Recent Articles

Quantum gravity

Quantum gravity is the field of theoretical physics attempting to unify the theory of quantum mechanics, which describes three of the fundamental forces of nature, with general relativity, the theory of the fourth fundamental force: gravity. The ultimate goal is a unified framework for all fundamental forces—a theory of everything.

Much of the difficulty in merging these theories comes from the radically different assumptions that these theories make on how the universe works. Quantum mechanics depends on particle fields embedded in the flat space-time of special relativity. General relativity models gravity as a curvature within space-time that changes as mass moves. The most obvious ways of combining the two (such as treating gravity as simply another particle field) run quickly into what is known as the renormalization problem. Gravity particles would attract each other and adding together all of the interactions results in many infinite values which cannot easily be cancelled out mathematically to yield sensible, finite results. This is in contrast with quantum electrodynamics where the interactions sometimes evaluate to infinite results, but those are few enough in number to be removable via renormalization.

Another difficulty comes from the success of both quantum mechanics and general relativity. Both have been highly successful and there are no known phenomena that contradict the two. The energies and conditions at which quantum gravity is likely to be important are inaccessible to laboratory experiments. The result of this is that there are no experimental observations which would provide any hints as to how to combine the two.

The general approach taken in deriving a theory of quantum gravity is to assume that the underlying theory will be simple and elegant and then to look at current theories for symmetries and hints for how to combine them elegantly into an overarching theory. One problem with this approach is that it is not known if quantum gravity will be a simple and elegant theory.

Such a theory is required in order to understand those problems involving the combination of very large mass or energy and very small dimensions of space, such as the behaviour of black holes, and the origin of the universe.

The incompatibility between quantum mechanics and general relativity

At present, one of the deepest problems in theoretical physics is harmonizing the theory of general relativity, which describes gravitation and applies to large-scale structures (stars, planets, galaxies), with quantum mechanics, which describes the other three fundamental forces acting on the microscopic scale.

A fundamental lesson of general relativity is that there is no fixed spacetime background, as found in Newtonian mechanics and special relativity; the spacetime geometry is dynamical. While easy to grasp in principle, this is the hardest idea to understand about general relativity, and its consequences are profound and not fully explored, even at the classical level. To a certain extent, general relativity can be seen to be a relational theory, in which the only physically relevant information is the relationship between different events in space-time.

On the other hand, quantum mechanics has depended since its invention on a fixed background (non-dynamical) structure. In the case of quantum mechanics, it is time that is given and not dynamical, just as in Newtonian classical mechanics. In relativistic quantum field theory, just as in classical field theory, Minkowski spacetime is the fixed background of the theory. Finally, string theory started out as a generalization of quantum field theory where instead of point particles, string-like objects propagate in a fixed spacetime background. Although string theory had its origins in the study of quark confinement and not of quantum gravity, it was soon discovered that the string spectrum contains the graviton, and that "condensation" of certain vibration modes of strings is equivalent to a modification of the original background.

Quantum field theory on curved (non-Minkowskian) backgrounds, while not a quantum theory of gravity, has shown that some of the core assumptions of quantum field theory cannot be carried over to curved spacetime, let alone to full-blown quantum gravity. In particular, the vacuum, when it exists, is shown to depend on the path of the observer through space-time (see Unruh effect). Also, the field concept is seen to be fundamental over the particle concept (which arises as a convenient way to describe localized interactions). This latter point is not uncontroversial, as it is contrary to the way quantum field theory on Minkowski space is developed by Steven Weinberg's book Quantum Field Theory.

Historically, there have been two reactions to the apparent inconsistency of quantum theories with the necessary background-independence of general relativity. The first is that the geometric interpretation of general relativity is not fundamental, but just an emergent quality of some background-dependent theory. This is explicitly stated, for example, in Steven Weinberg's classic Gravitation and Cosmology textbook. The opposing view is that background-independence is fundamental, and quantum mechanics needs to be generalized to settings where there is no a-priori specified time. The geometric point of view is expounded in the classic text Gravitation, by Misner, Wheeler and Thorne. It is interesting that two books by giants of theoretical physics expressing completely opposite views of the meaning of gravitation were published almost simultaneously in the early 1970s. The reason was that an impasse had been reached, a situation which led Richard Feynman (who himself had made important attempts at understanding quantum gravity) to write, in desperation, "Remind me not to come to any more gravity conferences" in a letter to his wife in the early 1960's. Since then, though, progress was rapid on both fronts, leading ultimately to string theory and loop quantum gravity.

