Monday, December 29, 2008

Bob McElrath, gravitons are not made out of dust

Attempts to "construct" gravity out of easy-to-imagine ingredients have become a modern counterpart of medieval alchemy.

The alchemists believed that by "cooking" the ordinary metals just a little bit differently from their predecessors, they could have produced gold, silver, or the elixir of life. 
A mostly unrelated commercial break: N. Sriram has sent me a beautiful essay by Paul Graham about heresies and taboos now and then, "What You Can't Say"
The contemporary gravitational alchemists believe that by combining random ordinary particles and mathematical indices just a little bit differently than their predecessors, they can explain the gravitational force in layman's terms. They're probably driven by the laymen's desire to make gravity look closer to our everyday life: see Feynman's comments about LeSage's theory of gravity at 5:20 of his Messenger 2 Lecture for a similar sociological example.

Needless to say, both beliefs are equally scientifically ludicrous and unsupportable. The difference between gold and iron is more profound than the question how much time you spend by "cooking" the iron. Analogously, the difference between gravitons and random composite states of random particles is more profound than the shape of mathematical indices or the percentage of different kinds of condensed matter papers that are being cited.

John Conway has promoted another paper about this new alchemy,
Emergent electroweak gravity
by Bob McElrath. Gravitons are bound states of neutrinos, the author boldly claims. I know that Prof Conway is able to do all kinds of things but his excitement about this type of manifest nonsense represents such a complete failure of judgment about so many fundamental questions of physics that I am simply unable to fully respect Prof Conway as a physicist. 

At the same moment, I realize that similar papers represent the kind of crap that the laymen and semi-laymen want to hear which means that any talk about serious physics in front of the broader public becomes casting pearls before swines: most people are just very stupid. Like hundreds of similar papers about the "subject", McElrath's preprint is based on the following sequence of seven steps:
  • the author has to convince himself that his paper will be better than the previous hundreds of analogous papers even though it is pretty much isomorphic garbage
  • a new favorite and surprising condensed matter phenomenon has to be picked and promoted 
  • it must be argued that this effect has something to do with gravity and its special features even though it obviously hasn't
  • spinors must appear somewhere in the story and because they are more mysterious for the laymen (and the author) than other representations, they play an important role in the self-brainwashing procedure
  • the meaning of the mathematical indices must be sufficiently obscured so that the author himself forgets what they mean and what is the actual spin of various particles in his construction
  • the no-go theorems are claimed to be "circumvented" because the "new" construction avoids an assumption; this assumption is either paramount for the inner workings of gravity (especially the diffeomorphism symmetry, linked to the equivalence principle, and the Lorentz symmetry), or it can easily be dropped or replaced in order to prove a morally equivalent no-go theorem (e.g. by adding a small cosmological constant)
  • because the "new" construction makes it necessary to replace pretty much all of cosmology by something else, the author must deny that he has ever heard anything about cosmology.
Let us now look at these steps one by one. At the very end, I will discuss why gravitons can "emerge" out of something else in string theory (e.g. a string) and why it is easy to see that this property of string theory can't be shared by any other idea that has ever been considered.

Fake originality

The first step needed to write a similar paper is for the author to convince himself that he has some original ideas - which should also explain why everyone else has previously failed. So McElrath also says that "no workable theory has been yet constructed". If he honestly looked at what he has, he would realize that no workable theory can be constructed by his methods, either. But he simply doesn't give a damn.

There are hundreds of people who are profoundly confused by the basic features of gravity and they have argued that gravity can "emerge" out of dozens of unrelated (but mutually related) phenomena. These people differ in details but they share the key belief that there is nothing special about gravity. Much like gold in the medieval alchemy, it can surely be "constructed" out of ordinary metals and liquids. Their goal is really not to look at (and explain) the precise numbers and principles that every event in the world seems to respect. They prefer sloppy theories that produce random chaotic junk - the material they really enjoy - which is later claimed to be equivalent to Nature. Well, it's not.

The list of people who have "worked" on similar silly stuff is long and includes names like Garrett Lisi, Fabrizio Nesti, Roberto Percacci, Lee Smolin, Ingo Kirsch, and many others. All of these authors seem to be confused by basic representation theory, the difference between spacetime and internal symmetries, the meaning of the equivalence principle, and other things. None of these papers is qualitatively better than others - all of them are extremely sloppy about issues that are completely fundamental for the very character of gravity.

