Asymptotic freedom and noninteger dimensionality

Abstract

This paper shows that below a critical value of dimensionality that lies between two and three, the potential between objects begins to fall as the energy levels increase. For dimensionality below two, the potential becomes constant irrespective of separation and the force between them disappears, which represents a new paradigm of asymptotic freedom. Since asymptotic freedom is at the basis of many applications such as those associated with strange metals, unconventional superconductors, and fractional quantum Hall states, the new paradigm can have novel applications. It also is of relevance to the study of anomalous mechanical effects that are important in metamaterials.

An Information Principle Based on Partitions

“…Subject-object interactions unfold via sensory processing [14[15] that is based on implicit partitions. One must pay attention to such interactions even in natural systems, if we accept the proposal that space itself is not quite 3-dimensional although our instruments and models map it into three dimensions [16][17] [18]. There is also substantial research on the noninteger dimensionality associated with natural phenomena [19] [20][21] that can either be seen as associated with physical or mathematical structures or emerging from the deeper nature of space time.…”

Weighted Linear Fractals

“…It is different from the Milky Way in that its bar is larger and the arms are less welldefined and not as symmetrical [13]. Considering fractals in nature, it should be noted that the dimensionality of e is optimal in the frame of physical space from an information theoretic perspective [14][15] [16]. Since data space in biology may be seen in a manner paralleling that of physical space, it is natural to encounter fractals in languages, organisms, and behaviors [17] [18], life in general and the structure of the DNA [19][20] [21], and in the neurosciences systems [22] [23].…”

Weighted Linear Fractals

“…It is different from the Milky Way in that its bar is larger and the arms are less welldefined and not as symmetrical [13]. Considering fractals in nature, it should be noted that the dimensionality of e is optimal in the frame of physical space from an information theoretic perspective [14][15] [16]. Since data space in biology may be seen in a manner paralleling that of physical space, it is natural to encounter fractals in languages, organisms, and behaviors [17] [18], life in general and the structure of the DNA [19][20] [21], and in the neurosciences systems [22] [23].…”