Ms Hossenfelder shows that she has vaguely yet mindlessly learned some mechanical procedures to construct quantum theories out of the classical ones – and she still seems to have a problem with this "addition of hats" – but she has never thought about the question whether this is the universal way how to find or define a quantum theory. It is not. And of course, we know that especially in quantum gravity, the reliance on a classical starting point is a brutal error.
2. Can we understand quantization?
(Up from 9. The more I think about it, the more I believe our problem with quantizing gravity is in the quantum part, not in the gravity part.)
Every pair of words in this question shows that the author of the question is confused about elementary things. The first sentence, the question, talks about "quantization" once again. But quantization is a simple procedure to construct operators and determine commutators out of their classical counterparts. An undergraduate student who is learning quantum mechanics should be able to understand and master quantization.

In the case of quantum field theories, the quantization leads to some additional complications – related to actual short-distance physical phenomena in the full quantum theory – that are addressed by regularization, renormalization, and the renormalization group. If we interpret an Einsteinian theory of gravity as a quantum field theory, these problems become fatal because the general theory of relativity isn't renormalizable at the quantum level.

However, this fact doesn't mean that there isn't any consistent theory of quantum gravity. This conclusion would be wrong because, as I have already said, it's not true that a correct quantum theory describing a physical situation must be obtained by a straightforward procedure from a classical starting point. Classical theories just aren't fundamental in any sense and you shouldn't assume that you will find one in every quantum research you will pursue. In the case of gravity, it's not true that one may get the right theory by a quantization. We only know that in a certain limit, the quantum theory should reduce to a classical theory. But this requirement isn't equivalent to the statement that the quantum theory should be constructed from the classical limit by a straightforward procedure, by "quantization". Instead, we must look at the set of plausible theories with desired properties and study them. Nature doesn't guarantee that our preconceived method how to find or construct these theories should work. It actually doesn't work.

Ms Hossenfelder's opinion in the parentheses proves that she is deluded about elementary points, too. The postulates of quantum mechanics are completely universal and can't be deformed in any way. Linearity, unitarity, and the quadratic formulae for the probabilities team up to create the unique viable framework different from classical physics that may produce predictions resembling the classical ones. There isn't any way to modify the quantum rules without destroying the entire theoretical structure.

On the other hand, the spacetime geometry is just one particular collection of observables in an effective theory; there may be and there are many other observables beyond the metric tensor. And the metric tensor isn't really a good degree of freedom at very short distances, away from the long-distance effective description. Also, the Einstein-Hilbert action (the Ricci scalar) is just one term in an effective Lagrangian. Once again, we know that there are many other terms, including interactions of the gravitational field with other fields as well as higher-derivative terms indicating more complicated self-interactions of the gravitational field with itself. It is totally obvious that at least a priori, the equations of general relativity may and do receive all kinds of corrections and deformations.

Ms Hossenfelder's opinion about all these things is upside down. She can't possibly understand the concept of the effective action – and I think she can't really understand the universal postulates of quantum mechanics – if she thinks that quantum mechanics should be modified while gravity should not be. It's certainly the other way around. Only incompetent would-be scientists and cranks can have a doubt about this basic point in 2012.
3. Do black holes destroy information?
What happens to the matter that collapses to a black hole?
(I think we spent enough time on the black hole information loss problem. It would be fruitful to instead think about what happens to matter at Planckian densities. Down from 2.)
The question about the black hole information loss was stricken by her; the justification is that "we spent enough time" on that problem. That's a very bizarre explanation why it was stricken. If we spend "enough time" on something, it doesn't mean that we have solved it or it has ceased to be a very important question. In many cases, having spent a long time with a problem may only highlight the depth of the problem.

At any rate, the black holes preserve the information even during the process of the Hawking radiation. We've known that since the late 1990s when explicitly unitary descriptions of these processes were constructed – in Matrix theory and the AdS/CFT correspondence. Stephen Hawking isn't a "canonical string theorist" but the evidence was so waterproof and overwhelming that he surrendered his bets and accepted that the information is preserved. Still, many questions that are more detailed and that are concerned with the way how the information gets out remain at least partially open. It's not quite easy to formulate them; Ms Hossenfelder hasn't even tried.

Her question about the Planckian densities could be refined and transformed into a meaningful question without misconceptions but it's not fine as stated. In the form it was stated, Ms Hossenfelder's question obviously assumes that there is some local description of "what is happening inside" in the very small regions where the densities are Planckian. But that's not how it works.

