Background independence

Lee Smolin has submitted "The case for background independence", hep-th/0507235. Background independence is definitely an interesting topic in philosophy of physics. Some of Lee's points can be agreed with, for example:

• It is desirable to find a background independent formulation of string/M-theory
• Such a formulation would likely to answer the questions whether the landscape approach to string/M-theory is correct; why it's not; what it should be replaced with.

These are the anthropic topics and it has been described many times why I agree with Smolin and others. However, I can't agree with the other points about background independence, especially Lee's opinions that

• We should try to revive Leibniz's relationism or Mach's principle
• Philosophical reasoning about background independence is relevant for derivation of physics of a particular background
• It's better if your theory contains no space (possibly not even an emergent one) rather than if it does
• Quantum mechanics should be replaced by something else that goes "beyond it"

and many others that will be discussed in this text.

See also: Background independence in AdS spaces

OK, let me start with the questions about relationism and Mach's principle. I highly recommend you the second popular book by Brian Greene, "The Fabric of the Cosmos", where the relative vs. absolute debate is covered in the first chapters. And the presentation is very nice.

What do I think about these issues? Unlike others, I have never been impressed by the relationist ideas and Mach's principle.

Leibniz's principles

It's easy to agree with Leibniz's "principle of sufficient reason": one must rationally justify every choice made in the description of Nature. However, this principle must be interpreted properly (justification: a proper interpretation is always a better choice than a wrong interpretation). A proper interpretation always allows you to make a choice because this choice leads to an agreement with this interesting world. More concretely, the coordinates and similar things are useful concepts to describe reality despite some redundancies and symmetries, as we will argue below. The success of Newton's theories is undoubtedly a sufficient reason to justify every single piece of his theory.

On the other hand, Leibniz's "identity of the indiscernible" - which says that the objects with the same properties must be identified - is technically wrong in all theories we've been using in the last 300 years. If two objects/states A,B are related by a global symmetry transformation, they have the same properties but they must still be considered as two distinct objects (configurations or states in the Hilbert space) - two objects that are not equal (=) - otherwise the mathematics would break down. Leibniz's approach to the "identity question" may be attractive philosophically, but in my opinion, it is more important that it is technically untrue in all successful theories of reality and we reasonably expect that it will remain untrue in the future theories, too. The only allowed interpretation is that Leibniz has defined another relation (equivalence) that is different from the usual mathematical identity.

Obviously, not all physicists share my viewpoint that the verifiable truth is more important than the philosophical prejudices; in other words, the philosophical prejudices may be incorrect even if their defenders sell them as deep ideas (and these chaps sell themselves as smart scientists and philosophers). But let us return to the question "Does space objectively exist?". There are aspects of "relationism" that are part of the standard physics cannon; and aspects that are an unnecessary philosophical addition that usually brings us on a wrong track.

In classical physics, the Galilean symmetry and the principle of relativity is alright. It's a well-known fact that you can't determine whether your train is moving or not. This fact is reflected by a mathematical property of the equations of motion: they only involve the acceleration and the differences between positions of objects; they don't directly depend on velocities. (Such a dependence may appear when you consider friction; friction typically picks a priviliged reference frame such as the frame associated with water in the ocean.)

Special relativity - an ideal amount of a deformation

In special relativity, the Galilean symmetry is deformed into the Lorentz symmetry which is in a sense deeper, as argued in the article about the depth. The Lorentz symmetry respects the same "beauty" as the Galilean symmetry (the beauty means, in this case, the equivalence of inertial observers) but it is more general because a parameter - equivalent to the speed of light - has a more generic, finite value. The Lorentz symmetry is a strong constraint on the possible form of the physical law. And every principle that has a chance to be true (or at least deep) and that has the capacity to constrain the equations of physics is welcome. The finiteness of the speed of light links mass and energy by Einstein's most famous formula and it reduces the number of independent physical fundamental concepts in many other cases, too.

The Galilean spacetime implied that the space and time were independent quantities (much like the energy and mass, and others). The Lorentz deformation is an ideal one (a golden compromise): it essentially identifies space and time (and mass and energy) with a power of the speed of light as the conversion factor. However, any choice of the speed of light leads to a physically equivalent theory (with a different choice of units). Had we made a larger deformation, there would be new undetermined dimensionless parameters. Special relativity shows the "optimum of beauty". Quantum mechanics is doing something similar and identifies time with energy (with hbar being the conversion factor), again without introducing new dimensionless parameters. Quantum gravity ideally sets another constant (Newton's constant or an equivalent) equal to one which allows to calculate all dimensionless numbers.

Coordinates: synthetic vs. analytical geometry

Also, as a kid, I was very impressed by coordinates and the possibility to analyze geometrical questions analytically, by looking at the equations involving coordinates. I don't know whether some of you have had the same feelings, but the mathematical tasks to solve a geometrical problem by "synthetic geometry" without the coordinates always looked like a useless childish exercise to me (which does not mean that one can't get good at it); it was recreational mathematics for children. If you can find the truth by using the coordinates, why shouldn't you use them? Coordinates are great and they are, to some extent, real. They are real modulo translations, rotations, and the Galilean (or Lorentzian) boosts. But there are only 10 parameters for this Poincare group in the whole Universe while the coordinates of the objects you want to study may be counted in thousands. No doubt, most of them are physical. We can't live without them or something more or less equivalent. The Cartesian coordinates, for example, look more fundamental than the angle between a bucket, Mercury, and a Mercedes, so why shouldn't we use them?

The relationist approach seemed to be an attempt to fight against the concept of coordinates; an attempt to pretend that they don't exist or they are unphysical; an attempt that must fail unless the coordinates are replaced by some assumptions that are equally powerful and essentially equivalent (but perhaps more awkward than the coordinates) because the space simply exists, to some extent, and you can't hide it. Also, the relationist approach did not look like a mathematical constraint on the possible form of physical laws. Instead, it was a way to make the questions quantitatively ill-defined. The relationist principles never looked like well-defined symmetries of a physical system; they were a method to show that no choice of the degrees of freedom is good enough for a sufficiently dogmatic person. We may summarize the situation: there was nothing that I would naturally like about the relationist approach.

Don't get me wrong: self-contained "bootstrap" systems that look non-quantitative and uncalculable at the beginning may be fine and very deep in physics but only if they're temporarily uncalculable. Relationism seemed to be a direction that wanted to make things permanently uncalculable.

Mach's principle

This description also holds for Mach's principle. According to Mach, the reason why you feel the centrifugal force when you rotate are the distant stars in the Universe; your rotation may be defined with respect to these static stars. If you remove all the stars, you can't distinguish a rotating yourself from yourself at rest and the centrifugal force disappears. While this idea was presented as a profound one by many popular books, it has always seemed obvious to me that it was a philosopher's nonsense. There can't exist any natural way to transform this paradigm into a set of mathematical objects and equations. The very goal of this approach is to show that everything about the coordinates is always unphysical. We simply know that it's not true: ideal solid bodies follow the rules of the Euclidean geometry (in a good approximation) and all the coordinates in this geometry are meaningful modulo a few symmetries we know. When we add dynamics, it's only the Galilean or Lorentz symmetry that must be subtracted from the reality of the coordinates. The fraction of the unphysical coordinates becomes arbitrarily small as we study ever more complex systems; and I just don't see anything wrong about auxilliary variables in physics.

Also, the Machian approach seemed as one of the confusions about the units. If the number of stars in the Universe were smaller, Mach's disciples argue, the inertial force would be smaller by the same factor. But in which units? It seemed clear that one can always use units in which the inertial force is independent on the number of stars. The exception is the case in which the number of stars is zero, but that's a singular case that can't agree with our Cosmos, and that could already be enough to make it uninteresting for a physicist.

Another technical problem with Mach's principle was the following.

Imagine that there are only two stars in the Universe. One is above you and one is below you. You will be able to distinguish rotational motion - except for the motion around the axis connecting the two stars. Does it mean that the magnitude of the centrifugal force should depend on the direction? Such a dependence would break the rotational symmetry of some laws of mechanics. Such a breaking does not seem to occur in reality. Moreover, it is ugly. Also, the argument seems to depend discontinuously on the size of the stars because if the stars have nonzero size (or if they have planets), you should be able to distinguish rotating objects once again. Let me summarize: Mach's principle always looked cheap, ill-defined, and nonsensical to me.

Mach's principle in GR

Einstein was strongly impressed by Mach's principle. It was one of the motivations why Einstein was developing General Relativity. And the resulting theory predicts some phenomena - such as frame dragging - that smell of the Machian flavor if you look at it from the right (or, equivalently, wrong) way.

But eventually, General Relativity had killed Mach's principle.

Mach's principle has not only been challenged: it became one of the weird prejudices that often leads you to wrong conclusions. Mach's principle was the main reason why so many people in the 1960s thought that the gravitational waves could not exist in GR; they thought that all such solutions always had to be pure gauge which means that they could be transformed into flat space by a coordinate transformation.

Of course, it's not true. If you analyze the equations in the linearized approximation and if you describe the diffeomorphism invariance using the same language as other gauge invariances - in other words, if you apply the rational and reliable tools of field theory - you will get the right counting of the physical polarizations in a few minutes.

A Nobel prize has been given in the 1990s for indirect experimental evidence of the existence of gravitational waves (a binary quasar is losing energy as it emits the gravitational waves). And I don't think it was an erroneous prize. LIGO, VIRGO, and LISA can tell us much more than just the answer to the simple question about their existence. Gravitational waves simply exist; they are a prediction of GR that is as much justified by the very basic principles of GR as any other phenomenon (such as the Mercury's perihelion precession, bending of light, or gravitational red shift). The existence of gravitational waves implies that there is something in the empty space that can oscillate; the "fabric of the cosmos" does exist, indeed. Any theory that wants to reproduce the successes of GR must agree with the existence of gravitational waves. In the low energy limit, they must be described by the same mathematical expressions. Moreover, in a quantum theory, gravitational waves must be coherent states of quanta called "gravitons" that are analogous to photons, quanta of the electromagnetic field.

An attempt to revive Mach's principle means to argue that the gravitational waves do not exist. It is a struggle to return us not only before General Relativity; it is a program to return the humankind to the pre-Newtonian era and the dark Middle Ages. Some people may be permanently impressed by Mach's principle and some people may find it shallow after a closer scrutiny. These two groups may be composed of equally nice people. But the difference is that the critics of Mach's principle have a good physical intuition; its advocates are philosophers who are unable to think analytically and quantitatively and they prefer to insist on prejudices that can be shown flawed by a five-minute-long quantitative argument.

Objects vs. relations

There is a lot of other philosophical waste around these questions that does not impress me much. On page 9, Lee starts with his theses. R1 says that "There is no background". We have discussed this one already. Using my language, R2 says that "The degrees of freedom should always be described as relations between the objects, not the objects themselves". I view it as a silly philosophical prejudice. There are great theories where at least some of the degrees of freedom are associated with the objects themselves, not just their relations. These are equally good degrees of freedom; the statement that relational degrees of freedom are "better" is unjustified (it violates a principle of Leibniz above, for example) and most likely incorrect, too. Also, you may view a property of the object A as a quantity describing the relation A-G between her and God, or whatever. There is no real difference.

Moreover, when there are some symmetries, the degrees of freedom assigned to the objects themselves may behave much like the degrees of freedom connected with their relations. R3 says that the degrees of freedom (the "relationships" in this case) evolve with time and the role of time is to order them; well, that's what time usually does except that Lee seems to mod out by the time reparameterization symmetry from the very beginning which I find awkward especially because a good absolute measure of time - including the reparameterization (not just ordering) may be measured by gadgets known as "clocks".

Let us agree that if background independence means to return us to the Machian dogmas that the space (and gravitational waves) can't exist, then it's a medieval silliness that we should no longer discuss in the 21th century. The assertion that "the relationist approach is powerful" is ridiculous simply because there does not exist a single relational theory that would describe anything in the real world, at least approximately. The field-theoretical revolution at the end of the 19th century has led us to exactly the opposite way of thinking: even in empty space, there can be fields whose existence is as real as the existence of material objects. They just describe other, field-theoretical degrees of freedom. The gravitational field is one of these fields that is connected with geometry of spacetime and with gravity; it exists much like the electromagnetic and other fields. Quantum field theory has shown that the positions of objects are not only on par with the values of fields in empty space; in fact, the former (particles) emerge from the latter (fields) once you quantize the fields.

Atoms of space

Another weird attempt is to say that the gravitational field only reflects long-distance properties of a complex system of "atoms of space" that can be found in very many different configurations. Well, such an opinion is nothing else than the gravitational counterpart of the luminiferous aether behind electromagnetism, i.e. the gravitational aether. It does not really matter whether one uses new terms such as "spin network", "spin foam", "background independence": these things mean nothing else than new versions of the gravitational aether and they are as discredited as luminiferous aether. If the "atoms of space" had many possible non-equivalent states in which they could be found - but all of these states would look like empty space - then the empty space would carry a (large) nonzero entropy density. Such entropy density is a four-vector whose nonzero value (probably the huge Planckian density!) would massively break Lorentz invariance of the vacuum.

It's clear that no such massive breaking is allowed in a realistic theory - not even a semi-realistic theory. In other words, the Minkowski vacuum must be locally unique. The requirement of the Lorentz invariance - even an approximate, local one - hugely constrains possible types of "compositeness" of space, and it definitely rules out all "chaotic models" of the vacuum. It is incredible that one may obtain something that looks like the empty space (or a gravitational wave) by making a condensate of seemingly complicated objects such as the closed strings with the graviton excitation. Nevertheless, we may show that these closed strings behave just like the metric. (At stronger coupling, the graviton is not composed "purely" of closed strings because they are not the only fundamental objects. For example, at very strong coupling in type IIB, the graviton is almost entirely composed of a D1-brane.) In virtually all other cases, we may show that the presence of some objects in space simply destroys the ability of the space to act as locally Lorentz-symmetric, empty space.

Comparison of aethers

Incidentally, the luminiferous aether in the 19th century was much more developed than the current versions of the gravitational aether. Maxwell has designed several models and FitzGerald has even produced a working model of aether based on wheels and gears. Be sure that it is not easy to create a system where only transverse waves propagate but Maxwell and FitzGerald were able to do it and immitate Maxwell's equation. (No model of gravitational aether that would mimic Einstein's equations has been constructed as of 2005.)

