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pmerriam
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new explanation for AdS/CFT??
Here is a possible new interpretation of AdS/CFT. (Just humor me for a moment.)
First, take a look at the pattens as photographed in Discover magizine: "Waves on a sphere follow the unpredictable Rules of Quantum Mechanics". (p. 53 of March 2011 Discover magazine).
Now, in a different article I read somewhere a few months ago, they were simulating the brain. On a sphere they planted nodes that would randomly go off. When nodes were connected to their neighbors, nothing happened (except the randomly turned on nodes would go on, then off). When the nodes were connected to a bunch of other nodes on the polar opposite of the sphere, the entire sphere would oscillate between all-on and all-off. (By a node being connected to another one I mean a wire through the sphere (and not just on the surface of it) that connects node 1 to node 2, and if node 1 gets turned on then it will turn on node 2.)
The point is this: when the nodes were connected to various in-between distributions of near and far nodes on the sphere, they got exactly the patterns of quantum waves on a sphere mentioned above!
This makes a great deal of sense if you think about it. In this scenario, the evolution of the waves on a sphere is due to two things. (Actually, instead of a sphere we may just as well talk about some more relevant manifold, such as M=AdS^5 times S^5, or whatever). 1. randomly briefly "turned on nodes" on the manifold—probably translated as virtual particles in any ordinary QFT. And 2. each node is connected to others, as given by some distribution of near and far nodes, on this manifold. The geometry of the manifold is thus a critical factor in the evolution of the set of nodes that are turned on.
On the surface of the sphere, the evolution of the nodes appears non-local (or partially local). But as a sphere situated in space (R^3) all that is happening is these electrical nodes are connected to others by a straight copper wire that goes through the inside of the sphere, and they turn each other on.
Similarly, take the manifold M. The evolution on some sub-manifold m is governed by what would *appear* to be non-local (or partially local) correlations. But they only appear that way on m. What really is happening is that randomly turned on nodes are turning on a distribution of connected other nodes through the whole manifold M (these nodes then turn on others, etc...). The connections do not appear to be local on the submanifold m, but they are "local" in the sense of being connected on the whole manifold M.
Admittedly, I don’t know if M needs an embedding space to get locality.
Now, for any quantum evolution E on a sphere, there is a function R that randomly turns nodes on, and there is a connection-distribution D of nodes on the sphere such that the pair (R, D) gives rise to precisely the evolution E (up to modulo something). The same thing would apply to quantum evolution E' on a submanifold m for a pair (R', D') on M.
That is the conjecture. There is enough freedom in the parameters that it is quite plausible.
In sum, this might be a possible explanation of why there is a string theory with gravity in a manifold dual to a QFT on the boundary.
Here is a possible new interpretation of AdS/CFT. (Just humor me for a moment.)
First, take a look at the pattens as photographed in Discover magizine: "Waves on a sphere follow the unpredictable Rules of Quantum Mechanics". (p. 53 of March 2011 Discover magazine).
Now, in a different article I read somewhere a few months ago, they were simulating the brain. On a sphere they planted nodes that would randomly go off. When nodes were connected to their neighbors, nothing happened (except the randomly turned on nodes would go on, then off). When the nodes were connected to a bunch of other nodes on the polar opposite of the sphere, the entire sphere would oscillate between all-on and all-off. (By a node being connected to another one I mean a wire through the sphere (and not just on the surface of it) that connects node 1 to node 2, and if node 1 gets turned on then it will turn on node 2.)
The point is this: when the nodes were connected to various in-between distributions of near and far nodes on the sphere, they got exactly the patterns of quantum waves on a sphere mentioned above!
This makes a great deal of sense if you think about it. In this scenario, the evolution of the waves on a sphere is due to two things. (Actually, instead of a sphere we may just as well talk about some more relevant manifold, such as M=AdS^5 times S^5, or whatever). 1. randomly briefly "turned on nodes" on the manifold—probably translated as virtual particles in any ordinary QFT. And 2. each node is connected to others, as given by some distribution of near and far nodes, on this manifold. The geometry of the manifold is thus a critical factor in the evolution of the set of nodes that are turned on.
On the surface of the sphere, the evolution of the nodes appears non-local (or partially local). But as a sphere situated in space (R^3) all that is happening is these electrical nodes are connected to others by a straight copper wire that goes through the inside of the sphere, and they turn each other on.
Similarly, take the manifold M. The evolution on some sub-manifold m is governed by what would *appear* to be non-local (or partially local) correlations. But they only appear that way on m. What really is happening is that randomly turned on nodes are turning on a distribution of connected other nodes through the whole manifold M (these nodes then turn on others, etc...). The connections do not appear to be local on the submanifold m, but they are "local" in the sense of being connected on the whole manifold M.
Admittedly, I don’t know if M needs an embedding space to get locality.
Now, for any quantum evolution E on a sphere, there is a function R that randomly turns nodes on, and there is a connection-distribution D of nodes on the sphere such that the pair (R, D) gives rise to precisely the evolution E (up to modulo something). The same thing would apply to quantum evolution E' on a submanifold m for a pair (R', D') on M.
That is the conjecture. There is enough freedom in the parameters that it is quite plausible.
In sum, this might be a possible explanation of why there is a string theory with gravity in a manifold dual to a QFT on the boundary.