Tuesday, July 03, 2007

Loop quantum cosmology

Shortcut to the discussion about the greenhouse effect

Many newspapers and magazines including New Scientist, USA Today, and Scientific American have recently promoted new "results" within a framework called loop quantum cosmology. I want to explain why 100% of this stuff is unphysical nonsense but we should find a logical place to start.

What is loop quantum gravity?

It is useful to first understand what is loop quantum gravity. Theoretical physics has been amazingly successful. Its basic theories can be summarized on a sheet of paper and they correctly predict the results of virtually all experiments and phenomena we have ever observed.

However, these theories correspondingly rely on difficult mathematics, they are increasingly abstract, and their mathematical and conceptual structure is not comprehensible to everyone. There is a lot of secret coding behind the sheet of paper from the previous paragraph. In order to understand the cutting-edge picture of the Universe or even extend the reach of the human knowledge, one must master not only quantum mechanics and classical field theories but also path integrals, renormalization, the Higgs mechanism, strong-coupling behavior of gauge theories, and many other subjects whose character is either intuitive, observational, or mathematical.

All really big open problems of current theoretical high-energy physics - such as the cosmological constant problem, the vacuum selection problem, a decent solution to the information puzzle, or the puzzle about the beginning of the Universe - only make sense as long as we consider all known qualitative aspects of our picture of the Universe seriously. We must include matter, too.

For example, the only reason why we would (incorrectly) predict that the cosmological constant should be Planckian (huge) is that there exist other forms of matter that can run in the loops. The only reason why we face the vacuum selection problem is that there exist many types of matter sectors that can be coupled to gravity - and this is true even within string theory although the degeneracy is reduced to a discrete set. Most of the information from the black hole that enters the information puzzle is stored in matter fields which also makes them crucial. And these additional matter fields are important during the Big Bang, too. They are never turned off. The fine-structure constants - the electromagnetic one or its generalizations - at the Planck scale are higher than what they are at low energies.

These facts make it clear that it is impossible to study any big question in theoretical physics without taking all other forces and particles into account: ignoring matter fields in these problems is the same thing as ignoring the problems themselves. Moreover, there exists huge evidence that "pure quantum gravity" without non-gravitational matter fields and without any complicated symmetries of the black hole microstates such as the monster group is simply inconsistent.

All currently known systems of ideas that are able to incorporate all essential ingredients of the contemporary picture of the world - including gauge theories coupled to scalars and fermions as well as gravity described by general relativity - turn out to be tightly connected and non-trivially connected within a mathematical structure that we continue to call string theory even though the term suggests a much more narrow-minded a theory than what string theory actually is today. In fact, it is likely that all mathematically possible systems of ideas that can do so are also parts of this string theory - if it is properly defined - but there exists no proof of such a statement. There cannot even exist such a proof right now especially because we can't even make this statement rigorous: we don't have a full definition of the term "string theory". Our knowledge of this structure is divided to "patches" analogous to patches that make up a manifold.

Oversimplifying physics

Some people find quantum field theories and string theory too complicated and they believe that it is possible to do serious or even "deeper" theoretical physics by ignoring most of the insights of the last 60 years or so. Loop quantum gravity is an example of such an approach. Loop quantum gravity violates every single obvious rule explained above - and many others - because
  • it wants to study quantum effects of gravity separately from other forces and forms of matter even though there exists no regime in which they can be decoupled and instead, there exists strong evidence that pure quantum gravity is inevitably inconsistent; the papers that try to discuss matter in loop quantum gravity look like albums of octopi and have clearly no connection with particle physics
  • it wants to use big words even though spiritually, the theory of loop quantum gravity is as naive as discrete theories of many ancient Greek philosophers such as Democritus; no results found after Democritus influence their thinking in any material way
  • it neglects effects that clearly can't be neglected, as exemplified below, and makes infinitely many unjustifiable assumptions
  • no "good features" of the theory that would indicate the consistency of the theory with reality or the internal consistency of the theory are ever found and no one cares: it is a classical example of a GIGO theory, garbage in, garbage out, because wrong assumptions are simply translated into wrong conclusions without anything interesting or encouraging happening in between; in the absence of observations, it is often important to know that a theory works and gives at least qualitatively meaningful answers - a coherent story - even though it was not a priori guaranteed: such a situation never occurs in loop quantum gravity.
Loop quantum gravity starts with the manifestly incorrect assumption that any classical theory must have a quantum counterpart and the only question is how to "add the hats". General relativity is such a beautiful theory that we shouldn't really change it at all, those people think, which is why they try to understand the problem of quantizing gravity along these lines.

How do we know that this assumption is incorrect? Well, classical theories may lead to anomalies that imply that no quantum theory with a given classical limit may exist. More generally, quantization of classical theories often leads to non-renormalizable theories which are no good as a starting point for predictions.

