Last time I had time to write a detailed physics post, I got to the point of declaring fields as the fundamental entities of nature. Since we can get particles from quantizing (certain kinds of) fields, and since the pointlike particles are confusing and paradoxical, we don’t really need them. Our basic theory of nature is then a (quantum) field theory.
Now, if you are contrarian, which I think everybody should be, you probably immediately think this is a rather dogmatic statement. We don’t really have a complete theory of nature yet, we haven’t unified gravity with quantum mechanics or explained consciousness, not to mention even finding the Higgs. As far as we know the universe may well be a computer, or it is human shaped, perhaps it is elephants (or turtles) all the way down, or angles dancing on a head of a pin. Wasn’t there also that theory of everything, something with a letter and a number? Once we get foundational and stuff, the possibilities are endless really…
The point is that it doesn’t really matter. Consider any example of continuous medium that we are all familiar with, say a rubber band or a surface of a pond. We all know these are all not really continuous, they are made of many small ingredients and the continuous description is only approximately true when we don’t look too closely. Be that as it may, if you want to describe the motion of a fluid, you’d better use the Navier-Stokes equations, rather than the quantum mechanics of the gazillion molecules making up that fluid.
Extending this logic leads to the idea of Effective Field Theory (EFT): when we don’t look too closely, anything at all will look like a field theory. Trivial as it sounds, it turns out that we can actually say quite a bit about the type of field theory we get, without knowing the precise details of microscopic physics. We can even get signs when that approximation stops making sense, without knowing much about the underlying structure. All of which makes EFT an extremely useful tool, one that dominates huge parts of modern theoretical physics, in fact.
If the description is only approximate, when do we have to replace it with something better? this is simply a matter of length scales. If we are interested in questions involving only long length scales, we are in effect averaging out all the small scale details, resulting in continuous description of the physics. If we look closer we may (or may not) see something else, which may itself be continuous or discrete (or involving turtles, or not).
For example, we describe the electrons and their electromagnetic interactions by a field theory called Quantum Electrodynamics (QED). This has to be a quantum field theory when we are interested in length scales for which quantum mechanics is important, for example when we want to discuss atomic transitions and emission and absorption spectra . It turns out that when we look at electrons at shorter and shorter distances (by smashing them together at higher and higher energies), the description by QED (or more accurately, by the full standard model of particle physics) is holding up to very high accuracy. Maybe in the future we will see some substructure, maybe not, in the meantime we call the electrons “fundamental” fields (just to tweak our condensed matter colleagues).
On the other hand, when we look at protons and neutrons- the basic ingredients of the atomic nucleus, we have a different situation. If we don’t have too much resolving power, we describe them by an EFT involving proton and neutron fields, interacting in specific way as to reproduce details of nuclear physics. However, we now do have more resolving power (also known as particle accelerators), and we know that when we probe the nucleus at even shorter distances, we find further substructure. The protons and neutrons are really made out of quarks, which interact (predominantly) via the strong force. The new structure includes quark and gluon (the strong interaction version of the photon) fields. Yes, it is still a quantum field theory, called Quantum Chromodynamics (QCD), but the fields visible at short distances are different from the ones visible when only probing long distance physics.
Now, finally coming to gravity. The classical physics of the gravitational force is explained by Einstein’s general theory of relativity (GR), one of the most beautiful and exquisitely tested theories in physics. In the center of the theory is the metric tensor, the basic field which explains the gravitational force, and describes the geometry of spacetime. There are currently no experimental results deviating from classical GR, it is certainly the correct description of gravitational physics at long distance scales.
Alas, there are many indications (which I may get to at some stage) that quantizing the gravitational field is problematic: when going down to length scales for which the quantum mechanics of gravity is important, we simply don’t know what to do. Unfortunately, this distance scale, the Planck length, is tiny. If we are not extremely lucky, we probably cannot probe this length scale directly. Nevertheless, we have now an incomplete story, full of interesting puzzles and paradoxes, and making that story coherent is the problem of quantum gravity.
So, what can happen when we go to such short distances? in other words, what is the quantum structure underlying classical general relativity? There are exactly two possibilities:
1. The description of gravitational physics by a field theory involving the metric tensor holds all the way down to the Planck length. This is similar to what happens in QED: this field theory describes the physics accurately all the way down to distance scales for which quantum mechanics is relevant. In this case, in order to describe quantum gravitational phenomena, one has to quantize the metric tensor, something we don’t really know how to do.
2. The metric field shows some substructure already at distance scales larger than the Planck scale. That substructure is what underlies the physics of classical gravity. In order to describe physics at extremely short distance scales, such as the Planck length, one has to quantize that substructure. This is similar to nuclear physics, when we are interested in very short scales we look at the quantum mechanics of the quark and gluon fields, QCD.
