Here ya go Carl … this IS an aspect worthy of consideration … this being because fractality may exist right down to the quantum level, and up to the opposite end of the scale. Almost no other theory or perspective bridges that scale expanse whilst displaying consistency.
Spacetime May Have Fractal Properties on a Quantum Scale
Quote:
As if extra dimensions weren’t strange enough, new research has probed an even more mind-bending possibility: that spacetime has dimensions that change depending on the scale, and the dimensions could have fractal properties on small scales. In a recent study, Dario Benedetti, a physicist at the Perimeter Institute for Theoretical Physics in Waterloo, Ontario, has investigated two possible examples of spacetime with scale-dependent dimensions deviating from classical values at short scales. More than being just an interesting idea, this phenomenon might provide insight into a quantum theory of relativity, which also has been suggested to have scale-dependent dimensions. Benedetti’s study is published in a recent issue of Physical Review Letters.
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In his study, Benedetti explains that a spacetime with quantum group symmetry has in general a scale-dependent dimension. Unlike classical groups, which act on commutative spaces, quantum groups act on nocommutative spaces (e.g. where xy doesn’t equal yx), which emerges through their unique curvature and quantum uncertainty. Here, Benedetti considers two types of spacetime with quantum group symmetry - a quantum sphere and k-Minkowski spacetime - and calculates their dimensions. In both spaces, the dimensions have fractal properties at small scales, and only reach classical values at large scales.
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Benedetti’s results match previous approaches to quantum gravity, which also point to the emergence of a ground-scale spacetime with fractal properties. Together, these studies may help scientists understand the unique Planck scale properties of spacetime, and possibly tie in to a quantum theory of gravity. For instance, as Benedetti explains, the fractal nature of quantum spacetime might enable gravity to cure its own ultraviolet behavior by dimensional reduction.
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Cheers