I've seen it said in various places that a major reason people like string theory as a theory of quantum gravity is that it does a good job of matching our prejudices about how a quantum gravity theory ought to behave. For example, the area law for black holes has been demonstrated for some black holes, and the lack of an off-shell formalism seems to be related to the non-existence of any observable aside from the S-matrix.

I'm wondering:

  1. What are these prejudices?
  2. Where do they come from?
  3. In particular, which by-now-classic papers/books/reviews should I be reading if I want to learn more about them?

Note that I'm not looking for papers on string theory or whatever. I'm trying to understand what a generic high energy theorist might have thought about gravity circa-1983.

For the sake of this question, let's suppose that I have a PhD in theoretical physics, but focused mainly on computing structure functions, and that my knowledge of GR is essentially limited to what's in Wald.

[A Late Addendum: It's become clear that I didn't ask my question clearly. I've been lucky and gotten some excellent answers anyways. But-- just for the record -- what'd I'd been wondering is this: Which bits of the historical literature led us to our picture of how a 'generic' quantum gravity theory ought to behave? (This is the reason I brought up string theory in the original question. I have no desire to discuss its relative merits here. I only mentioned it because its relative popularity indicates that there are some criteria we think a theory of quantum gravity ought to satisfy.)

This is obviously a tricky question to answer, for several reasons: 1) there might not be such a thing as a generic quantum gravity theory, 2) more recent developments in theoretical physics have shaped our perspective on what's important, and 3) people writing early papers on the subject didn't necessarily know what was important.]

  • $\begingroup$ This probably should be community wiki... $\endgroup$
    – user1504
    Commented Oct 25, 2011 at 0:41
  • 2
    $\begingroup$ Personally, I am not so crazy about catch-all questions. There could be hundreds of good answers to this question, each with different flavours depending on the required level and background of the OP. Maybe there is a way to make the question more narrow and specific? $\endgroup$
    – user566
    Commented Oct 25, 2011 at 1:37
  • 1
    $\begingroup$ Alright, CW it is. Hope for some interesting answers. $\endgroup$
    – user566
    Commented Oct 25, 2011 at 3:06
  • 1
    $\begingroup$ "my knowledge of GR is essentially limited to what's in Wald." Modulo the fact that Wald was written after 1983, this could very well apply to most high-energy physicists at the time :) $\endgroup$ Commented Oct 25, 2011 at 16:52
  • 1
    $\begingroup$ A nice review of quantum gravity may be found in Claus Kiefer's Quantum Gravity, Third Edition; it covers the "classic" results, and ought to be read as a sort of "Annotated Bibliography++"... $\endgroup$ Commented Jan 13, 2013 at 21:22

6 Answers 6


I will try to answer the narrowest reading of this question: what expectations do we have of quantum gravity based on general principles, perhaps combined with semi-classical reasoning and other clues (regardless of history, which I’m not qualified to comment on). I'm not going to discuss in detail how this distinguishes string theory from other approaches to quantum gravity. Let me just express my personal opinion, which is that following only what we know with great confidence to be true, some of which is specified below, inevitably leads to string theory or something very much like it.

Also, since this is such a general question and an appropriate answer can be very long, I'll just write a short list off the top of my head for now and wait for things to focus a bit. I can edit my answer later as needed (if I have the time). For the same reason, and since looking for references is time consuming, please let me know which of these points you'd want to look into, and I'll add references as needed. I’m also not sure if your question is mainly historical, or is defined more by the content (which is the way I treated it, namely: what do we know of QG independent of specific approach) so correspondingly I am not sure which references you want.

Lorentz Invariance:

It is nearly impossible to break Lorentz invariance at short distances without getting large number of huge violations of any test of LI at observable energies. It is nearly impossible to write a consistent quantum theory with small violations of LI. Therefore, any theory of short distance physics has to be exactly LI. Luckily, this is a very stringent constraint, this by itself eliminates most of the approaches to QG out there, or many things you'd want to try if you didn't know better.

Non-Renormalizable theories are "effective":

GR is non-renormalizable when quantized around flat space (or any other smooth background). Though some miracles may sometime happen, by and large non-renormalizable theories indicate that the degrees of freedom and action you use at low energies are not "fundamental", they are effective description of short distance physics which may be radically different. To steal a slogan from Ted Jacobson (who used it in a different context), you don't quantize the metric for the same reason you don't quantize ocean waves.

