## Monday, October 24, 2011

### Why I don't quite agree with Tom Banks on eternal inflation

My former PhD adviser Tom Banks (Rutgers/UCSC) wrote a guest blog for the Cosmic Variance,
Guest Post: Tom Banks Contra Eternal Inflation
in which he presents arguments against eternal inflation and promotes his holographic theory of everything, "HST". Tom is undoubtedly an out-of-the-box thinker. After all, this is also the main reason why your humble correspondent, a former undergraduate student from a country largely invisible on the map of modern physics research, has spent 10 years (1997-2007) in the U.S., something that I have never planned or dreamed about, after Tom Banks became the world's #1 person who liked my papers on Matrix theory posted to the arXiv, including one that started screwing string theory (often misnamed as "matrix string theory" these days).

Just to be sure, I have never had substantial political problems as a grad student at Rutgers (and not even as a fellow at Harvard); I surely don't count an irrelevant feminist hysterical outburst of Eva Silverstein after she learned from me that the average number of neurons in a female brain is 5-15% lower than that of an average male brain as a problem. When Tom Banks would give me one of the stupid petitions circulating among the left-wing Academia – for example, I remember one that was trying to harass John Ashcroft for no good reason – and I told him that I really had nothing in common with the petitioners' values, he would immediately stop.

He has done many things for me and one could talk about some amusing stories from the filming. But instead, we will look at Tom's long guest blog presented to the world via Sean Carroll. First, in order to introduce a photograph (most TRF blog entries should have a picture near the top), let us return to 1999.

TASI '99, group photo

In Spring 1999, we spent a month in Boulder, Colorado – much like every year, some high-energy physics grad students were making hikes to the beautiful Rocky Mountains and listening to lots of talks on string theory and related subjects. You may find your humble correspondent near the lower right corner. If you have complaints about my shorts or something like that, you're just like Nadiya Tkachuk, third from the left at the bottom. ;-)

You will find lots of other well-known people (mentioned on TRF or elsewhere) over there, too. Tom Banks is near the middle top and Sean Carroll is on the left upper side from him. Michael Peskin and Veronika Hubený are right above me and you may also locate lots of other people you may have heard of, including Natalia Saulina, Shamit Kachru, Eva Silverstein, Matt Headrick, Mark Van Raamsdonk, and so on, and so on (sorry if I skipped exactly you: it wasn't deliberate).

Tom came to TASI a few days after most of us, the grad students, and he was giving lectures on Matrix theory. I was excited and kind of naturally proud of my adviser, of course. However, I had to listen to fellow students who were saying that Tom's lectures were very confusing. He said that he would want to remove some fog of confusion and controversy from Matrix theory; however, a large part of the early lectures was dedicated to somewhat bizarre speculations about holography and nonlocality in time etc. that probably went well beyond Tom's new blog entry at CV.

Exactly when Tom came to Colorado, I was also informed about the newest discoveries related to his holographic theory of everything. My task was simple: to understand it and to complete the missing details so that the theory would obey the standard mundane requirements of the Nobel prize committee, among others. (Just to be sure, Tom didn't use this exact language, but it was the spirit as I understood it and still understand it.) Of course, I have failed. Even though Tom would almost always say things about the big-picture questions that looked manifestly right and self-proving to me, his holographic TOE musings left me utterly confused. That wasn't another Matrix theory I was able to work upon.

Going through the article written for Cosmic Variance

Over the last decade, Tom wrote dozens of articles about his holographic concepts and loosely related ideas. I've spent dozens of hours by trying to understand them and while I have been intrigued by some (but not all) philosophical properties of his proposals and some of the spirit of his thoughts has always been familiar to my soul, I could never find anything that really solves any mystery I wanted to be solved (an insight that makes things "fit together") and I could never find an argument that would answer a previously unanswered question. I could only see lots of general propositions, many of which disagreed with what I believed to be true, and no genuine evidence that I should change my beliefs (which, I think, are supported by much more tested formalism than Tom's ideas). This unfortunately continues to be the case as of October 2011.

First, let me summarize what I think about eternal inflation.

I rather strongly believe that inflation (or something de facto equivalent to it) is a part of the early cosmological evolution of our visible Universe. But is the inflation eternal? My belief in this situation is much weaker but I do think that the tunneling on the landscape or the configuration space does occur, does resemble the Coleman-DeLuccia instantons and processes at least in some situations and limits, and may even lead to the complicated hierarchical "multiverse" geometry as envisioned by the eternal inflation's champions. I have doubts about our control over the probability of different tunneling events between different points on the landscape – for example, whether or not the "faraway" tunneling events are suppressed, as believed by the KKLT-like cosmologists, or whether they may be enhanced due to the hugely increasing number of possible destinations and due to other things. (Over the years, I promoted a couple of papers offering this point of view.)