One can't construct a fully local description of such extreme situations. Instead, meaningful physics reflects what can actually be measured about such systems, e.g. via scattering. So it doesn't really make sense to ask "what happens at the Planckian densities". Instead, we may ask what probes and observers will observe in situations that would be naively assigned Planckian densities.

Moreover, Ms Hossenfelder's formulation of the question shows that she denies the holographic principle. In fact, you may see that in her whole "top ten list" of quantum gravity, there's not even a hint of holography although most genuine experts consider it the most important discovery of the last 20 years in theoretical physics. She's just detached from all these things.

Trans-Planckian densities can't really exist. If you try to find the densest object of a given size, you inevitably end up with a black hole. The smallest black holes have the highest density. But there can't be any black hole – an object admitting a general relativistic description as a black hole with small corrections – that would be smaller than the Planck length. So the maximum density one can achieve is the density of these tiniest black holes. It happens to be close to the Planck density.

Such a tiny black hole quickly evaporates – within a Planck time. It follows that one can't make any detailed measurements what was happening inside; there's not enough time e.g. for an accurate measurement of the energies. In the Planck time that is available, the error in the measured energy is inevitably greater than the Planck energy, too. There is simply no "large body of knowledge" about the internal behavior of materials that have similar densities simply because these materials don't exist as (meta)stable states.

Her focus on "volume densities" also contradicts the holographic principle. In the text above, I showed that only the tiniest black holes may reach close to the Planckian densities. But these objects are small and heavy. You can't fill a larger volume – a volume much larger than the Planck volume – by this "material". If you try to place too many (a million of) similar black holes next to each other, they will coalesce into a larger black holes whose radius is much (a million times) larger than the original one. Its density will be inevitably much lower.

The very idea that one should imagine that matter may be arranged into Planckian (volume) densities has been shown invalid by the holographic principle. It's a completely wrong way to think about the extreme conditions in quantum gravity. The modern legitimate replacement is to think about the maximum concentration of entropy per area – and that's nothing else than the event horizons. And one may also try to study the black hole interior or even the vicinity of the black hole singularities. But one must also realize that these questions are incompatible with "fully precise measurements" because only a limited amount of time is available for such measurements. And what happens in the very vicinity of the Schwarzschild singularity is arguably unphysical because no measurement can be done over there – and if it could, its results can't be broadcast to long-lived scientists.

Quantum gravity just doesn't work in the way that Ms Hossenfelder suggests in between the lines. Her questions could have looked OK thirty years ago but for decades, we have known that they're not good questions. One must be very careful when he discusses the black hole interior because it's unavailable to the scattering methods etc. It's likely that everything that may be said about the observations inside the black hole is equivalent to "matter on a curved background" which is an approximate description whose errors are matched by the unavoidable errors of the measurements, anyway.

It would be much more interesting to ask about the ways how the horizons store the information and how the viewpoints of the external and internal observers may be translated in between but of course, Ms Hossenfelder is nowhere close to these actually open questions in quantum gravity.
4. Are the electroweak and strong interaction unified at high energies? If so, are they also unified with gravity?
(That is, is there a theory of everything? Up from 8. I'm undecided whether or not unification is helpful to the problem of quantizing gravity.)
We don't know for sure whether the electroweak and strong interactions unify in the strict sense of grand unified theories – whether the GUT field theories are good effective descriptions of Nature at some scale. It may be a good assumption (and the gauge coupling unification in the MSSM is positive circumstantial evidence) but it could be wrong. However, we do know that at high enough energies, the seemingly differences between individual interactions (between the individual non-gravitational ones; as well as between the non-gravitational and gravitational ones) have to go away.

They surely go away in string theory but even if you pretended that we don't know string theory, one may also offer general arguments based on quantum gravity in the general sense that imply that the strict separation between different kinds of elementary particles has to go away.
5. Are the currently known particles of the standard model (SM) elementary? Are there more so far unobserved particles? Why are the parameters of the SM what they are and are they in yet unknown ways related to each other? Why are the gauge groups of the SM what they are? Is it even possible to uniquely answer this question?
(Formerly 8, minus the question for unification plus the question whether there's a unique answer.)
This question is obviously a purely stringy question; no other framework has even tried to dream about finding tools to address such conglomerates of questions.

Whether the particles of the Standard Model are point-like is a particle physics question – within string theory or outside string theory – that is probably unrelated to the characteristic problems of quantum gravity. One could say that this question shouldn't have appeared in a quantum gravity list. It would be OK in a string theory list but quantum gravity is a term that only describes those aspects of string theory that depend on the validity of the postulates of quantum mechanics as well as on the existence of the gravitational field. Questions about the inner structure of very light particles are unlikely to belong to this subset.