Gauge "symmetries" are redundancies:

This is a more modern line of reasoning, it goes to what precisely in meant by the expression "quantum gravity." For many older approaches diffeomorhpism invariance is the defining feature, for example they will tell you that an operator algebra representing the diffeomorphism group defines a quantum gravity theory. In more modern approach gauge symmetry is more of a technical tool -- there can be many definitions of the same quantum theory utilizing different sets of gauge redundancies, and each such gauge redundancy is part of the language most appropriate for a specific classical limit of the theory. Defining QG by what redundancies it possesses seems besides the point - QG should be defined rather as any quantum theory which reduces to classical general relativity at long distance scales.

Background Independence and the problem of time:

Quantum theory needs some structures, for example a non-dynamical time, for its formulation. That can be done when fixing a background spacetime, but if you want spacetime to be fully dynamical, no such structure can be treated as fixed, and you are stuck. Holographic approaches to quantum gravity (like matrix theory or ads/cft) sidestep this issue by using auxiliary variables to define a background-independent quantum gravity theory. The key point that the structures defining the quantum theory are not identified as part of the resulting dynamical spacetime.

Holography vs. locality:

Following from black hole quantum mechanics, and from the fact that there are no local observables in the theory, it is clear that the maximal entropy you can fit in a spatial region scales like the surface area of that region, and not like the bulk volume. Any approach that quantizes a local field will get an entropy scaling like the volume; most of these degrees of freedom are unphysical -- they correspond to local excitations that pack lots of energy in small volume and therefore should correspond instead to black hole microstates. Any approach that insists on strict locality in the quantum theory will treat almost all excitations of the system in the wrong way.

This is also related to the non-existence of off-shell formulation you mention — the theory cannot be probed locally for very physical reasons. Any attempt to calculate these unphysical quantities (say, off-shell Green’s functions which are the basic observables in a local QFT) is bound to get you very confused.

Unitarity in black hole evaporation:

More recent and more tentative line of reasoning, which I am including only because it is so beautiful. This is a line of reasoning that leads to string theory, or something very much like it, as the only way to fully resolve (sometime in the future) the black hole information paradox. Look for one of the latest reviews by Samir Mathur on "fuzzballs" to see this very elegant line of reasoning.

  • $\begingroup$ Let me ask you this Moshe: are you really qualified to speak about, say, what LQG/spin-foams have to say on these topics? If you are, fine. But otherwise, I'd like to see some higher standards of intellectual rigour on TP.SE. Again, what I said to Lubos: we're all physicists here --- let's focus on the physics and leave the spitting at the door. $\endgroup$
    – genneth
    Commented Oct 25, 2011 at 23:52
  • 3
    $\begingroup$ After briefly expressing my personal opinion, clearly labeled as such, and which everyone is invited to distegard, I see only one parenthetical reference to any specific approach to QG. Everything else represents model-independent constraints on any approach to QG. Of course, some of these criteria don't reflect too well on some approaches (including for example, closed string field theory), but I was careful not to get into this kind of food fight. Since we are all physicists here, let me also say that the "argument from civility" is equally a distraction from a substantive discussion. $\endgroup$
    – user566
    Commented Oct 26, 2011 at 0:11
  • 3
    $\begingroup$ To respond directly to your question: LQG and the spin foam variant are attempts to canonically quantize gravity, using the Ashtekar variables as the fundamental degree of freedom. Certainly one of the "prejudices" the OP refers to is that directly quantizing Einstein gravity as a QFT (in whichever variables) is both hopeless and misguided, and that a quantum mechanical theory in which you don't have to do that, but still get gravity as part of the story, is a god sent. Pointing out many of the reasons for this attitude is a perfectly rigorous and on-point response to the question. $\endgroup$
    – user566
    Commented Oct 26, 2011 at 1:49
  • 3
    $\begingroup$ I truly don't see any part of my answer which even refers to LQG directly (not even indirectly, if you don't think of it as quantization of a classical theory), so I am puzzled by your comments. Besides that, I am also not precisely sure what the OP was asking about, and for what purpose. So for all these reasons, I am afraid I have lost interest in any further discussion. Maybe the lesson for the future is concentrating more on concrete and technical issues, and not get into unfocused discussions, which to be honest are not all that much fun. $\endgroup$
    – user566
    Commented Oct 26, 2011 at 7:34
  • 1
    $\begingroup$ I thought the OP was asking for quasi heuristic expectations that a theory of QG ought to conform too. Well thats one of them. Here are more: There are no global symmetries in such a theory and there are no local observables. References shouldn't be too hard to track down, especially since most of them are in the relevant textbooks.. Like Wald, Birrel and Davies the original papers by Wheeler etc $\endgroup$
    – Columbia
    Commented Oct 26, 2011 at 19:25

The only full-fledged, genuine quantum theory of gravity we have (and most likely, the only one that is possible for mathematical reasons) is string/M-theory so textbooks of string/M-theory represent the only canonical literature on quantum gravity that you may find as of 2011 and that is ready to be presented pedagogically to students as material they can further work with, see e.g. this list


Things that have been proposed as "alternative theories" can't really compete with string theory when it comes to the degree of rigor, strength of the connections with the previous established physics, and just simple pure internal consistency and the discouraging quality of canonical textbooks on these subjects is one of the simplest ways to see this fact.