On the other hand, the tunneling events in eternal inflation are rather discontinuous which makes it questionable whether the time coordinate may be continued in any physically meaningful sense – much like the space (and momentum) in different vacua is different from that in others (another vacuum's momentum and the dual space may be closer to our vacuum's winding number and its dual space, for example), we should also admit that vastly different environments belonging to different vacua have non-convertible time coordinates (which are linked to the spatial ones by the respective Lorentz symmetries) and the unification of the patches to a bigger spacetime may be meaningless. Most importantly, because I don't believe that the total volume of space or spacetime occupied by inequivalent vacua in such a multiverse has anything to do with the probability that we live in a particular vacuum, I have serious doubts whether the big "family tree" of granddads, uncles, and cousins of our Universe in the multiverse can have any implications for science in our Universe, for our ability to explain or predict observable phenomena.

More precisely, I feel almost certain that this is not the way how to figure out something about the reasons why we live in one vacuum or another or how to determine which vacuum is the right one. As far as I can say, this is an unanswered question and if there exists a probability distribution on the landscape which "picks the right (or more right) vacuum (or vacua)", we should start from scratch and find it, while acknowledging that we hadn't found the right distribution so far, and we shouldn't make arbitrary (and extremely unlikely) assumptions such as that this distribution has something to do with the volumes in some semi-physical multiverse or with the counting of objects that we're ready to identify as "observers" and equip with "human rights".

Tom and technology of eternal inflation

In the section "Why I don't believe in eternal inflation", Tom starts with the following complaint against the instanton-based understanding of the tunneling processes needed in eternal inflation:
The theory [of eternal inflation] was developed in the 1980s, when it seemed plausible that quantum field theory in curved space-time was a good approximation to a real theory of quantum gravity whenever the energy densities and curvatures of the background geometry were small in Planck units. This idea is simply wrong. The fact that its falsification came through a back door...
Of course, the main reason why Tom thinks that the "idea" is wrong is holography. The holographic principle establishes that in a theory of quantum gravity, the adjacent volumes of space can't be quite independent – the total Hilbert space can't include all the degrees of freedom from the tensor product, like in local quantum field theory – because the degrees of freedom may effectively be organized on the surface of the volume rather than in the bulk and the surfaces don't add additively.

This is a very rough idea but one must be extremely careful about all the details surrounding the validity of the holographic principle and its implications. First of all, the holographic principle was first promoted by speculative papers by Gerard 't Hooft and Leonard Susskind in the early 1990s. They wanted the idea to be applied to any situation in quantum gravity. In 1997, Juan Maldacena de facto proved that the idea was right in anti de Sitter spaces, at least a couple of them. However, the impressive body of evidence hasn't established the same thing about holography in general spaces.

A nontrivial feature of the AdS/CFT is that the CFT theory living on the boundary is local: it's a Yang-Mills theory in the most familiar AdS_5 example. This fact is probably linked to some special properties of the AdS space such as the infinite stretching of the proper distances near the AdS boundary. For generic finite volumes, I am pretty certain that the hypothetical holographic theory living on the surface of the volume can't be local; in fact, this boundary sees all the Planckian areas and physics at the Planck scale simply isn't local. Once we admit that the theory controlling the "nats" on the surface isn't local, it can be any theory governing the Hilbert space of the corresponding value and the whole proposition of the holographic principle becomes vacuous in the worse case and equivalent to the entropy bounds (on the size of the Hilbert space) in the optimistic case.

While the evidence for AdS holography is huge, there are also reasons why holography in the AdS space is less counterintuitive than the holography in a finite volume of a flat space would be. One of them is that a "regularized AdS space" has the proper volume scaling just like the proper surface area – the same relationship as you experience in the negatively-curved Euclidean-signature Lobachevsky plane which is just the Euclidean AdS space, after all. So while Maldacena has shown that holography works really accurately, his setup doesn't automatically validate all speculative properties of finite regions that 't Hooft, Susskind, or someone else could have "deduced" from the speculative holographic principle.

