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Thread: the various dimensions

  1. #1 the various dimensions 
    Forum Radioactive Isotope
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    Is it fair to say that all the dimensions that have been identified are actually mathematical abstractions?

    What I mean is ,when for example in the holographic principle theory they talk of a 2- dimensional plane that all the objects existing in that plane are actually in same the 4 dimensions as we , the observer is ?

    Since we do not know the interior structure of any object with certainty it makes no sense to me to say that the third dimension is absent.


    Last edited by geordief; February 16th, 2012 at 02:49 PM.
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    Moderator Moderator Markus Hanke's Avatar
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    Please allow me to quote from the Wikipedia entry for "Holographic Principle" :

    "The holographic principle is a property of quantum gravity and string theories which states that the description of a volume of space can be thought of as encoded on a boundary to the region—preferably a light-like boundary like a gravitational horizon. "

    What this basically means is that one may be able to reduce the mathematical description of a 3-dimensional system down to a 2-dimensional problem formulated over the boundary of that system, very much like a 3-dimensional picture being encoded on a 2-dimensional surface in a classic hologram. In other words, the surface boundary contains all relevant information about the interior of the higher-dimensional volume. This does not necessarily mean that the spatial dimensions of the volume of space itself aren't real.
    This is actually a very difficult concept when applied to the universe as a whole, because the cosmological horizon is not stationary and has only finite area, thus can only hold a finite amount of information. It isn't clear what the implications of this really are.

    Very interesting problem though !


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    Forum Radioactive Isotope
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    thanks
    I appreciate the holographic principle is interesting but I was wondering whether the 2-dimensional boundary was in fact 2- dimensional or rather an extreme version of the 3- (or 4 - or >4- ? ) dimensional reality that we can presumably be confident actually exists .

    Maybe my point is only nitpicking but has anyone actually arranged matter onto a 2 dimensional plane?

    I presume that that plane would be oriented in the pevailing space time curvature (which would itself vary along the "plane") so isn't a 2 dimensional object an approximation only?
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    Moderator Moderator Markus Hanke's Avatar
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    Quote Originally Posted by geordief View Post
    thanks
    I appreciate the holographic principle is interesting but I was wondering whether the 2-dimensional boundary was in fact 2- dimensional or rather an extreme version of the 3- (or 4 - or >4- ? ) dimensional reality that we can presumably be confident actually exists .

    Maybe my point is only nitpicking but has anyone actually arranged matter onto a 2 dimensional plane?

    I presume that that plane would be oriented in the pevailing space time curvature (which would itself vary along the "plane") so isn't a 2 dimensional object an approximation only?
    I think it is not clear yet how that principle is to be interpreted physically - is it a purely mathematical statement, or do we actually live in a lower-dimensional universe, and the extra dimensions aren't actually real ? So far as I know this is an area of ongoing research.
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