In the same way, you can't really find any meaningful pre-1983 textbooks on quantum gravity, either, because this discipline wasn't understood, almost at all. Right before 1983, people working on the most similar kind of physics (except for 5 string theorists) would do research in supergravity which is really just a field theory generalizing Einstein's general relativity, adding extra fermionic fields and a fermionic symmetry (local supersymmetry) but it's a field theory. Most of the calculations they did were classical, just like in classical GR, and the attempted quantum calculations using the tools of quantum field theory were seen to lead to a divergent short-distance behavior. That changed in 1984 when superstring theory was shown to be free of anomalies and UV problems while it was capable of producing all the right classes of physical phenomena known from supergravity and gauge theories coupled to matter.

While the theories – quantum gravity and string theory – almost certainly have to be the same thing, the two names are used differently. "Quantum gravity" is reserved for the research of questions that can only be asked or that only become hard if the physical system respects both the postulates of quantum mechanics as well as those of general relativity (gravity). They're the questions of the type "how do the postulates or effects of quantum mechanics influence one or another situation where the curved geometry plays a key role?".

Some of these questions are answered by string/M-theory in its current state; some of these questions were approximately answered even by QFT tools before string theory; some of these questions remain open.

For example, the Wheeler-DeWitt equation (together with its various solutions such as the Hartle-Hawking state) mostly belongs to the third category (the things not yet established). It's the equation $H\Psi=0$, expressing the idea that the Hamiltonian constraint in GR actually encodes the full evolution in time, something that is possible due to the ambiguous meaning of the word "time" in diffeomorphism-symmetric theories. To solve it, one must first define his own time, by linking it to some coordinate-independent evolving quantity, and so on.

Partial arguments why this equation should be true exist, much like some approximate demonstrations how it could work in truncated schemes. However, at the end, this equation should only be applied to the Hilbert space of a full working theory of gravity. At this moment, and most likely not only at this moment, string/M-theory is the only theory that satisfies this condition. Unfortunately, the understanding of the Wheeler-DeWitt equation, if one exists, at the level of string theory is highly incomplete, to put it euphemistically. In fact, the equation itself is unnatural because the diffeomorphism symmetry is just one among infinitely many similar symmetries and the Hamiltonian linked to it is just one of many operators that should be treated on equal footing if they are treated at all. So it's questionable whether the Wheeler-DeWitt equation will ever tell us something new again or whether it has been superseded. Maybe, it should be replaced by some more complex structure we don't know.

Before 1983, the Wheeler-DeWitt equation was as confusing as today and our knowledge about it boils down to one or a few papers, most of which remain confusing. This has never been a stuff ready to be printed in textbooks and taught to students. It's a speculative suggestive work in progress that doesn't have to lead anywhere.

The Hawking (black hole) radiation is sometimes included into quantum gravity but Hawking's original calculation was done within effective quantum field theory, really ordinary non-gravitating quantum field theory on a curved background. So strictly speaking, it shouldn't really be considered a part of quantum gravity. In this way, he could have derived the black hole temperature. Indirectly via thermodynamics, this also implies that black holes should have an entropy and many microstates. Why they possess the required entropy had been a mystery through the mid 1990s when the entropy was microscopically computed in string theory – for the first black hole and then for dozens of others (lots of multi-parameter supersymmetric black holes, near-supersymmetric i.e. near-extremal black holes, and some completely non-supersymmetric black holes in which the stringy "tricks" may be applied as well). Aside from consistent and convergent formulae for graviton scattering amplitudes, this became a huge piece of new evidence that string theory is a consistent theory of quantum gravity and it remains the only theory that is able to solve either of these problems.

It's not true that all questions surrounding the information loss paradox have been resolved. While we know that the information isn't lost after all, the non-local processes that (as we know indirectly) surely take place in string theory are not well-understood. How far they operate? Why? How much can they change at all? Could they become observable in non-black-hole experiments? And so on. These questions remain mostly open.

A special part of quantum gravity is quantum cosmology. Here, we're not really talking about the common description of inflation that is needed to explain the cosmic microwave background; the latter is, once again, governed by quantum field theory on fixed curved backgrounds and shouldn't really be included in quantum gravity per se. Most of it remains inconclusive within string theory – even though people have already taken their fast interpretations what important processes happen when they talk about the multiverse etc. – and once again, it is not addressed by other approaches at all.

