What Are Curled-Up Dimensions and Their Implications?

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Discussion Overview

The discussion revolves around the concept of "curled-up dimensions," exploring their nature and implications within theoretical frameworks such as string theory. Participants engage in geometric interpretations, mathematical reasoning, and philosophical considerations regarding the existence and characteristics of these dimensions.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • Some participants describe "curled-up dimensions" using analogies from video games, suggesting that such dimensions could allow for a return to the starting point after moving a short distance.
  • Others argue that string theory's claims about curled dimensions lack empirical support and remain more philosophical than scientific.
  • A participant proposes a detailed geometric analogy involving maps to illustrate how one might perceive a curled-up dimension, questioning the difference between curled and non-curled dimensions.
  • Another participant suggests that a curled dimension could allow for different experiences of motion, as demonstrated by sending light beams in opposite directions and observing their collision points.
  • Some participants introduce speculative ideas about semi-curled dimensions and dimensions that do not interact with others, raising questions about their existence and implications.
  • There is a discussion about the nature of mathematical theories and their relationship to reality, with some participants expressing skepticism about the existence of mathematically consistent but unobservable dimensions.

Areas of Agreement / Disagreement

Participants express a range of views, with no consensus on the nature or implications of curled-up dimensions. Some agree on the conceptual differences between curled and non-curled dimensions, while others challenge the validity of these concepts without empirical evidence.

Contextual Notes

Participants highlight limitations in understanding curled dimensions, including the dependence on definitions and the lack of observable evidence for certain theoretical constructs. The discussion remains open-ended regarding the implications of these dimensions.

  • #31
Hurkyl said:
Fortunately, things become simpler when the dimension is very tiny (e.g. if quarks can 'span' the entire dimension) -- you simply don't (directly) detect it at all!

Yes indeed, Hurkyl. But then it's hard to say what curled-up dimensions are "like" and, with the rest of folk beyond the standard model, one is left literally grasping at straws (or strings?), not having detected anything new lately!

Let's hope that the LHC soon turns up something new, if it doesn't blow us all to Hades.
 
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  • #32
Dcase said:
Curled-up dimensions have been discussed in papers ...and probably others... the ubiquity of helices...

Add:

7. It's very old and all relative: "..a geometrically straight, but eccentric (line) line parallel to the axis of a twisted (crystal lattice) is in fact a helical line in lattice coordinates" Phil.Mag. 34, 1105 (1958).
 

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