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Apr. 6th, 2014 12:30 pm
symbioidlj: (Oculus)
[personal profile] symbioidlj

Amplituhedron.  Holy shit.

A talk by Nima Arkani-Hamed, regarding their discovery of this mathematical object called the Amplituhedron.



Here's an article from the Simons Foundation magazine Quanta.

Here's a link to the PDF article at Arxiv, which is given in the above article.

Here's a diagram showing the 3D Face of one form of this 4D object.  (One that solves for N=4 Supersymmetric Yang-Mills Theory):



There's also this poorly colored image which really is pretty, but I think it actually does not convey how this works as a 3D Structure:



Basically, if this theory is right, SpaceTime and Quantum Mechanics are emergent from a multi-dimensional (I think he said infinite dimension at some point, but his examples are 3D surfaces of a 4D object.  He claims that he could do on one paper on a plane flight what would be many many pages worth of Feynman diagrams to calculate the scattering trajectories of  particular particles.

Clearly, since his example is limited to one form and there are many many possible things, he says that he thinks more forms of this type of calculation can lead to better insights and new unificiations (in the example, he removes the conflict between unitarity and locality).

The vertices of this object, if I am understanding it properly, act as potential pathways for various particles (he uses gluons as an example a few times, so I'm guessing this is about gluon interaction in protons and neutrons?).  That is the potential paths they can take are calculated by the structure of this object...  The internal structure is the array of potential amplitudes in some manner.  If you give it a specific value and feed it in at a point, it will go through a given path and output at another predetermined point (I think.  He has a separate diagram for that, but I believe it's the same concept - he's essentially talking about graph theory/nodes in this case)

It sort of makes me think of the holographic principle and the holographic universe theory in the sense that there is some "eternal"/static object that has, embedded in it/on its surface, the rules for the universe.

What I am so very curious about, though, is how does this arise?  WHAT is it that causes our reality to arise?  In a hologram, we have light shining onto the surface to create that 3D space/projection.

If you think in Platonic terms, you have the 3d object casting a shadow on the 2d surface.  Only, the interesting thing here, is that it's almost the opposite, the 3d "shadow" is casting a 3d object.  (in our case, we have a 3d surface of a 4d space-time.  this 3d surface projects 3 space dimensions and one time dimension) as our universe.

Anyways, I saw another topic where someone asked if Mathematicians were Platonists, and one guy said "in private they'll tell you they are but in public, they'll be less candid and say we use math as a tool to help describe reality, of course these things, numbers, exist as a real thing outside of our mind"...  But it's certainly interesting if you think that mathematics is a pure structural external entity through which our universe arises in some manner.

It's the question of WHAT causes it that fascinates me.  I think it's like Indra's Net (to use the Jewel metaphor with these faceted 3D objects) in that there's a complex web of interactions and reflections between all the facets/jewels/faces/ of/in this THING (Terence McKenna's UFO/Oversoul/Ultimate Tool) that self-arises and self-causes.  In effect, this pure eternal mathematical form is "god" and we are "god thinking" or dreaming in some sense.

Even more interesting if you think of consciousness as the flow of things via nodes and pathways (in the same way the vertices of these objects form pathways along which rules create the structures that we see).

Yet again, there is something that flows/moves through and causes things to arise, and that, I think, is the real mystery.  We're focusing so hard on the WHAT, that we really don't know HOW (or even necessarily WHY, though some say science isn't about "WHY" I think that's a copout.  "Why is the speed of light 300,000km/s?"  When I ask this I'm told "Science doesn't have an answer for that, it just IS a constant" That really really really bothers me.  I mean, we know it's the limit that at which mass becomes infinite, but... then I suppose we end up with some weird Anthropological argument  that it is because we're here to observe it and ask why it is... I hate the fucking anthro argument, there is no "argument" there, except that "we exist in the universe due to the laws that allow us to exist" no fucking shit sherlock.

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