Recently, Subhash Kak proposed that space is e-dimensional, rather than the commonly supposed 3-dimensions, where, e is Eulers number that is about 2.71828, and he used this to provide a resolution to the problem of Hubble tension, which is the disagreement between values of the rate at which the universe is expanding obtained using two different methods. Now, Kak has provided further support to this theory by a model that may explain why quarks, constituents of matter, don’t interact with each other when they are up close, but are bound strongly when pulled apart.
“Noninteger dimensionality leads to the anomalous situation of strong interaction at large distances and much weaker interaction at short distances, which is a characteristic of asymptotic freedom,” writes Subhash Kak, Professor in the School of Electrical and Computer Engineering at Oklahoma State University.
His new paper shows that, as the dimensionality falls below the value of critical dimension (dcrit), which lies between 2 and 3, there arises strange behavior where increasing energy reduces the strength of interaction between the particles.
And when the value is 2 or below, the potential becomes constant (independent of separation) and force between objects or particles completely disappears. This new version of asymptotic freedom, which arises from the squeezing the dimensionality of space, could be of use in studying the anomalous mechanical properties of metamaterials.
“Future investigation will reveal whether this phenomenon based on dimensionality of space has any connection with other models of asymptotic freedom,” he concludes.
Featured image: Potential with respect to dimensionality; blue line p3,B(d), and red line p3,C(d) © S. Kak
Reference: Kak, S. Asymptotic freedom and noninteger dimensionality. Sci Rep 11, 3406 (2021). https://doi.org/10.1038/s41598-021-83002-9
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