by twistor59 wrote:But those conceptual reasons can't carry much weight because according to some formulations of the holographic principle, space may be essentially two dimensional and the 3rd dimension may not be fundamental. If space is two dimensional then objects which occupy it may be at most two dimensional.
"Susskind and 't Hooft stressed that the lesson should be general: since the information required to describe physical phenomena within any given region of space can be fully encoded by data on a surface that surrounds the region, then there's reason to think that the surface is where the fundamental physical processes actually happen. Our familiar three-dimensional reality, these bold thinkers suggested, would then be likened to a holographic projection of those distant two-dimensional physical processes.
If this line of reasoning is correct, then there are physical processes taking place on some distant surface that, much like a puppeteer pulls strings, are fully linked to the processes taking place in my fingers, arms, and brain as I type these words at my desk. Our experiences here, and that distant reality, would form the most interlocked of parallel worlds. Phenomena in the two—I'll call them Holographic Parallel Universes—would be so fully joined that their respective evolutions would be as connected as me and my shadow."
(Greene, Brian. The Hidden Reality: Parallel Universes and the Deep Laws of the Cosmos. New York: Alfred A. Knopf, 2011. pp. 260-1)
So, according to the holographic model, all the 3D things existing in the "shadowy" bulk world are unreal projections of the real physical (information) processes taking place on the 2D boundary world.
The holographic model obviously presupposes that surfaces as 2D boundaries of space regions are real physical things. For if they are not, there cannot be any real physical (information) processes taking place on them.
Well, it all depends on your conception of space. Most physical models and theories are based on the assumption that space is fundamentally composed or made up of 0-dimensional space points. Given this conception, 2D boundaries are real parts of space as surfaces of 3D regions which are composed of points just like regions.
But I doubt that this conception is true, thinking it more plausible that points, lines, and surfaces of or in space are but mathematically abstracted limits which aren't physically real, aren't concrete physical things.
(My approach to physical space/spacetime is holistic rather than atomistic.)
If I'm right, then the holographic model is an ontological nonstarter because it operates with fictional things: two-dimensional physical things.
"boundary. The boundaries of extended objects may be thought of in two ways: as limits or as thin parts. Limits of the object have fewer dimensions than it has itself: a three-dimensional brick has surfaces without thickness; the edge where two faces meet is a one-dimensional line; the corner where three faces meet is a point. An enduring event like a kiss has a beginning and an end without duration. There are also inner boundaries, like the half-way point in the flight of an arrow. Boundaries in this sense raise many ontological questions. Do they really exist or are they mathematical fictions? Are they parts of their objects, or of the surroundings, or neither? Alternatively, boundaries are simply 'thin' parts of the same dimensionality as their wholes. At stake is whether the highly successful mathematics of continuous structures, like the real numbers, which treat extents as composed of extensionless points, truly depict reality."
("Boundary," by Peter Simons. In A Companion to Metaphysics, 2nd ed., edited by Jaegwon Kim, Ernest Sosa, and Gary S. Rosenkrantz, 155. Malden, MA: Wiley-Blackwell, 2009.)
