Thursday, August 27, 2015

Embrace your 5th dimension.

I found this awesome photo at
What does it mean to live in a holographic universe?

“We live in a hologram,” the physicists say, but what do they mean? Is there a flat-world-me living on the walls of the room? Or am I the projection of a mysterious five-dimensional being and beyond my own comprehension? And if everything inside my head can be described by what’s on its boundary, then how many dimensions do I really live in? If these are questions that keep you up at night, I have the answers.

1. Why do some physicists think our universe may be a hologram?

It all started with the search for a unified theory.

Unification has been enormously useful for our understanding of natural law: Apples fall according to the same laws that keep planets on their orbits. The manifold appearances of matter as gases, liquids and solids, can be described as different arrangements of molecules. The huge variety of molecules themselves can be understood as various compositions of atoms. These unifying principles were discovered long ago. Today physicists refer by unification specifically to a common origin of different interactions. The electric and magnetic interactions, for example, turned out to be two different aspects of the same electromagnetic interaction. The electromagnetic interaction, or its quantum version respectively, has further been unified with the weak nuclear interaction. Nobody has succeeded yet in unifying all presently known interactions, the electromagnetic with the strong and weak nuclear ones, plus gravity.

String theory was conceived as a theory of the strong nuclear interaction, but it soon became apparent that quantum chromodynamcis, the theory of quarks and gluons, did a better job at this. But string theory gained second wind after physicists discovered it may serve to explain all the known interactions including gravity, and so could be a unified theory of everything, the holy grail of physics.

It turned out to be difficult however to get specifically the Standard Model interactions back from string theory. And so the story goes that in recent years the quest for unification has slowly been replaced with a quest for dualities that demonstrate that all the different types of string theories are actually different aspects of the same theory, which is yet to be fully understood.

A duality in the most general sense is a relation that identifies two theories. You can understand a duality as a special type of unification: In a normal unification, you merge two theories together to a larger theory that contains the former two in a suitable limit. If you relate two theories by a duality, you show that the theories are the same, they just appear different, depending on how you look at them.

One of the most interesting developments in high energy physics during the last decades is the finding of dualities between theories in a different number of space-time dimensions. One of the theories is a gravitational theory in the higher-dimensional space, often called “the bulk”. The other is a gauge-theory much like the ones in the standard model, and it lives on the boundary of the bulk space-time. This relation is often referred to as the gauge-gravity correspondence, and it is a limit of a more general duality in string theory.

To be careful, this correspondence hasn’t been strictly speaking proved. But there are several examples where it has been so thoroughly studied that there is very little doubt it will be proved at some point.

These dualities are said to be “holographic” because they tell us that everything allowed to happen in the bulk space-time of the gravitational theory is encoded on the boundary of that space. And because there are fewer bits of information on the surface of a volume than in the volume itself, fewer things can happen in the volume than you’d have expected. It might seem as if particles inside a box are all independent from each other, but they must actually be correlated. It’s like you were observing a large room with kids running and jumping but suddenly you’d notice that every time one of them jumps, for a mysterious reason ten others must jump at exactly the same time.

2. Why is it interesting that our universe might be a hologram?

This limitation on the amount of independence between particles due to holography would only become noticeable at densities too high for us to test directly. The reason this type of duality is interesting nevertheless is that physics is mostly the art of skillful approximation, and using dualities is a new skill.

You have probably seen these Feynman diagrams that sketch particle scattering processes? Each of these diagrams makes a contribution to an interaction process. The more loops there are in a diagram, the smaller the contributions are. And so what physicists do is adding up the largest contributions first, then the smaller ones, and even smaller ones, until they’ve reached the desired precision. It’s called “perturbation theory” and only works if the contributions really get smaller the more interactions take place. If that is so, the theory is said to be “weakly coupled” and all is well. If it ain’t so, the theory is said to be “strongly coupled” and you’d never be done summing all the relevant contributions. If a theory is strongly coupled, then the standard methods of particle physicists fail.