Although the 19th century luminiferous aether was much ahead of the current proposals for gravitational aether, it was exactly luminiferous aether whose complete destruction and humiliation became one of the most important symbols of the Einsteinian revolution in physics. Einstein updated and clarified Lorentz's observations that only one electric and one magnetic vector exist in the vacuum and they are not made out of anything more fundamental; he found a symmetry - namely the Lorentz symmetry - relating the electric and magnetic phenomena and showed that this valuable, precious symmetry would be broken by any system of wheels or anything else that you imagine to occupy the empty space. Wheels in empty space have been moved to the trash bin of physics. They have been superseded by a powerful, beautiful, and restrictive symmetry that tells you that no aether is possible. Undoubtedly, this conclusion holds for the luminiferous aether much like the gravitational aether.

I hope that most readers are intelligent enough not to be manipulated by a slightly fashionable philosophical term "background independence" into believing these patently false and discredited ideas about the origin of electromagnetic and gravitational fields. No doubt, many proponents of loop quantum gravity have tendencies to revive Mach's principle, aether, and other things. But these are not debates that should excite 21th century physicists since they are completely unrelated to any experiments, observations, and conceptual problems with the current theories that explain the cosmos; these are debates whether we should forget everything we have learned in the last 100 or 300 years and return to the era when philosophical and religious dogmas, not experiments and their lessons, should dictate what is the truth. I guess that we should not.

Background independence of GR

Lee is trying to argue that GR is a "partly relational theory". The "partial relationism" stems from the diffeomorphism invariance. Well, from a rational viewpoint, diffeomorphism invariance is nothing else than an example of a gauge symmetry; an example that prevents us from defining local gauge-invariant fields/operators. It seems that it's the absence of local gauge-invariant fields/operators that Lee sees as the source of his "partial relationism". I don't care about these fancy words; the diffeomorphism group is nothing else than a gauge symmetry, much like Yang-Mills gauge symmetry. In fact, we know that Yang-Mills and diffeomorphism symmetries may be dual to each other in the Kaluza-Klein theory and string/M-theory; in the latter case, they can also transmute into each other. It is definitely a misunderstanding to assign the diffeomorphism invariance with a philosophically deeper role than the Yang-Mills symmetry has, for example. Both of them are local symmetries - redundancies of the description.

Also, if someone says that the diffeomorphism symmetry is qualitatively different from Yang-Mills symmetry and its philosophical implications are different and more far-reaching, he or she shows the flawed opinion that the space and the degrees of freedom associated with it are special. They are not special and in string/M-theory, we know that all degrees of freedom - gravitational as well as matter fields - are generating from the same fundamental starting point. This unification is an important philosophical paradigm: all degrees of freedom in a completely satisfactory theory should stem from the same starting point; the existence of one group of degrees of freedom should be deducible from others via consistency requirements and symmetries. Why is my principle deeper than Lee's or Leibniz's principles? It's because it's respected by a theory that is capable to describe the real world at a very fundamental level. Leibniz's are just words that are - as far as we can say - simply wrong and the evidence for his words is purely sociological.

On page 13, Lee also argues that there is no kinematics without dynamics in GR. Well, it's because the diffeomorphisms are able to mix space (kinematics) and time (dynamics) almost arbitrarily. Note that this important rule is also violated in loop quantum gravity. Its proponents argue that it is perfectly OK to study kinematics first, and pretend that the results are independent of dynamics (about which they know absolutely nothing). It's not OK in a generally covariant theory as explained above; the ability of loop quantum gravity to separate kinematics from dynamics reflects its struggle with the time-like diffeomorphisms that will probably never be well-defined in the theory.

Lee says many statements that can easily be seen to be flawed. On page 13, he says that if we construct a physical description of GR, Leibniz's "identity of indiscernible" will be respected. However, light-cone gauge string theory in the Minkowski space is a completely physical picture, but it still has non-trivial global symmetries that can transform a state into an analogous, but different state. A similar statement may also be said about the AdS/CFT correspondence or Matrix theory (which is similar to the light-cone gauge example); in both cases, the diffeomorphisms are also removed but global symmetries survive.

On page 15, Lee argues against perturbative quantum general relativity but his arguments actually seem to be directed against perturbative general relativity itself (without the word "quantum") because the word "quantum" plays no role in his arguments. The reality is that perturbative general relativity is the most important technical tool to study it - one that was instrumental in deriving all major predictions of GR such as the gravitational waves, Mercury's perihelion precession, bending of light, gravitational redshift, and others. The same perturbative techniques are also critical in the investigation of the quantum theory; they allowed Hawking to calculate his radiation and the details of his and Bekenstein's black hole thermodynamics; they tell us that gravitons must exist; they inform us that they become strongly coupled at the Planck scale where a UV complete theory (string/M-theory) must take over. Once again, virtually all tested and reliable conclusions of GR at the classical and quantum level could not have been derived without the help of the perturbative method.

On the other hand, there are no successes whatsoever of the approaches that Lee wants to call "non-perturbative approaches". The main problem is that they don't care about physics, experiments, and the new principles that are revealed by them; they prefer philosophical dogmas from the 16th century. It is a waste of time to discuss these "non-perturbative" speculations in detail. In all cases (causal set theory, loop quantum gravity, triangulation models), the speculations are based on the naive picture of space as being composed of infinitely sharp points - like in the classical theory - which are moreover exactly discrete. All these approaches make incredibly strong assumptions about the physics at the Planck scale whose probability to be incorrect safely exceeds 99.9999999999%; all of them belong to the discredited category of "gravitational aether theories" and no 16th century philosophical principle is strong enough to transform this intellectual waste into a topic for a meaningful physical debate in the 21st century.

Background independence in string/M-theory

This subsection starts with the statement of the physicists that physics around a particular background of string theory may be studied without a background-independent formulation of the theory. This statement is obviously correct as shown by Matrix theory and especially the AdS/CFT correspondence. Lee responds with a quip (or a serious assertion??) that it is not clear whether the AdS/CFT correspondence is a valid conjecture. After 4000 papers of agreements, "no comment" seems to be the only plausible reaction to Lee's speculation.

There is no doubt today that many superselection sectors of the string/M-theory Hilbert space admit a description in terms of theories that are completely well-defined. Locally, we may move into different places of the configuration space (or the landscape). Physics of "other backgrounds" is always, to some extent, encoded in every background dependent description of string/M-theory.

What we don't like is that the descriptions depend on the starting point too strongly. It would be much better to have a universal description that treats all places in the landscape on par with others. Such a description is likely to make the spacetime locality and causality more manifest, too. When a background-independent description of string/M-theory is found, it will provide us with a global view on the landscape. If there are any special places in the landscape, we should see them. The transitions between the different places of the landscape during the cosmological evolution would probably become well-defined mathematically. A background-independent formulation would also be more powerful in revealing new subtle inconsistencies or instabilities of particular backgrounds.

Most of us dream about a background-independent formulation of string theory; but once again, we don't need it to study a particular background (superselection sector) of string theory. If Lee really predicted that one cannot deduce physics of a larger class of backgrounds if we start from a background-dependent description, then his prediction has already been safely falsified.

Relationism and reductionism

I don't understand the logical flow of the discussion that starts on page 25. Lee mentions the importance of emergent phenomena for complex systems; he says that it is not a contradiction to reductionism but rather a "deepening" of it. There is no justification. Common sense dictates that the more role emergent phenomena play, the less powerful reductionism becomes. While I believe that reductionism is a generally valid idea and it is always just a matter of approximation to rely on emergent phenomena, it's impossible to agree that Lee has justified that the emergent phenomena are "deepening" reductionism.

For string/M-theory, Lee postulates three principles that - as he believes - are widely believed: unification, uniqueness, maximal symmetry. Unification means that all elementary degrees of freedom in the theory are manifestations of the same elementary entity; one group of the degrees of freedom can't be removed without destroying the structure. Lee says that the elementary entity in string theory "is" a string - which is somewhat perturbative, obsolete interpretation - but otherwise he's right. I have already discussed this principle above.

The second principle is uniqueness: the right description of all the interactions and particles is unique. Although Lee connects this principle with insults such as the adjective "postmodern", there is no doubt that there can't be two fully correct but different theories that describe reality. Two theories may be exactly equivalent; then we call them one theory. If they're not, there must be a difference between them, and an accurate enough measurement is sufficient to distinguish which of them is correct. Lee's doubts about uniqueness suggest that even if we found the ultimate description of string/M-theory that accurately predicts the particle masses etc., Lee would object that the correct theory can still be a different one. In this hypothetical situation, I would find any doubts to be a bizarre kind of craziness. Also, our experience suggests that it becomes increasingly clearer to decide whether a theory is a correct one as we approach to the more fundamental layers of reality. And the theories become more unique.

The third principle of maximal symmetry has not become a component in the active, successful research yet. One thing is grand unification: the gauge group in Yang-Mills theory should be as simple (technically) as possible. Another thing is its generalization to the whole physics; this has not led anywhere so far. One must distinguish gauge symmetries and global symmetries. A gauge symmetry is a redundancy of a description, not a property of a physical system. It depends on the description and equivalent descriptions of the same physics may come with different gauge symmetries (AdS has diffeomorphisms; CFT may have a Yang-Mills symmetry). The representation group of a gauge symmetry is physically irrelevant because the trivial singlets are the only allowed physical states.

Global symmetries are different (although they can arise as a subgroup of "large" transformations in the group of gauge symmetries). Their representation theory is very important because the physical states form their representations that don't have to be trivial. But I don't know a reasonable physicist who is trying to maximize the global symmetries. We know what they can be - for example, the Poincare group. The possibilities for global symmetries are very limited in string theory because a global symmetry is typically extended into a local symmetry. For example, a symmetry current on the worldsheet may be multiplied by "del X" to create a vertex operator for a gauge boson. This gauge boson implies that the symmetry was actually a local one, at least perturbatively. For rotations and translations, this means that string theory always contains spacetime diffeomorphisms and gravity. For other global symmetries, the prescription also works. Whether or not non-singlet states are allowed depends on dynamics (whether or not a gauge field is confining or not and whether it is spontaneously broken, for example). In a sense, I agree with Lee (page 27) that the precise identification of the (global) symmetry group depends on the background; it is a background-dependent question.

As we move through the moduli space, the natural symmetry that we imagine to be "fundamental" is changing. Heterotic strings on a circle may start with an E8 x E8 symmetry; one may adjust the Wilson lines and get to a point with an SO(32) symmetry. Both of them are 496-dimensional groups that are not contained in one another; they are equally profound, in a sense. There does not seem to be any natural finite-dimensional group that contains both; the full "stringy gauge invariance" seems to be the only conceivable unifying framework.

The comments about the global vs. local symmetries above are valid for the theories as we know them today. If a very large symmetry is relevant for the theory of everything, something about the separation to local and global symmetries must be generalized. Morally, it is true that the unified structure of string theory also unifies its symmetries, but it is harder to see technically how a particular large group could be relevant for the whole picture and why it would be exactly this group and not others. The intriguing idea to get "all of physics" from one very large group (such as one of the groups beloved by Thomas Larsson) remains an unsuccessful speculation.

There are errors in Lee's reasoning on page 30 and around that are too numerous to enumerate. Lee does not distinguish effective theories and UV complete theories; he claims that there are no good interacting quantum field theories above 4 dimensions (what about the (2,0) in d=6?) and so on. I don't know how anything reliable can arise from this philosophizing if one half of the input is just plain wrong. In my opinion, it is enough to overlook one error in order to destroy an argument. Whether or not a 6-dimensional quantum field theory may be UV complete and interacting is an important question, and the answer is Yes. It may not be an expansion around a gaussian fixed point; but it is a consistent theory with operators and their correlators nevertheless.

Fortunately, these technical points are completely independent from the general discussion about the anthropic hope, which is why I can easily agree with Lee's comments about the anthropic hope once again.

In the following section, Lee unifies relationism not only with reductionism but also with Darwin's theory. While I also enjoy these deep ideas about "metaunification", let me admit that similar constructions proposed by others usually look weird to me. Natural selection could possibly share something with relationism but it is definitely too vague to be of any use. Incidentally, Lee's prediction that the parameters of our Universe are optimized for black hole prediction has been safely falsified. It is easy to adjust some parameters in such a way that we produce many more black holes than those seen around.

Cosmological constant puzzle

It's interesting to see a debate about the C.C. problem that is based on four speculations all of which seem completely vacuous and flawed. Statements such as "the C.C. problem is just an artifact of the evil background-dependent thinking" look ridiculous. No doubt, the background dependence is also responsible for the latest terrorist attacks. But such an emotionally loaded combination of words does not show how to calculate the right (tiny) value of the cosmological constant in a theory that contains the known particle physics - which is the true content of the C.C. problem. Some people apparently think that a solution to the C.C. problem means to construct a grammatically correct English sentence that contains a quote by a 16th century philosopher as well as the happy end that the C.C. problem is eventually solved. I beg to differ.

"Relational quantum theory"

On page 37 Lee starts an attack against the quantum theory itself. It's hard for me to read this kind of material. There is one valid point - that Bohr argued that the boundary between the "classical observer" and the "quantum observed object" may be drawn more or less anywhere which was not satisfactory. Today, we solve this question by decoherence that may be used to calculate the scale at which the classical concepts become a good approximation and the quantum coherence and interference disappears because of the interactions with the environment. Decoherence is a part of the modern neo-Copenhagen interpretations, especially the picture based on Consistent Histories.

The emergence of the classical world from the universal framework of quantum mechanics was a well-defined puzzle associated with the interpretation of quantum mechanics - one that has been solved. It is much harder to see which problems Lee is trying to solve now but I suspect that they are not my problems.

Lee combines various valid but usually invalid objections against various interpretations of quantum mechanics with relationism and cosmology. Because the length scale above which the meaning of the text seems to evaporate is around 1-3 sentences, I can't unfortunately say anything nice about these comments. As far as I can say, "relational quantum theory" is an incoherent conglomerate of weird assertions about quantum theory from people who have never understood it and who kind of confuse the lessons of relativity with the lessons of quantum mechanics. Concerning the "relational approaches to go beyond quantum theory", let me just state that as far as I can say, there exist no approaches to go beyond quantum theory (certainly not "relational ones") and all statements I have seen that claim the opposite are rubbish.

While the word "rubbish" may sound harsh, you should not forget that if you rearrange the electrons and nucleons in rubbish properly, you may obtain anything, including a piece of gold. This is what many of us should try to do with these questions.

See also Moshe Rozali's comments about background independence that are pretty much equivalent to mine.

