Noncommutative Geometry
The Planck scale is a set of natural units that define the smallest measurable length and energy scales in the universe, specifically at approximately $1.6 \times 10^{-35}$ meters for length and $1.2 \times 10^{19}$ GeV for energy. These scales are significant because they mark the boundaries where quantum gravitational effects become significant, suggesting a need for a theory that unifies quantum mechanics and general relativity.
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