There are some other partial questions of quantum gravity that have been understood such as the changing effective dimensionality or topology of spacetime and so on (those things are allowed, do occur, and sometimes they are under complete calculational control). All these things have mostly been clarified by string theory. If you summarize the successes and failures of string theory as a tool to answer general questions about quantum gravity, the situations (including singularities) that are close enough to static ones (where supersymmetry may be preserved etc.) are well-understood in string theory; the heavily time-dependent situations such as the Schwarzschild singularity or the very initial point of the Big Bang are (mostly) not understood. But let me return to the original questions.

Prejudices vs insights

The word "prejudices" is clearly emotionally loaded. Such emotional labels don't belong to the realms of science that investigate totally plausible – and in fact, given the quantitative evidence, very likely – statements. I think that "insights" would be far more accurate but let's call them "general propositions" to be impartial.

String theory's general framework that quantum gravity should belong to is closer to the intuition of particle physicists who have worked with relativistic quantum field theories for decades before they were superseded by string theory. Even though string theory is no longer a local quantum field theory in spacetime, it still broadly agrees with some general propositions about quantum gravity, including

  1. the dynamics has to be locally (at very short distances) invariant under the Lorentz or Poincaré groups, otherwise we would inevitably end up with contradictions with successful tests of special relativity even in the context of doable, long-distance experiments

  2. the metric tensor field is another field in an effective field theory, a degree of freedom; it is fluctuating (in the quantum mechanical sense) which is why some unlikely effects (like information tunneling at the end, against the naive classical causality, see the last point) may be possible

  3. the metric tensor has its particle-like excitations, the gravitons, whose existence (waves that solve Einstein's equations, the effective classical low-energy equations) and energy quantization (due to the periodicity of the wave function in time) may be deduced in a full analogy with the photons, independently of string theory

  4. a related point is that the Hilbert space is naturally organized in terms of multi-particle states which may be created, in the long-distance limit, by Fourier-transformed linearized fields; perturbative expansions of the calculations should be possible (and are possible in string theory) and in the stringy context, they implicitly include linearized general relativity (which is just a tool to approach calculations, not any "violation" of any sacred principles, and one that is pretty much necessary to talk about particle scattering in any field-like theory at all)

  5. the diffeomorphism symmetry acts on the spacetime coordinates but it's just a technical difference from the Yang-Mills gauge symmetries; in principle, both of them play the same role and in fact, they may be shown to unify in string theory or at least in some vacua (e.g. in the Kaluza-Klein way: but in a broader sense, string theory always unifies all particle species and all forces)

  6. scattering amplitudes for the gravitons (and other particles) must be calculable (and the calculations must be anomaly-free, convergent etc.) because the scattering experiment may be done whenever the spacetime has a non-empty particle spectrum and an infinite, solvable asymptotic region (the flat space and the AdS space are typical examples)

  7. local off-shell Green's functions that depend on $x^\mu_1, x^\mu_2$ etc. can't be defined in manifestly Lorentz-invariant descriptions of quantum gravity because the association of the coordinates $x^\mu_i$ with physical spacetime points is ambiguous due to the diffeomorphism symmetry; that's why these Green's functions wouldn't be gauge-invariant and why a consistent theory should only be able to produce the on-shell scattering amplitudes, unless we gauge-fix the gauge symmetry which is inevitably breaking the manifest Lorentz covariance (e.g. by using the light cone gauge)

  8. the evolution should be unitary so the information shouldn't get lost even in the presence of evaporating black holes; the superficially inevitable proofs of information loss were shown to have loopholes and pretty much every professional physicist thinks that the conservation of the information has been shown to hold

Most of these propositions were really just guesses prevailing among particle physicists at the beginning (so they were never "codified" by textbooks) but have become pretty much indisputable (in some of them, I attempted to sketch the relevant proof in the very description) because of contemporary research and indeed, all known proposed "alternatives" to string/M-theory violate at least one of them or most of them.

The alternative attempts to construct a quantum theory of gravity generally start from the "classical general relativity" culture, taking the causal structure of spacetime completely seriously even though it should be a fluctuating quantum variable in any theory of quantum gravity. So these approaches want to "quantize" the classical starting point in a new way. A priori, this could look like an equally sensible and promising attempt. However, when one actually does the research, the symmetry evaporates: there doesn't exist any "reliable" or "systematic" way to obtain a consistent quantum theory from any classical theory; the relationship goes in the opposite direction only: quantum theories usually have classical limits.