Rich aliens from strings

Totday, the India Daily Technology Team has informed the large Asian country that

• The superstring theory in contemporary physics proves the existence of parallel universe with many higher dimensions where advanced alien civilizations prosper.

Actually, this sentence is the title.

Rich aliens seem to be one of the first practical application of string theory; they may live in a new kind of landscape. ;-) Their existence has also been shown by "rich spectroscopy at the Large Hadron Collider", our Indian colleagues argue and demonstrate it by a photograph of a fully operational collider. After the article in India Daily, The Reference Frame is the second source that informs you about the great news - and moreover tells you that you should not accept the news uncritically. ;-)

You should not think that India is the only place where such encouraging news occur. Yesterday, Canada was told that the work of Donald Coxeter from Toronto found applications in the Nobel-prize-winning carbon 60 molecule and string theory. A nice combination.

Also yesterday, another article about the liquid behavior of the "matter produced by Big Bang" appeared and the liquid behavior of the quark-gluon plasma may be "explained by some versions of string theory". Details are not specified.

Strings as Microsoft

This is my (first) reply to the discussion over at cosmicvariance.com under Sean's article called "Two cheers for string theory", especially the article itself.

There are many points in the text that I agree with and the author seems to have a remarkably sane idea what string theory is all about even though he is not a practitioner. There are other, more technical points, where corrections are necessary. Sean has not really considered the implications of the last 10 or 20 years in string theory but most of the non-professional readers of their blog misunderstand these implications as well, so it does not seem to matter and the readers are satisfied.

No doubt, it would be more encouraging if more than string theory as of 1985 presented by a non-string-theorist was needed for a full satisfaction. But one should not forget that there are many people, often outside the blogosphere, who care about the difference between string theory as of 1985 and 2005.

Let me start with some comparisons mentioned in the discussion.

String theory is Microsoft of quantum gravity. Unlike Robert, I have no serious problems with this comparison. Microsoft is more about success and competition while string theory is about the lasting intellectual value. But the degree to which string theory dominates the research in quantum gravity is analogous to the extent to which Microsoft dominates the world of operating systems. On the other hand, our loop quantum gravity colleagues should definitely feel flattered if someone compared them to the Apple or Linux of quantum gravity.

The reason is that the Apple computers more or less work, and sometimes the same thing holds even for the Linux computers.

Microsoft is gonna release a new operating system in 2006; a successor of Windows XP. It used to be called Longhorn, but on Friday they announced that it will be called Microsoft Windows Vista. I am looking forward to see this system, and I hope that string theory will offer something comparably striking by 2006. Meanwhile, many of us will continue to admire Microsoft and Bill Gates whose acts have been critical for the PC industry. When I learned that the BASIC for Commodore 64 - a home computer we played with as kids - was made by Bill Gates, my admiration doubled. And it did not disappear even when Bill Gates praised the brand new type of capitalism in China (formerly known as communism) and helped the Chinese bastards to ban MSN blogs containing the word "democracy".

Don't get me wrong: Linus Torvalds and Steve Jobs are also amazing guys! It would be harder to say the same thing about all the activists whose goal is to eliminate commercial software and force everyone to use their favorite semi-functional open source software.

String theory vs. QFT and Standard Model

Another comparison Sean offered was between string theory and quantum field theory. His goal was to suggest that string theory was not a particular model - such as the Standard Model - but a whole framework - such as quantum field theory. Definitely, string theory provides us with a new set of mathematical tools and concepts to study spacetime physics that goes beyond quantum field theory.

But in a specific technical sense, string theory is more analogous to the Standard Model, indeed. It's because string theory is one theory. While different quantum field theories are physically disconnected - although they can be mathematically similar - different backgrounds in string theory are solutions of the same underlying equations. We should imagine the Hilbert spaces of backgrounds in string theory to be unified into one Hilbert space. Moreover, the conditions of one background can usually be locally reconstructed in another background.

The haystack (or landscape) of these classical solutions of string theory is much more complex than in the case of the Standard Model, but the analogy holds. In fact, string theory is an even more specific model than the Standard Model; the Standard Model (with neutrino masses) has about 30 free parameters. String theory, on the other hand, is a completely unique theory and it has no free, continuous, adjustable, dimensionless parameters.

In some sense, string theory may look as a framework and a loose network of new ideas. But in a very technical sense, string theory is a completely rigid and unique conglomerate of these new ideas.

Sean's argument that string theory is a framework, not a specific model, is being used to justify the opinion that string theory does not have to predict particular numbers that can't be extracted from the Standard Model and GR. From a general intellectual or mathematical viewpoint, I agree with this thesis. String theory is continuously generating a lot of new mathematical ideas and new physical intuition that helps us to solve mathematical problems and compute things in new ways. It is also an amazingly consistent mathematical structure that is deeply rooted in physical reasoning. This itself justifies the research.

The value of a unification of GR and QM

From a physics point of view, I disagree with Sean's comment that string theory is justified as a physical theory even if it makes no new predictions. He emphasizes that string theory should be sold as the leading candidate to unify GR and QM. That's fine. But the only physical reason why we need to unify GR and QM is the fact that our world apparently respects both the postulates of QM much like it contains phenomena of GR. In other words, we need to unify them because we need to make predictions for our real world where electroweak, strong, and gravitational forces operate together and happily.

A consistent reconciliation of QM and GR in d=4 or higher turns out to be an interestingly constrained and difficult mathematical task whose solution is most likely unique up to dualities and equivalences. The solution is called string/M-theory. But we would never know that such a reconciliation is an interesting problem if we did not see both GR and QM in the world around us. And the only useful and physically valuable result of such a reconciliation are new predictions - qualitative or quantitative. For the reconciliation to be meaningful, we must be able to say something that the previous theories were silent and ignorant about. In particular, this includes the "overlap" regions where both GR and QM are necessary, such as the black hole singularity and the Big Bang.

There seems to be no argument about the fact that string theory has provided us with new sensational insights into many corners of mathematics and mathematical physics: into geometry of Calabi-Yau spaces (including mirror symmetry), equivalences between objects and phenomena that a priori look completely different (dualities), holography and the AdS/CFT correspondence, the role and fate of fields such as tachyons, geometrical realization of many mathematical systems that looked non-geometrical before, and so on.

It has also given us many new ideas how new interesting physics "behind the corner" may possibly look like and in 2005, most stringy as well as non-stringy phenomenologists admit that the majority of new good ideas for model building in the last 10 years came from string theory. We don't need to argue about these things; everyone who wants to be "in" tries to extract some valuable insights from the reasoning discovered by string theorists.

Value for physics as opposed to mathematics

But all these things are victories in physically inspired mathematics and the search for better mathematical tools to study physics. They're not victories in physics itself. I consider string theory to be more than just a miraculous generator of new mathematical insights about objects inspired by physics. I believe string theory is a new, deeper theory to accurately describe actual physical phenomena; probably a theory of everything. By a "new" theory, I mean that it is not physically equivalent to the previous theories such as the Standard Model (an example of a QFT), but it contains all of their wisdom and something more.

I don't see what the unification of GR and QM would be good for if it did not allow us to calculate new numbers about a world containing both GR and QM, at least in principle. Notice that this is the same comment that is emphasized whenever I explain why the attempts of loop quantum gravity to unify pure GR with QM are not only failing but also misguided from the very beginning. It is not exactly just some abstract QM that we want to unify with pure GR and we have no experimental evidence that pure GR should be compatible with pure QM without other forces: we want to unify the well-known quantum phenomena - namely gauge theories with fermions - with gravity.

Loop quantum gravity can't do it because these sectors remain independent, even in the most optimistic case in which the Standard Model is successfully added to LQG with the right low-energy limit. String theory does achieve this goal because gauge theories, fermions, and gravity are all parts of its low-energy limit. But in order to achieve the goal fully, it should also be used to derive the right spectrum of particles with the right parameters either from no input or from a smaller set of assumptions than required by the previous theories.

Concerning loop quantum gravity, I also disagree with another point of Sean: that all of us should offer our support to loop quantum gravity and other problematic directions in order to create an environment of competition. In my opinion, scientists should provide hints where to go according to their best knowledge. My best knowledge about loop quantum gravity implies that it is a misguided approach to physics. There undoubtedly exist people with a different opinion but it is impossible to lend your support to a particular human activity just because some other people like it. These people may only like it because a third group of people likes it - and the source of the love may remain obscure. That's wrong. Scientists' responsibility is to offer their independent opinion. Mine is that loop quantum gravity is a wasted time and money. And social-engineering of competition is plain wrong.

Ann Nelson and Occam

Occam's razor dictates me to agree with Ann Nelson in one point: if the prediction of the parameters or other numbers absent in the Standard Model is impossible, then the Standard Model should be favored as a physical description of reality because it is simpler and requires the same (or smaller) number of input parameters as the stringy landscape picture, for instance. My feeling is that some colleagues of ours truly love mathematical derivations and translation of one kind of physics into another kind of physics; even if the amount of predictions agrees, they will prefer a starting point that is as different from the final outcome as possible and that is as complex as you can get.

My opinion - and I suspect that the opinion of Ann Nelson and most phenomenologists as well - differs. A more convoluted starting point and a longer chain of reasoning from this starting point to the final result is only justified when either the explanatory power is extended, or the amount of parameters or independent assumptions and concepts is reduced.

String theory as we know it today may be used to calculate the Planckian scattering in some backgrounds. (Incidentally, for Peter Woit, the gravitational potential of an electron is "-M_e.G/r".) That's a stimulating progress, but the real victory in physics only occurs once we become able to calculate the Planckian scattering - the transition between low energies and the black hole creation - in the real world. The importance of this next step - to describe the effects in the real world - has become particularly pressing at the moment when we decided that the number of backgrounds in string theory is probably large, and therefore the collective predictions for all backgrounds are potentially highly ambiguous and essentially arbitrary until we find a selection principle. A larger number of critical points in the landscape does not mean that we should give up the goal to extract predictions beyond the Standard Model from string theory; it just means that the vacuum selection mechanisms will be a more important part of the full story than we had thought previously.

If the string theorists ever give up the task to calculate the numbers that can't be predicted by the previous theories, the string theory research should be moved to mathematics departments. Physics is about understanding the actual material physical world we live in. Mathematical beauty is a great thing, but for a physicist it should be just a hint that she is on the right track. It cannot be the ultimate justification of a proposed theory. Progress in physics always means that a larger number of phenomena can be calculated and predicted more accurately using a theory with less independent assumptions, defining concepts, and parameters.

String theory has the capacity to achieve this goal maximally, and if we transform ourselves into pessimists and fool ourselves by pseudo-arguments that the progress is impossible and that we should be even happy with such a postmodern and I would say scary expectation, we're gonna be in a big trouble.

Strings are just a piece

Also, another problem with Sean's text is that he paints string theory as we knew it 20 years ago or so. (It's not such a big problem at their blog whose typical readers who are not professionals - and some of those who are - are more interested about the YES/NO wars about string theory rather than the difference between string theory in 1985 and string theory in 2005.)

Today, string theory is not just a theory of strings. The perturbative approach to string theory based on one-dimensional elementary objects was a very fruitful point to start with, but we know today that it is far from being the whole story. The strings may be viewed as fundamental objects in the weakly coupled regime only; in other limits, other objects may "look" fundamental even though they were interpreted as solitons in the weakly coupled limit. In a recent article about the depth of ideas, I also explained that the very idea to replace point-like particles by strings is not deep. It only becomes a powerful idea once the special properties of two-dimensional conformal field theory are revealed.

In other words, when a person who does not understand conformal field theory in 2 dimensions at the technical level says that the idea to replace point-like particles by strings does not look deep to her but rather shallow and convoluted, I completely understand where she's coming from. But I would also like to tell her that if she learns how the relevant mathematics works, she will understand why strings are so special. But it requires a lot of calculations and the power of strings can't be obvious to a layman after 1 minute.

This point is rarely emphasized, so let me say it again. The laymen who consider strings as the elementary building blocks to be a shallow idea are correct at the beginning; but there is a lot of mathematical facts that can't be obvious from the very beginning that eventually make strings much more remarkable than one might have thought. This implies a recommendation for the laymen: slow down your far-reaching conclusions about string theory until you learn how its machinery works at the technical level.

Today, "string theory" is a kind of misnomer. The theory is based on many other concepts, too - but it does not make it less reliable. On the contrary. Clifford Johnson is very right when he disagrees with Sean and mentions that M-theory in 11 dimensions which has no strings is an equally valuable and qualitatively understood limit of the whole theory as the five superstring theories in 10 dimensions.

Point-like terminology

Sean mentions that he does not understand why the regular quantum field theories are said to be based on "point-like particles". It's because the quantum fields assign an operator to every point in spacetime. In string theory, it is different, indeed. For example, if you formulate string theory using the language of string field theory, you must assign an operator to every one-dimensional contour (string) embedded into spacetime. The number of degrees of freedom you see perturbatively is just much larger than in quantum field theory. (But at the very end, paradoxically, you end up with a holographic theory whose number of degrees of freedom is smaller than in any local point-like quantum field theory.) The fact that the operator at a given point can't be quite identified with the actual physical particle is an irrelevant technical complication that does not reduce the large technical difference between point-like field theories and string theory.

Wrong attempts to separate str-ing theory

Several participants in the discussion try to follow Peter Woit and divide string theory to the "good" stuff - new approaches of QCD including the AdS/CFT correspondence, insights about mirror symmetry - and the bad stuff - which includes the 10-dimensional and 11-dimensional vacua as the unifying starting point to include all of physics.

Only a person who is completely ignorant about the way how string theory works - and Peter Woit and Ohwilleke are not the only ones - can say something so absurd. There is no way to eliminate the critical dimension and all other basic insights about string theory from the other, "good" applications of string theory. For example, the best understood example of the AdS/CFT correspondence involves the N=4 super Yang-Mills theory. The dual bulk description is the AdS5 x S5 background of type IIB string theory. Note that the total dimension is 5+5=10, as always required in type IIB string theory. All the detailed features, including the excited type IIB strings and branes of all kinds, can be derived not only from the bulk description but also from the gauge theory defined on the boundary!

String theory, at least in the highly supersymmetric vacua with 8 or more supercharges, is a fantastically rigid theoretical structure that holds together perfectly. If someone says that one can preserve the successes (as enumerated above) of string theory without preserving everything we know about its critical dimension and the basic knowledge of stringy dynamics in 10 and 11 dimensions and the compactifications, then she or he only shows that she or he is uninformed about the very basic facts of the field. String theory simply can't be separated in this way. It would be similar to the attempt to remove photons from QED.

