Classical gravity, Supergravity and strings

In summary: The equivalence principle is not a law of nature, but an empirical statement that has been verified many times.b) There is no 'correct' way to quantize gravity, as all such quantizations are consistent with the equivalence principle.2) Supersymmetry preceded string theory, if my recollection is right, and has been pursued independently of string theory.3) Thus one could posit that a research program aiming to be more in touch with experiment would look for ways choose a preferred SUSY extension to SM that had appropriate dark matter candidates, and perhaps combined with effective quantized gravity explained dark energy.
  • #1
Haelfix
Science Advisor
1,964
233
So the following questions were posed in an another thread by Pallen, and I thought i'd give an attempt at answering them, since they tend to show up over and over again.

"
1) It is not clear that GR and QFT must be considered in conflict that must be resolved somehow. I've seen a growing number of papers arguing several related points:

a) The need for quantum gravity at all should be considered subject
experimental verification. Maybe some form of QFT in curved
space is a valid model.

b) Progress in quantizing GR as an effective field theory
least raises the question of whether the conflict is as deep or
needful of whole new frameworks.

2) Supersymmetry preceded string theory, if my recollection is right, and has been pursued independently of string theory.

3) Thus one could posit that a research program aiming to be more in touch with experiment would look for ways choose a preferred SUSY extension to SM that had appropriate dark matter candidates, and perhaps combined with effective quantized gravity explained dark energy. "
 
Physics news on Phys.org
  • #2
I will try to go through these, one at a time. Keep in mind, I am not a quantum gravity theorist, so I do feel somewhat underqualified to answer. Otoh I think I know the arguments well enough by now to make people at least consider the motivations (the exact and more precise statements may be found in the literature or in textbooks).

A) Why Quantum gravity at all? Well several reasons. The first is that classical GR containts certain types of singularities. Some of them are coordinate artifacts, but some of them are lethal. IN particular, if you read Hawking and Ellis, you will note that our own FRW dust universe possesses one of these (see eg chapter 10, for the proof of the existence of a closed trapped surface under minimal assumptions about the nature of the primordial radiation fields)

The second is that at the very least, *some* if not all matter must be quantized. In particular, all the matter that we have ever measured in a lab so far (eg the standard model). Thus you need to consider a very formal object or at least a part of a very formal object.. Namely, the expectation value of the stress energy tensor < Tuv >. This is no longer just a pseudotensor, but the expectation value of a full quantum operator.

So if you want to keep gravity classical, you are left with a very weird statement:
Ruv - 1/2 Guv R + Guv lambda = < Tuv >

Now, the left hand side is a statement involving differential geometry quantities, (eg smoothly varying classical quantities) and this is supposed to be equal to a quantum mechanical object that is highly nondifferentiable. The instant observation is that this cannot possibly work. Einstein's equations are manifestly nonlinear in the metric guv. If you solve for the time evolution of the matter system, by solving Einsteins field equations you will immediately notice that the Hamiltonian is no longer given by a Hermitian operator (indeed not even a linear operator) and is not even bounded from below. This is therefore a theoretical inconsistency as the system violates a primary postulate of quantum mechanics.

The immediate conclusion is that the geometry must also be quantized. Classical gravity is not compatible with quantum mechanics!
 
  • #3
Now that we have determined that classical gravity with quantized matter is inconsistent, we are led to quantum gravity, including the quantization of the metric. I'll leave the lengthy details for a text like Birrel and Davies or Wald, but suffice it to say you can kind of do this. The problem is that it is a technically challenging and mathematically difficult subject. Again, I highly recommend any and all to read the first 10 pages of B&D if you are serious about quantum gravity. It is subtle but necessary information to even begin to tackle this subject seriously.

In fact, it should IMO be *REQUIRED* reading to even be allowed to post on this board as anyone posting about strings, SUGRA or loops or any quantum gravity proposal who hasn't mastered this material, is in quite literally over there heads. Seriously, nothing makes sense if you haven't mastered the basics first, you simply cannot avoid it.

