What are particles in the holographic principle?
According to Verlinde, gravity is emergent from the holographic principle as an entropic force. According to this, attempts to find a quantum carrier of the gravitational force are fundamentally misguided and will never be successful.
Taking this paradigm as given for the sake of argument, what are particles like electrons and photons in terms of the holographic principle? How do they arise?
edit: I'd like to clarify that the question is asked from the perspective of the holographic principle where everything is information on screens. That is the answer I'd like to know...not presupposing other fields, nor criticizing the holographic principle.
Posted Oct 7, 2016, 2:11 AM UTC · edited
1322
First of all I don't think most physicists working on holography agree with Verlinde's idea that holography entails that gravity is entropic, but the core of your questions doesn't really depend on that because it's true that in the holographic dual of a spacetime there isn't any gravity.
Does that mean that if the holographic principle is true that we shouldn't be able to see gravitons? No. One big misconception that is perpetuated by the popular depiction of holography is that the holographic description is somehow the 'more real one' whereas really they're both equally valid. And in the ordinary description of spacetime, unless we're really really wrong about a lot of thing regarding quantum field theory, there simply has to be gravitons. Even if gravity where entropic or somehow emergent there has to be some regime in which the graviton description of gravity is valid the same way there's a regime where you can think of sound in terms of phonons. If something has waves then it has a quanta of those waves. This has to do with the fact that really matter is more 'wave-like' than 'particle-like'. Quantum waves or 'fields' really only look like particles in certain regimes.
So how do gravitons and other particles arise from the holographic dual description of spacetime? The problem with trying to picture it is that the mathematical relationship between the two descriptions is between the fields not between particles. Things which look like particles on one side might correspond to configurations that don't on the other.
Roughly speaking though the graviton corresponds to pairs of gauge bosons in the dual theory. The orientation of the pair of bosons corresponds to the 'orientation' of the graviton and the distance between the two bosons corresponds to how far away from the holographic boundary the graviton is.(see u/hopffiber's post below) Other particles are often realized as supersymmetric partners of the graviton, which I know is utterly unhelpful and unvisualizable. They also can be Kaluza-Klein modes in compact extra dimensions, i.e. gravitational oscillations of compact extra dimensions, which at large scales look like independent fields (Kaluza-Klein theory was originally a way of getting E&M from 4+1 dimensional general relativity, where the photon is now this kind of oscillation of the extra dimension). I think there are other ways but I can't really remember.[deleted]
This is assuming reality is actually fundamentally quantum. Some people think that gravity is ultimately going to be 'more fundamental' and we'll have to 'relativize' quantum mechanics rather than quantizing gravity.
In a purely quantum system every degree of freedom is quantized, even bulk/emergent degrees of freedom. This is why you can do the double slit experiment with buckyballs. The center of mass degree of freedom behaves like a single large particle and so mathematically it's equivalent. Similarly in a system with waves by definition there are degrees of freedom that behave like waves.
There is a big caveat though which is that you need to be able to see the waves while the system is cold enough that it won't decohere very quickly. IIRC part of the trick with that buckyball experiment is shooting them out without heating them up. Similarly while you can see phonons in cold crystalline lattices, you're unlikely to be able to detect them in say, ocean waves, even though you can get 'ripplons' in cold enough liquids like superfluid helium.
Does this correspond to when the dual is some complicated gauge theory (maybe N=4 Super Yang-Mills)? I have some vague notion that in AdS/CFT the AdS graviton is dual to the stress-energy tensor of the CFT, is this equivalent to what you're saying?
Looking around I think you're right and in general the graviton is the stress-energy tensor since that's the only spin two thing in the CFT side. I'm pretty rusty with AdS/CFT and I only vaguely remember the qualitative picture with the pairs of bosons, so I don't know what qualifications it has.
u/mofo69extreme is correct that the dual of the graviton is the stress-energy tensor of the CFT; as you point out it's the only thing that makes sense.
The picture you're describing where the graviton is related to a pair of gauge bosons sounds like another idea, the KLT relations from string theory that relates a closed string (=graviton) to two copies of open strings (=gauge bosons). This has a non-stringy corresponding idea that is quite modern, the color-kinematic duality (BCJ relations), where gravity is described as "two copies of a gauge theory"; but this is not really directly related to AdS/CFT.