Strong leadership of supersymmetry

Possibly, there are many intellectual directions - bosonic string theory, non-critical string theory, topological string theory, the landscape approaches - that will eventually be considered to exist outside the realm of "the" string theory (or will be considered inconsistent because of some non-perturbative subtleties). By "the" string theory, I mean the theory that has the beauties and that is relevant for the real world. But the different phenomena and relations between physical insights about the supersymmetric vacua of string theory can't be undone, and they will always be essential for our understanding of many things, including holography etc.

The less we rely on spacetime supersymmetry, the less reliable the different dualities and relations are. For example, the holographic dual of pure QCD in 4 dimensions probably has a different bulk dimension than 10 or 11 and it may be called a non-critical string theory (it is an ambiguous task to define the number of tiny dimensions in a background of string theory; only the large and nearly flat dimensions can be counted without doubts). But it is also the case where the existence of a quantitatively predictive dual (bulk) theory is uncertain and where string theory has not told us too much - at least not too many quantitative results.

The maximally supersymmetric backgrounds - such as the N=4 gauge theory - are best understood, and one can show that the dual is not just some generic five-dimensional gravitational theory, but the ten-dimensional type IIB string theory on a very specific background. All details work. It is not possible to eliminate some known aspects of ten-dimensional string theory from this picture! While various other approaches to quantum gravity are incoherent and dividable conglomerates of ideas, string theory is united.

United we stand, divided we fall.

Hawking and unitarity

The previous blog article about the very same topic was here.

Stephen Hawking who may currently be the world's most famous applied string theorist among the public has finally submitted a paper that many of us were eagerly expecting for a year or two. The paper is titled "Information Loss in Black Holes" and its preprint number is hep-th/0507171. Because it is less than 5 pages long, I recommend you to read it.

On the first page, he summarizes the history of the information loss puzzle. In 1967 the no-hair theorems started to appear: the black holes are classically more or less unique solutions determined by a few parameters. Because they don't have any hair, they can't wear any haircuts that would distinguish them from other black holes with the same value of conserved quantities; they don't have any features that could give them a large entropy.

This is strange because the black holes seem to be the final outcome of a gravitational collapse, and according to the 2nd law of thermodynamics, the final states should maximize the entropy. The apparently vanishing entropy seems to contradict this law. However, the black holes in the classical theory are eternal and we may envision the information as being stored inside the hole; it is just not accessible to the folks outside.

This argument fails in the quantum theory because of the line of reasoning pioneered by Jacob Bekenstein and Stephen Hawking. Black holes eventually evaporate, via the Hawking process, which eventually uncovers all the details of their interiors. The nonzero temperature may be used to derive their entropy via the equations of thermodynamics; the entropy happens to be proportional to the horizon's area (for large black holes; the extensive progress in determining all the corrections from string theory is discussed elsewhere), as first predicted by Bekenstein.

However, Hawking's semiclassical calculation leads to an exactly (piecewise) thermal final state. Such a mixed state in the far future violates unitarity - pure states cannot evolve into mixed states unitarily - and it destroys the initial information about the collapsed objects which is why we call it "information loss puzzle". A tension with quantum mechanics emerges.

There have been roughly three major groups of answers that people proposed.

1. One of them is essentially dead today; it is the remnant theory. It argued that the black hole does not evaporate completely. Instead, a small light remnant with a large entropy remains after the evaporation process - and this remnant is what preserves the information. This approach is highly disfavored today because such small seeds simply should not be able to carry large entropy (because it violates holography). Moreover, this approach does not save unitarity anyway because the scenario still assumes the thermal radiation to be in a mixed state.
   
2. The other two general answers are obvious. One of them says that the information is lost, indeed. The qualitative features of Hawking's semiclassical calculations - the evolution into mixed states - survive in the exact analysis, too. Such an approach is popular among the General Relativity fundamentalists who believe that the fabric of spacetime is exactly what we think it is classically; causality in particular must be exact and no information can ever get out from a black hole. I formulated the argument in a way that makes it clear that it looks dumb to me - especially today when we know that topology of space may change and that black holes exist in unitary backgrounds of string theory. The Hawking process itself is an example of a violation of the strict rules of locality and causality by black hole physics!
   
3. The last answer, the only one that has always respected the principles of the 20th century physics, says that the information is preserved in the same way as in any other process in the world - burning books is an example. (Only later, I noticed that Hawking has independently chosen the very same example.) When we burn books, it looks as though we are destroying information, but of course the information about the letters remains encoded in the correlations between the particles of smoke that remains; it's just hard to read a book from its smoke. The smoke otherwise looks universal much like the thermal radiation of a black hole. But we know that if we look at the situation in detail, using the full many-body Schrödinger equation, the state of the electrons evolves unitarily.
   
   The same thing must hold for black holes. And the feeling that such a transfer of information is impossible because of the horizon is just an illusion; it is an artifact of the semiclassical approximation that paints the rules of locality and causality as more strict than they are in the full theory. Locality and causality are, in general, approximate emergent concepts that appear in the (semi)classical limit. The power of the full theory of quantum gravity to violate locality and causality in a subtle way is manifested whenever horizons develop, and it is responsible for the conservation of the information.

Note that the conservation of the information is the only answer that can be acceptable for a physicist who treats the postulates of quantum mechanics seriously. No doubt, the postulates of quantum mechanics seem rigid and un-modifiable, while the exact degrees of freedom and terms in the Lagrangian that describe general relativity are flexible. The quantum mechanical postulates have a higher priority, and they tell us that the information must be preserved in the details of the nearly thermal Hawking radiation that remains after the black hole disappears.

While Stephen Hawking has believed that the information was lost - and he has made bets of this kind - he eventually switched to our side in the summer of 2003 or 2004 (I am uncertain now). As you could hear from CNN and other major global new agencies, he officially admitted that his opinion was incorrect. The deep insights in string theory have convinced him that John Preskill was right and the bet is lost; Hawking gave an encyclopedia to Preskill as promised.

Among these insights that have convinced Hawking, you find Matrix theory and especially the AdS/CFT correspondence. Gravity in asymptotically AdS spaces has an equivalent description in terms of a conformal field theory living on its boundary. This conformal field theory is manifestly unitary and has no room for destruction of the information. This answers an equivalent question about gravity, too.

This brings most sane physicists to the opinion that the information is preserved and gravitational physics is not that special after all. But it does not give us a quantitative, calculable framework that would explain how does the information get out of the black holes and what do these subtle correlations that remember the initial state look like.

Hawking's recent solution

Hawking has announced that he had solved the problem. The main ideas of his solutions are the following ones:

• The scattering S-matrix is the main "nice" observable that should be calculated in a theory of quantum gravity. (I fully agree.)
• The scattering does not prevent a black hole from being formed, but such a black hole is just like any other intermediate state or resonance. (I fully agree.)
• The thermal nature of the resulting radiation is a consequence of an approximation (that becomes accurate for large black holes) but there is no qualitative difference between black hole intermediate states and other intermediate states; the transition if smooth. (It was actually just me who formulated this point in this way.)
• Just like in quantum field theory, the Euclidean setup combined with the Wick rotation is an essential technical tool to do the calculations; Hawking refers to Euclidean gravity as the "only sane way" to do quantum gravity. In the gravitational context, this approach was promoted and improved by Hawking and Gibbons. In fact, the Euclidean approach may be even more important in quantum gravity than it is in quantum field theory and its procedures may represent am even larger fraction of the derivations in the gravitational context. (I agree, and as far as I know, the people who disagree - such as Jacques Distler - have not offered any rational and valid arguments so far.)

OK, so Hawking tells you to calculate the S-matrix by a Euclidean path integral over topologically trivial configurations (spacetimes) - those that are continuously connected to the empty spacetime. Such a process may involve a production of a large number of particles in the final state which is a hallmark of an intermediate black hole. Once you calculate the Euclidean S-matrix, you Wick rotate the results to get the amplitudes for the Minkowski signature.

Note that we have only included the topologically trivial spacetimes and this is a good choice that preserves unitarity.

On the second page, Hawking proceeds with some technical subtleties. He wants to allow strong gravitational fields to occur even in the initial and final states, it seems. (It does not seem necessary when one talks about the generic S-matrix elements but it is conceivable that these strong fields appear in the Euclidean spacetime anyway.) With strong gravitational fields in place, one can't meaningfully define the wavefunction at time "t" because there is no preferred diff-invariant way of slicing the spacetime.

Hawking solves this by a seemingly bizarre operation. He calculates a partition sum with periodic Euclidean time instead of the transition amplitude; it is not 100% clear at this point how will he introduce the initial and final states to this setup. (Note that the Euclidean time is spacelike and it should therefore not be interpreted as a source of the usual violation of causality.) Moreover, this partition sum has a volume-extensive divergent factor. Hawking regulates this infrared problem by introducing a small negative (anti-de-Sitter-like) cosmological constant that does not change local physics of small black holes much.

He obviously deforms the picture into an AdS one in order to get a background that is as well-defined as the usual AdS/CFT backgrounds in string theory. Hawking states that because we are making all measurements at infinity, we can never be sure whether a black hole is present inside or not.

This looks like cheating to me; equivalently, it suggests that no true solution is being looked for. Of course that if we only work with the boundary degrees of freedom, we will see no unitarity violations and no problems associated with the black hole dynamics. It's simply because all these things are encoded in the CFT which is unitary. The true surviving question is how is this unitary description reconciled with the bulk interpretation in which a macroscopic black hole is demonstrably present and has the potential to cause information loss headaches.

Hawking does not have a working convergent path integral beyond the semiclassical approximation, but let us join Hawking and pretend that this problem is absent. He computes the partition sum over geometries whose boundaries are topologically S^2 (the sphere at infinity) times an S^1 (the periodic Euclidean time) at infinity; he works in four spacetime dimensions. There are two simple spacetimes with this boundary: B^3 times S^1 is the empty flat (or anti-de-Sitter) spacetime while S^2 times D^2 is the anti-de-Sitter Schwarzschild topology.

While the empty spacetime can be foliated, the S^2 times D^2 cannot because it has no S^1 factor, roughly speaking. Because it can't be foliated, you can't even define what the conservation of the information should mean in this topologically non-trivial case. The contribution to the correlators coming from the topologically trivial case are conserved as the Lorentzian time T grows; the contributions from the topologically non-trivial backgrounds decay.

On page 3, Hawking confirms that he was inspired by Maldacena's hep-th/0106112 about the eternal black holes in anti de Sitter space. In that case, you also have two - actually three - geometries that fit into the S^1 times S^2 boundary: empty space, small black holes, large black holes (compared to the radius of curvature). The large black holes dominate the ensemble; they have a large negative action. Nevertheless, using the bulk techniques you may calculate that a correlator of O(x)O(y) on the boundary decays for large separations (while it has the usual flat-space behavior if x,y are nearby).

Such a decrease looks much like other cases of information loss; nevertheless in this case you may argue that there is a unitary CFT behind it and the exponential decrease may be in principle reduced to repeated scattering. Maldacena also showed that the contribution of the empty spacetime does not decay and it has the right magnitude to be consistent with unitarity; Hawking argues that he strengthened this observation by having showed that the path integral over topologically trivial spacetimes only is unitary. (Again, it is not obvious whether his formal argument holds in reality because of the usual loop UV problems of general relativity.)

The large black holes are not too interesting because they don't evaporate. Instead, we want to look at the small black holes. Hawking has been trying to find a Euclidean geometry corresponding to an evaporating Lorentzian black hole for years. Now he says that he failed because there is no such geometry. In the Euclidean setup, only the metrics that can be foliated - empty space and eternal black holes - should be added to the path integral.

One of the main question that you must certainly ask is: Why does dynamics over topologically trivial spacetime look like the creation of a long-lived black hole with horizons in the Lorentzian signature? I believe that Hawking does not fully answer this question; he only says that "thermal fluctuations may occasionally be large enough to cause a gravitational collapse that creates a small black hole". Let me re-iterate that such a short comment is deeply unsatisfactory. What we want to understand in the first place is the bulk description of the process in which we can see that the usual long-lived black hole is there; we want to see how are the concepts of locality and causality corrected so that the information can escape.

Hawking only says that this solution of the information loss puzzle is possible. We could have said the same thing just because there is a dual unitary CFT description. But the local bulk dynamical mechanisms that make these things possible remain nearly as cloudy as before.

Some of Hawking's conclusions say:

• There are no baby universes branching off - which is what Hawking used to think. The information is preserved purely in our Universe.
  
• The black hole can form while remaining topological trivial because its evaporation may be viewed as a tunnelling process (Hartle-Hawking). Although this comment can't be considered to be a quantitative answer to my main question, I like it, and let me describe an analogy.

Imagine quantum mechanics of a particle on a line. The classically inaccessible regions (E smaller than V) may be compared to the black hole interior. Classically, these are qualitatively different regions from the rest. However, quantum mechanically, the qualitative difference disappears because of tunnelling. All points on the line are qualitatively on equal footing. You can get there. This is why the black hole should be thought of as having a trivial topology quantum mechanically. The situation would change for an infinite inaccessible region (infinite black hole) where you can't tunnel.

Let me summarize: Hawking's argument why the evolution is unitary probably works and The Reference Frame agrees with virtually all of Hawking's broader opinions, but such a solution is not much different from the observation that the dual CFT is unitary. The question why these unitary processes look like a small long-lived black hole and how the necessary correlations are created remains mostly unanswered.

Hawking has lost a bet but he seems to think that he has made the critical steps to solve the information loss puzzle. While he has given the encyclopedia of baseball to John Preskill, next time he will give him the ashes from a burned book (or the nearly thermal Hawking radiation) because John Preskill can always reconstruct the information out of them.

Cosmic variance

A new blog named Cosmic variance has been started by five well-known cosmologists.

For example, Sean Carroll contributed a piece that argues that the "other" physicists should like string theory. I agree with his basic points. As you can imagine, the owner of this blog is not among the string theorists who are unaware of the large amount of negative emotions that many scientists outside string theory feel against string theory. In 95 percent of cases, they are plain wrong. Believe me that the remaining 5 percent cases are even more annoying.

Measuring the depth of ideas

In this philosophical text, I would like to open the question what it means for a mathematical or physical idea to be deep. Are there some rules that may be used to quantify the depth? At the very beginning, you should know that no exact and objective definition will be found. And I believe that no such a definition may ever be found, even in principle. But let us try to identify some qualitative features of the deep ideas.