These insights are robust conclusions of a paramount section of theoretical physics, the renormalization group, a theoretical machinery that is important both in high-energy physics as well as condensed-matter physics and other fields.

The proponents of loop quantum gravity realize that adding hats to general relativity is somewhat subtle so loop quantum gravity combines the hats with a field redefinition. All hopes that this step is any useful in removing the problems of quantized general relativity violates another fact about theoretical physics - namely that field redefinitions may make things more transparent and easier to manipulate with but they can never make an inconsistent theory consistent. Indeed, it is obvious that any inconsistency on one side can be mapped to the corresponding inconsistency on the other side as long as a dictionary exists. Also, infinitely many undetermined terms in one language can always be translated to infinitely many undetermined terms in another language.

In loop quantum gravity, the degrees of freedom in the metric tensor are randomly re-expressed in terms of a gauge field. This field redefinition is only legitimate locally on the configuration space; globally, it imposes new periodicities (of the Wilson lines) and corresponding quantization rules for the dual variables (areas) because the field redefinition is not one-to-one. The resulting quantization rules are often mentioned as predictions of this approach to quantum gravity; instead, they are nothing else than a measure of inadequacy of their particular field redefinition. The quantization rules are not derived from any robust assumption: they are an assumption itself because they can be easily shown to be equivalent to the incorrect field redefinition.

Our conclusion that by making this particular field redefinition, one loses any contact with the original theory of gravity, can be seen more explicitly. The resulting discrete theory has no traces of Lorentz invariance - a lethal problem that arises from the discreteness of the areas itself - or other basic principles of modern physics, making it extremely obvious that loop quantum gravity has nothing to do with insights of 20th century physics.

The pathological infinite number of unknown parameters of quantized general relativity have their counterparts in loop quantum gravity, too. The situation is more problematic here because the new infinite-dimensional space doesn't contain a single representative theory that would locally obey the Lorentz symmetry, among other key laws. Having an infinite-dimensional space of theories is clearly not enough for having the correct theory anywhere on the space.

Relation of loop quantum gravity and loop quantum cosmology

The theory of loop quantum gravity constructed above is comprehensible to most schoolboys and even to many journalists: the whole world is made out of vertices and links. This "comprehensibility to masses" is the main reason why these otherwise manifestly unphysical ideas continue to be studied. This whole enterprise is driven by crackpots - those guys from the discussion forums who know how to draw a combinatorial graph and who like to think that once they can do it, they surely understand the secrets of the Universe because gauge theories and renormalization groups are just irrelevant technical details that these "geniuses" may generously ignore.

And it looks cool, doesn't it? Especially if you make "Milde Marketing" do the P.R. for you - apparently the main thing that scientists need these days to defend their theories

There exists no sense in which the extraordinarily strong statement about the structure of spacetime at short distances can be derived from reasonable or robust assumptions and there doesn't exist a single consequence of it that would indicate that this feature of spacetime is desirable i.e. connected with any observation or principle of physics, either directly or indirectly.

The specific discreteness of spacetime - and any discreteness, for that matter - is an extremely unlikely religious belief. A belief that those people don't want to question. They like it so much because it makes their world so simple. Results that confirm this belief are interpreted as successes of loop quantum gravity. You may view these "successes" as consistency checks except that they are qualitative self-consistency checks only - something that theoretical physicists should never find enough in the absence of direct observations. There exists no truly quantitative, exact logical link between the different myths about quantum gravity that the loop quantum gravity believers want to assume.

Another part of the religious belief is the so-called background independence, a notion that the whole loop quantum gravity community completely misunderstands and treats very irrationally. For example, Carlo Rovelli has been unable to understand that propagators such as the graviton propagator can't be background-independent because they encode the second derivative of the action around a particular background. The term "background-independent propagator" is exactly the same oxymoron as "Taylor expansion without any point to expand around" but these guys don't care because the adjective "background-independent" is equivalent to "God" and the spiritual content of this adjective is more important than any logical contradiction.

From gravity to cosmology

You might think that loop quantum cosmology is nothing else than the application of loop quantum gravity to the context of cosmology i.e. that loop quantum cosmology will agree with loop quantum gravity, whatever these words mean. You would be wrong.

While loop quantum gravity is an extremely naive model that clearly doesn't have the capacity to incorporate the basic features of the real world as understood during the last 70 years - matter coupled via gauge fields, obeying the proper rules of renormalization, anomaly cancellation as a non-trivial condition on matter spectrum, black hole thermodynamics (the coefficient of the black hole entropy in loop quantum gravity is wrong, among other things), and many others - the people who work on loop quantum gravity don't find loop quantum gravity naive enough.

