Can anyone clarify Brian Greene's relation of holographic parallel universes with Plato's cave/ The string theorist Brian Greene recently came up with the book The Hidden Realities. In Chapter 9, and also in the article http://discovermagazine.com/2011/jun/03-our-universe-may-be-a-giant-hologram , he argued that our universe might be a hologram with a holographic parallel universe and compares our world to shadows in Plato's cave. Can anyone point me to where I can read up more on this/ Are we living in a black hole. Are we puppets pulled by strings from some distant surface
 A: The "Plato's cave" analogy is due to Polyakov: http://cdsweb.cern.ch/record/364444/files/9809057.pdf. The precise formulation is that a mathematical description of bulk gravity should be considered as living on a null surface (like a black-hole horizon) far away. This doesn't make us puppets, but it does mean that our perception of bulk space-time is not correct at short distances, and we are like 3-d shadows of a 2-d reality (more likely higher dimensions, but that's the idea anyway).
The "parallel universes" stuff is only in an extremely speculative, in my opinion completely experimentally excluded, offshoot of string theory called "large extra dimensions". There you can put extra universe "parallel" to ours, and they would only interact with us through gravity. This idea might appeal to people because they might think it explains astral projection or something like that, but in these theories, there is no way project yourself into an extra dimension unless your consciousness is made out of gravitons. It is logically independent of the holographic principle.