A new favorite condensed matter effect

The second step requires the author to pick a favorite effect by which "gravity" can "emerge". For no good reasons, McElrath chose neutrinos to be the fundamental building blocks of gravitons. Gravitons are supposed to be massless and because the Goldstone bosons are also massless, many of the contemporary alchemists are led to believe that gravitons are Goldstone bosons of some kind.

Because Goldstone bosons also appear in superconductivity, many authors like to argue that gravity is a kind of superconductivity. McElrath is one of them. So he wants gravity to arise from superconductivity of something like Cooper pairs of neutrinos of some kind. His favorite phenomenon is the Kohn-Luttinger effect, a mechanism as old as half a century that implies that Cooper pairs may arise from a strictly repulsive interaction, too.

Non-existent links between Cooper pairs and gravity

It's surely interesting that one can obtain a replacement for these "bound states" in a strictly repulsive condensed matter system. But does it have something to do with gravity and its defining characteristics? The answer is a resounding No. The only valid and transparent enough relationship between Cooper pairs and gravity is that Sheldon Cooper is a string theorist. ;-)

The defining characteristics of gravity is the equivalence principle, the masslessness of its carriers (the infinitely long range of the force, related to the well-known power-law decrease), and the gravitons' spin equal to two (its coupling to the stress-energy tensor that has two indices). None of these features has an explanation in terms of the neutrino Cooper pairs. In fact, all of these features directly contradict the superconducting picture, as we will see. The repulsive superconductivity may look "cool" but it has nothing to do with gravity. 

One may drink a lot of alcohol so that this obvious conclusion becomes fuzzy but the sober people may still realize that the conclusion is true and unchanged: there doesn't exist a single rational link between gravity and these condensed matter papers.

Mysterious spinors

Spinors are representations of orthogonal groups that are more surprising than more ordinary tensor representations with vectorial indices. I guess that at some moment of her life (perhaps as a college student), pretty much every physicist was surprised by the very existence of spinors. However, it is also important to make another step. At the end, spinors must become just another mundane representation, just another piece of basic knowledge that can be used as a building block for more advanced research.

Most people simply never become "adult physicists" in this sense. For example, Peter Woit wrote exactly one preprint during the last two decades that pretends to offer "positive material" rather than just hateful anti-scientific whining. The very idea of this nonsensical 0-citation paper is a mysterious role that the author attributes to spinors and the Dirac operator.

Once a student learns her representation theory, there is nothing mysterious about spinors whatsoever and one simply can't make a paper look more "cool" or "serious" or "promising" just by including spinors. Nevertheless, a divine task is associated with spinors in most of the "emergent" papers about gravity. McElrath's is no exception.

The spin of the graviton

The most widespread technical "trick" in these papers is a confusing notation concerning mathematical indices. The authors often convince themselves that objects have a different spin than they actually have. What do I mean?

Almost all of the alchemists introduce some kind of internal symmetry group whose meaning is being obscured until the authors themselves begin to think that the symmetry group geometrically acts on spacetime, after all. Well, there's still a huge difference between spacetime symmetries and internal symmetries but these alchemists simply fool themselves so that they don't see it.

There are many ways to see why this distinction cannot ever evaporate and why these people are just brainwashing themselves.

Begin with the spin of the messenger particles. If your force resembles gravity in general relativity, the messengers' spin must equal two. That's because they arise from perturbations of the metric, "h_{mn}", and this tensor has two indices because it must be coupled to the stress-energy tensor. The latter has two vectorial indices, too. It must be so because it determines the density-and-current vector (one index) of the energy-momentum vector (another index).

Now, the statement that the graviton's spin equals two is not just about some bureaucratic sleight-of-hand or a feature of your conventions how you write your indices. It is a very physical feature of the excitation. Take the minimum nonzero energy of the gravitational waves at a certain frequency. By basic rules of quantum mechanics, the energy must be quantized in units of "E=hf". 