The same comment applies to the question whether additional particles exist. It's what particle physics model building is all about and its existence is mostly independent from quantum gravity; this separation is legitimate and justifiable, at least according to the current level of understanding of these topics.

Whether the field content and the values of parameters are calculable is nothing else than the usual vacuum selection problem. Some people would promote the anthropic reasoning as an answer in recent years; there is a large (but finite) number of possibilities and our Universe is a pretty random one. It may be very hard to isolate the right one. Alternatively, there may be a vacuum selection rule we don't know yet but it will be found in the future (or it won't be found but it may still exist).

At any rate, I find it bizarre that Ms Hossenfelder tries to "squeeze" the whole field of particle physics phenomenology and model building as the question number 5 in her quantum gravity top ten list. One either studies these things seriously, as good phenomenologists do, or she doesn't. Suggestions that questions about the short-distance architecture of the Standard Model particles is just a tiny subset of Ms Hossenfelder's "field" is yet another dishonest proposition because Ms Hossenfelder knows almost nothing about particle physics.
6. Did the universe start with a big bang, a big bounce or something else entirely?
(This is a reformulation of the earlier question number 4 which focused on singularities specifically. Down from 3.)
Because of the second law of thermodynamics – a law dictating that the entropy can't decrease – the visible part of the Universe had to have a beginning. Bounces can't be quite eliminated but they're neither natural nor motivated. Cyclical cosmologies have to have a beginning, too.

None of these questions are quite settled at this point but I think it's a wrong intuition to expect some new great insights about the prehistory of the visible Universe around us. It started 13.73 billion years ago and it's almost certain that there exists nothing that wouldn't fit on the semi-infinite axis from the Big Bang to the present.

If there are interesting insights to be found in related contexts, they're about the incorporation of our visible Universe into a grander scheme of things, e.g. an eternally inflating multiverse. It seems obvious that the eternal inflation is the more convincing proposed theory for a "broader context" in which our Universe lives; on the other hand, it's equally obvious that the existence of such a prehistory is likely to have no genuine yet calculable physical implications.

Again, what I don't like about the formulation of the sixth question is that it feverishly tries to overlook the actual progress that's been done in the relevant field – in cosmology, in this case. Ms Hossenfelder is asking the question in the same way as people would ask it 40 years ago or so. I don't think questions like that have any value if nontrivial insights collected over a 40-year period don't affect the wording of the questions at all.
7. Why do we experience 3+1 dimensions? Are there extra dimensions? Does the effective dimension of space-time decrease at short distances?
(This is an extension of the earlier question 7, taking into account that dimensional reduction to 2 dimensions has received some attention recently.)
Inside the parenthesis, this question tries to hype a random unimportant fad in the fringe literature.

At any rate, there are 6 or 7 extra dimensions but one should be much more careful when she talks about them. Before we count them, we should know what they are and how we define them. In quantum field theory, fields are functions of a certain number of spacetime coordinates and strict locality allows us to identify the spacetime manifold and measure its dimension. But quantum gravity is not a quantum field theory in the strict sense (and in the same spacetime); it is not strictly local and the usual definitions of the dimension don't apply to the short-distance space according to quantum gravity which is "fuzzy".

This fact makes the definition of the number of dimensions subtle. The counting of the dimensions is only "unambiguous" if we decide to count the dimensions whose size as well as the curvature radius is much longer than all fundamental length scales. However, the number of tiny compactified or strongly warped dimensions depends on the description. We know that because of dualities, the number of compactified dimensions (e.g. in the heterotic/K3 duality) isn't well-defined. In the AdS/CFT correspondence, the number of dimensions is ambiguous, too: depending on the description, the holographic radial dimension in the warped geometry may be seen or invisible. These are the actual important discoveries that are relevant for the seventh question; however, Ms Hossenfelder pays absolutely no attention to them. She has no clue.

Ms Hossenfelder is asking questions but she seems totally uninterested in the answers. That's why particle physics doesn't appear in her questions about particle physics, holography doesn't appear in her questions about holography, cosmology doesn't appear in her questions about cosmology, and so on. As far as I can say, she just wants to look smart by asking similar questions even though she doesn't have the slightest clue what the contemporary science knows about these matters.
8. Why is gravity so much weaker than the other interactions?
(Up from 10.)
The fact that gravity must be weaker – when the strength is properly defined – than all the other interactions seems to follow from consistency conditions in quantum gravity; it is implied by constructions in string theory, too.