Ah okay. There's way too many things in high energy physics.
Do you know how the following terms relate to this: instantons, corners in
modularizedmoduli space, Berry phase, crossing eigenvectors?From this talk.
I know or am vaguely familiar with those terms but I'm not sure what relationship they have to this issue. I'll have to watch the talk.
Edit: Looking at the section of the talk you linked to those terms are all involved in Verlinde's description of entropic forces in his approach to trying to exhibit gravity as an entropic force. It's not particularly related to the stuff I was talking about aside from being related to gravity and holography in the first place.
Thank you for the follow-up edit. I guess I'll have to wait for Verlinde to publish so as to observe the responses from the rest of the field and see whether his approach is generally acceptable.
A lot of this post is predicated upon gravitons existing and I don't see a reason why they should. GR is a perfectly self-consistent theory that requires no mediation on the quantum level, why must gravitons exist?
Since you didn't seem very satisfied with the other explanation, maybe another approach would help. In GR, in order to calculate the spacetime curvature, you need to input the classical stress-energy tensor of the matter in the Einstein equations. But our fundamental theory of matter is quantum mechanical, and the stress-energy tensor which is an operator on a Hilbert space.
So what do we input into the right-hand side of Einstein's equations? A first guess might be to input the expectation value of the matter stress-energy operator, but you can quickly see how it's absurd to treat the Einstein tensor classically in this case. If we set up an experiment where the matter is in a superposition of being in region A and region B (assume these regions are disjoint), then the average stress-energy is concentrated at a point between them (where there is zero probability of there being matter!), and your gravitational theory predicts a force pointing towards the middle of these two regions.
Now what happens if you measure whether matter is in region A or region B? If the gravitational field changes discontinuously, the nonlinear parts of Einstein's equations will simply make the theory go beserk.
Quantizing the gravitational field, such that the Einstein equation only holds as expectation values of quantum operators (where the Einstein tensor is also an operator which can describe superpositions of quantum gravitational configurations), is really the much more sensible thing to do.
(I stole the above argument from Robert Wald's general relativity textbook.)
Doesn't this approach lead to a non-renormalizable theory? From what I understand, treating the action metric as a perturbation about the Minkowski metric and trying to solve the field equations leads to nonsensical answers. I'll admit this isn't my field so I'm not up-to-date on the literature but how would you rectify this?
Non-renormalizable quantum field theories are not nonsensical; they are predictive at low energies. Hence the amazing utility of Four-Fermi theory, Chiral Perturbation theory, and most of the field theories that condensed matter theorists like myself work on.
The issue with non-renormalizable theories is that they fail to be predictive at high energies. It might be easier if I just link to a previous comment I made explaining how things break down.
Anyways, whether the naive construction of quantum gravity using quantum field theory is complete or not, most physicists believe that there is some theory of quantum gravity that should work to high-energies, and will simply reduce to the field theory description at low energies. This theory might look very different from GR or QFT at high energies, but there are good reasons to think that low energy quantum gravity will look like the non-renormalizable theory. (I discuss the latter point in this recent thread.)
GR is self-consistent but it's not possible to make classical GR consistent with quantum mechanics. I'm not talking about renormalization or anything but rather the internal logic of GR and QM. I don't like Luboš Motl but his blog post about this issue is very good.
It's possible that QM is the thing that's only approximately right and then it's possible that there aren't gravitons, but if the world is ultimately quantum every field needs to be quantized and any field that has propagating degrees of freedom (which we know gravity has because we recently saw them) has to have quanta.
That's a really interesting post, thanks. I'll read it and get back to you.
Whoa, I completely, utterly disagree with this. Gravitational waves are entirely analogous to the multipole expansion of the electromagnetic fields for l=2. We don't need a "photons are spin 1 therefore no l=0 radiative fields exist" explanation for why the lowest electromagnetic radiative mode is l=1 (sphere of harmonically increasing and decreasing radius will not radiate) and we certainly don't need one for gravitational waves.
Perhaps I'm missing something here. Could you clarify?
What he's saying applies to plane waves as well as spherical waves. Also he's saying 'if you accept that everything is quantum mechanical in nature, then waves have to have quanta'. I don't really see how what he's saying has something to do with spherical wave expansions.