It's not the first time when Nima Arkani-Hamed gave a "totally negative" talk on a similar issue but it's a fun time.
Twelve days ago he came to The Space Telescope Science Institute (STScI) in Baltimore, Maryland – the terrestrial headquarters for Hubble (past) and James Webb Telescope (future) and a loose part of Johns Hopkins University – and had the following things to say.
Video:
Don't Modify Gravity—Understand It! (video, 85 minutes)He is introduced by a host who enumerates some prizes Nima has received, including a nice one from Milner, and mentions that the only person over there who would understand the talk is Mario Livio who is just recovering from an illness (fortunately for his health, unfortunately for the readiness of the audience).
Nima claims to have a special moral right to give an entirely negative talk about the sinfulness of modifications of gravity because he's been a dirty sinner himself. ;-) So that's why he has the credentials to crawl from his hole, confess, and repent. Of course, he means it's wrong to modify gravity at long distances. Of course, GR isn't adequate at super short distances, an issue he later (around 15:00) talks about, too. Gravity just becomes an intrinsically strong force over there (at the Planck scale).
Nima debunks the usual vague philosophical attitudes about general relativity's being justified by the beauty, sexiness of geometry, and similar stuff. Instead, GR works because it's inevitable; it's dictated by consistency on top of special relativity and quantum mechanics. This provable inevitability shows how deep our knowledge of physics has become. He sketches his plans to discuss the cosmological constant problem and learn from the epic failure of every single attempt to solve the problem by modifying gravity at long distances. He divides the theories to the deeply flawed ones that he would spend his time with, anyway; and complete idiocies that are not worth talking about at all, despite a thousand of deluded papers about them.
The experience has numerously shown that physicists have to be radically conservative instead of conservatively radical. Well, in this case, he claims that the conservatism leads to the landscape. OK, his more technical comments start with the proof that gauge theories and gravity are inevitable.
Nima attacks the claims in the popular books that "we don't know how to combine gravity and quantum mechanics". Obviously, neutron interferometry may be done and measured (and used to show that Erik's Verlinde entropic gravity is crap). Obviously, we may talk about gravity and quantum mechanics in the same sentence – otherwise we couldn't have discovered quantum mechanics on planet Earth (where we have gravity) at all. In fact, we may even calculated the leading-corrected Newton's law:\[ F = \frac{G m_1 m_2}{r^2} \zav{ 1 - \frac{27}{2\pi^2}\frac{G\hbar}{r^2c^2} +\dots} \] We can questions like that! The effect is minuscule but we may still calculate it. Quantum mechanics is a robust framework that can deal with anything. The real difficulty – sad properly – is that we don't know what happens with various terms in gravity at short distances which is why GR needs a replacement. I couldn't agree with him more. Note that Nima attacks not only really crappy popular books such as Lee Smolin's ones but even the really mainstream ones such as Brian Greene's books. Needless to say, I think that Brian's confusing presentation of the conflict is biased towards his completely flawed tendency to modify quantum mechanics whenever he sees a vague opportunity or excuse for that. ;-)
Fine. Nima returns to long distances. Photons would produce a wrong negative-norm polarization. Gauge invariance ("redundancy", using his more favorite words) is needed. The same goes for the diffeomorphism redundancy and gravity and spin-2 fields. These gauge redundancies aren't real symmetries – they're artifacts of our imagination. He continues with Weinberg's arguments from the 1960s that the interactions with added photons – regardless of the nature of the theory – have to depend on the polarization vectors for these interactions to remain nonzero at long distances. Now, pure gauge polarizations have to decouple (interaction amplitude going to zero) which implies that the total charge is zero and therefore, there has to be the "symmetry".
The same with spin-2. You don't have to know anything about the "culture" of gravity or the word. The spin-2 needs to decouple the bad polarizations. This forces the conservation laws for the momentum in this case. As I have explained many times, the allowed spins of massless/light particles are \(0,1/2,1,3/2,2\) and the last three choices inevitably arrive with increasingly constrained gauge redundancies.