Loop quantum gravity is the fruit of the effort to formulate a background-independent quantum theory. Topological quantum field theory provided an example of background-independent quantum theory, but with no local degrees of freedom, and only finitely many degrees of freedom globally. This is inadequate to describe gravity in 3+1 dimensions, which even in vacuum has local degrees of freedom according to general relativity. In 2+1 dimensions, however, gravity is a topological field theory and it has been successfully quantized in several different ways, including spin networks.

Theories and Proto-theories

There are a number of proposed quantum gravity theories and proto-theories including:

• String theory
• Loop quantum gravity of Ashtekar, Smolin and Rovelli
• Noncommutative geometry of Alain Connes
• Twistor theory of Roger Penrose

The "direct" way of quantizing gravity comes with many choices. Do we use functional integrals over Wick rotated Riemannian metrics (e.g. by Hawking)? See Euclidean path integral approach. Do we use the covariant Peierls bracket? Do we use BRST/Batalin-Vilkovisky formalism or gauge fixing or gauge factoring? If we pick canonical quantization, do we use the Einstein-Hilbert action with only the metric as dynamical to get the Wheeler-deWitt equation? Or do we treat the metric and the affine connection independently? Or do we have the whole Poincaré group as the gauge group starting with the Einstein-Cartan theory? Or do we use the Cartan method of moving frames with the Palatini action to get second class constraints? Do we eliminate the second class constraints using the Ashtekar variables to get loop quantum gravity or do we do something else? The existence of spinor fields may force us to work with the Cartan formalism or something comparable. Or maybe we should look at representations of the diffeomorphism group just as Wigner looked at representations of the Poincaré group.

String theorists' criticisms of Loop quantum Gravity

Lubos Motl is a string theorist who is highly critical of loop quantum gravity. On sci-physics research, Lubos debated Steve Carlip and John Baez, and offers the following criticisms of loop quantum gravity:

• loop quantum gravity makes too many assumptions about the behavior of geometry at very short distances. It assumes that the metric tensor is a good variable at all distance scales, and it is the only relevant variable. It even assumes that Einstein's equations are more or less exact in the Planckian regime. The spacetime dimensionality (four) is another assumption that cannot be questioned, much like the field content. Each of these assumptions is incorrect in a general enough theory of quantum gravity, for example all models that emerge from string theory. These assumptions have neither theoretical nor experimental justification. Examples will be listed in a separate entry.

• according to the logic of the renormalization group, the Einstein-Hilbert action is just an effective description at long distances and it is guaranteed that it receives corrections at shorter distances. String theory even allows us to calculate these corrections. There can be additional spatial dimensions; they emerged in string theory and they are also naturally used in many other modern models of particle physics. An infinite amount of new fields and variables can appear, and indeed does appear according to string theory. Loop quantum gravity ignores all these 20th and 21st century possibilities, and it insists on a 19th century naive image of the world.

• loop quantum gravity is not a predictive theory. It does not offer any possibility to predict new particles, forces and phenomena at shorter distances: all these objects must be added to the theory by hand. Loop quantum gravity therefore also makes it impossible to explain any relations between the known physical objects and laws. Loop quantum gravity is not a unifying theory. It is not just an aesthetic imperfection: it is impossible to find a regime in real physics of this Universe in which non-gravitational forces can be completely neglected. For example, the electromagnetic and strong force are rather strong even at the Planck scale, and the character of the black hole evaporation would change dramatically had the Nature omitted the other forces and particles. Because loop quantum gravity claims that the ultraviolet divergences of all fields and their interactions are regulated by loop quantum gravity, this theory allows any new fields and interactions to be added, which can change the result arbitrarily; the predictive power is therefore exactly equal to zero. The situation strongly contrasts with serious theories of physics; quantum field theories are constrained by the requirement of renormalizability while the consistency constrains string theory completely.

• unlike string theory, loop quantum gravity has not offered any non-trivial self-consistency checks of its statements and it has had no impact on the world of mathematics. While string theory smells by God, loop quantum gravity smells by Man. It seems that the people are constructing it, instead of discovering it. There are no nice surprises in loop quantum gravity - the amount of consistency in the results never exceeds the amount of assumptions and input.

• loop quantum gravity is isolated from particle physics. While extra fields must be added by hand, even this disappointing procedure seems to be impossible in some cases. Scalar fields can't really work well within loop quantum gravity, and therefore this theory potentially contradicts the observed electroweak symmetry breaking; the violation of the CP symmetry, and other well-known and tested properties of particle physics. Loop quantum gravity also wants to deny the importance of many methods and tools of particle physics - e.g. the perturbative techniques; the S-matrix, and so on. Loop quantum gravity therefore potentially disagrees with 99% of physics as we know it.