The strong nuclear force for example has the peculiar property of “asymptotic freedom,” meaning it becomes weaker at high energies. But at low energies, it is very strong. Consequently nuclear matter at low energies is badly understood, as for example the behavior of the quark gluon plasma, or the reason why single quarks do not travel freely but are always “confined” to larger composite states. Another interesting case that falls in this category is that of “strange” metals, which include high-temperature superconductors, another holy grail of physicists. The gauge-gravity duality helps dealing with these systems because when the one theory is strongly coupled and difficult to treat, then the dual theory is weakly coupled and easy to treat. So the duality essentially serves to convert a difficult calculation to a simple one.

3. Where are we in the holographic universe?

Since the theory on the boundary and the theory in the bulk are related by the duality they can be used to describe the same physics. So on a fundamental level the distinction doesn’t make sense – they are two different ways to describe the same thing. It’s just that sometimes one of them is easier to use, sometimes the other.

One can give meaning to the question though if you look at particular systems, as for example the quark gluon plasma or a black hole, and ask for the number of dimensions that particles experience. This specification of particles is what makes the question meaningful because identifying particles isn’t always possible.

The theory for the quark gluon plasma is placed on the boundary because it would be described by the strongly coupled theory. So if you consider it to be part of your laboratory then you have located the lab, with yourself in it, on the boundary. However, the notion of ‘dimensions’ that we experience is tied to the freedom of particles to move around. This can be made more rigorous in the definition of ‘spectral dimension’ which measures, roughly speaking, in how many directions a particle can get lost. The very fact that makes a system strongly coupled though means that one can’t properly define single particles that travel freely. So while you can move around in the laboratory’s three spatial dimensions, the quark gluon plasma first has to be translated to the higher dimensional theory to even speak about individual particles moving. In that sense, part of the laboratory has become higher dimensional, indeed.

If you look at an astrophysical black hole however, then the situation is reversed. We know that particles in its vicinity are weakly coupled and experience three spatial dimensions. If you wanted to apply the duality in this case then we would be situated in the bulk and there would be lower-dimensional projections of us and the black hole on the boundary, constraining our freedom to move around, but in such a subtle way that we don’t notice. However, the bulk space-times that are relevant in the gauge-gravity duality are so-called Anti-de-Sitter spaces, and these always have a negative cosmological constant. The universe we inhabit however has to our best current knowledge a positive cosmological constant. So it is not clear that there actually is a dual system that can describe the black holes in our universe.

Many researchers are presently working on expanding the gauge-gravity duality to include spaces with a positive cosmological constant or none at all, but at least so far it isn’t clear that this works. So for now we do not know whether there exist projections of us in a lower-dimensional space-time.

4. How well does this duality work?

The applications of the gauge-gravity duality fall roughly into three large areas, plus a diversity of technical developments driving the general understanding of the theory. The three areas are the quark gluon plasma, strange metals, and black hole evaporation. In the former two cases our universe is on the boundary, in the latter we are in the bulk.

The studies of black hole evaporation are examinations of mathematical consistency conducted to unravel just exactly how information may escape a black hole, or what happens at the singularity. In this area there are presently more answers than there are questions. The applications of the duality to the quark gluon plasma initially caused a lot of excitement, but as of recently some skepticism has spread. It seems that the plasma is not as strongly coupled as originally thought, and using the duality is not as straightforward as hoped. The applications to strange metals and other classes of materials are making rapid progress as both analytical and numerical methods are being developed. The behavior for several observables has been qualitatively reproduced, but it is as present not very clear exactly which systems are the best to use. The space of models is still too big, which leaves too much room for useful predictions. In summary, as the scientists say “more work is needed”.

5. Does this have something to do with Stephen Hawking's recent proposal for how to solve the black hole information loss problem?

That’s what he says, yes. Essentially he is claiming that our universe has holographic properties even though it has a positive cosmological constant, and that the horizon of a black hole also serves as a surface that contains all the information of what happens in the full space-time. This would mean in particular that the horizon of a black hole keeps track of what fell into the black hole, and so nothing is really forever lost.

