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Thinking Outside Euclid's Box

  1. Nov 13, 2005 #1
    The following is not intended as a definitive explanation of other dimensions, but a suggestion for other ways of looking at the idea of physical dimensions.

    Supporters of string theory occasionally remark that the reason we cannot "see" other dimensions is that they must be very small. Such comments represent thinking inside Euclid's geometric box. We have been conditioned to believe that physical dimensions are limited to the 3 dimension of Euclidean geometry (length, width and height) and maybe time. But, are these the only characteristics of physical reality that can qualify as dimensions in the mathematical sense.

    A dimension is basically a characteristic or variable. Length, width and height are not the only variables that can be represented geometrically. Social as well as physical data can be represented as 2-dimensional images. Social data may not qualify as a physical dimension of reality, but what about other physical data?

    How many dimensions do we actually "see"? Each eye sends a flat image to the brain which then interprets the visual as showing length, width and height using differences between the two images and certain visual clues such as closer objects appearing larger to add a dimension of depth to the image.

    However, length, width and height are not the only physical characteristics the eyes perceive. The eyes also see variations in color. Color is a function of the electromagnetic characteristics of sources of emitted or reflected light.
    Objects of the same length, width and height may be of different colors. The existence of color implies the existence of other physical dimensions.

    Euclidean geometry theory begins with points which have zero dimensions. A point is at a specified location or there is no point at the location. If physical reality had only 3 dimensions there would be something (such as a quark) at a location or there would be nothing. If the quark can have more than one possible characteristic, then quarks are variables and imply the existence of other dimensions. Variations in the types of quarks could be additional physical dimensions of reality. Perhaps gravity is another physical dimension, or perhaps there is an energy dimension.

    Dimensions are sometimes viewed as having a heirarchy with additional dimensions being higher than the others. However, math theory allows for separate spaces that may intersect in one or more dimensions and we perceive reality as having 3 dimensions because each of the spaces shares the dimensions of length,width and height. For example, each flavor of quark might have its own space in which there is a quark of that flavor at a location or there isn't a quark at that location. There might be a gravity space. Perhaps the weak force and strong force are two dimensions in a force space.

    The intersection of these different spaces might be static or dynamic. A dynamic intersection could explain certain aspects of quantum physics. The apparent winking in and out of particles could result from those particles being within the area of intersection at one time but not at another. Tunneling might result from shift in the locus of the intersection.
  2. jcsd
  3. Nov 14, 2005 #2
    When I think of the three dimensions(Length, width and height), I think of a cube. But when I think of dimensions as relates to a sphere, it takes on a whole new relationship. Since events occuring at the level in question, the conservation of angular momentum provides a number of considerations when addressing the merging or convergence of light waves produced by any number of sources. In other words, is it possible that additional dimensions only become necessary in order to satisfy the math requirements dealing at the sub-atomic level.

    I've thought about this problem for some time and think the answers will eventually be found at this level.

    Just my thought....John
  4. Nov 14, 2005 #3
    When you think of a cube, that is flat space. When you think of a sphere, that is curved space - so curled that it makes a circle. Add in open or hyperbolic curvature, where all paths diverge, and you have covered all three possibilities.

    Cheers - John McCrone.
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