Anyway its important to note the following about these 'semiclassical' solutions:

1) The equivalence principle states that all forms of matter and energy must couple equally strongly to gravity, including gravitational self energy. Said another way, a graviton will feel gravity just as strongly as say a photon would. Likewise, the quantum vacuum can just as easily spit out a graviton as it can a photon. In other words, you have to consider everything at once and you can never find a limit where various quantities decouple smoothly. Said yet another way, the nonlinearity of gravity frustrates all attempts to ignore quantum gravity. This is of course nasty, b/c in principle we don't know what the lagrangian for all matter is, as well as being forced to consider the full backreaction of all metric variations onto itself.

Still, we can perform a trick. The trick is to take the small linearized graviton contribution and pull it into the matter source term. This is similar in spirit to looking at photon emmision from a background object (like an atom) immersed in a rapidly changing relativistic electric or magnetic field. This kind of works, so long as one keeps the backreaction small and controlled.

2) The effective field theory of quantum gravity requires an expansion around a small parameter in order to have a valid perturbative setup, as well as to keep the aforementioned backreaction small and under control. The only such number available is given by dimensional analysis and is epsilon = E^2/Mpl^2. Expansion around this quantity is well defined, so long as an energy or length scale is chosen that forces it to be smaller than unity. Unfortunately, once it is larger, the system becomes strongly coupled and the approximation breaks down.

3) Note that the nonrenormalizability of gravity is in force ('G' has units of length and is thus by powercounting nonrenormalizable) and you will find dangerous divergences for even pure gravity appearing at 2 loops. Consequently, you must truncate the series at one loop and throw out all the higher order terms (terms that involve R^3, R^4 and so forth). Thus you have a finite theory with a finite amount of couplings, that is perfectly predictive but also incomplete (technically you have a renormalization of G, a renormalization of the cosmological constant, as well as two additional couplings from new geometrical tensors).. As described, it makes no sense at very high energies (even approximately), but suffices for many intermediate regimes (such as questions about the nature of black hole radiation, simple graviton exchange diagrams, or even inflation). However, it is most assuredly not going to help you much when you get too close to a black hole singularity, or alternatively for questions about the very early universe. Right there, the full strong coupling behavior is necessary and the infinite set of couplings that you threw out (both matter and gravitational), comes back to bite you as they require an infinite amount of experiments to pin down.

Long story short, you are left with one of only two possibilities for what the tentative full high energy theory can be. Either the original theory is UV completed, where new degrees of freedom emerge, or alternatively there is a nontrivial fixed point (asymptotic safety). There is no other consistent alternative that also retains a measure of predictivity.

Now, there are a number of good arguments against even this, and in fact you can make an argument that whatever the UV completion is, it cannot be a local field theory (this arises from arguments centered around the black hole information loss paradox, see eg hep-th/0605196 for a partial review). In any event, the additional problem posed by the existence of black holes, is that we have apparently lost unitarity. Therefore the correct high energy theory must also unitarize the semiclassical physics somehow. No one has ever found a way how to do this in full generality although of course it is expected that holography is necessary (likely implying the need for stringy states)
 
  • #4
3) Supergravity. Why bother with strings, when we have a good theory of supergravity?

Well, historically this is basically what everyone doing quantum gravity believed in during the late 70s and early 80s. It was known that supersymmetry was the most logical, minimal and obvious solution to the hierarchy problem. Therefore there had to be a theory of supergravity, since gravity also exists! =)

The excitement really started when it was noticed that a lot of the bad divergences of regular gravity could be canceled by the extra supersymmetry. In particular, extended supersymmetry could *maybe* make the whole thing finite! Also there were very interesting Kaluza-Klein reductions between extended supergravities in different dimensions that could also explain part of the group structure of the standard model. People really expected that compactifying the maximal supergravity solution down to N=8 d=4 would constitute the first theory of everything. There were of course difficulties. Like for instance the lack of a viable chiral phenomenology, and just as seriously: uncancelled gauge anomalies.

Nowdays, I think the only remaining possibility that stands by itself is just the minimal N=1, D=4 supergravity (mSugra), which of course still has the aforementioned nonrenormalizability problem and the need for a suitable UV completion.

