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Help with Dimensions

  1. Sep 27, 2009 #1
    There are 'four' experimentally proven dimensions. Anything and everything must be defined by 'four' dimensions.

    It doesn't make sense to me to say "An Object exists in two dimensional space" or "Three dimensional."

    To mean there is one dimension, what everything exists in, defined by (x,y,z,t).

    For example: A circle on a piece of paper is called two dimensional. But it has a height, albeit small, and exists in some reference frame.

    So what is the first dimension, the second dimension, the third dimension. My logic tells me since nothing can exist in these dimensions, they themselves don't exist.
     
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  3. Sep 27, 2009 #2
    What...

    It all depends on if you consider time a dimension in the same sense as spatial dimensions.

    It also depends on a definition of dimension.


    A common definition for geometry defines a dimension as the minimum number of coordiantes to specify a spcific point on its geometry.

    Using 3 coodinates x,y,x means 3 dimensions.
     
  4. Sep 27, 2009 #3
    Has anyone ever seen a circle on a piece of paper, or anywhere else in nature for that matter? I mean a genuine, perfect circle, as opposed to a picture of a circle. Of course not! A circle, a sphere, a cube, the Mandelbrot set... they're all abstract mathematical objects. They're ideas, not something that can exist on a sheet of paper, except as an approximation. What you see on a page or a screen will look less and less like a circle the closer you look at its image, as you start to see all its flaws and roughness, its height (in the case of a drawing on paper), or its pixels (if on a screen).

    And because circles and two dimensional spaces are ideas, which come into existence in our minds by the act of defining them, their existence can't be disputed with reference to the dimensions of the physical universe, although we can debate how useful they are as models of aspects of nature.
     
  5. Sep 28, 2009 #4
    What? Time and space are one in the same. How would YOU consider them different? Type in SR Albert Einstein on Wikipedia Albert Einstein's and see the proof.

    Saying is 2-dimensional is as ridiculous as saying its 60 - dimentional. Neither is possible. The 60th dimension doesn't exist (as of yet). Neither should the '2nd' dimension.
     
  6. Sep 28, 2009 #5

    diazona

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    Schrodinger's equation:
    [tex] i \hbar \frac{\partial \psi}{\partial t} = -\frac{\hbar^2}{2m}\nabla^2\psi + U(\vec{x})\psi [/tex]
    Time and space are completely different there. Or classical mechanics: the velocity of a particle, which is a very important quantity, is defined as a time derivative, but spatial derivatives don't hold the same importance. Equations of motion describe the changes of a system over time, not space. Even in relativity, if you look at the Minkowski metric
    [tex]\begin{pmatrix}-1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1\end{pmatrix}[/tex]
    you'll see that it has a -1 in the time dimension but +1 in the spatial dimensions. So time and space are not the same, though Einstein's hypothesis (well, a consequence of his hypothesis) was that they're not completely separate concepts either.

    And think about this: what if the universe is actually 10-dimensional, as some variants of string theory are claiming?
     
    Last edited by a moderator: Sep 28, 2009
  7. Sep 28, 2009 #6
    Thank you for proving my point. The equation and matrix above prove that space and time cannot be described seperately. Taking either out of the equation or matrix renders them meaningless.

    As far as 10-dimensions go, yes there is a working theory describing all 10 dimensions, but has yet to be proven experimentally, alas we are stuck in this one dimensional world involving (x,y,z,t).
     
  8. Sep 28, 2009 #7
    If you're goimg to say there's only one spatial dimension but you need three values to locate any point in it, why not just say there are three spatial dimensions? Time must also be considered a dimension, because as you move through the spatial dimensions you also move through time.
     
  9. Sep 29, 2009 #8
    Four dimensional spacetime, the simplest instance of which is Minkowski space (the geometrical setting for special relativity), isn't the same thing as a four-dimensional Euclidean space (the place where a tesseract lives). For one thing, in Minkowski space, the three dimensions of space have a differenent sign to the one dimension of time, whereas the four dimensions of Euclidean 4-space are identical.

    But they're ideas. An idea exists when we think of it, as an idea. 3d space and 4d spacetime are also ideas, ones which happen to have particular usefulness in describing nature.
     
  10. Sep 29, 2009 #9
    The notion of an object "Existing" in x-dimensional space is in itself a statement which is not true. So as far as this goes, dimensions and more broadly mathematics are all constructs of a human mind to aid in understanding what he sees around him.

    As for what you asked, its all about perspective, think about this:

    if you were an ant walking on a curved piece of paper, would you notice the curvature of the paper? no! for you, all would be either front-back or left-right. So your existence would be two dimensional! So you see, saying we live in a 2-D,3-D or 10-D world is really an abstract way of approximating nature. We so firmly believe we live in a 3-D world (or 4-D if you want to include time as a disparate dimension) because our senses are tuned to only make sense of reality in 3D. so our eyes see 3-D, our ears hear in 3-D and so on and so forth. if we were really small, like maybe as big as a quantum point, we would have no use for any dimension at all.
     
  11. Sep 29, 2009 #10
    I'm an engineer so pretty much base everything on classical mechanics and consider time and spacial dimensions seperate, i.e. dont really give a crap about time as a dimension as its not useful for practical purposes.

    Dimensions are stuff I can measure with my ruler, when I design a box I use 3 dimensions, x,y,z.


    So as I said before... it depends on definitions and considerations in context.


    Rasalhague said it better than me. Are you talking about Minkowski space or Euclidean space.
     
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