So they have invented loop quantum cosmology that is even more naive and oversimplified than loop quantum gravity. Here, you don't try to rewrite a general spacetime geometry (ignoring all other degrees of freedom) in terms of gauge fields. Instead, you only try to rewrite a very special kind of spacetime geometry - a uniform and isotropic FRW cosmology - in easier variables that show similar signs of discreteness of time as the degrees of freedom in loop quantum gravity show discreteness of spacetime.

It is absolutely manifest that you are once again throwing the baby out with the bathwater. Our world is neither uniform nor isotropic and the inhomogeneities clearly become very important at the very beginning of the Universe - e.g. before the inflationary era if there ever was one. Whoever uses the FRW cosmology to study a supertiny Planckian universe lacks a completely basic ability to decide what is the range of validity of various approximations, an ability that is absolutely crucial in physics as well as other sciences. There can't be any question that conclusions based on this preposterous assumption will be scientifically worthless and whether or not they qualitatively agree with the correct answers is a matter of pure coincidence.

Fine, so loop quantum cosmology doesn't even start with loop quantum gravity but with something that is even more naive and more unphysical. These approaches nevertheless share most of the problems - for example, there are also infinitely many undetermined parameters about the dynamics and it seems that not a single point in this infinite-dimensional space of theories describes a theory that would at least qualitatively agree with some features of the known observations. There exists not a single encouraging sign of another type - as we have mentioned, e.g. no consistency check is known. The space of loop quantum gravity cosmologies is an infinite-dimensional dumping ground.

How to be both stupid and ambitious

And now these people take this ancient Greek nonsense and they start to argue that it is relevant for solving big open problems in physics of 2007, without a glimpse of evidence. They randomly construct variations of their discrete models that have a beginning or that have a bounce even though it is manifest that no prediction of the model near the Planck scale can be trusted and no feature of the model can really be predicted anyway because of the infinite number of unknowns.

They also want to argue that these primitive models "explain dark energy". Can these models describe anything that would share any quantitative properties with dark energy? The answer is, of course, a resounding "No". Observations make it clear that dark energy is almost certainly a cosmological constant, with pressure equal to minus energy density. Can you get the right equation of state - the very basic, defining feature of observed dark energy - from any framework such as loop quantum gravity or loop quantum cosmology?

The answer is obviously "No". The reason why "p=-rho" is special is called the Lorentz invariance. This special kind of the stress-energy tensor that is relevant for the cosmological constant is proportional to the metric tensor which is why it doesn't break the Lorentz invariance of local physics. But loop quantum theories have no Lorentz invariance at the Planck scale which is why it is infinitely unlikely that a form of matter should ever have the right equation of state. It almost certainly doesn't. Suggesting that some random objects found in some random primitive discrete models are mapped to some highly abstract features of reality - such as the problems of high-energy physics - is stupid beyond imagination.

This whole approach of loop quantum gravity returns us (or at least them) to the era of early primitive religions. Tens of thousands of years ago, people would also believe irrational links between observable phenomena and mysterious hypothetical portions of deeper reality - such as their gods. They have never had a good reason to believe in these links but they were extremely excited about the grandiose connections they were imagining. Reasons to believe in links proposed by loop quantum gravity are absent, too. If people lose the ability or the right to realize that this whole reasoning is absurd, many more people will be returning to the pre-scientific era every day.

And that's the memo.

1 comment:

  1. Wearing hats, haha: http://images.search.yahoo.com/images/view;_ylt=A0PDoTC2FSJS8hoAW6CjzbkF;_ylu=X3oDMTF1NW1kMXZpBHNlYwNmcC1leHAEc2xrA2V4cARvaWQDZjliNWM1YjgzYTE2OGIxZDNiMDU4M2YzMTE5MjI5NjAEZ3BvcwMx?back=http%3A%2F%2Fus.yhs4.search.yahoo.com%2Fyhs%2Fsearch%3Fei%3DUTF-8%26p%3Deinstein%2Bhat%26fr%3Dgoodsearch-yhsif&w=150&h=109&imgurl=www.ias.edu%2Ffiles%2Fimages%2Fnotedfigures%2Feinstein-hat.jpg&rurl=http%3A%2F%2Fwww.ias.edu%2Fpeople%2Feinstein%2Fin-brief&size=3.1KB&name=%3Cb%3Eeinstein%3C%2Fb%3E-%3Cb%3Ehat%3C%2Fb%3E.jpg&p=einstein+hat&oid=f9b5c5b83a168b1d3b0583f311922960&fr2=&fr=&tt=%3Cb%3Eeinstein%3C%2Fb%3E-%3Cb%3Ehat%3C%2Fb%3E.jpg&b=0&ni=114&no=1&ts=&tab=organic&sigr=11bq73ros&sigb=12mcr7ca9&sigi=11m2ajrvo&.crumb=qH/G9DzWZku&