In the commercial world or the world of applied physics, one may measure the depth by the amount of U.S. dollars that the idea will earn in five years, for example. (The Reference Frame considers 1 USD to be an international unit analogous to 1 meter, 1 kilogram, 1 second - and the speculations about 1 euro replacing 1 USD as the main unit in the next 20 years to be unrealistic.)

When this approximate concept of depth is combined with the invisible hand of free markets, a mechanism appears that looks for and helps the deep ideas to be created and to propagate. Capitalism works as many readers will agree. The exceptions may be those who call themselves communists in Europe or who call themselves - because of much better skills in the P.R. - progressives in the U.S.

We may leave this approximate notion of depth to the free markets, but I am sure that most of us will feel unsatisfied. We can't really believe the markets in assessing such complex questions as the depth of ideas in theoretical physics undoubtedly is. After all, the markets are driven by the people. This includes ordinary people. Clearly, the rich people - those who have shown their ability to earn money - have bigger statistical weight in the ensemble that controls the markets. While it is natural to believe that this fact may improve the ability of the markets to measure depth, it is obvious that it does not improve it enough. It is simply not the depth that is valued by the markets. We simply feel that an idea does not have to produce much money for it to be deep, and the more pure research we do, the more we feel so.

We need an objective - and more abstract - description of the deep ideas. One of their features is their unification power. For an explanatory idea to be deep, it should be able to explain many diverse phenomena or many ideas of a more concrete type. For a constructive idea to be deep, it should be vital for constructing a large group of new objects (either material objects or theoretical constructs).

Even if we accept this definition, we still face the task to determine how should one count the phenomena or concrete ideas and how should we assign them an appropriate weight. It's not shocking that if a more concrete idea is deep itself and it is explained by another, more general idea, it makes the more general idea deeper than if it had explained a shallow idea only. How do we solve this self-consistent problem to measure the depth?

This mathematical problem seems somewhat analogous to the question what is the importance of a web page; a basic question that the guys at Google and its competitors have faced for years. As Alex Wissner has told me, the solution is expressed in terms of eigenvectors.

Consider the matrix "M" whose size is "N times N" where "N" is the number of web pages you monitor. The matrix entry "M_{ij}" is equal to zero or one if the i-th page refers to the j-th page. If I have mistakenly exchanged "i" and "j", let me hope that a careful reader will correct me. Note that this distinction between "i" and "j" is important because the matrix "M" is not symmetric and because we are gonna work with its eigenvectors.

We want to determine which web pages are important etc. The best solution turns out to be the eigenvector of "M" corresponding to the highest eigenvalue; it is essentially the principal component. The coordinates of this eigenvector inform you about the importance of the individual web pages. Note that this importance is not simply the number of other web pages that link to a given web page; it is affected by the influence of your referrers and their referrers, and so forth.

A thoughtful reader should ask: Is the world of ideas truly analogous to the world of the web? Does this algorithm treat the repeated web pages correctly? How is it affected by the attempts of someone to promote his or her own false ideas or shallow web pages? Will we improve the counting if the entries of "M" won't be either 0 or 1, but will take one of many possible values instead? There are many other questions to be asked.

In our reasoning, we are still pretty close to the free markets. We still talk about the ability of general ideas to explain the phenomena that have actually been observed in the real world. It is understood that we want to formulate as compact and general idea as possible as long as it remains relatively straightforward to specialize the general idea and derive its consequences for particular situations and concrete examples.

Of course, we would like to attack an even more abstract question, namely the depth of the ideas in the world of mathematics - that does not have to be connected with the observed phenomena at all - or ideas from theoretical physics that are ambitious enough so that they can't be directly tested with the current equipment. How deep a given idea from this category is? Someone may offer the citation count - that would be analogous to the profit counting above and would be slightly unsatisfactory because of the very same reasons. The main point I would like to solve is the difference between a robust, general, far-reaching idea on one side; and a random idea or construction from recreational mathematics on the other side.

One can see that the main feature of the ideas from the former, deep category is their perfect or nearly perfect uniqueness. Consider chess. One must be pretty intelligent and a fast thinker to play the chess well. There are zillions of possible scenarios how a chess match may advance and a good player has to use many emergent ideas to make the right decisions.

But on the other hand, there is a whole landscape of board games similar to chess you may imagine. That's not a big problem for those who want to train their minds and show others how powerful they are. Every board game in this landscape may be applied more or less in the same way. The detailed rules of chess are a matter of historical accidents; they are not arbitrary for the game to be meaningful, but we can certainly envision millions of other civilizations where the details of the rules differ but where the counterparts of Karpov and Kasparov enjoy more or less the same status.

But you should notice that when this status is discussed, we are focusing on the ability of the brain to deal with certain complex systems; we are not focused on the details of the ideas themselves. The rules of chess are not "true" in any profound way. Different rules would work, too. It is a matter of cultural heritage that we prefer the usual rules. This description is a typical feature of recreational mathematics: in this case, it is important that you train your mind but the details of the ideas are less crucial.

The terminology I used makes it clear that the analysis of a particular convoluted background of string theory is an example of recreational mathematics. In this case it is also true that one may (and has to) learn many things when she studies a particular background. She acquires skills that can be used to study other, similar backgrounds, too. But this fact is very different from the truth. It is very unlikely that one random vacuum from a huge landscape is "true". It should be obvious that a brute force analysis of a particular setup is not deep, and we don't need to discuss these things, I would say.

The real question is what conceptual ideas and visions are deep. For example, there are very deep ideas involving symmetries. It is by no means obvious that the observers in motion may be equivalent to observers at rest. Once you recognize this possible equivalence, you may postulate a Galilean symmetry. Then you may look for classical deformations of this group. You will only find a few examples and the Lorentz group is the only one that makes the speed of light finite and universal.

I don't only want to say that these symmetries are deep. Another observation is that the Lorentz group is deeper than the Galilean group. What do I mean? I mean not only that it is more correct in the actual world. It is more general given some assumptions we want to impose - such as the equivalence of observers in the state of uniform motion. The Galilean group and the Lorentz group have the same number of generators and respect the same basic consistency requirements.

Nevertheless, the Galilean group is a special example in which some commutators (of the boosts) are set to zero. This choice may be obtained from the Lorentz group by setting the defining speed - which is called the speed of light - equal to infinity; the Galilean group is a contraction of the Lorentz group. On the other hand, the speed of light is finite in relativity which allows one to unify the space and time; to unify electricity and magnetism; to identify the mass and energy by Einstein's most famous formula. The Lorentz symmetry also severely constrains the possible forms of the physical laws.

This comparison of the Galilean and Lorentz groups clarifies that I believe that the physical laws should be "as deformed as possible" as long as they are compatible with certain general aspects of beauty and physical consistency. If we continued to talk about symmetries, we would have to solve many other problems. For example, is quantum deformation of a group a very deep idea? My feelings are mixed. A quantum-deformed group only acts as a group in the context of quantum mechanics. The classical systems can't really have quantum symmetries. Is that a problem?

While my opinion about the quantum groups is uncertain, I truly feel that more deformed classical groups are deeper in a very similar sense in which the (technically) simple groups such as those in GUT theories are more profound than the non-simple groups.

I would also have to discuss the difference between global and local symmetries. The local symmetries are not true symmetries; they are redundancies of a description. Their representation theory is physically irrelevant because the trivial singlet representation is the only one that occurs in the physical spectrum. Moreover, the identity of a gauge symmetry is not uniquely given by a physical theory as we learned in the 1990s (S-duality, AdS/CFT, Matrix Theory). These facts reinforce the impression that the local, gauge symmetries are not really deep. Such a conclusion may be exaggerated a bit because the local symmetries remain an excellent guide to construct theories in which unphysical, ghostly modes of higher spin fields decouple (in Yang-Mills theory, general relativity, and elsewhere). Moreover, the global symmetries are typically a subgroup of the local symmetries.

This discussion would bring us too far from the main topic. Instead, let us ask: is quantum mechanics deep? Yes, I think that quantum mechanics is perhaps the deepest idea we know. It is once again a deformation of a conceptually simpler picture of classical physics. Much like the speed of light is finite in relativity and it unifies space and time, the Planck constant is finite in quantum mechanics which allows us to identify the energy with the frequency, among many other things - quantities that would otherwise remain as independent as space and time without relativity.

Quantum mechanics is the broad framework that controls thousands of interesting theories we know. Again, it is a deformation of the concept of a theory in classical physics. It is a generalization that may reduce to the previous, classical framework, but a generalization that still allows arbitrarily precise predictions of some measurable quantities, namely the probabilities. A non-trivial idea is that the total probability of all alternatives must be 100 percent which is guaranteed by the fact that the time evolution is a unitary operator. Because of the well-known relations between unitary operators and Hermitean operators (whose eigenvalues are real and eigenvectors are orthogonal), the whole picture makes a perfect physical sense. It is increasingly likely that the basic postulates of quantum mechanics will stay with us.

Are there some generalizations of quantum mechanics? I doubt it. But there can be, on the contrary, special versions of quantum mechanics where some postulates are added. For example, the group U(N) acting on the Hilbert space is reduced to a subgroup. But let me not speculate too much.

The successful framework of quantum mechanics does not tell us what is the theory of everything yet. We must still learn the right "Hamiltonian" (or at least the "S-matrix" or whatever replaces them). In other words, we must learn what are the right degrees of freedom and what is their dynamics. What deep ideas do we know in this direction of research?

We know the deep basic idea of quantum field theory - a theory whose relation to classical field theory is analogous to the relation between quantum mechanics and classical mechanics; and moreover a theory that implies that the energy of the field is quantized which transforms every field into an arena for particles - the fields' quanta. Quantum field theory (QFT) is the simplest framework that unifies two previous deep ideas, special relativity and quantum mechanics.

Once we calculate loops etc., we encounter infinities and other things. The deepest idea about these facts is the idea of the Renormalization Group. A quantum field theory is an effective description valid below a certain energy scale. Moving from one scale to another generally requires to change your effective field theory or at least their parameters, according to a certain flow. There can be QFTs valid at all energy scales - UV complete ones - but it is not necessarily true that the world is an example. In fact, the existence of gravity makes it pretty likely that the language of QFT must be completely invalid above the Planck scale (or earlier); in this context, the whole procedure of organizing physics according to the scale must be revisited.

The Renormalization Group is deep because it allows us to understand many features of QFTs - the divergences; the relation between different theories; the methods to construct QFTs - in a unified fashion. Let us now assume that the full theory is not just a QFT, and let's think about the nature of the most fundamental degrees of freedom.

Perturbative string theory is an example of a generalization of the concepts of QFT. Point-like particles are replaced by one-dimensional strings. Is that a deep idea? A priori, I definitely think that it is not a deep idea. One could replace points by strings or little green men. When the founding fathers established string theory, the profound idea was not the sentence that you may invent in less than one minute. The profound aspect were the special mathematical features of the theory that are only manifest once you spend years to investigate it. The fundamental stringy worldsheet is the only kind of worldvolume of an object that is described by a quantum field theory whose ghosts, worldsheet UV divergences, and other problems are under control, which is also able to generate spacetime physics whose spacetime UV divergences are harmless and which permits finite spacetime interactions reducing to the usual QFTs.

This special status of the fundamental string follows from the huge size of the two-dimensional conformal group and other features. Are these technical things a deep idea? Well, definitely. But it is not quite clear whether they are a human idea. The people who kept on - and keep on - discovering all the miracles in string theory are more like cowboys who accidentally discovered a ton of gold. It is not necessarily their unique ingenuity that makes all this progress. It is a combination of their intelligence, good luck, and especially the objective fact that the ton of metaphorical gold is simply there - somewhere in the world of crucial mathematical ideas that could be used by Nature to make the world work.

Once we appreciate the fact that the string theorists are not inventing but rather discovering something that objectively exists, it is OK to admit that these technical features of two-dimensional conformal field theory are deep ideas. It is definitely worth asking what are exactly the abstract features of a two-dimensional conformal field theory that make it work and make it profound. These theories describe all weakly coupled string theories which is a significant fraction of the backgrounds of string theory we know of.

And it is natural to think that all backgrounds of string theory may be described by a system that follows the same requirement of beauty and physical consistency as two-dimensional conformal field theory, but one that is more general. The more general setup may avoid any explicit quantum field theory description of the worldvolume; it may be generated by self-consistent bootstrap conditions; the worldvolume may be a target space of some deeper string theory (or generalized string theory) which itself may be a target space of something else, and perhaps ad infinitum. This approach is also natural because the worldsheet has a two-dimensional theory of gravity on it, and string theory is a way to describe a quantum theory of gravity.

Unlike the very general framework of string theory, this line of reasoning has not led to huge progress so far, but I definitely believe that these are very deep ideas.

What about some other ideas that people think are deep? For example, what about discreteness of space and physics? Something that Stephen Wolfram, Ed Fradkin, and the majority of the loop quantum gravity community would consider deep? And they may even find a much more thoughtful support from people like Cumrun Vafa?

In my opinion, the very bare statement that everything in physics should be discrete is not deep at all. It is a program of fundamentalism. It seems that we have known discrete and continuous features of the real world for quite some time. There are many observables in the real world that look completely continuous and the discrete people can't offer any replacement - at least not a replacement that would preserve all physical consistency rules as well as the "amount of beauty" - as represented by the symmetries, for example. In this situation, the call to abandon all continuous theoretical constructs is a call to throw away a huge portion of our vital current knowledge. It is unrealistic fundamentalism, not unsimilar to the Islamic one among others - not a deep idea.

Discrete systems may approximate continuous ones but in the actual systems we know, the continuous description is the more correct one.

There are more detailed reasons why I think that such calls are shallow. One of the deep abilities of quantum mechanics is to construct a discrete spectrum of observables that are defined as continuous functions of variables with continuous spectrum. The spectrum of a Hamiltonian can simply be discrete (or have a discrete sector) because of the uncertainty principle and the miraculous abilities of the theory of linear operators. Quantum mechanics admits many bases of the Hilbert space. The discrete bases are more appropriate to teach the truly new interpretational features of quantum mechanics - which is what Feynman did in his lectures. But if the task is to find the right Hamiltonian, it seems completely clear to me that the continuous language is deeper and more fundamental. The continuous language based on "x" and "p" (or their generalizations) as the elementary operators is better in explaining symmetries (both global as well as local ones) and locality.