The elementary quantum of energy carried by these waves, the physical graviton, will have the projection of the angular momentum to the direction of motion equal to "+-2 hbar". You may imagine that your graviton is composed out of neutrinos or dust or dirt. But if the physical spin won't be "+-2 hbar" once you're finished, it is easy to show that the induced interactions won't agree with general relativity. And the difference won't be small in any sense. The theory will be instantly falsified.

What is the spin of the Goldstone bosons arising from a broken symmetry? Well, inconveniently enough for the alchemists, the spin is equal to the spin of the conserved charge associated with the broken symmetry. Any theory qualitatively resembling the real world that has nontrivial interactions only admits conserved charges whose spin is one of these three numbers:
  • 0
  • 1/2
  • 1
Most of the conserved charges, such as the electric charge, have spin zero. If the corresponding symmetry is spontaneously broken - like in superconductivity - the resulting massless Goldstone bosons will have spin zero, too. You will never construct spacetime tensors out of these objects. Ordinary Goldstone bosons, such as the phase of the Cooper pair "wave function", are massless spinless fields. Whenever the broken symmetry is a part of a local symmetry, the Goldstone bosons are eaten to become the longitudinal polarizations of the massive gauge bosons.

Supersymmetry is the only type of symmetry with nonzero spin that can come in many "flavors" - I am talking about the extended supersymmetry algebra with many spin-1/2 generators. If supersymmetry is spontaneously broken, one encounters Goldstone particles, too. In this case, the generators of the symmetry were fermionic, so the Goldstone particles are fermions rather than bosons: they are called the goldstinos and they have spin-1/2. In theories where the supersymmetry is local - which are inevitably supergravity theories (because the anticommutators of local supersymmetries involve local translations, thus including diffeomorphisms to the local algebra) - goldstinos are eaten to become new polarizations of massive gravitinos.

The only other conserved continuous quantity in Nature is the energy-momentum vector associated with the space-time (actually time-space, to match energy-momentum) translational symmetry. There can only exist one copy of such a conserved current. There can exist neither additional spin-1 conserved quantities nor higher-spin conserved quantities. If you assumed that such additional conservation laws exist, you could easily prove that the interactions would effectively have to vanish (as in the Coleman-Mandula theorem and its variations) because the required conservation laws for so many components of tensors would be far too constraining.

The rotational (and Lorentz) symmetries change the asymptotic location of points in spacetime so dramatically that the corresponding modes are not normalizable and one can't get any new "Goldstone bosons" out of them. So let me only mention what are the Goldstone bosons arising from the spontaneous breakdown of the spin-1 conserved (translational) symmetries. Indeed, these symmetries may be broken, too.

For example, if you place a brane at "z=0" in space, you break the SO(3,1) Lorentz symmetry (semidirectly multipled by R^4 of translations) down to SO(2,1) (semidirectly multiplied by R^3 of translations). Because of this breakdown, it makes sense to consider the SO(2,1) vector indices to be the only geometric ones. In this classification, the Goldstone boson is nothing else than the "z = z(x,y,t)" coordinate of the brane. Because of the translational symmetry of the laws of physics before we included the brane, the brane can be anywhere and it can wiggle: its height "z" is a massless scalar field in 2+1 dimensions.

None of these Goldstone particles can ever look like the graviton. Every single paper that claims that the author can obtain a spin-2 tensor out of similar Goldstone particles is fooling himself by assuming that an internal index is actually a geometrical one. For example, some other authors think that diffeomorphisms are related to SO(3,1) or GL(4,R) or something like that. Because the latter are similar groups to Yang-Mills gauge groups, these people think that it is pretty much the same thing.

But technically speaking, it is not the same thing at all. The Yang-Mills symmetry doesn't act on spacetime while the diffeomorphism symmetry does. The corresponding messenger particles have spin-1 or spin-2, respectively. These are technically different things and there exists no "duality" or "equivalence" between spin-1 fields and spin-2 fields in the same spacetime. Everyone who thinks that he has found such an equivalence is fooling himself by a mistake that is as obvious as the mistake in the identity "1=2" - if you look at it from the correct angle.

This particular alchemist, Bob McElrath, "proves" the "1=2" equation using his own trick. He argues that there is an enhanced symmetry of his neutrino dynamics, "SO(3,1)_{space} x SO(3,1)_{spin}". It is broken "only" by the kinetic terms, he says (and by most other physical phenomena, he doesn't say). If things were described by his theory and if objects couldn't move and interact ;-), there would be an enhanced symmetry. Well, but it's broken: there is only one set of independent rotations of space and boosts of spacetime in Nature. 