In the particular case of gravity, all attempts to find a quantum version of the theory in a straightforward way immediately lead to highly discouraging results. One either runs into the usual problems of non-renormalizability when he tries to follow the methods of quantization from quantum field theory; or, when one tries to introduce some discreteness etc. by hand, one ends up with theories that violate the local Lorentz symmetry and most likely don't admit any "nearly flat" solutions at all. The infinite collection of undetermined non-renormalizable operators is just translated to completely equivalent pathologies and ambiguities in any discrete picture as well.

Aside from these general lethal problems, none of those theories could have ever addressed any of the serious "theory-independent" problems of quantum gravity such as the information loss paradox; the fate of the black hole singularities, Big Bang singularity, and the Big Crunch, and many others. Whenever one wants to address any of these issues, he has to add new arbitrary assumptions to the theory (the word "theory" therefore isn't really legitimate because this set of guesses doesn't really allow one to learn anything about anything). So the things that have been said and calculated about the alternative "theories" mostly remain a superficially quantitatively looking, but otherwise completely ill-defined, set of structures used as an excuse for the people who want to say that they're quantum gravity physicists but who don't want to learn string theory even though it covers a vast majority of the substantiated insights we know about quantum gravity today.

  • 6
    $\begingroup$ A typical Lubos answer, starting by completely disparaging other lines of research. The meat of the answer is fine, but the social commentary is not. I think physics.SE suffered enough of the pointless rhetoric, so I would like to see TP.SE kept "cleaner" and to a much higher standard. String theory is not the only research line in town, and comments to that effect are bordering on libellous. $\endgroup$
    – genneth
    Commented Oct 25, 2011 at 9:49
  • 7
    $\begingroup$ Dear Genneth, string theory is the only textbook-ready theory of quantum gravity on the market – now as well as at any point in the history of quantum gravity – and this is pretty much the core of the question that was asked, indeed. Physics.SE has suffered a lot from ignorant people who try to spread their opinion which was one of the reasons why a new server with higher standards, protected against unsubstantiated and unjustifiable comments such as yours, became necessary. $\endgroup$ Commented Oct 25, 2011 at 11:35
  • 4
    $\begingroup$ Lubos, I'm strongly tempted to downvote your response. I was asking for references to the early literature, and -- despite writing some 2000 words -- you didn't mention even one. $\endgroup$
    – user1504
    Commented Oct 25, 2011 at 12:11
  • 1
    $\begingroup$ @LubošMotl: your dogmatic view that string theory is the only game is town is (I hope) well-known. But it doesn't hold up to any kind of scrutiny (citebase provides a lower bound). I don't mind the content, but why have the unnecessary comments about sociology? We are all practising physicists here (I hope) so we can all use our critical thinking to evaluate theories when presented with the work. $\endgroup$
    – genneth
    Commented Oct 25, 2011 at 14:52
  • 5
    $\begingroup$ FWIW, this contains lots of ingredients for a good answer. The question is a bit unfocused (which is one reason I find it hard to formulate an answer myself), but in one reading one is asked how string theory improves on older approaches to QG. I think the sharp distinction to other (=older, because all other approaches are in fact older) is that string theory does not treat the metric as a quantum variable, rather it is something that emerges in the classical limit of the theory. Lots of the detail on how that improves the situation are in this answer. $\endgroup$
    – user566
    Commented Oct 25, 2011 at 16:27

I feel I can add a little. Most of the serious "prejudices" (I don't think this is a fair description--- these are not prejudices at all, these are solid physical arguments, along the lines of Bohr's pre-quantum correspondence principle arguments, and are validated by their correctness in string theory) come from 1976 Hawking evaporation discovery, and are probably best found in the 1979 Einstein centenary conference proceedings, when people were very excited about Hawking radiation. If you read this, you will come up with all the conditions yourself without any further prompting, this stuff was in the air.

Before Hawking, people just expected that there would be a quantum version of Einstein Hilbert action with spin-2 gravitons interacting with a stress tensor. They really couldn't say much more. One expected a Hamiltonian formulation along the lines suggested by Wheeler-DeWitt, and some sort of small-distance magic to fix non-renormalizability. The demonstration of Hawking radiation changed everything, because you have for the first time solid physics that guides you in making a theory of quantum gravity, a real understanding that black holes are special thermodynamic things.