The old quantum mechanics of Bohr was a system which implied some discreteness by its very assumptions. The new quantum mechanics allows us to derive these things - the spectrum of the Hydrogen atom, among millions of others. The old quantum theory was a naive phenomenological theory that captured some features of the real world; the transition to the new quantum mechanics was an amazing progress, I think. Those who want to present the discreteness as a fundamental idea are returning us to the age of the old quantum theory, to say the least. More likely, they want to return us to the age of luminiferous aether or even Democritus' atoms. I don't think that they have made much progress since Maxwell's and Fitzgerald's aether or Democritus' atomic school.

There exists an opposite fundamentalist approach in which everything must be derived from a continuous framework. In my opinion, it is much much deeper than its main enemy ("discrete physics"). Why do I think so? In some sense, the analysis of number theory (especially the prime integers) using zeta functions is one of the achievements of this way of thinking in mathematics. The distribution and properties of prime integers are encoded in a continuous (holomorphic) functions and the continuous tools of functional analysis may shed a lot of new light on questions from number theory. The discrete interpretation of the number-theoretical facts may count as the set of emergent phenomena. Yes, we need to know them, but it is still legitimate to consider the zeta functions to be the more fundamental description of the same data. Analogous statements hold for various generating functions etc.

In a similar fashion, the continuous theories such as topological string theories may be used to calculate many discrete and combinatorial features of Calabi-Yau manifolds. Also, Chern-Simons theories may generate many features of knots in knot theory. I believe that these continuous descriptions are deeper than the original, purely discrete form of the questions. In some sense, I would like to believe that all of theoretical physics and mathematics is about emergent phenomena found in some theoretical structure that is as continuous as you may imagine.

How can you construct highly continuous theories? What does it mean? Spaces of higher dimensions are "more continuous", in a sense. For example, the description of a background in terms of M-theory is more "geometrical" and "continuous" than in terms of perturbative string theory because more degrees of freedom are "geometrized" (into 11 dimensions). Whether or not you also say that it is more fundamental is a matter of taste. I would not say so - they are just different pictures to organize an infinite number of continuous degrees of freedom.

And the infinite-dimensional spaces are "more continuous" still. For example, when you quantize a system in classical physics, you obtain a smoother system because the sharp, discrete, point-like particle is replaced by a smooth wavefunction. If you perform a second quantization, the amount of continuity increases again. This could lead you to try to make a third quantization (something mathematically isomorphic to the situation that appears in string field theory) or a fourth, fifth quantization; infinitely many, if you wish. Can we learn something from these "higher order" hyper-functional methods (for example, from functionals defined on the space of functionals), or is it a generalization of successful ideas that was dragged too far?

At any rate, if a discrete, combinatorial, finite conclusion is derived from a continuous starting point, in my opinion, the depth of our understanding increases.

What are other deep ideas in string theory? For example, Polchinski's framework to calculate with D-branes is a very profound discovery. The broader message is that strings with more general boundary conditions can have oscillations that are connected with fields that describe a large spectrum of physical observables of a large number of new kind of objects (D-branes, in this example). That's definitely a deep idea because it shows that some previous ideas (fields from vibrating strings) are much more general and far-reaching than what was thought previously once the right subset of their features is extracted and imposed. Note that the previous sentence reflects a rather successful template to search for new profound ideas: preserve most features of a successful theoretical construct from the past, sacrifice some unimportant ones, and find new classes of solutions.

Holography is another deep idea; this statement is strengthened once mathematically controllable examples of holography are found in the context of the AdS/CFT correspondence. Holography tells you that a certain physical system should be described in terms of another physical system that lives in a space whose dimension is smaller. If formulated in this fashion, the idea is essentially unique. The details of the idea - the fact that the first system is gravitational, the second system is non-gravitational, and the dimensions differ by one, among other observations - are not unique a priori, but the correct answer may be derived mathematically. These are the features of a research direction that often leads to deep conclusions.

What about some ideas that seem much more shallow? For example, rewrite your metric in terms of some new variables in such a way that some observables will have discrete eigenvalues. It's not hard to see that I talk about loop quantum gravity. These new variables seem shallow because of many reasons: they are not unique at all. Writing a system in new variables may be a good way to solve it if the change of variables is legitimate, and if you're lucky to choose the right one that will help you to solve a well-defined question. That's not the case of the new variables in loop quantum gravity. In that case, you don't solve anything you wanted to solve. What you derive is the discrete spectrum of the areas - which is not a consequence of quantum gravity but a consequence of your particular choice of the new variables (that is not legitimate globally on the configuration space, and therefore it implies some discreteness that does not really exist in quantum gravity itself).

Some people may like the discrete spectrum of the areas for some reasons that I find irrational; one of them is the confusion between discretization and quantization. In a deep contrast with the beliefs of many people, a quantum theory does not have to have a discrete spectrum of all observables.

There are zillions of other globally invalid field redefinitions that could lead to discreteness of other observables - various integrals of the Riemann tensor, for example. There is no reason why one of these observables should have a well-defined discrete spectrum while another one should not. There is nothing deep about one particular choice compared to others. It's just recreational mathematics, and because it has led to no consistency checks or insights that are independent of the particular choices, it is unsuccessful recreational mathematics. One of the completely critical features of a deep idea worth scientific investigation is that it must explain more than the input - measured by the extent to which the assumptions are non-trivial and "unlikely" - that you used to construct it. My huge respect for this principle may partially reflect the influence of Feynman's books on me.

If you explain a seemingly unlikely value of an observable - call it Lambda, for example - by postulating an equally unlikely network of new objects, a whole new decoupled sector of new fields, or a plethora of Universes - call it a landscape - whose only achievement is to explain a single thing, then you have not really explained anything. Occam's razor dictates that these unnecessary quasiexplanations should be jettisoned as excess baggage in order to make progress. (Thanks to Murray Gell-Mann and his cute commercial for Enron.)

The observation that Lambda is small and has an unlikely value that we can incorporate into effective field theory is a deeper description of the situation than a new system of theoretical constructs that can only describe one thing. However, some of us simply like recreational mathematics. Imagine that you want to explain one number (Lambda) and in order to do that, you add a new mostly decoupled sector to your theory with a lot of new degrees of freedom and new parameters (c_1, c_2, ... , c_N). Then your Lambda is a function of these numbers "c_i" and perhaps other things, and it may be fun for you to calculate what Lambda would be in this hypothetical situation.

You may call it physics, but it is not a scientific explanation of anything because you actually *increased* the number of things that remain unexplained. It is a mental image that someone may like to have in mind, much like luminiferous aether that was thought to underlie electromagnetic phenomena. But until there is an independent prediction of these things, you can't think that it is an intriguing or deep idea. And once the experimental tests are doable, the history teaches us that these ideas whose only ability was to explain one thing that was used to construct them are nearly always falsified at the very end. The aether wind does not exist, for example.

Let me summarize. Deep ideas are those that are unique among conceivable similar statements at comparable levels of complexity and that are able to cover a large set of particular examples (models, phenomena, metaphenomena) and explain a large number of patterns using a small number of independent assumptions and parameters, especially if the deep ideas are inevitable. Whether or not a given idea is unique among ideas that a priori look analogous, may often require hours or years of calculations. These calculations are crucial because we must choose our deep ideas not only according to the impression they make in the first 3 minutes, but also according to their ability to offer us true insights in the long term.

In order to make progress, we must not be too dogmatic - so that we would believe that an idea that looks intriguing in the first 3 minutes must be studied despite decades of failures. But we should not sacrifice all of our principles either - so that we would study whatever requires some calculations. But we should know that being in the middle is not a sufficient condition either.

The next revolution

Most of the talks and discussions at Strings 2005 in Toronto already belong to the history. There have obviously been many talks about interesting calculations of medium importance. And there have been important conceptual discussions about the big questions.

Jacques Distler and Peter Woit have written quite a bit about the talks and especially about the panel discussion called "The Next Superstring Revolution". As expected, I can agree neither with Peter Woit nor with Jacques Distler.

Peter Woit's main profession is to find, extract, and artificially produce poison in string theory and for string theory. If you gave him a bottle of Coke with a label "String Theory", he would extract several atoms of arsen from the bottle and claim that you gave him a bottle of poison.

Jacques Distler argues that the students should not ask where string theory is going because they must think what to work on right now and forget about some "exercises" associated with the medium and long term future of the field. This is what the graduate students - who are deciding whether they should dedicate their lives to a scientific field - are being told. Does this answer describe the actual state of communication we have reached? Should the young physicists join the field with the plan to look around every three months what kind of activity is helpful for their careers because this is the only thing that they should really be interested in? I hope not.

I hope that even among the readers of this blog, there are people with great goals and dreams. Some of these goals and dreams will remain unfulfilled. But the dreams and visions are important nevertheless. One of the primary general goals of string theory is to achieve a deeper and more quantitative understanding of the world of high energy physics and quantum gravity than the Standard Model and General Relativity may offer us. And nothing has changed about the fact that we have very good reasons to think that string theory can do it.

Because July 2005 is definitely not among the most optimistic moments in the history of the field, no one will tell you that we will complete the theory of everything (or calculate the correct masses of the elementary particles around us) in 2005 - even though this is exactly what the leaders of the field thought back in 1985, for example. An exception may be a secretary who is often reading the grant proposals that always look like if the field is living in the most fantastic era right now. Don't ever trust your secretary in these important matters because her or his understanding of the situation is as twisted as the grant proposals. ;-)

If we rely on theoretical considerations, most of us would probably guess that it would take decades before someone will make the "final" steps that will convince everyone that string theory describes reality.

A student who wants to join a scientific field because of some of her scientific dreams simply cannot avoid the question what string theory is going to look like in 5 or 10 years and what is the framework into which the small pieces of the research should fit. Sure, no one knows the answer - much like they did not know in 1992 that the Second Superstring Revolution was behind the corner. But we must still ask this question and try to find the best answer we can because we study string theory - at least I believe so - because of some important things that are emerging and will emerge.

I totally agree that if the string community became a collection of people, neither of whom knows why they're doing what they're doing, the support for this community should decline. And let's hope that this is not the atmosphere we are approaching.

Those who think about joining string theory to build their careers can be assured that string theory won't disappear in the next 5 or 10 years. In the competition between the theories going beyond the language of Quantum Field Theory, string theory has been the winner for 20+ years and it will remain the winner for the years to come. The people who have been saying that the whole field of string theory is a fad that would disappear because there is nothing deep about it have been saying wrong things for 20 years and it has been shown that they have been wrong - and I assure you that the primary statement of their blogs will remain nonsensical in the near future, too.

Despite some increase in the quality of the contributions, Peter Woit's blog will remain a propagandistic web page addressed primarily to the readers who are not terribly demanding - and a web page that gives you wrong answers to many essential questions.

The two previous paragraphs mean that any potential difficulty of string theory is actually a difficulty of the whole theoretical high energy physics; these two things have already been heavily correlated and you can't separate them anymore.

The people who ask whether string theory lives in one of its most optimistic eras should clearly be told that the answer is No. But unlike some other candidate theories, we have not discovered a mathematical consistency in string theory. We have not discovered a serious discrepancy between string theory and the broad features of the real world either. We have learned many things that simply work and will undoubtedly remain a solid piece of mathematical physics and a foundational pillar for future investigations.

Another important question is whether we know what is the most direction where the field is and should be going, and the answer is probably once again No. Of course, the people with their own proposals may disagree because they believe that their proposals should determine the direction.

In the discussion under Jacques' article, Dan noted that it was unexpected that Jacques would work on the fashionable anthropic business. Well, yes, I definitely agree that the anthropic landscape business is fashionable; it is in fact one of the dirtiest fads in the history of theoretical physics. Jacques argues that he never does anything because it's fashionable. Unfortunately it is easy to see that this sentence of Jacques is not true because I still happen to remember Jacques' description of his early days in string theory that he offered when he was blogging from Sidneyfest; it was disappointing enough so that I could not forget about it. Jacques wrote:

• Sidney Coleman is my hero.
• That statement requires a little bit of an explanation, as Sidney was my PhD thesis advisor. Truth be told, his direct influence on my thesis was negligible. Midway through my graduate career, string theory swept through high energy physics. As a sensible young man, I dropped everything I’d been doing and rode the wave.

I suppose that someone could argue that "riding the wave" is different from "doing things because they are fashionable". But I would not be terribly impressed by such an argument. This revelation why Jacques became a string theorist was simply a sad thing to learn for me. But not catastrophically sad ;-) because it is pretty clear that "riding the wave" is what a majority of the people are thinking about anyway.

There is no need to say whether I belong to this majority because the readers know it anyway.

Once again. Some graduate students can have a feeling - a very justified feeling - that something is being hidden from their attention. They're not being told the complete truth. But they should know that they are being told the truth about the basic question - namely the question whether string theory will remain the primary direction to attack questions that go beyond the language of quantum field theory. It will and we are aware of no serious problems with string theory. With a help from the LHC (that may generate some fantastic data) and perhaps a next revolution in the theory, we may come closer to God's mind.

Before it happens, people will probably have to get rid of many incorrect ideas and prejudices - the anthropic craziness is almost definitely one of them. And things will be a lot of fun. And one more thing for the students: there is a lot of stuff for a student to learn - stuff that will remain a part of theoretical physics forever. It actually takes some time before one learns enough to be able to judge whether the stock price of a field is increasing or decreasing and whether a particular project is gonna be a breakthrough that will amaze everyone else. And before you learn all these things, the trend can be completely different and you don't want to miss the next explosion of stimulating ideas.

And don't forget: you are not expected to follow someone else throughout your life. All of string theorists can be doing something silly, and you will be the first one to point it out. But if you want to be serious about these things, you must first learn a lot of material and work on some serious things. Good luck to all of us.

Tachyons and the Big Bang

Let's start with a general description of the tachyons, their history, their meaning, and their role in string theory; we will get to the current questions whether the tachyons are important for cosmology later.

There have been many twists and turns in the history of the tachyons. As soon as Albert Einstein discovered his special relativity 100 years ago, it became clear that no particle, no object, and no carrier of information can travel faster than light. The reason is that an observer in a different reference frame would realize that such an object not only travels faster than light but it in fact travels backwards in time. Lorentz transformations make superluminal propagation equivalent to propagation backwards in time. That would destroy causality; it would allow you to kill your father before he met your mother - and such a possibility would transform our Universe into a pile of logical absurdities and oxymorons.

