The Fractal Dimensionality of Space
hubie writes:
Noninteger dimensions are fairly well known in mathematics, but they are also used in various branches of physics and engineering to explain the emergence of scale invariant phenomena, such as atmospheric turbulence, or for measuring coastlines. Subhash Kak of Oklahoma State University in the United States published a paper that shows that if you look at physical space through the lens of information theory, the optimal number of dimensions turns out to be not an integer.
Kak shows the optimal dimension associated with the representation of information is e=2.71828... and he argues that physical space is e-dimensional instead of 3-dimensional if one accepts optimality as a fundamental physical principle. He argues the discrepancy between 3 and e can be seen in existing data, and the example used has to do with the large scale structure of the universe.
One of the "crises" in physics is reconciling the two different values of the Hubble constant, H0. The two values are 67 km s-1 Mpc-1 if you use early universe data, and 74 km s-1 Mpc-1 if you use late universe data. If physical reality is e-dimensional and we insist on viewing it as being 3-dimensional then there is a discrepancy equal to e/3=0.9060. This number is very close to the divergence of 67/74=0.9054 from the experimental data.
Journal Reference:
Subhash Kak. Information theory and dimensionality of space [open], Scientific Reports (DOI: 10.1038/s41598-020-77855-9)
Read more of this story at SoylentNews.