These guiding principles can be summarized as a series of folklore thought experiments:

  • No global symmetries: black holes evaporate, so throw neutrons in a black hole, you'll get photons out. So Baryon number is not conserved. This is folklore, you won't find it in a paper, the argument was too simple to publish.
  • No tiny couplings: every process not protected by gauge symmetry is violated by black holes, so there is a nonzero amplitude for any process, due to virtual black holes, and generic terms of size only suppressed by renormalizability considerations.
  • Black holes are the same as white holes: since thermodynamic states are time-reversal invariant (or CPT invariant if you like). This is an extraordinarily unlikely equivalence considering the complete difference of the Penrose diagram of the two, and suggests holography and complementarity strongly. This argument is made by Hawking in the late 1970s.
  • Monopoles: Quantum gravity requires magnetic monopoles, since you can solve the Einstein/Maxwell equations and find a magentically charged black hole. While classically, you wouldn't form this in the absence of magnetically charged particles, quantumly, you expect pairs of oppositely magnetically charged black holes to form from the vacuum when there is a constant magnetic field over a long enough region (just like electron positron pairs spotaneously appearing in the Schwinger effect). So you expect magnetic charges in quantum gravity.
  • Black holes can break in two: again, forbidden classically, but quantum mechanically required, since a black hole can emit another smaller black hole in the Hawking radiation. So if you stretch a horizon enough, like if you apply a strong magnetic field, it will snap. The snapping in this case will produce oppositely magnetically charged black holes.
  • There exists an asymptotically approximately degenerate fermionic/bosonic black hole spectrum: a black hole of large area can absorb a fermion and turn fermionic (throw in a slow neutrino) without hardly any change in area. This means the fermionic and bosonic black hole states are nearly degenerate. Further, the fermionicity travels along the black hole surface as fermions enter and are emitted, just as they travel along a world-sheet. So the fermionicity should be associated to a fermionic current of some kind. This strongly suggests that if there are fermions in the universe, large black holes should carry a supercurrent. This argument is not in the literature either, but it suggests you want a SUSY theory at high energies for the black hole spectrum, and this is validated by Ramond's construction for fermionic strings, which required a supercurrent on the world-sheet.
  • No infinite renormalization: This is based on the fact that a mass renormalization in gravity can't blow up because at some point gravity provides a negative attractive contribution that always smoothes out the blow up, because gravitational attraction dominates at ultra-short distances. The proper way to say it (with hindsight) is that a small particle in a gravity theory is always some sort of spatially extended black hole, and there are no pointlike blowups. This is related to...
  • Infrared/ultraviolet duality: you expect that high energies at some point become long-distance physics, because a high-energy collision makes a big floppy black hole.

In addition to these thought experiments and physical principles, there was the following legacy of the 1960s:

  • The S-matrix should be the only observable in flat space: this was mentioned in other answers, but it was directly coming from the 1960s push for a pure S-matrix physics, expanded in the 1970s to the gravitational domain. This is not emphasized by the GR people. It is appreciated by Witten.

The path integral for gravity was giving uncomfortable things too:

  • There is a mode of the gravity path integral which doesn't get regulated in imaginary time. This mode corresponds to the overall conformal factor in the metric. Coleman uses this to argue that the CC vanishes, but the argument is not very persuasive. It is easier to just say the path integral for gravity doesn't make sense.
  • Penrose (I think) argues that the path-integral for gravity is summing over all 4-manifolds, and this is an uncomputable summation, since there is no classication of 4-dimensional first homotopy groups (the fundamental group can encode any generators with any relations, something which was known to be equivalent to Turing computation). So summing over topologies can't happen in quantum gravity.

In addition to these things, there were several extremely uncomfortable results due to Witten that serve as a prelude to the 1984 string revolution.

  • Witten argues that the sum over topologies is not necessary because you can't make topology in topology/anti-topology pairs! Handles don't have anti-handles. But this restriction means that we fundamentally don't have any idea how to do the quantum gravity sum--- what do you sum over? You can't sum over glued flat-looking pieces (like glued simplices), since the gluing will reproduce all the topologies, and you need to quotient by diffeomorphism equivalence.
  • Gravitational instantons wreck KK compactification: Witten in a famous paper shows that there is an instanton that renders the KK circle vacuum unstable. This paper is unsettling in a much broader context than KK theory--- the type of instability is not something you would notice from the Hamiltonian for small perturbations--- it really a global screw up. So you start worrying that the formulation of quantum gravity is just completely off, because how would you know the Hamiltonian is bounded below? The positive mass theorem still holds in circle KK, the initial vacuum is flat, yet here is an instability you would never guess in a million years. This makes you worry again that you have no clue about something as simple as vacuum stability.
  • No chiral fermions in SUGRA compactification: Witten was very much for the 11 dimensional SUGRA, since this was an elegant unique thing that existed by a miracle. But then he shows that compactification on manifolds doesn't make chiral fermions. So how the heck can you get the standard model out? This is very unsettling. It suggests that we need some new structures to determine the nature of a higher dimensional theory, beyond SUSY.