In other words, the four-momentum of acceptable particles must be a time-like vector. Let's choose the convention in which "p squared" is positive in these good cases. Particles with negative values of "p squared" are banned. They are called "tachyons" - the Greek word "tachos" means speed and the name is apt because the tachyons have to be very fast; they would always move with superluminal velocities.

In quantum field theory it is still useful to think of tachyons as particles with space-like four-momenta but it is not the most realistic description of their behavior. Instead, the typical configuration involves a time-like imaginary four-momentum of a tachyon field - a configuration of the field that exponentially grows with time instead of oscillating. The potential energy "m squared times phi squared (over two)" for a scalar field "phi" has a minimum if "m squared" is positive - the regular massive particles - and it has a maximum for negative values of "m squared".

The latter case corresponds to tachyons. As you can see, tachyons signal instabilities akin to Columbus' egg standing on its tip. For example, the Higgs field in the Standard Model would be a tachyon if the symmetry remained unbroken. However, the Universe with such a Higgs field would be unstable much like the egg. It would spontaneously choose a random direction and "fall"; the speed of the fall would be growing exponentially, at least for a little while.

The key question is what happens with the egg if you make it stand on its tip but it eventually falls. The ordinary egg will find another, stable position. Whether or not this occurs for a tachyon in a physical theory depends on the details. The final fate of the Universe with a tachyon - a counterpart of the egg - depends on the existence of a minimum of the tachyonic potential. For example, the potential has a minimum in the Standard Model (a whole sphere of minima whose points are, however, equivalent due to the original gauge symmetry). This minimum describes the spontaneously broken electroweak symmetry - a situation in which our world lives today. If you expand the potential energy around this point, you will find out that the squared masses are never negative. Higgses becomes massive particles and the tachyons disappear if the theory is described as a small perturbation around a stable point - around a minimum of the potential as opposed to a maximum (or a saddle).

Let's turn our attention to string theory. The original "bosonic" string theory found in the late 1960s and early 1970s lived in 26 dimensions. Its closed strings could behave not only as gravitons or (infinitely types of) massive particles but also as tachyons. Regular closed strings are free to move throughout the space. In the case of the closed strings that vibrate as gravitons, the previous sentence implies that gravity is always a property of the whole spacetime; string theory agrees with general relativity that gravity is dynamics of spacetime's geometry. In the case of the closed string tachyons, the same sentence means that these tachyons signal an instability of the whole spacetime. Something brutal has to happen with the whole Cosmos - for example, it can lose most of its dimensions.

People in the 1970s tried to get rid of the tachyons; to pretend that they were not there; to find a minimum of the potential. All these attempts have failed. A well-known story from the history of physics is that the "bosonic" string theory in 26 dimensions was superseded by superstring theory in 10 dimensions in the middle 1970s. The latter has no tachyons; it is a consequence of spacetime supersymmetry that allows you to write the energy "E" as "Q squared" where "Q" is another operator, namely the supersymmetry generator; this makes it obvious that the energy can't be negative which would have to be the case for a specific tachyonic particle. (Superstring theory also predicts the existence of fermions which is pretty useful to match the real world, but matching the real world of particle physics is not the topic of this text.)

It is fair to say that the tachyons played very little role in the string theory research between 1975 and 1998. Much progress in these two decades relied upon spacetime supersymmetry - especially the supersymmetric calculational revolution sparked by Seiberg in the early 1990s. Tachyons were viewed as an uninteresting disease of unrealistic or toy model versions of string theory.

In 1998 or so, people decided to return to the question of the tachyons. However, they did not need to return to 26 dimensions; tachyons may be found in superstring theory, too. It's enough if you compactify string theory in certain ways that break supersymmetry (such a breaking is not a sufficient condition) or if you include unstable configurations of branes.

Ashoke Sen was the first person who has understood the fate of some string-theoretical tachyons. Consider two (nearly) coincident parallel D-branes as found by Joe Polchinski; a D-brane or a Dp-brane is a p-dimensional membrane defined by the property that open strings are allowed to end on it so that some of their coordinates (namely those transverse to the D-brane) have Dirichlet boundary conditions "x=x_0" at the endpoints (which is where "D" comes from). Rotate one of these two D-branes by 180 degrees in a "mixed" 2-plane (spanned by 1 parallel direction and 1 transverse direction); this changes the D-brane into an anti-D-brane because the direction of the arrow (or the volume form) is inverted. Its charge - something like a higher-dimensional winding number - thus gets reversed, too. What you get is a brane-antibrane pair.

Much like the positronium, the bound state of an electron and a positron, the brane-antibrane pair is unstable because these two guys may annihilate with each other. How do you see it in string theory? Once you have two D-branes, it is always allowed for an open string to terminate on one D-brane with one end and the second D-brane with the other end. These open strings describe physical quantities that these two D-branes share; in the case of intersecting branes, such open strings want to shrink near the intersection of the D-branes because the string can then be shorter (and henceforth lighter). This is why the resulting fields arising from such open strings are localized at the locus of the intersection. The ground state of such a string is a priori a tachyon; incidentally, note that tachyons are always excitations of a scalar field in string theory as well as any other consistent physical theory. For example, you won't be able to write down a Hermitean mass term for a Dirac fermion with an imaginary mass.

If these two D-branes are really identical, the tachyon is removed by the superstringy GSO (Gliozzi-Scherk-Olive) projection and it is not a part of the physical spectrum. Two parallel D-branes are stable. On the other hand, if one of these D-branes is an anti-D-brane, the sign of the GSO projection is inverted. The projection preserves exactly those particles that are banned in the "brane-brane" case which includes the tachyon. Now, because the open strings are attached to the D-branes, their excitations describe fields that are geometrically attached to the D-branes. A negative squared-mass scalar field is a sign of instability; but because this field is only defined within the D-branes, it is an instability of the D-branes only. It cannot directly destroy the rest of the spacetime.

Ashoke Sen conjectured that the potential energy for this tachyon has a minimum and one can exactly say what is the value at the minimum. The energy density at the minimum is exactly the energy density at the maximum (where you found the tachyon) minus the total tension of the D-branes. This means that once the tachyonic scalar field rolls from the maximum to the minimum, the D-branes are destroyed completely and their full energy "E=mc^2" is released. Such a scenario has many implications. For example, it quantitatively predicts the energy at the minimum which has been tested in string field theory - a formalism that describes (open) string theory as a quantum field theory with infinitely many fields. They have found, numerically, roughly 99.9999% of the right value of the energy difference and everyone was happy. The numerical calculations were needed in the cubic string field theory; in the boundary string field theory, analytical proofs were possible.

A more sophisticated gedanken experiment involves a brane-antibrane pair whose antibrane (for example) has a non-trivial gauge field so that the two branes can't annihilate completely. After the annihilation, something (a lower-dimensional object) is left. All possible objects that are left are classified by certain topological data. This line of reasoning showed us that the allowed D-brane charges are not classified by homology - the possible cycles onto which the D-branes are simply wrapped - but by something else, namely K-theory that is physically closer to topologically non-trivial configurations of gauge fields. K-theory is similar to homology but it differs in details; for example, new D-branes conserved "modulo k" have been found. A link with another mathematical field has emerged.

More convoluted thinking along these lines has led people to conjecture that not only K-theory but also the "derived categories of coherent sheaves" are useful and relevant for understanding of D-brane charges as well as some of their dynamics. The string theory community is a community of mathematically oriented physicists, but most of them are not mathematically oriented enough to transform coherent sheaves into the most exciting object to study. But you should remember that those who propose these coherent sheaves and other notions from category theory - Paul Aspinwall, Dave Morrison, Michael Douglas, among others - as a new language (and maybe not just language) for string theory are very smart people and there can be something deep in it although I have personally not understood what it should be.

Despite many attempts, I still have not understood the basic question whether the category-theoretical description is just a different language to describe known features of string theory; or whether it implies new physics that is not contained in the CFT; in the latter case, I also don't understand whether the compatibility of this category theory with the "usual" string theory is a conjecture or a proven fact. The status of these ideas remains unclear and it is likely that they're valid in the perturbative realm only. (D-branes can only be singled out among other branes in the weakly coupled regime.)

It is fair to say that these developments have convinced all of us that the fate of the open string tachyons has been understood completely. It was natural to look at the closed string tachyons. Because the bulk tachyons seem to signal an instability of the whole Universe and the whole theory and the fate of the Universe that collapses completely seems uncertain, people focused on the closed string tachyons that are localized much like the open string tachyons. How can you localize closed string tachyons? They can be localized if they appear in a twisted sector of an orbifold - a fact that Adams, Polchinski, and Silverstein (APS that does not mean American Physical Society) exploited in 2001 or so.

Consider the "C/Z_N" orbifold - a two-dimensional plane whose points are identified if they are related by a rotation by "360.k/N" degrees around the origin for integer values of "k". In field theory this would be equivalent to a new field theory defined on a cone (recall how can you produce cones by gluing a wedge of paper appropriately). In string theory, you also reduce the number of independent "points" and "fields", but you must compensate this reduction by adding twisted sectors. The twisted sectors are new sets of closed strings that are not exactly closed in the original plane "C" but they are closed up to a rotation by "360.w/N" where "w" runs between "0" and "N-1" and labels one of the "N-1" twisted sectors (plus "1" untwisted sector for "w=0").

The twisted strings would be long (and heavy) unless they are localized near the origin - the fixed point of the rotation. That's analogous to the open strings living near the intersection; the open string case is actually a worldsheet orbifold of the closed string case. The punch line is that the twisted closed strings describe fields that are localized at the origin.

This APS example is a non-supersymmetric orbifold and you will find a lot of tachyons in the twisted sectors. What do these tachyons tell us? They tell us that string theory does not like the sharp tips of the cones. The tachyons condense near the tip which smears out the tip of the cone which makes the tip nice and round. Although this picture does not offer truly quantitative predictions analogous to Sen's energy difference, there are many qualitative consequences of such a story that can be checked and have been checked.

Tachyons made of winding closed strings are analogous to the twisted closed strings. Their squared mass is the sum of the tachyonic basic squared mass plus the squared circumference of the circle (multiplied by the squared stringy tension). This means that these modes only become tachyonic if the circle onto which the closed strings are wrapped is short enough. It has been shown that they have the capacity to change the topology of the space. Unlike the case of Sen's open string tachyons and unlike the supersymmetric topology changing processes, this scenario itself does not offer quantitative predictions either but it is a nice and self-consistent picture that shows you how non-supersymmetric "handles" may be removed - a picture proposed by Adams plus four more authors.

As you can see, these considerations are inevitably becoming less quantitative, more uncertain and kind of frustrating, but potentially also deeper conceptually. Recently it has been proposed by John McGreevy and Eva Silverstein - who were building on some comments by Polyakov; calculations of some correlators of tachyons by Strominger and Takayanagi; the general philosophy to study time-dependent background, especially time-dependent tachyon fields, in the early 2000s; the stories explained above - that the bulk closed string tachyons are an important key to understand the initial singularity in string theory.

They study various backgrounds in string theory where a tachyon - or a tachyon-like operator in the conformal field theory (whose main component is a relevant operator) - has a vacuum expectation value that is large at the moment of the singularity but exponentially decreases later. Such a tachyonic condensate behaves much like the Liouville wall in two-dimensional string theory. Recall that the Liouville wall is useful in two-dimensional string theory because it acts as an additional potential that repels the strings from the strongly coupled region. John and Eva are using their tachyonic potential in a similar way: the tachyon near the singularity "turns off the lights" and it repels strings and all physical phenomena for that matter. The authors believe that this solves the problems and infinities of the initial singularity.

I don't really understand these claims and let me try to specify what I don't understand about them.

First of all, even in the Liouville case itself, the Liouville wall is not something one should be proud about. It is a method how perturbative string theory may remain internally consistent without telling you what is the physics at strong coupling: the places where the coupling is strong have also a powerful Liouville wall that does not really allow the observers to probe these regions. It's closing your eyes. My personal belief is that physics at strong coupling in two-dimensional string theory is not really uniquely well-defined and the folklore about the uniqueness of quantum gravity does not really apply in 2 spacetime dimensions (not even 3 spacetime dimensions) because of the topological nature of gravity in these low dimensionalities. Quantum gravity is only tough if at least 4 dimensions are rather large and flat; this is where one expects uniqueness and where string theory can show (and, in some cases, does show) its predictive muscles.

The situation in John's and Eva's setup is even more difficult. In the two-dimensional case, the tachyonic condensate eventually becomes infinitely large in the infinitely strongly coupled region and the screening is "perfect". The tachyon of John and Eva has always a finite vacuum expectation value as long as the coefficient is finite. Some of their qualitative conclusions depend on the coefficient's being infinite which seems as a confused order of limits to me. The problems they claim to have solved are not solved for any finite value of the tachyon which may always be viewed as a small perturbation of the original singular background. The larger value of the tachyonic field they choose, the more thoroughly they may solve some problems, but the more their solution is similar to simply cutting the cosmology at some moment "t=BBC", an abbreviation that I will explain below.

We may forget about these non-perturbative worries, of course, and ask whether we have removed all dangerous singularities from the perturbative expansion of string theory. My worries continue. Some of my primary questions are the following ones:

Are their conformal field theories really conformal? A reason to doubt this statement is that the expanding Universe near the singularity looks like a conical singularity, and much like a regular cone, it has a deficit angle and violates the Ricci flatness by a delta-function at the very tip of the cone. There exist orbifolds in string theory that admit a nonzero deficit angle, but they are very special and moreover a small condensation of the tachyon leads to a destruction of the whole cone, not just the stringy neighborhood of the tip that is needed in John's and Eva's setup.

If there are no conformal field theories of this type, the discussion would end and the idea would be ruled out. So let us assume that there are such conformal field theories in which the tachyon is only condensed in the stringy vicinity of the singularity. The next pressing question is:

How unique is this CFT? It is unlikely to be completely unique - John and Eva themselves offer many examples how the initial singularity could look like. The real question is really: How many continuous adjustable parameters each of these backgrounds has? Zero, finite number, or infinitely many? I think that this question must be answered before some correlators are computed because the correlators are only physically meaningful if the answer to the previous question is "zero" or, in the worst case, "finite number".
There are no predictions if infinitely many parameters are undetermined.


The most interesting point of their paper - as far as I can say - is that they show that the two-point functions have a thermal behavior whose temperature is "kappa/pi" where "kappa" is the rate of the tachyon's decrease; the tachyonic vev is "C.exp(-kappa.X0)". Note that this could be a universal temperature in the whole Universe. If such things worked with a small number of adjustable parameters - or a larger number of parameters that do not change the gross behavior - one would not even need inflation to explain the uniform temperature of the CMB radiation in the visible Cosmos. The temperature would simply be related to some universal properties of the tachyon near the Big Bang.

