Friday, December 13, 2013

"Holographic" Universe?

There's a recent article that I've seen circulating around Google+, namely:

Simulations back up the theory that Universe is a hologram, Published on Nature.com, Dec. 10, 2013.

This is a bit of a synchronicity for me in some ways as I've been revisiting some ideas regarding notions of a "holographic" universe and, indeed, have been planning on doing some review/analysis here on Drifting Labyrinths of a few YouTube videos on the subject, which I have watched this past week. But this is an aside--now let's get to the matter at hand.

I've seen some comments regarding this article, and I think that some people misunderstand what the article is actually saying. It does not say that we are living in a hologram and it certainly does not say we are living in something that is similar to The Matrix. What it does say is that certain interpretations of string theory--ones which use nine spatial dimensions with one dimension of time (for a total of ten dimensions)--can be seen as a projection, or "hologram," of a specific sort of one dimensional model of quantum mechanics. From the article:

The mathematically intricate world of strings...would be merely a hologram: the real action would play out in a simpler, flatter cosmos where there is no gravity.

and the article later says of this "simpler flatter universe":

The lower-dimensional, gravity-free [universe] has but a single dimension and its menagerie of quantum particles resembles a group of idealized springs, or harmonic oscillators, attached to one another.

What some people seem to miss in the article is where theoretical physicist Juan Maldacena is paraphrased as saying:

Neither of these model universes...resembles our own.

What the article is actually reporting on is the fact that there are problems/solutions which are translatable from the more complicated and thus, mathematically more difficult, ten dimensional model of superstrings to this simpler one dimensional model. In the article, these problems and solutions concern properties of certain kinds of black holes.

Now, the fact that a specific one dimensional model has some sort of equivalency with a ten dimensional model does not seem particularly surprising in this instance: in string theory the strings themselves are seen to be one dimensional objects and these one dimensional objects are "vibrating" in the ten dimensions. It seems at least intuitively possible that a simplified model of the ten dimensions of certain formulations of string theory would be able to be expressed in a single dimension--perhaps not much differently from how we can think of and express four dimensional "light cones" in two dimensions, how we can explore four dimensional geometry by the projection of four dimensional objects onto a two dimensional surface, or how we create a three dimensional visual experience from the two dimensional representation of images on our retinas. What I am getting at here is that it seems there are several instances of translating phenomena from such and such a dimensional configuration to another, and so, it's not like such translations are something new.

Moreover, it's not like the discoveries reported in this article are conclusive that certain ten dimensional string theories are entirely translatable into this specific one dimensional model. As the article itself says the research being reported upon is not a proof but provides "...compelling evidence that Maldacena's conjecture is true."

What was this conjecture? It's not that we are living in a hologram or The Matrix that's for sure; rather, the conjecture is that there exists a model of the universe such that a "...model of the Universe in which gravity arises from infinitesimally thin vibrating strings [i.e., in the context of the content of the research reported on in the article, specific models of ten dimensional string theory] could be reinterpreted in terms of well-established physics [and this would be, apparently, the physics of the one dimensional model reported on in the article]". In other words, the "compelling" evidence is in regards to the fact that there is a simplified model of a more complex model.

And that's the so-called "rub" here: we are talking about models of the universe and not the universe itself. Pretty much by definition all models are going to be simplified versions of whatever it is the model is modeling. Further, since all these models in current physics are essentially mathematical in nature, I can't help but think that any model is going to run up against some problematic manifestation similar to Gödel's Incompleteness Theorem, by which I mean that, for any given model of the universe, it will be impossible for it to be both complete and consistent. Put differently, it seems likely that there will always be truths of the universe that are unable to be fully represented within a physical model of the universe.

There are more things in heaven and earth, Horatio,
Than are dreamt of in your philosophy.

3 comments:

  1. This is a subtle point: In GIT(s) it is the first order theory that is used to describe the model that is incomplete or inconsistent, not the model. Given an FO axiomatisation that allows us to axiomatise certain basic properties of integer arithmetic there are certain statements that are true in the model but that cannot be proved so using the axioms and rules of inference. basically it means (as far as I understand it) that i might have a very nice model of the universe but i can't use logic (in any commonly understood scientific sense of that term) to prove everything that is true about that model (if that model includes very basic number theory): I could define a very nice mathematical model of the universe and not be able to prove everything that it says is true.

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    1. Oops sorry for repeating that last point twice in the last sentence

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  2. First, no need to apologize: repetition can help to clarify or otherwise assist in understanding.

    Second, thanks for taking the time to read and comment!

    Third, and to the meat of the matter, you are entirely correct, and I have erred: Gödel's Incompleteness Theorem *is* about the first order language, specifically about arithmetic, yes, and not about the model the language exists in! My bad for running the two together and thanks for keeping me honest, heh.

    I guess what I was trying to get at is: if the language of any given model is itself unable to express all the truths about the objects which the language represents, then how can the model itself ever be fully representational of that which it is modelling? Does that make more sense in the context of first order languages, Gödel's Incompleteness Theorem, meta-theory and models (because I don't think that this says quite the same thing you say about having a model and not being able to prove that everything the model says is true)?

    I must admit it has been awhile since I've considered any of this stuff with any degree of rigour--I've definitely got some rust to be rid of--so, again, I appreciate the feedback!

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