Nima says many things I repeat many times. Someone comes to you and tells you that he may have a completely new spiritual viewpoint on gravity, based on some torsion, wakalixes, or any other word. We just don't need to care about these vague words and fog! We may study what the theory predicts for the interactions and whatever it is, it will either agree with the "gauge descriptions above" or violate the general postulates of relativity or quantum mechanics. That's it, we're finished, "anything goes" is just wrong.
At 35:40, he begins to talk about the cosmological constant problem, the most frequent excuse for modifications of gravity at long distances. Everything is Planckian in the fundamental theory, so should be the density or curvature of empty space, but it is empirically 123 orders of magnitude smaller. There are contributions to the C.C. that are Planckian, after all, and they must cancel with the huge relative accuracy (classical terms against quantum corrections etc.). The cancellation isn't an inconsistency, however ludicrous it may seem. People used to believe in the fantasy that there was a deep so far unknown reasons why the C.C. ultimately exactly cancels. Its nonzero value made this scenario far less plausible: it almost cancels but there must still be a tiny leftover. Oops.
Nima compares this situation to the fantasies in the 1930s when the first divergent loop corrections to QED were seen. It was believed that those infinities were fantasies that would ultimately see a redefinition of QED that makes all of them zero. Well, they were finite but they were definitely not zero. Loop corrections at every order matter and are nonzero, although much smaller than the naive (infinite) value. As a stumbling block, the case of the C.C. is more serious; as a stimulation of the progress, the story of the loop corrections to the magnetic moment was far more dramatic.
When written as an energy density, the C.C. is the fourth power of the inverse millimeter. So some new physics could be appearing at the millimeter scale. Except that we have looked and there seems to be nothing over there. (We think that the analogous solution does explain the hierarchy problem, the unbearable lightness of the Higgs' being, however.)
Now, at the level of linguistics, a great idea to explain why the C.C. is so small is to "degravitate" the vacuum energy, all the modes of the fields or those whose wavelengths are shorter than the millimeter (this refinement is needed to preserve the tested behavior of gravity at distances longer than 1 mm). Everything else gravitates but this form of energy just happens to exert no gravitational influence, the proposal says. However, physics only starts once you begin to convert the word-level ideas to equations and 99.9% of the word-level ideas simply fail at that point.
A slightly clever mechanism to realize similar ideas was "dumping curvature in the bulk" of a higher-dimensional space. Of course it's easy to "solve" the C.C. problem if you're allowed to modify the behavior of gravity, e.g. by changing the exponent in Newton's power law. The discussion turns to examples in lower-dimensional gravity (3D gravity with deficit angles), too.
A modification of the idea is based on Randall-Sundrum who managed to "trap" gravity on the brane. At the beginning, it looked like the tower of apparently massless Kaluza-Klein modes of the gravitons may provide you with a loophole. However, one may ultimately see that the RS theories end up being effectively equivalent to normal four-dimensional theories, GR with massless matter. I know that Lisa doesn't like these "RS is equivalent to..." comments but I am afraid (or happy to see) that Nima is right. It's not just the full-fledged AdS/CFT methods that argue in this direction.
More exotic ideas (53:00) came from DGP, Dvali-Gabadadze-Porrati (it's a messed up GDP; I really disliked those things from the beginning and without an interruption because they seemed so contrary to all the lessons I learned from string theory). The Einstein-Hilbert term is weighted by a coefficient that only makes gravity matter on our brane; it's extra 4D gravity added on top of the normal 5D gravity. Your humble correspondent thinks it's inconsistent at the quantum level (swampland). Surely in string theory, it looks like gravity only affects "all of space" and the "\(D\)-dimensional space with all the dimensions one can find". At any rate, Nima shows that if the crossover state obeys the inequality needed to dump the curvature etc., gravity on the brane will be modified at millimeter-like distances, too.