That is the basic dichotomy of quantum gravity (and not background independence, as is often claimed). There are many clues, about which I will write at some point, that it is the second option that is more likely. Among those clues are the myriad of conceptual and practical problems we encounter when we try to follow the first route, and the fact that nearly 80 years of attempts have not resulted in much progress. On the other hand, after countless failed attempts, we do now have in string theory a few working examples of general relativity emerging as long distance approximation to something more fundamental, lending us confidence this is indeed the right scenario.
As a result, most researchers interested in quantum gravity (almost all of whom are labeled string theorists) have abandoned the attempt to quantize the metric tensor directly. There are still a few holdouts, who take at least some features of classical general relativity seriously all the way down to extremely short distances, I hope everyone can join me in wishing them good luck in their quest.
Update: Lubos lists some of the reasons why quantizing the metric tensor directly is unlikely to work.
How does a predictive theory of gravitation evolve without theorists knowing if weak founding postulates doom everything from the start?
Euclid cannot navigate the globe; the Fifth Postulate fails. Metric and quantum gravitations (e.g., string or lattice) postulate the Equivalence Principle (or BRST invariance to the same end). Theory lacking testable predictions is nicht einmal falsch. EP falsification lifts quantum gravitation from its refractory messes through a loophole.
PSR J1903+0327, arxiv.org/0805.2396, ends all composition, physical spin, quantum angular momentum, binding energy… EP tests, neutron star vs. Sol’s twin. The only unexamined disjoint remainder between metric and teleparallel (no EP) theory is trivial: Do chemically identical opposite parity mass distributions violate the EP?
The resolved chiral drug market exceeds $100 billion/year. It matters which enantiomer goes down your mouth. Nexium, [S]-omeprazole, has twice the activity and little of racemic Prilosec’s toxicity. Perhaps spacetime cares what goes down its mouth.
Do enantiomorphic space groups P3(1)21 and P3(2)21 quartz test masses in an Eötvös experiment reproducibly violate the EP? Somebody should look. When you know the empirical answer, create theory from it – or ignore it and risk being nicht einmal falsch from the start.
3. The procedure of quantization does not hold all the way down to the Planck scale.
Bee,
1. While there are some attempts to modify quantum mechanics, I am not aware of any attempts to apply those to QFT, which is what really counts.
2. In particular, once applied to QFT, I don’t see an apriori reason modifications to QM would be organized by length scale. This is necessary if you want to modify QM at short distances without spoiling its success at observable ones. Wilsonian EFT, with its cascade of new theories at ever shorter distances, does that very naturally.
I definitely opt for number 2. One only needs to take the old argument that Planck’s constant h tends to values of the Planck length squared as the maths get closer to the initial singularity at t=0. If you think about it, contracting the metric backward in time is going to ensure that constants such as h and the Planck length are going to be on top of each other. Definitions may blur then but I am willing to bet that h thus gets exponentially very small. If it is nearly equivalent to an area (Planck length squared) then h itself is an inherent part of structure and it maybe that h is encoded into an euclidean or an orbifolded structure close to t=0. A very small number ~10^-65 will be involved.
Which class do the loop quantum gravity theorists belong to?
Loop quantum gravity is an attempt, really a series of attempts, to quantize gravity using different variables, and possibly different rules for quantization. As far as I can tell, just about the only thing those different programs have in common is that they belong in the first class.
Would you say then that a quantum theory of gravity would likely supplant any notion of the metric tensor in GR?
How would gravitons warp space? What exactly would space be (non-mathematically). Would gravitons bend light, or influence other things by somehow coming out of stuff with mass, recognizing other gravitons coming out of other stuff with mass, and somehow pull on each other?
Would the gravitons, even at a large distance, be able to sense other gravitons? How? Do they pull on each other, or do they pull on their associated objects with mass, toward the other graviton? Is space even necessary in that scenario?
But if space is being created as the universe expands, it must be something, other than nothing, I would think.
So maybe the gravitons go pulling on it instead of other objects? And if that’s the case, isn’t the tensor still there?
Hi Moshe,
I didn’t have a specific modification in mind, I’m not aware of anything that would fall into category 3. It was more meant as an in principle existing possibility that I believe shouldn’t be discarded prematurely. Best,
B.
Hello Moshe,
I am an engineer not a physicist but I’m generally interested in physics. I don’t understand why you describe LQG as a holdout. The fact that it predicts quantization of space at plank length and thus eliminates the divergences by introducing a natural cut-off, is not a promising result? What else you would expect from a canonical quantization of GR? Isn’t this a success? You said “almost all of whom are labeled string theorists”. Could you give percentages? You would say 99% for example?