The problem is that we now know that many of these theories are in some ways, just limits of string theory in disguise. That in order to render them internally consistent (either phenomenologically or theoretically), you have to add structure to them and essentially perform the same set of operations that string theorists do with their own constructions. Further, and most importantly that it is extremely difficult to 'decouple them' mathematically from string theory.

Lubos wrote an interesting article about this here:
http://motls.blogspot.com/2008/07/two-roads-from-n8-sugra-to-string.html
 
  • #5
Haelfix said:
So the following questions were posed in an another thread by Pallen, and I thought i'd give an attempt at answering them, since they tend to show up over and over again.

...

2) Supersymmetry preceded string theory, if my recollection is right, and has been pursued independently of string theory.

3) Thus one could posit that a research program aiming to be more in touch with experiment would look for ways choose a preferred SUSY extension to SM that had appropriate dark matter candidates, and perhaps combined with effective quantized gravity explained dark energy. "

I can add my 2cents for these.

I agree on 2), there is not such a deep relationship between string theory and supersymmetry as it is often claimed.

As for 3), this reseach program exists and is usually called "Beyond the Standard Model Phenomenology". I think (based on experience at a large institution, ie from job applications) that at least as many people work in this field as in strings. Thus there is no shortage in research on these matters. Typically this research is more speculative and less based on firm grounds than strings, it tries to be more close to experiments but doesn't care much about conceptual and foundational issues, it is rather of the "everything goes" style.
 
  • #6
Very good and useful review, thanks for posting this. However, in my more radical moments, I'm not completely sold on the idea of the need for a quantization of gravity, due to holding out some hope for 'emergent gravity'-theories in the vein of Sakharov or Jacobson/Verlinde... That's just personal prejudice, however.
 

1. What is classical gravity and how does it differ from quantum gravity?

Classical gravity refers to the laws of physics that describe the behavior of large-scale objects, such as planets and galaxies, under the influence of gravity. It is based on Isaac Newton's theory of gravity and Albert Einstein's theory of general relativity. On the other hand, quantum gravity attempts to unify the laws of gravity with the principles of quantum mechanics to explain the behavior of subatomic particles. While classical gravity is well understood and has been extensively tested, quantum gravity is still a subject of ongoing research and has yet to be fully understood.

2. What is supergravity and how does it relate to classical gravity?

Supergravity is a theory that combines the principles of supersymmetry and general relativity to describe the behavior of gravity at both the classical and quantum level. It extends the classical theory of gravity by introducing additional dimensions and new particles called superpartners. Supergravity plays an important role in string theory, which is a theoretical framework that attempts to reconcile general relativity with quantum mechanics.

3. What is the relationship between supergravity and string theory?

Supergravity and string theory are closely related. Supergravity can be seen as a low-energy approximation of string theory, which means that it is valid in certain limits of string theory. Supergravity also provides a framework for studying the properties of strings in a curved spacetime, which is necessary for understanding the behavior of strings in the presence of gravity.

4. What are strings and how do they differ from traditional particles?

Strings are one-dimensional objects that are theorized to be the fundamental building blocks of the universe in string theory. Unlike traditional particles, which are considered to be point-like, strings have a finite length and vibrate at different frequencies. The way in which strings vibrate determines the properties of the particles we observe in the universe, such as their mass and charge.

5. Can classical gravity, supergravity, and strings be experimentally tested?

While classical gravity has been extensively tested and confirmed through experiments, supergravity and string theory are still theoretical and have yet to be experimentally confirmed. However, there are ongoing efforts to test predictions made by these theories, such as the search for supersymmetric particles at the Large Hadron Collider. Additionally, there are ongoing studies of gravitational waves, which could provide evidence for string theory and other theories that attempt to unify gravity with other fundamental forces.

Similar threads

  • Beyond the Standard Models
4
Replies
105
Views
10K
Replies
2
Views
1K
  • Beyond the Standard Models
Replies
7
Views
1K
  • Beyond the Standard Models
Replies
24
Views
4K
  • Beyond the Standard Models
Replies
3
Views
2K
Replies
1
Views
2K
Replies
72
Views
5K
  • Beyond the Standard Models
Replies
15
Views
3K
  • Beyond the Standard Models
Replies
10
Views
2K
  • Beyond the Standard Models
Replies
2
Views
2K
Back
Top