• loop quantum gravity does not guarantee that smooth space as we know it will emerge as the correct approximation of the theory at long distances; there are in fact many reasons to be almost certain that the smooth space cannot emerge, and these problems of loop quantum gravity are analogous to other attempts to discretize gravity. While string theory confirms general relativity or its extensions at long distances - where GR is tested - and modifies it at the shorter ones, loop quantum gravity does just the opposite. It claims that GR is formally exact at the Planck scale, but implies nothing about the correct behavior at long distances.

• loop quantum gravity violates the rules of special relativity that must be valid for all local physical observations. The spin networks represent a new reincarnation of the 19th century idea of the aether - environment whose entropy density is probably Planckian and that picks a priviliged reference frame. The Lorentz invariance was the only real reason why Einstein had to find a new theory of gravity - Newton's gravitational laws were not compatible with his special relativity. Despite all the claims about the background independence, loop quantum gravity does not respect even the special 1905 rules of Einstein; it is a non-relativistic theory. It conceptually belongs to the pre-1905 era. It also depends on the background in a lot of other ways - for example, the Hamiltonian version of loop quantum gravity requires us to choose a pre-determined spacetime topology which cannot change.

• the discrete area spectrum is not a consequence, but an assumption of loop quantum gravity. The redefinition of the variables - the formulae to express the metric in terms of Ashtekar variables (a gauge field) - is legitimate locally on the configuration space, but it is not justified globally because it imposes new periodicities and quantization laws that do not follow from the metric itself. The area quantization does not represent physics of quantum gravity but rather specific properties of this not-quite-legitimate field redefinition. One can construct infinitely many similar field redefinitions that would lead to other quantization rules. It is probably not consistent to require the new quantization rules - one can see that these choice inevitably break the Lorentz invariance which is clearly a bad thing.

• the discrete area spectrum is not testable, not even in principle. Loop quantum gravity does not provide us with any "sticks" that could measure distances and areas with a sub-Planckian precision, and therefore a prediction about the exact sub-Planckian pattern of the spectrum is not verifiable. One would have to convert this spectrum into a statement about the scattering amplitudes.

• but loop quantum gravity provides us with no tools to calculate the S-matrix, scattering cross sections, or any other truly physical observable. It is not surprising; if loop quantum gravity cannot predict the existence of space itself, it is even more difficult to decide whether it predicts the existence of gravitons. The S-matrix is believed to be essentially the only gauge-invariant observable in quantum gravity, and any meaningful theory of quantum gravity must allow us to calculate it, at least in principle.

• loop quantum gravity does not really solve any UV problems. Quantized eigenvalues of geometry are not enough, and one can see UV singular and ambiguous terms in the volume operators and most other operators, especially the Hamiltonian constraint. Because the Hamiltonian defines all of dynamics, the whole dynamics of loop quantum gravity is at least as singular as it is in the usual semiclassical treatment. We simply do have enough evidence that a pure theory of gravity, without any new degrees of freedom or new physics at the Planck scale, cannot be consistent at the quantum level, and loop quantum gravity advocates need to believe that the mathematical calculations leading to the infinite and inconsistent results (for example, the two-loop non-renormalizable terms in the effective action) must be incorrect, but they cannot say what is technically incorrect about them.

• despite various claims, loop quantum gravity is not able to calculate the black hole entropy, unlike string theory. The fact that the entropy is proportional to the area does not follow from loop quantum gravity. It is rather an assumption of the calculation. The calculation assumes that the black hole interior can be neglected and the entropy comes from the surface area - there is no justification of this assumption. Not surprisingly, one is led to an area/entropy proportionality law. The only non-trivial check could be the coefficient, but it comes out incorrectly (see the Immirzi discrepancy). The Immirzi discrepancy was believed to be proportional to the logarithn of two or three, and a speculative explanation in terms of quasinormal modes was proposed. However it only worked for one type of the black hole - a clear example of a numerical coincidence - and moreover it was realized in July 2004 that the original calculation of the Immirzi parameter was incorrect, and the correct value is not proportional to the logarithm of an integer.

• loop quantum gravity has no tools to answer other important questions of quantum gravity - the details of Hawking radiation; the information loss paradox; the origin of holography and the AdS/CFT correspondence; mechanisms of appearance and disappearance of spacetime dimensions; the topology changing transitions (which are most likely forbidden in loop quantum gravity); the behavior of scattering at the Planck energy; physics of spacetime singularities; quantum corrections to geometry and Einstein's equations; the effect of quantum mechanics on locality, causality, CPT-symmetry, and the arrow of time; the interplay of gravity and other forces; the issues about T-duality and mirror symmetry. Loop quantum gravity cannot answer real questions; it is a philosophical framework that wants us to believe that these questions should not be asked, and general relativity is virtually a complete theory of everything (even though it apparently can't be).