This by itself isn’t a new idea. What is new in this work with Malcom Perry and Andrew Strominger is that they claim to have a way to store and release the information, in a dynamical situation. Details of how this is supposed to work however are so far not clear. By and large the scientific community has reacted with much skepticism, not to mention annoyance over the announcement of an immature idea.

[This post previously appeared at Starts with a Bang.]


  1. If the holographic pictures is true, how could be face the interior singularity of spacetime from the boundary? What is its final destiny?

  2. Schlegel diagrams project polytopes into one fewer dimension. 3D fullerenes project as 2D nets with no edge (bond) overlap. Of some 60 million indexed organic compounds, about a dozen do not cooperate.

    If the "bulk" contains Kuratowski's theorem non-planar graphs, subgraphs homeomorphic to K_5 or K_(3,3), what then of projecting them one dimension fewer? Perturbation theory fails given emergent symmetries, right? One cannot perturb a sock into a shoe (which shoe?).

    "4. How good does this duality work?" "good" (adjective) describes a thing; "well" (adverb) describes an activity. It's "well" not "good." "8^>)

  3. Since quantum theory of strong,em and weak interactions is reasonably well understood,are people trying to get at quantum theory of gravity by duality arguments? Any success yet?

  4. If we live in a universe with an exact dual to its physics, then why do we experience only one side of the duality?

    Maybe the universe is self-dual?

  5. Thanks for this excellent overview.

    My mother majored in English and was an English teacher, and relentlessly corrected my grammar. Also I have read a lot of good books. So I have a heuristic feeling that "... exactly how information may escapes a black hole" should be "... exactly how information may escape a black hole". The first sounds wrong and I can hear my mother correcting me to the second (another example of M-Theory). I think it has something to do with "the conditional tense", e.g., "Susan escapes the hole," versus "John may escape the hole".

  6. Could you say a few words about the way dualities mechanically arise?

    On the side of the non-string dual, it can only ever be precisely what we define it to be. Because on the string side we use over-complete functions and curve fit everything into position.

    Which means there has to be a precise concept of what we're steering towards. It's a 1:1 resolution. You can only curve fit to the resolution you are upfront defining the other side.

    Are you satisfied arrangement like this can produce fundamental new insight and knowledge, even in principle? what sense?

  7. Hi Uncle,

    Thanks, I've fixed that. Should have known this of course... Best,


  8. JimV, sorry I've fixed that typo. Best,

  9. Arun,

    Well, we experience both of course, it's just that the way we interpret it is the computationally easier way, which means it's the description in which there are weakly coupled localized particles. Best,


  10. Chris,

    I don't know what you mean with how they "mechanically arise". If you want more technical details, I recommend Joe Polchinski's brief review which is really well done and informative. Best,


  11. Sorry in my above question, I should have used the word *holography* rather than duality.

  12. A couple of days ago I was at a barbeque explaining a theory idea that I had to one of my nephews. He then began telling me about the Holographic Universe idea and also mentioned black holes. While I had heard about the Holographic Universe concept I wasn't too familiar with it. Your post really clarified in my mind what this is all about. Thank you.

  13. Hi Bee,

    I think this article sets the stage for what we want to examine further regarding black hole evaporation. What this might mean regarding supertranslations. I am interested to see how this term is explained, regarding the continue exploration of information that is not lost, and what this might mean regarding blackholes.


  14. At a small enough scale, there's no such thing as a uniform spherical infalling shell: it has to be made out of individual particles. Even a spherical infalling shell made up a single photon (a tricky thing to construct) has to have a polarization, and when it falls into the black hole its position presumably gets measured (or for the non-Copenhagen inclined, the quantum state of the black hole becomes entangled with the state of the photon it ate, so the phase of the incoming photon wave becomes encoded in a phase in the Hilber space of the black hole), so its position gets localized.

    In AdS/CFT holographic models, distance from the surface (the radial information) in the N-dimensional model gets encoded as excitation scale in a scale-independent N-1-dimensional model. I don't know if that's the case for BRS charges: from what I read the physics of the BRS charges resembles fluid mechanics, but I'm unsure what that means for scale-invariance.


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