Because it's broken, we should classify the generic physical objects according to the unbroken SO(3,1) Lorentz group only. I am always free to classify things according to the unbroken group, in order to gain an insight. Other people may hide their eyes from such insights but that doesn't make these insights disappear. Under this real, physically meaningful group, one that actually has to exist, the gravitons have spin-2 while the Goldstone bosons have spin-0. There's simply no way to make the "1=2" or "0=2" identities valid. People may fool themselves by choosing confusing indices or confusing names for their groups and by combining these groups into half-internal, half-geometric symmetries but they can't fool Mother Nature: gravitons have different spins than Goldstone bosons and they will always have.

Circumventing no-go theorems

All these papers are safely killed by the Weinberg-Witten theorem, among others. Bob McElrath agrees with this assertion but he seems to suggest that his model can survive. The Weinberg-Witten theorem is an extremely powerful physical argument - a more valuable and robust result than all the alchemist papers combined. The theorem actually tells us how Nature can work or does work and how it cannot work - which is often a different thing from the laymen's desires how Nature should work. That's a fact that the alchemists generally misunderstand. They just find the theorem inconvenient so they just try to throw it away in one way or another.

But in physics, what matters are correct results, not convenient results.

Many alchemists find an assumption in the theorem that they claim not to be satisfied which - they believe - allows them to ignore the theorem completely. For example, Garrett Lisi has argued that the theorem assumed the cosmological constant to be zero. Because it is now believed to be nonzero - a fact that is supposed to be incorporated into Lisi's theory - the assumptions of the theorem don't apply and the theorem can be ignored, Lisi thinks.

Of course, if someone is both lazy and stupid, he can say that the rigorous proof no longer applies. But if he were somewhat more intelligent and if he understood the essence of the Weinberg-Witten argument, he would know that the logic still kills the theories: it is easy to construct a variation of the Weinberg-Witten proof that is still doing the same job. 

Local physics of our Universe agrees with a theory with a vanishing cosmological constant up to small corrections of order 10^{-123} in Planck units. So any conclusion about the local physics based on the assumption of a vanishing cosmological constant is going to be correct up to small errors of order 10^{-123} (or its reasonable positive power), too. 

An effect that is as tiny as the cosmological constant in the real world simply can't "qualitatively" change these conclusions. Composite gravity remains impossible. In fact, variations of the theorem hold exactly for spacetimes with a nonzero cosmological constant even though my argument only guaranteed that they must hold almost exactly.

However, McElrath chooses another assumption of the Weinberg-Witten theorem that is invalid in his model which is why he thinks that he can ignore the theorem. Because of the presence of a physical background, the diffeomorphism symmetry is broken and the theorem ... doesn't apply. 

But if the diffeomorphism symmetry is broken, it is a huge problem for any model of gravity. In fact, even if it is broken, one can reformulate any theory as a diffeomorphism-invariant one by adding some auxiliary fields. If the symmetry is broken, there will be symmetry-breaking terms. It can be shown that these diffeomorphism symmetry breaking terms will violate the equivalence principle, too (unless they can be absorbed to field redefinitions). Because the latter holds - either completely accurately or almost accurately - these terms must be extremely tiny.

Unless someone claims to have a theory that explains all the dimensionless parameters in Nature, including the very tiny ones, in terms of fixed and calculable constants, his theory must allow a "simplified" limit where the diff-breaking terms are set to zero (much like the cosmological constant). That's really the zeroth approximation he should be talking about in the first plcae because it is surely much more relevant as a description of reality than a theory where the diff-symmetry is broken by terms of order one. If he can't construct any diff-symmetric theory, it pretty much proves that he can't possibly have any theory that agrees with the observed effects of gravity.

The diffeomorphism symmetry plays a completely crucial role in the inner workings of gravity. It is the actual gold inside the gravitational jewel. The equivalence principle is the "miracle", the feature of gravity that is actually both experimentally supported (with an impressive accuracy) and theoretically far-reaching. McElrath throws this gold into trash bin in order to replace it with some superconducting crap. Other champions of "spinor gravity", "superconducting gravity", "graviweak gravity", "surfer dude gravity", and their siblings are doing the same thing.