In the previous paragraphs, I discussed whether the holographic principle is true in general and found some likely limitations. However, even when it's true, we may ask what are the implications. Tom's quote reproduced above shows that Tom is convinced that holography has truly far-reaching consequences that de facto completely invalidate locality. I don't believe it. I am convinced that the bizarre effects made necessary by holography – such as the non-local effects needed to conserve the information during the black hole information – are very subtle and can only be observed by extraordinary probes with a very high resolution, very high frequency, very high mass so that they would destroy the experiment, or a very large size so that the new holographic effects have no observable regional consequences. The regional consequences of the non-local effects that get the information out of the black hole are exponentially tiny and I believe that in any operational sense, they're unphysical for observers living in a small enough region of space.

One would need far more precision to describe the inequalities beneath which the locality shouldn't be violated; I have some guesses what the more accurate statements could look like but let me say that I admit that the formulations above lack rigor. However, so do Tom's propositions about the complete violation of locality by holography. When there is this disagreement, one still has the experimentally established locality as well as the approximate versions of locality that may apparently be derived from many descriptions of string theory we know.

So I see the situation with locality and holography as follows: I think that all of us have seen evidence that the exact locality can't hold but locality should still hold rather accurately in many situations and what we're missing is the demarcation line or a more accurate and universal quantification of the magnitude of non-local effects in the context of various measurements. I haven't told you what (or where) the exact demarcation line is; Tom hasn't given you an exact calculation of the line, either. This is not a universal criticism; no one else in the world knows the full answer. However, in this situation, we should still realize that among these two competing realms, the "realm trying to respect locality" and the "realm rejecting locality in any form and using the holography as an excuse", the former one is the established one which is connected with observations and quantitative, well-defined laws of physics while the latter is the one that is not established. So we shouldn't just say "screw locality". If you do so, you must revisit every single situation and every single theory or explanation which respected locality and you must show that your "completely non-local" new theory doesn't contradict observations and/or doesn't contradict other established features of string theory.

Tom has apparently chosen the audacious path to build all of physics from scratch so it's simply his duty to explain – in all inequivalent situations we know – why his proposed, "completely non-local" new theory doesn't lead to contradictions or falsifications in all the contexts where we have thought that locality works. This task of building physics from scratch may in principle be fulfilled but it is an extremely ambitious task and as far as I can say, Tom hasn't completed the task (yet). Because of this simple reason, he simply shouldn't expect other rational physicists to jump en masse from the "mostly local" platform to his shaky "completely non-local" platform. Such a jump simply seems as a transition from science to a non-science. Let me also mention that despite the apparent (modest?) violations of locality needed to solve the information loss paradox, string theory obeys many conditions normally derived from locality. Perturbative string field theory apparently saturates some bounds of the growth of amplitudes at high energies (with the angle scaling in a certain specific way) that may be derived from locality – which morally means that perturbative string field theory is barely local but still local – and I am not ready to dismiss all these observations, either. There's a lot of relatively deep maths in this business. You can't really throw away locality without any replacement.

With some more details, Tom's objection against the usual lore used in derivations of eternal inflation looks like this:
There are, in my opinion, two serious conceptual errors behind the theory of eternal inflation. The first is the notion that space-time geometry is a fluctuating quantum variable. The second is that de Sitter (dS) space is a system with an ever increasing number of quantum degrees of freedom. The increase is supposed to take place as the global dS time coordinate, or the time coordinate in flat coordinates, goes to future infinity.
Well, I have no clue what the first "error" is supposed to mean. The space-time geometry may not be a particularly natural or fundamental quantum variable – the CFT description in the AdS/CFT offers some potentially "more elementary degrees of freedom" – and the metric fails to be a good (or the only) degree of freedom at very short distances or high energies but it is surely a quantum variable, much like everything else than can be measured in any and every quantum theory. In the path integral formulation, all continuous degrees of freedom are integrated over with Feynman's integrand (phase) which is why all of them, including the metric tensor, are fluctuating. String theory unifies gravity with everything else so if other things are fluctuating quantum variables, the metric tensor must obviously satisfy the same condition. We may talk about superselection sectors and the suppression of fluctuations by requiring some boundary conditions at infinity or the horizon or the boundary of a causal diamond but it's clear that at generic points in the bulk, the spacetime geometry must be a fluctuating quantum variable. So as far as I can say, this "error" should simply be ignored because it is not an error.