You have the tremendous pressure of a small but growing group of people, who keep insisting that strings make sense. There are also hints of Montonen Olive electric/magnetic duality emerging, which is something you only expect to come out of something consistent with gravity, and SUSY theories have strange relationships which are only clear if you think of them as reductions of 10 dimensional N=1 SUSY gauge theory. The 1981 superstring breakthrough (the major breakthrough, the Green-Schwarz action) made it clear that spacetime SUSY was present in the GSO projected strings, and this means that the theory's vacuum is fine. You can't destabilize a SUSY vacuum by any sort of gravitational instanton. Further, the theory comes from a pure S-matrix theory, so it obeys one of the prejudices automatically.

Then Witten and Alvarez-Gomez do gravitational anomalies, and Schwarz and Green respond by showing the cancellation mechanism, and Witten learns string theory. Once he does this, he sees that all the problems are solved. No anomalies, no fields (so no path integral, and no diverging modes), an elegant infrared ultraviolet duality that makes finiteness almost manifest.

Further, in string theory, there are no global symmetries, since a global symmetry comes with a massless gauge field automatically (the symmetry acting on the string action produces the vertex operator for the gauge boson). The emergence of gravity is very elegant, through the Yoneya argument (also described by Schwarz and Scherk, although less elegantly), since it's the same argument for the space-time symmetry. So the theory incorporates gravity naturally.

But this is not all the prejudices. The black hole prejudices weren't shown to work in strings until the 1990s. This is after t'Hooft (who isn't thinking directly about strings) formulates holography, and argues that black holes are described by a string-like action, and Susskind formulates black-hole complementarity, and notices that this resolves the information paradox.

AdS/CFT is the final nail in the coffin for alternative theories, because it shows that strings obey holography, and also it shows what kind of insanity it is to obey holography--- the duality requirements are that the theory of oscillations of any extremal black hole in the theory must reproduce the same stuff as any other extremal black holes. This is so ridiculous, it would be the basis of a no-go theorem if strings didn't show that it was possible.


Perhaps a good idea of what at least part of the community trying to quantise gravity was up to prior to 1984 can be gleaned from the Supergravity Physics Reports by Peter van Nieuwenhuizen. Some of the excitement about the two-loop finiteness of certain supergravity theories (in 4 dimensions) is still palpable from the report and in particular the question of the finiteness of $N=8$ supergravity is mentioned, a topic which is still very much alive today. Of course, these are really quantum field theories of gravitons (and cousins), but that was at the time at least a valid approach towards a quantum theory of gravity.

  • $\begingroup$ Dear José, of course, in the late 1970s and early 1980s, this was the branch of physicists closest to e.g. string theorists today - later absorbed by the string/M-community. However, I wouldn't say that their research was really a part of "quantum gravity". They studied it because they were excited by supersymmetry and wanted to apply it to GR as well. At those times, it only gradually became well-known that quantized GR suffers from the 2-loop non-renormalizable problems which energized the SUGRA research but wasn't really ever the deciding issue. SUGRA folks never studied quantum foam etc. $\endgroup$ Commented Oct 25, 2011 at 12:13
  • $\begingroup$ Dear Luboš, I agree that perhaps this is not what we now would call 'quantum gravity', but I think that if you had asked them at the time, they really were thinking of quantising gravity by standard QFT techniques. The supergravity crowd were the same people who in the early 1970s were computing one- and two-loop graviton-graviton scattering. $\endgroup$ Commented Oct 25, 2011 at 13:44
  • $\begingroup$ I agree, @José. Dan Freedman was telling me about those approaches in those time. QFT techniques were simply believed, kind of naively. $\endgroup$ Commented Oct 25, 2011 at 19:11
  • $\begingroup$ Well, it is good as the OP was asking for the hep-th community, not the gr-qc. But some hints about the later could make a more complete answer. $\endgroup$
    – user135
    Commented Oct 26, 2011 at 0:37
  • $\begingroup$ Alas, I have no idea what the gr-qc community was up to before 1984 :( $\endgroup$ Commented Oct 26, 2011 at 10:11

In 1983 a "generic high energy theorist" would have known that superstring theory could describe quantum gravity. However, they could have thought superstring theory was anomalous or they could have thought it was not anomalous. The Green–Schwarz mechanism, the anomaly cancellation mechanism in type I superstring theory with the gauge group SO(32), was discovered in 1984.