Ignoring cosmology

McElrath et al. ignores the equivalence principle and other essential features of gravity. But of course, he has to ignore much more. For example, he wants you to believe that gravity as we know it only works at distances longer than the neutrino length scale. This meme has been marketed as the "fat graviton" in the past in order to explain the smallness of the cosmological constant. There was at least some motivation - one that McElrath seems to be unfamiliar with.

Instead, McElrath tells you that gravity didn't work in the way it does today when the energy density was much higher than it is today. In fact, with his particular version of a "fat graviton", the gravity would be modified almost instantly - whenever the density is higher than today. However, the Big Bang cosmology has been verified at least up to the Big Bang Nucleosynthesis - when the energy density approached the QCD values - about 50 orders of magnitude higher than it is today (i.e. 50 orders of magnitude higher than what McElrath's theory could explain even if you ignored all the trouble with the wrong spins and the equivalence principle).

McElrath is silent about these issues. Does he care? Does he think that anyone who denies the modern relativistic description of gravity has to give his own, completely new explanation for the equivalence principle as well as all the observed aspects of cosmology? An explanation that must surprisingly lead to pretty much the same results - otherwise it is experimentally ruled out - even though the essence of his theory seems completely different? There seems to be absolutely nothing about these alchemist theories that works. What is driving its champions? Is it a rational driver?

Emergent gravity in string theory

Gravitons can't emerge out of neutrinos, dust, bottles of beer, or any other "random" ingredients, as argued above. Gravity is very "universal" and it is inevitably associated with the only spin-1 conserved charge (energy-momentum) that can exist in an interacting world. It couples to all forms of energy and momentum, as checked by the tests of the equivalence principle.

However, you could be puzzled why there are gravitons in string theory. For example, in perturbative string theory, gravitons are identified with a particular energy eigenstate of a vibrating string. A string is just another object. Shouldn't all the anti-neutrino arguments apply?

Well, they don't because a string is not "just another random object". In fact, everything in a stringy world is made out of strings (or their nonperturbative "generalization", M, if you wish). The real difference between strings and neutrinos is that one can actually prove that the equivalence principle and/or diffeomorphism symmetry is exactly satisfied in string theory while it is certainly violated in the case of neutrino bound states.

In perturbative string theory, it is the state-operator correspondence that saves the day. There exists a one-to-one map between the states of a single string and the local operators on the string world sheet. According to this map, the state of a closed string identified as the "graviton" is mapped to a local operator that equals the variation of the world sheet Lagrangian with respect to the external geometry (metric tensor).

It follows that if you add closed strings in the particular graviton internal vibrational mode in your spacetime, the effect on other strings will be exactly identical as if you instruct all other strings in the world to propagate on a modified geometric background. And because everything is made out of strings, the equivalence principle will hold for everyone. All strings will accelerate equally in the gravitational field - in the field with a condensate of the particular closed strings.

But this argument hasn't changed anything about the precious value of the equivalence principle and its ability to kill almost every wrong idea instantly. Instead, it has replaced this jewel by its perturbative stringy counterpart - by the state-operator correspondence. We can actually show that the equivalence principle is going to be respected if the particular closed strings fill the space. If we couldn't prove such a thing, we would have no right to say that string theory is a theory of gravity.

Analogously important but surprisingly different arguments exist in other approaches to string theory, including Matrix theory (where gravitons are made out of D0-branes or noncommutative membranes) and AdS-CFT (where they're represented by the stress-energy tensor of the boundary theory). All these mechanisms how gravity may "emerge" are connected - we may say that the unifying principle is the existence of string theory itself.

But if your theory ignores the equivalence principle, doesn't guarantee that the principle is valid, and doesn't replace the principle by any other effectively equivalent principle, it simply makes no sense to argue that your theory is a theory of gravity. As a theory of gravity, your theory is instantly and safely dead: it is ruled out by very accurate measurements that it has no chance to agree with. If you say that you have a theory of gravity nevertheless, you are a crackpot, and if you promote such "theories of gravity" in your articles, you can't distinguish crap and gold.

And that's the memo.

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