The second error is more subtle. The evolution in which the size of the Hilbert space is increasing can't be unitary: it's a problem. Well, I think that at any moment, the dimension of the Hilbert space for which any description of de Sitter space really works is at least equal to the dimension extracted from the area of the cosmic horizon (determined by the cosmological constant, in the empty space, which means by the lowest possible energy density). More precisely, I believe that the relevant dimension to describe de Sitter space really exactly is inevitably infinite; a finite-dimensional Hilbert space is at most relevant for some effective description. As the de-Sitter-like space is expanding, more degrees of freedom get "activated" (they were forced to be "frozen" by the limitation on the volume but they have always been there).

Many of Tom's arguments rely on the strict – and I would say naive – finite dimension of the Hilbert space relevant for de Sitter space so they carry a vanishing ability to change my mind about any of these questions. Instead, let me say that I don't believe in fundamentally correct finite-dimensional Hilbert spaces describing de Sitter space (and quantum gravity in it) for many reasons. First, there is no finite-dimensional unitary representation of the de Sitter isometry group (although there could exist examples for its quantum deformation, something that had made Tom excited a decade ago but that I consider it irrelevant because the non-quantum limit of the group and its representation should still be a more interesting object to study and because non-quantum isometry groups lead to too much non-locality, much like the recently discussed kappa-Poincaré symmetry).

Second, I just don't believe that there exist canonical finite-dimensional Hilbert spaces with preferred operators on them that would describe something like physics on de Sitter spaces (which may be nearly flat). After all, every Hermitian operator on a finite-dimensional Hilbert space is determined by its eigenvalues (up to a unitary transformation) and one finite set of eigenvalues doesn't look "more correct" than another. For this reason, I don't believe that one could find principles that would say that one of the "Hamiltonians" or other operators is right and the others are wrong. Such principles that allow us to say that a Hamiltonian is the right one while its small deformations are not are only possible for infinite-dimensional Hilbert spaces, I think. The constraints on the spectrum of the Hamiltonian come from the requirements of renormalizability, good behavior in the UV, and so on: those things are absent in finite-dimensional Hilbert spaces and even in non-relativistic quantum mechanics which is why undergraduate quantum mechanics i.e. 0+1-dimensional field theory is just a toy model with a couple of important or solvable problems (and approximations to the real QFTs), not the "real story" that could be constrained and fundamental. (Any potential is as good as any other.)

Those comments of mine may be referred to as heuristic guesswork, intuition, vague feelings, whatever. However, they're morally extracted from the body of knowledge and they're consistent with the things that have worked in physics (for example, the transition from undergraduate QM to QFT wasn't a mistake: it was needed both to reconcile relativity with QM as well to be able to constrain the actual allowed Hamiltonians); it seems to me that Tom's picture isn't consistent with the spirit of known physics. When he promotes some privileged gravitating theories with finite-dimensional Hilbert spaces, he should have some data about them before we can see that something interesting is going on. As far as I can say, none of the theories that Tom envisions and that would deserve to be called "theories" – rather than a collection of many assorted unconstrained eigenvalues – may exist and unless Tom tells me either what the theory is or what are the conditions that are supposed to have a rather special but nonzero set of "solutions" (solutions that we could be looking for), where the solutions would be his theories, I think that there's simply nothing to talk about.

Independent bubbles and instantons

Even more specifically, Tom claims that what breaks down in the calculation of the tunneling instantons is the "dilute instanton gas approximation". One needs instantons at different places of a de Sitter space to be pretty much independent and Tom claims they are not. I believe that they're largely independent and the first moment when I would start to worry would be the point when the number of the bubbles per causal patch parameterically reaches or surpasses the de Sitter entropy i.e. the surface area of the cosmic horizon in the appropriate units. I just don't believe that the non-locality imposed by holography starts to manifest itself much earlier than that. As far as I can say, one may show that the target spacetime physics resulting from string theory is local at distances much longer than the string length (and in some sense, the locality holds even at shorter distances), at least for low-energy localized probes (plus some other disclaimers). And I am not ready to abandon this conclusion without a substantial amount of evidence – something I don't see in Tom's texts. While many details of the situation and the proofs are vague, I feel that the claim that some holographic non-local effects prevent a larger number of instantons from being squeezed into the Euclidean de Sitter space simply contradicts the proofs of approximate locality in string theory.