Unfortunately, I think - especially after discussions with Nima - that such a scenario is extremely unlikely. The uniform character of the CMB temperature also depends on the flatness of the Universe at the very beginning. John and Eva have not really showed that the Universe with flat spatial slices near the beginning is preferred in any way. It is critical to decide whether all shapes can lead to CFTs or whether some of them are preferred. Only if the choice of the initial configuration is more or less unique, we have solved something. The main problem of a naked singularity is that predictions are impossible because of infinitely many choices. A singularity can emit anything.

It seems that John and Eva declare that the tachyon provides us with a BBC - these letters do not stand for "British (or Bin Laden's?) Broadcasting Company" ;-) but rather "Big Bang Cutoff" - and the times before "t=BBC" - such as "t=0" - are unphysical. If this is what they mean, the prescription does not solve anything because we may equally well call "t=BBC" to be the new physical Big Bang. The calculational strategy is then nothing else than extrapolation of arbitrary initial conditions at "t=BBC" to "t=TODAY". We could have always thought that this is the only thing that physics can do. If we follow this strategy, we close our eyes to avoid the moments before "t=BBC". Moreover, such a philosophy has nothing whatsoever to do with the tachyons.

Once again, the only hope would be to show that the CFT and its non-perturbative completion near the Big Bang is essentially unique and it gives us a stringy counterpart of the Hartle-Hawking wavefunction. Note that it is allowed for the non-perturbative phenomena to help us to make this choice unique - in analogy with various non-perturbative terms that stabilize some moduli in flux vacua and elsewhere. It is tollerable that the CFTs are degenerate but non-perturbative effects require us to choose a specific one. At any rate, my feeling is that if the initial singularity is not unique, the rules of the game are ill-defined and all correlators that one calculates in these theories are physically meaningless.

Some people could say that "string theory won't be capable to predict some things but only some other things". I find these statements either incorrect or vague because no one has found a key in string theory to separate physical questions to "predictable" and "unpredictable" and those who claim to have found such a key have not shown any arguments that their key is better than zillions of other keys to divide quantities to "predictable" and "unpredictable" differently. My prediction is that such a key will never be found in string theory because of its "everything-or-nothing" nature.

As far as the very beginning and the "initial conditions" of the Universe go, physics will either be able to make predictions, or it won't. Note that the inflationary era makes most of the details of the "initial conditions" almost exactly irrelevant for the present observations. But still, if you assume a finite inflationary era, nothing is changed qualitatively about the question whether the conditions before the inflation can be studied scientifically.

The statement that the tachyon condensation is an essential key to understand the Planckian/stringy cosmology is an interesting, bold, and extraordinary statement, and it requires extraordinary evidence.

Anonymous remailers

Some people think that if they use anonymous remailers to send hate mail, no one can ever find them. That's not right.

Well, since the infamous March 15, 2005 - which is not only the anniversary of the Nazi occupation of the Czech lands in 1939 but also the date of a certain problematic FAS faculty meeting at Harvard - there have been several episodes that have temporarily but severely reduced optimism and self-confidence of people like me.

Some of these episodes involve pressure by seemingly nice people - our friends and colleagues, in some cases - who have forced some of us to apologize for our opinions many times, to become silent, and perhaps to create five more women's committees. OK, you could have read these (or similar) stories in the media.

Be sure that the president was not the only person who has been subject to this kind of influence. Those who believe that it's only the president who is not allowed to have certain heretical opinions - because they could be interpreted as the official policy - are very naive people. Obviously, the less powerful a person at a university is, the easier it is to impose the "official" opinions upon her or him.

In my case, there have also been roughly two anonymous senders. One of them was directly inspired by the controversy at Harvard. He has sent two slightly entertaining but very embarassing PDF files that contained a mostly fictitious story about me and a professor of humanities at Harvard (plus the officials at Harvard). The goal was to damage my name and my good relations with the other professor. The recipients were all physics professors at Harvard and probably many others; thankfully, they understood that they should not trust the text. I still don't know who was the anonymous sender although he or she is probably living in San Diego. Maybe I should finally find time to investigate this episode...

After March 15th, I have also received very ugly anonymous e-mail messages about Prof. RW and probably Prof. SP - senior professors who had similar opinions to mine about the whole story. The mail about Prof. RW looked like a message from Al-Qaeda because it was heavily anti-Jewish and the author was apparently a radical Arab. Its goal was to transmute a debate about the role of the sexes (indeed, not genders) to something much more serious. I want to assure Prof. RW and others that this message has not damaged the positive image of them in my eyes, not a single bit.

The other sender related to myself - one whom I dedicate the rest of this text - has informed me through ten or so anonymous remailers and through a web form on a website of mine that she or he was going to kill me; the apparent correlation with the controversies at Harvard was most likely accidental in this case.

Those roughly 100 messages - that were sent more or less every week between April and early July - contained a detailed description how the author was going to strangle me and then masturbate because it was so arousing. In other e-mails, he or she just declared himself or herself to be my personal assistant who would help me to kill myself. Some of these e-mails argued that it was necessary to do the same thing with

• all males - the ultimate source of the evil
• all foreigners - especially the Slavs
• all conservatives

The e-mails contained hundreds of copies of the word "die". They have also informed me that the sender had installed a spycam in my apartment and was going to publish the videos. ;-) After some time, I did not read all of these weird messages.

Because these themes were so stable, I eventually became convinced that the author was probably a liberal female scientist born in the USA who was moreover very likely to be pretty fat. ;-) Well, unfortunately the sender was sending e-mail messages through my website rather carelessly; this website happens to be one of a very few web pages of mine that record the IP addresses of the visitors.

So I learned that the sender was from the University of a state whose name starts either with "Q" or "D" and I asked the network administrators over there to help me to stop these messages. They thought it was sufficiently serious and their police started to study this case - very skillful and pleasant guys, by the way. I admire this kind of policemen who are not only strong but who deal with the "real stuff" and who know how the world really works. Some compliments for the computer administrator are attached at the end of this text.

I always emphasized that my goal has never been to create problems for the person because he or she needed help and compassion rather than punishment. It was a great relief to learn that the sender came from a rather remote university and has probably never seen me. You can imagine that my list of possible suspects used to contain several people I knew which was very unpleasant.

Because the visits to my website that were clearly correlated with the hate mail came from particular IP addresses reserved for modems at their university, the authorities knew the identity of the sender by June 20th; they could not get a confirmation from the remailers but it turned out that the sender was the only person at that university who had connected to these re-mailers from that university at all so that the identification could be re-confirmed by analyzing the log files at the university.

The whole story was a sensitive issue, so they were checking and rechecking and trying to think about alternative explanations; a very professional approach. The person was finally interviewed yesterday (7/11). A very bizarre person, I was told, not really a dangerous one.

Needless to say, my instinct has failed completely. The sender was not a fat female born in the USA but a petite male born in Asia - between 20 and 25 years of age. Yes, the author who wants to eliminate the males was male himself. He spends nights gazing at the skies. His landlord is a very authoritative person. I hope that the one way correspondence he has had with me has helped him psychologically.

Please don't ask me for more details; I won't tell you because I want this story to remain partially anonymous. The only exception are people from the CIA and FBI and the Homeland Security Department; I would give these Gentlemen and Gentlewomen contacts to the skillful computer administrators whose analysis was either nearly perfect or perfect - especially one particular administrator - and who could be very helpful for the security of the U.S. or the whole Western world for that matter. The main message of this story is that all of us should avoid writing anonymous hate mail because this is how things can get out of control. And moreover, they are never quite anonymous.

It may be useful to find the sender of the PDF lies, too - it could help one to focus on creative things as opposed to this kind of stuff.

Strings 2005

The annual conference on string theory in Toronto is underway. I can't write effectively with this modem, so let me give you basic links:

• Speakers and titles
• Slides
• Jacques Distler's blogging
• Peter Woit's comments

Bombings

Let me begin with my personal memories of 9/11. I was visiting New Jersey for two weeks and 9/11 was the day in the very middle of that period. More importantly, 9/11/2001 was the day of my PhD defense at Rutgers. It started at 9:30 am, about 50 miles from the World Trade Center.

I woke up at around 8:00 am in what used to be my office (equipped with an airbed) - the housing did not work out and it would be too far from the Physics Department anyway. I took a shower and then opened the e-mail. At 9:00 am, an e-mail message from a Czech friend of mine contained a copy of the report of the Czech Press Agency (CTK) about the first airplane abused in New York.

It sounded very bizarre. Nevertheless, it was completely clear to me that it was true. Another e-mail said that the second tower had been hit. I was conveying the message to the people around and no one believed me, except for a few guys who had already heard it on radio. Well, I grabbed an overhead projector and started to defend.

At the beginning, I said that two airplanes were hijacked and used to attack the Twin Towers by the terrorists. Some members of the committee did not believe it. The thesis continued as expected. 30 seconds before it ended, Edward Witten appeared in the room and told me that he liked the defense.

He was giving a seminar at Rutgers the same day. As far as I remember, it was about the G_2 holonomy manifolds. Before the seminar we had a toast to celebrate my PhD. It was one of the most painful toasts in my life. I made a comment that we may remember that day not only as one of the most disastrous days in the U.S. history, but perhaps also as a day of an interesting seminar by Edward Witten at Rutgers. Witten said that he wished I would have had never used his name in that sentence.

From the highest floor of the math department, we were able to see smoke above Manhattan. The elevators were switched off.

It was only after the defense when we saw the first pictures and videos and the full psychological impact started to affect our minds. People, especially my advisor Tom Banks, were making predictions that our way of life had to change. Although some security measures had to be tightened after 9/11, my feeling today is that these scenarios were exaggerated. Many servers such as CNN.COM were overloaded, and because I (incorrectly) thought that all such servers had to be down, I developed a new website that contained pictures and translations of the basic stories from the Czech internet media that worked fine. The website had thousands of visits within a couple of hours.

I am not sure about you but I was silently frustrated and also upset. My anger was not directed exclusively at the small group of terrorists because they were just a tip of the anti-American and anti-capitalist iceberg. For example, a Czech journalist called Pecina published an article in which he endorsed the attacks against the U.S. Later he argued that it was a way to prove his journalistic independence.

I wrote him an e-mail that argued that the main differences between him and Al Qaeda is that most members of Al Qaeda were born in problematic conditions; and most of them are, unlike Pecina, able to sacrifice their lives for their sick ideas; on the other hand, Pecina has similar goals and emotions and is expressing them in a society where he knows that he can't be punished. This "hate mail" was published and it still appears among the best Google's hits if you search for my name. Needless to say, I would write a similar mail again if the context were similar.

The casualties were often estimated to top 10,000 people. I made a bet that the total number would exceed 10,000. Fortunately, I lost this bet. A week after the attacks, I tried to see Wall Street but the air was still so unpleasant that I did not make it to the Ground Zero.

About three years later, Madrid was also attacked by the terrorists and Al Qaeda helped to elect the Spanish socialists whose relations with Al Qaeda were widely viewed as the more friendly ones. The number of casualties was smaller by an order of magnitude.

The casualties in yesterday's attacks against the city of London seem to be one order of magnitude lower still. While it is still an alarming number of lost lives, the counting suggests that the capabilities of Al Qaeda to end lives are going down the hill. Let's hope that these attacks reflect the typical maximum scale what they can do today. You know, the impact is not so different from a lunetic with an automatic gun who simply starts to shoot as many people as possible in the subway.

London was just chosen to host the 2012 olympics (54 vs 50 for Paris). It's very likely that some votes would have been missing if the vote took place after the attacks and Paris would win instead. Great Britain also succeeded Luxembourg to become the semi-annual leader of the European Union. The Reference Frame officially supports Tony Blair's major policies (with the exception of the climate change agenda). Undoubtedly, Margaret Thatcher is one of the great living examples for the "labourist" Tony Blair and he is doing great steps not exactly to match her greatness but at least to become a comparable leader.

Unfortunately, it is this kind of a leader and his country who is likely to become a target of the acts of human trash such as Osama bin Laden and his disciples.

Some friends of mine are very frustrated by the London attacks. They say that the world is so bad that it is not worth living here. I don't know how to cure these feelings; the best thing I can do with them is to disagree. The world as of 2005 is a pretty good one. Look into the history textbooks and you will see that our world is better than it was at most moments in the past. 65 years ago, it was common sense in most of Europe that people should be killed if they were Jews. 500 years ago, you could have been executed for stating that the Earth orbits around the Sun or for trying to figure out how the guts or the brains work; today it is much better because you will only get a "lack of confidence" vote for the same thing.

The successors of the Inquisition may be obnoxious, but they are not directly threatening your life. (My apologies go to the sexual deviant and killer from the University of Delaware who counts as an exception.) Al Qaeda is a successor of the mass famines, tuberculosis, and other diseases. Except that it is killing many fewer people than the diseases did. And much like in the case of the diseases, we are getting better in fighting with these threats.

A few million years ago, you would be eaten by another mammal if you did one error. 14.3 billion years ago (without 300,000 years), the global warming was so bad that you could not even form the Hydrogen atom. 3 minutes after the Big Bang, all the nuclei would be transmuting into each other all the time. One Planck time after the Big Bang, even the very concept of space and time would be so crippled that even the best string theorists from 2005 could not tell you what to do - even what (and how) you should calculate.

Let me summarize. We should not expect that some threats and annoying things will disappear completely. Moreover, I think that the desire to eliminate an annoying thing completely underlies most totalitarian ideologies. There will always be some risks and some threats. In the case of the terrorists, virtually all of us realize that they are a real problem and we are trying to deal with it. But don't forget that the risks will never disappear totally because it would violate the uncertainty principle. Just like an evil dog can bite you on the street and kill you, you may also be killed by a lunetic (terrorist) in the subway. The probability is small in both cases. And many people are employed to keep the vacuum expectation value of the rate of such deaths low enough.

The terrorists and their ideas and ideals simply cannot be dominating over the world of the 3rd millenium.

NASA's collider

NASA has constructed a collider with the center-of-mass energy well above 10³⁰ GeV. The collision took place during the Independence Day. Unfortunately, the huge energy was not focused into a single pair of elementary particles. Therefore, NASA only saw a dirty cloudy images instead of new physics. ;-)