In 1983 a "generic high energy theorist" could have thought quantum gravity based on general relativity was perturbatively renormalizable or they could have thought is was not perturbatively renormalizable. Quantum gravity based on general relativity was proven to be perturbatively non-renormalizable by Goroff and Sagnotti in 1985.

In 1983 a "generic high energy theorist" could have thought supergravity with N supersymmetries in D dimensions was perturbatively renormalizable or they could have thought is was not perturbatively renormalizable. As far as I know, this is still not settled for some N and some D. See for example Green.

In 1983 a "generic high energy theorist" would have known nothing about Ashtekar variables and thus Loop quantum gravity, and all related formalisms, as Ashtekar variables were discovered by Ashtekar in 1986.

As you can see, the "modern" picture of quantum gravity only started to emerge around 1986. In 1983 a "generic high energy theorist" could have believed almost anything about quantum gravity.

Oh, a good, but old, review of pre 1983 views of quantum gravity is Ashtekar and Geroch written way back in 1974!

  • 1
    $\begingroup$ Also, a GHET in 1983 could be interested on supergravity only because of the turmoil caused by Witten 1981 "Search for a realistic Kaluza-Klein theory". For instance A. Salam got very interested and a good bunch of his team was mobilized to study this particular subtopic. $\endgroup$
    – user135
    Commented Oct 28, 2011 at 17:15
  • $\begingroup$ And a personal thinking: a hep-th theorist could be more inclined towards strings for gravity that a gr-qc one, because the later are used to think of Riemann tensor as a [set of] bidimensional object[s], so to them it is not so surprising that a 1+1 worldsheet can feel gravity. My guess is that Gr-Qc practicioners probably felt initially that strings were just a very convolved way to measure curvature. $\endgroup$
    – user135
    Commented Oct 28, 2011 at 17:21
  • 1
    $\begingroup$ I don't think this is correct--- the anomaly cancellation paper was not that important in convincing people strings were viable. If the known type I strings were anomalous, you would have just stuck to type II (and eventually discovered type I through branes). The main purpose of anomaly cancellation was that it was Schwarz vs. Witten, and Witten liked Schwarz's calculation better than his own, and jumped ship. People on the east coast then felt comfortable openly studying strings. It's mostly politics, not science (although the Green-Schwarz mechanism is lovely science). $\endgroup$
    – Ron Maimon
    Commented May 29, 2012 at 4:36

One reference is the 1986 paper by Syracuse U. and UC Santa Barbara researcher A. Ashtekar

Ashtekar, A. New Variables for Classical and Quantum Gravity. Phys. Rev. Lett. 57 no. 18, 2244–2247 (1986). doi:10.1103/PhysRevLett.57.2244. Free version at weylmann.com.

This paper marks the start of a new orientation in Quantum Gravity, so perhaps you could want to set the milestone here.

Anyway, FIND DK QUANTUM GRAVITY AND TOPCITE 500+ AND DATE BEFORE 1985 gives only ten papers. And three of them are actually "Quantum Theory of Gravity", by Bryce S. DeWitt, in 1967.

  • $\begingroup$ Upvoted for the Spires search. Those papers were exactly the sort of thing I was looking for. The Ashtekar paper is a 4 page PRL, and consequently says next to nothing about the history. $\endgroup$
    – user1504
    Commented Oct 26, 2011 at 1:33
  • $\begingroup$ @user388027, the prejudices you ask about are an outcome of early attempts to quantize gravity, they are unlikely to be discussed as part of these early attempts. I think one of my problems of figuring out what you are asking for precisely is that your point 1+2 are not the same, and in fact contradict point 3. Are you asking about early attempts to quantize gravity, or are you asking which expected features of quantum gravity resonate best with string theory? those are two separate questions. $\endgroup$
    – user566
    Commented Oct 26, 2011 at 3:49
  • $\begingroup$ BTW, thanks to the anon user who edited the spires link to do it clickable :-D $\endgroup$
    – user135
    Commented Oct 26, 2011 at 12:24
  • 2
    $\begingroup$ Ok, but common lore like the one I tried to specify in my answer, will not have been explicitly written anywhere at that time. Anyhow, in my mind, the Dewitt papers were the most influential ones, not a bad place to start. $\endgroup$
    – user566
    Commented Oct 26, 2011 at 15:04
  • 1
    $\begingroup$ Upvoted because arivero's answer supplies concrete citations. I'd like to commend also Ashtekar's work with Troy Schilling on non-relativistic non-Hilbert quantum dynamical state-spaces (arXiv:gr-qc/9706069v1). $\endgroup$
    – John Sidles
    Commented Oct 26, 2011 at 18:44

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.