• most loop quantum gravity advocates are not good physicists, and they try to avoid learning anything from particle physics and other fields even though it is clearly necessary for a proper understanding of many questions in quantum gravity. They believe that a very narrow-minded understanding of reality that they propose - and that has not made any real progress for decades - is everything we need. They are making incorrect mental links between different concepts and they are unable to learn better. For example, it is often said by loop quantum gravity proponents that unitarity is no longer necessary because it only follows from time-translation symmetry. Well, the right answer is that unitarity is equivalent to the conservation of the total probability - something that must hold in any context in which basic rules of logic hold - while time-translation symmetry is equivalent to the existence of a conserved (time-independent) Hamiltonian, because of Noether's theorem, which is an entirely different issue.

• the criticisms of loop quantum gravity regarding other fields of physics are completely misguided. They often dislike the perturbative expansions. While it is a great advantage to look for a framework that allows us to calculate more than the perturbative expansions, it should never be able to calculate less. In other words, any meaningful theory must be able to allow us to perform (at least) approximative, perturbative calculations (e.g. around a well-defined classical solution, such as the flat space), and the fact that loop quantum gravity cannot do it is definitely a huge disadvantage, not an advantage as many advocates try to claim. A good quantum theory of gravity should also allow us to calculate the S-matrix.

• also, the loop quantum gravity calls for "background independence" are misguided. The first constraint for a correct physical theory is that it allows the (nearly) smooth space(time) - or the background - which we know to be necessary for all known physical phenomena in this Universe. If a theory does not admit such a smooth space, it can be called "background independent", but it is definitely a useless theory and a physically incorrect theory. It is a totally different question whether a theory treats all possible shapes of spacetime on completely equal footing. However, it is not a priori clear on physical grounds whether it must be so (it can be just an aesthetic feature of a particular formulation of a theory, not the theory itself), and moreover, for a theory that does not predict many well-behaved backgrounds the question is meaningless altogether. Physics of string theory certainly does respect the basic rules of general relativity exactly - general covariance is seen as the decoupling of unphysical modes of the graviton. This exact decoupling can be proved in string theory quite easily. It can also be seen in perturbative string theory that a condensation of gravitons is equivalent to a change of the background; therefore physics is independent of the background we start with, even if it is hard to see for the loop quantum gravity advocates.

• loop quantum gravity is not science because every time a new calculation shows that some conjectures were incorrect, the loop quantum gravity advocates invent a non-quantitative explanation why it does not matter. They usually borrow concepts from completely unrelated and irrelevant fields of human activity, including noiseless information theory and philosophy, and some of their explanations why previous incorrect results should be kept are hard to believe. No questions can ever be settled down if one adopts these extremely low scientific standards.

Loop quantum gravity theorists criticisms of string theory

Carlo Rovelli has summarized many of the criticisms moved by loop quantum gravity theorists to string theory in the following article, written in the form of a dialog, and inspired by Galileo Galilei's famous Dialog on the Copernical and Ptolemaic systems

• Carlo Rovelli, A Dialog on Quantum Gravity, .

Quantum gravity theorists

• Abhay Ashtekar -- Author of Ashtekar variables, he is one of the founders of loop quantum gravity.
• John Baez -- Mathematical physicist.
• Julian Barbour -- Author of The End of Time, Absolute or Relative Motion? and The Discovery of Dynamics.
• Martin Bojowald -- Has developed the application of loop quantum gravity to cosmology.
• Louis Crane -- Theorist.
• Rodolfo Gambini -- Author of Loops, Knots, Gauge Theories and Quantum Gravity.
• Brian Greene -- Physicist who is considered one of the world's foremost string theorists.
• Stephen Hawking -- Leading theoretical physicist.
• Peter Higgs -- Proposed the 1960's theory of broken symmetry in electroweak theory,
• Christopher Isham -- Theoretical physicist, main figure of the quantum gravity field.
• Ted Jacobson --
• Michio Kaku -- Theoretical physicist with significant contribution to the string field theory.
• Renate Loll --
• Fotini Markopoulou-Kalamara -- Theoretical physicist interested in foundational mathematics and quantum mechanics
• Roger Penrose -- Mathematical physicist. Invented the spin networks.
• Jorge Pullin -- Theoretical physicist.
• Carlo Rovelli -- One of the founders and major contributors to loop quantum gravity.
• Lee Smolin -- One of the founders and major contributors to loop quantum gravity.
• Andrew Strominger -- Theoretical physicist who works on string theory
• Thomas Thiemann -- Researcher.
• Edward Witten -- Mathematical physicist who does research in M-theory.

Related topics

• Centauro event
• String theory
• M-theory