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I Could a Negative Dimension exist

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  1. Mar 25, 2017 #1
    Instead of the 10,11, and 26 dimensions proposed by various theories, could there be, let's say 10 positive dimensions, existing of 9 of space and one of time, but also 1 negative dimension? This is just a random theory. I have no idea what a negative dimension would hold, but I think it would be worth looking into
     
  2. jcsd
  3. Mar 25, 2017 #2
    I don't think the word 'negative' makes any sense in regards to dimensions. One could choose a coordinate system that reversed the sign of the bases for a given dimension, which would affect the sign related to any such results appropriately, but this would only serve to hindet or facilitate calculation, it would not impact on the reality at all.

    I suspect you're not really proposing a theory so much as a fantasy without foundation, rationale nor potential for testing.
     
  4. Mar 25, 2017 #3
    True, but I'm saying would it be possible for there to be a dimension where everything worked inversely as we see things happen? I suppose a more suitable name would be a reversed time dimension
     
  5. Mar 25, 2017 #4
    Dimensions are not parallel or alternate realities/universes.
    They are merely directions / degrees of freedom.

    You could, as mentioned, orient your personal coordinate axes to gve time the opposite sign*


    *ironically enough, relativistic spacetime events & intervals historically have time's future direction as negative sign, since the spatial dimensions were prioritised as positive.


    ____

    Edit: Sorry just noticed this is in QM section. My answer was more classical, but I don't believe there is much specifically QMechanical in the question
     
  6. Mar 25, 2017 #5

    fresh_42

    Staff: Mentor

    This is a false understanding of what a dimension is. A dimension is in any of its uses I know of a synonym for some kind of extension: whether it's mathematically a coordinate, or physically a quantity like length, time, mass, energy or whatsoever. @_PJ_ mentioned a reverse measurement of such an extension, but this is still an extension. That's the additive version of what you called "inverse". The multiplicative version would be a quotient, like frequency is. This, too, is physically a dimension. The fact that it counts something per second is only of technical interest and doesn't affect what is meant by a dimension. Therefore, there cannot be something of negative dimension. As soon as it is there, it has a positive dimension of some kind.
     
  7. Mar 25, 2017 #6
    Oh. I see what you mean. So there can be no negative dimensions
     
  8. Mar 25, 2017 #7

    fresh_42

    Staff: Mentor

    Yes. As far as I know, the weirdest you can get are some non-integer dimensions in fractal theory or topology. The smallest thinkable is a point, which has dimension zero. It "exists" without any extension.
     
  9. Mar 25, 2017 #8
    No, a dimension is stuff that can be measured (or hypothesized), the units you measure it in and whether you call them positive or negative units is arbitrary.
     
  10. Mar 25, 2017 #9
    As Fresh42 says, you can mathematically introduce arbitrary mathematical spaces with dimensions to represent quantities - I could have a "lunch space" with an icecream dimension - where any amount of icecream had at lunchtime represented by a position along that icecream dimension - but it would only serve as a construct to use as a calculation or modelling tool.
     
  11. Mar 28, 2017 #10
    Some definitions of dimension used in fractal theory are correlation dimension, box-counting dimension, and Hausdorff dimension. It's not possible for these to be negative, because it would mean that you somehow have more points within a neighborhood of a point as you shrink the neighborhood. That seems impossible by any sensible definition of distance.
     
  12. Mar 29, 2017 #11
    There are also degenerate metrics. In the metric you can have zeroes but this changes nothing to the theory I think.
     
  13. Mar 30, 2017 #12
    Depending of course where a is pointing, a[-6][-5] can be a perfectly valid reference. Negative subscripts are valid and could be said to represent negative dimensions... although, a is still an array of +2 dimensions. The statement, declare a[-2] makes no sense. So never mind.
     
  14. Mar 30, 2017 #13

    Drakkith

    User Avatar

    Staff: Mentor

    I think the question has been adequately answered. Anyone with further questions about dimensions in physics or math can make a new thread in the appropriate forum.

    I'm locking this thread before it starts attracting crackpots. Thread locked.
     
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