Deficit angle didn't work because it can't go over \(2\pi\) or so. With an excess angle, this limitation seems to be lifted. Things look fine. However, if you're diligent, you derive the propagator in your theory and alas, it is modified, too. Some \(2\pi\) becomes \(2\pi+|T|\), in some units; the tension is added. For a large tension, the tension term dominates. You recalculate at what distances gravity starts to behave properly and you find out that these distances must be larger than the Hubble scale (the size of the Universe). Too bad. ;-)
A model after model after model fails like that. Why all of them fail? It's useful to hit your head with a hammer 10 or 20 times, then you may start to get the message. ;-) The reason behind the failure of all these things is relativity. Relativity relates space and time. If you modify physics at some distances, you modify it at some time scale, too – or break relativity or causality.
More technically, your stress energy tensor \(T^{\mu\nu}={\rm diag}(\rho,p,p,p)\). The different components have different sources – the C.C., visible matter, radiation – and there's simply no relativistically invariant way to "isolate" the piece that you would like to make non-gravitating without spoiling the proper behavior of matter and radiation at the same moment! The only way to avoid the conclusion would be to modify gravity by "knowing in advance" what the impact would be, and that would violate causality.
At 1:00:00, he switches to the question whether one may modify gravity at all – a purely theoretical question. Can one make gravity a bit massive etc.? Every modification of gravity has to add a new degree of freedom, typically a scalar field that couples to \(T_\mu^\mu\). That's morally nothing else than boring extension of GR with scalars such as Brans-Dicke etc., something that's been around since the 1940s. If you add the scalars, you modify gravity in a boring way – e.g. you modify the bending of light so that you are in conflict with the observations at the same time unless you boringly choose the coefficients of the extra terms to be much smaller than one (obnoxious imitators/deformations of GR that can't solve its fundamental problems such as the C.C. problem).
Exciting possibilities are those where the scalar fields are more exotic, e.g. massive gravity or Galileons or ghosts or fields with specific non-linear self-interactions. Lots of phenomenology but as I always said, these theories lead to deep conflicts with locality and/or thermodynamics. At any rate, Nima promotes the Galileons. Scalar fields are equipped not just by symmetry \(\phi\to\phi+c\) but also \(\phi\to\phi+v_\mu x^\mu\), a "Galilean symmetry" but acting on fields rather than \(\vec x\). Lunar phenomenology, fun, but to make the story short, some radial modes propagate superluminally. Despite formal Lorentz invariance, the "nice structure" is inseparable from the lethal acausality.
Similarly, "higgsed gravity" allow you to produce "black hole hair" which is enough to create a perpetual motion machine of second kind by making a cycle between two distinct event horizons of a black hole valid for two different particle species/fields. Too bad. Nima spent 8 years of his life with similar things, he says. Gravity is much more constraining than other types of dynamics. He declares that the eternal inflation plus the multiverse are the only possible way to the C.C. problem given the failures discussed above. I disagree with that. I don't have to modify gravity at all but the selection that makes the C.C. tiny may still reject the existence of any multiverse.
Of course, I agree with Nima that one has to be radically conservative instead of a left-wing as*hole because the declaration that the previous knowledge was "just wrong and may be scratched" has never been successful. Even quantum mechanics overthrew classical physics in a very respectful way – when it explained some surprising features of classical physics that should have been asked even by classical physicists, e.g. "Why can the equations of motion be derived from a Hamiltonian as well as the principle of least action?" No trashing here.
Radical conservatism – the right attitude – means that one is prepared to push the tested principles as far as they can go and only when one becomes absolutely sure that there is a problem, he may think about modifications. Nima repeated his slogan, Don't modify gravity, just understand it. And the host proposed not to modify Nima's talk by stupid questions, instead, let's drink some beer which is what they are conservatively good at.
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