The fact that it's much weaker is the core observation of the hierarchy problem.

Let me start more slowly: we know why gravity is weaker than the strong nuclear force. Or to say the least, we may transform this proposition into a more fundamental one. This fact boils down to the value of the strong coupling constant at the fundamental (Planck) scale which is smaller than one but not insanely smaller than one. By the logarithmic running and dimensional transmutation, we may calculate the scale at which the strong coupling constant grows larger than one – the QCD scale – and it inevitably ends up exponentially smaller than the Planck scale.

For the electroweak force, the calculation can't be done in this way assuming that the Higgs boson is a point-like particle. The reason why the electroweak force is much weaker at low energies than gravity is the hierarchy problem and much of the activity in particle physics phenomenology of recent decades has been dedicated to this problem. While no detailed complete answer is known, it seems obvious that attempts such as technicolor and compositeness have been eliminated after the 125 GeV Higgs was observed and supersymmetry is by far the most motivated solution to the hierarchy problem.

Of course, it's also plausible that there's no "mechanism" that explains the gap and one needs to refer to some anthropic explanations etc. in order to explain it.
9. Does dark energy exist? If so, what is it? Is the coincidence problem more than a coincidence?
(Down from 4. I think that the dark energy puzzle is possibly a relevant hint for quantum gravity. But then, maybe not.)
The case for the dark energy in the form of the cosmological constant has been getting stronger since the initial discovery in 1998. It has led to largely unsuccessful attempts to explain the small but nonzero value of the cosmological constant; the anthropic multiverse is the only at least plausible explanation that may agree with everything else we know and it's been briefly discussed above.

On the other hand, there exist various reasons to think that the dark *matter* exists. The 130 GeV gamma-ray line recently isolated in the Fermi data could become the most explicit evidence in favor of the existence of dark matter.

The coincidence problem isn't a problem. There are two reasons. First, we may compare many pairs of time-dependent quantities in a cosmology so it's not shocking that some of them are close to each other, within half an order of magnitude. Second, Weinberg's calculation of the optimum cosmological constant for life indeed does indicate that life tends to arise when the cosmological constant is comparable to the upper bound compatible with life – which is comparable to the density of dark matter when the life is actually thriving.

It shouldn't be shocking that I refer to Weinberg's arguments which are "anthropic" and depend on our existence because the very question "why now" depends on our existence, too. There is nothing objective about the moment we call "now". To describe it objectively, we need to link it to some properties of the Universe that exists today – such as the existence of stars or life on Earth.
10. How do we correctly assign an entropy to gravitational degrees of freedom? Is this testable at all?
(Newcomer.)
Yes, the gas of gravitons carries a calculable entropy much like any other gas; moreover, the event horizons carry the extra huge Bekenstein-Hawking entropy $S=A/4G$ that's been known from the mid 1970s and verified by totally independent methods in string theory. The appearance of this question does indicate that Ms Hossenfelder has no idea about quantum gravity, indeed.

If one isn't satisfied with independent calculations of the thermodynamic properties of black holes etc., she has to observe them. However, only very small black holes have high enough temperature for its radiation to be detectable experimentally. There are not too many objects around. And of course, one always needs some indirect reasoning to talk about entropy because the entropy isn't ever "directly observable". We may determine the changes of the entropy of macroscopic objects from the first law of thermodynamics in an appropriate form but there's no "entropy-meter"; this disclaimer is true both in black hole thermodynamics as well as any other thermodynamics.

Moreover, the whole language she uses is sloppy and naive. One of the lessons that we have learned in recent decades in theoretical physics is that we can't sharply separate gravitational degrees of freedom from others. This is related to the unification discussed above. In fact, AdS/CFT-like holography is another manifestation of this unification. Degrees of freedom that look completely gravitational in the AdS description are physically identical to degrees of freedom that look completely non-gravitational in the exactly equivalent CFT description. Ms Hossenfelder's wording implicitly denies all these facts because it pretends that a "gravitational degree of freedom" is a uniquely well-defined concept. It's not.

The impressive amount of deep insights that theoretical physics has learned in recent decades – but Ms Hossenfelder has not learned them – has shown that not only some naively guessed answers of people like her were wrong; even most of the questions are wrong, as you have seen above.
Dark matter has dropped off the list. I think we're well on the way to finding some direct evidence for dark matter. It will be difficult to pin down, but at this point it seems unlikely to me that it will be relevant for quantum gravity.
There may be surprises but I agree with these particular comments. Too bad they're not a part of the top ten list.