BR
Dear Giotis, I think the scientific evidence accumulated over many decades suggests (to me) that canonical quantization of GR cannot work, at least not without a dramatically new idea. Maybe I am wrong, but I have trust myself when deciding what to spend my time on. If I see some promising results in the future, I may change my mind. Looking forward to such results.
(I know I did not write anything about that evidence, this piece is long enough, and there will be future ones).
Yes, it would be great if you could present the evidence in this blog. There is a long dispute about that evidence and it would be very helpful if you could contribute to clarify the confusion. I’m looking forward for future posts.
BR
Moshe will surely present additional or better evidence but here’s some:
http://motls.blogspot.com/2008/10/why-canonical-gr-cannot-work.html
Thanks Lubos, I already linked your discussion to the main text.
A confused, rambling, question: naively, it seems that some problems dealing with quantum gravity, can be posed entirely within the low energy setting. More specifically, consider energies much lower than the lowest neutrino mass, where we get an EFT of a metric plus EM gauge field. There are macroscopic black hole solutions, and we can think about the black hole information problem. We have solutions based on a UV complete description (AdS/CFT), but why can’t the problem be addressed entirely in the low energy effective field theory?
gs, this is an excellent question, the essence of the information paradox is explaining where the low energy EFT breaks down. I don’t think there is a universally accepted answer, but one place to be suspicious of EFT is when trying to describe correlations in the Hawking radiation, which is presumably where the information is stored. In other words, EFT like any other approximation scheme is not uniformly valid for all questions asked, and detailed questions involving huge number of quanta may require the full quantum gravity theory. Of course, those are all words, calculations would be more impressive.
Your background independence paper has the statement:
“In this sense spacetime is inherently a derived concept in string theory, even perturbatively”.
The above has “the metric field shows some substructure already at distance scales larger than the Planck scale”.
Are these two statements intended to mean the same thing?
Yeah, more or less, maybe “substructure” is slightly less precise. Certainly the metric is subsumed by something else in perturbative string theory, long before we reach the Planck length.
Hello,
I read Lubos post and i thank him for his answers and his effort. I tried to follow as much as i could. This is even harder if there is only text. As far as i know the kinematical Hilbert space is well defined in LQG. The gauge and the spatial diffeomorphism constraints have been resolved. The role of the local lorentz invariance in discrete quantum gravities is a general issue and a number of papers have been published for it (Rovelli has some answers about that for example). The definition of the physical Hilbert space in LQG and the troubles with the Hamiltonian constraint is also a very well known issue and is currently a subject of research e.g. Thiemann’s Hamiltonian etc. The lack of a well defined formalism for the calculation of scattering amplitudes and the semiclassical approximation again are important obstacles.
But basically these are the current weaknesses of LQG. Every theory has its weaknesses more or less and LQG is not a finalized theory yet. On the other hand the central property of GR -background independence- is not mentioned.
I mean we have GR and QFT. These are the only theories we can currently rely upon since these are the only theories that have been verified in a large extend by experiment. It is only natural to use them to establish a quantum gravity theory.
Now GR tells me that i have a dynamical field; the metric. QFT tells me how to quantize dynamical fields. The new thing though is that GR is background independent. The field is the space-time itself. QFT on the other hand quantize only background dependent fields i.e. i must have a background metric where fields propagate. In GR there is no background metric, the whole metric is dynamical and thus following the usual perturbative approach around Minkowski space-time leads to divergences. In general terms LQG investigates the non perturbative approach by using this crucial property of GR; background independence.
So is it possible that this peculiar property of GR is the key to its quantization? LQG answers yes to this question and argues that all the previous attempts have failed because we followed the perturbative approach and ignored this fundamental property.
It might exist new physics at Planck scale from which GR emerges after all but this does not change the fact that you can’t have a background metric. GR tells you that. What ever you do, you can’t break general covariance. This is not only a technical but more important a conceptual issue.
BR
PS BTW Moshe you said: “we do now have in string theory a few working examples of general relativity emerging as long distance approximation to something more fundamental”.
Could you please indicate some papers about that? Thanks in advance.
Dear Giotis, for description of my view of BI (including my opinion that it way too often used as cure-all slogan) you can read my post and the article linked there. In brief, the fact that we have a metric in the low energy limit does not imply our only option is to quantize the metric as a fundamental field. If you don’t attempt this feat, issues like background independence are much easier to resolve – if there is no metric at all in the underlying description of the theory, in particular there is no background metric in that description, and both background independence and general covariance are achieved more easily. This is the way it works for example in AdS/CFT.
[...] reader called Giotis at Shores of the Dirac Sea asked why we almost certainly know that canonical quantization of general relativity cannot work. [...]