Even if I ignored the fact that I don't see any evidence for Tom's viewpoint that the proofs of locality have loopholes and the locality breaks down in Tom's drastic way, I also fail to see what we gain if we start to believe that the locality breaks down. Do we explain some observed data – either experimental data or "data" computed from some stringy models and other lessons? Do we resolve some outstanding paradoxes? I simply don't see anything of the sort so it seems irrational to me to abandon beliefs in propositions that seem correct and replace them by some other propositions that seem incorrect, especially if such a step seems to be a complete lose-lose situation. I don't say that we have a completely rigorous proof that Tom is wrong; it just seems likely.

Somewhat more generally, Tom argues that the Coleman-DeLuccia and similar instantons shouldn't be viewed as moral extensions of the Coleman instantons in (non-gravitating) quantum field theory. Well, that's exactly how I understand them and I think it is the very correct way to look at them. The instanton itself is also "localized" in some broader space. In its core, the metric tensor is allowed to have a non-trivial profile, much like other (scalar) fields in Coleman's QFT example (that's because we're dealing with a gravitating theory), but it's still true that the instanton approaches the original vacuum in some asymptotic region so there is a localized object in the vicinity of one point. As long as the spacetime dimension is high enough, such a local object or local disturbance in the Euclidean spacetime (and similarly in space) may be viewed as a localized object in quantum field theory.

I mean something pretty specific by this statement. People agree that special relativity emerges from general relativity in small enough regions where the space is approximately flat and gravity may be neglected e.g. by choosing a freely falling frame. That's one way to get a special relativistic limit out of general relativity. However, even if you have objects with hugely curved regions of space (such as black holes), you may still restore special relativity. Far away from a black hole, the geometry may approach the Minkowski space in which special relativity holds. So whatever the black hole is, must be representable by a localized object with a certain energy-momentum, charges, angular momentum, and other observables. From this viewpoint, the large curvature is only relevant for the description of the "internal structure of the object" at distances comparable to the black hole curvature radius scale or shorter.

If there is a large surrounding space, I am convinced that the usual locality expected from special relativity and its most straightforward embedding in general relativity has to be restored. In fact, even the fact that the information gets out of the black hole is just about some "internal issues" of the object we call the black hole.

Summary

I have no idea why the Blogger dog ate one-half of this text of mine: this sucks. But I am not going to write the missing piece again tonight, especially because when I got to checking this text, I decided it is less important than I thought. In the text that disappeared, I was going through many other technical statements by Tom and argued why there's no evidence supporting them while there seems to be evidence supporting the claims that Tom disagrees with. I have been explaining why it is very strange to associate finite-dimensional Hilbert spaces with arbitrary regions such as intersections of diamonds (which seem almost as generic regions with null boundaries), why it's anti-holography to expect tensor factorization for Hilbert spaces linked to regions split into pieces (something like that doesn't really hold even for QFT and holography makes the clustering property even more problematic), and I presented the reasons why I disagreed with most of Tom's principles that he wants to be satisfied by the axiomatic holographic TOE and why I think that they're unrelated with each other (e.g. with the cosmological SUSY breaking, and so on). There was a long discussion of "fake effects implied by holography", something one must be careful about (a point I agreed with Raphael Bousso and Dan Holz when we reviewed some bizarre literature about new counterparts of the uncertainty principle that were actually just signs that the author didn't know how to measure things more precisely, and he presented his sloppiness and inaccuracy to a principle of Nature).

So let me just sketch the original summary that was at the end of the text that evaporated (after a single Chrome tab kind of froze) and that was also much longer than here: if Tom is right, we will probably need many more centuries for other physicists to understand his brutally original axiomatic ideas that so far seem to be arbitrary, decoupled from each other, decoupled from experiment evidence, and decoupled from well-defined successful theories and theoretical evidence in the field. I wish him to be on the good track and to find some convincing evidence. Instead, I find it much more likely that the picture that will emerge in the future will confirm our expectations (such as locality, I don't really mean Tom's expectations here) much more robustly than we can confirm them today and that will allow us to calculate the demarcation lines and show that the regimes in which the expectations are violated differ in some remarkable ways from the "normal situations", ways that we can't really imagine. But it's unlikely that we will be just throwing away principles without any "equally constraining" replacements. We have learned something and it can't be quite unlearned.

And that's the memo.

#### 1 comment:

1. I don't agree with him either, and I think he ought to be explaining

- why spacetime is evidently curved to no more than to the second degree, and if so, what Riemannian manifolds are consistent with closure and unboundedness

- Why is entropy an apparent macroscopic invariant everywhere

- Why is action (more properly, action density) an apparent invariant everywhere (even microscopically - the Planck quantum of action is as much independent of motion of observers as the speed of light is)