On the Isomorphism between Dissipative Systems, Fractal Self-Similarity and Electrodynamics. Toward an Integrated Vision of Nature

Abstract

In electrodynamics there is a mutual exchange of energy and momentum between the matter field and the electromagnetic field and the total energy and momentum are conserved. For a constant magnetic field and harmonic scalar potential, electrodynamics is shown to be isomorph to a system of damped/amplified harmonic oscillators. These can be described by squeezed coherent states which in turn are isomorph to self-similar fractal structures. Under the said conditions of constant magnetic field and harmonic scalar potential, electrodynamics is thus isomorph to fractal self-similar structures and squeezed coherent states. At a quantum level, dissipation induces noncommutative geometry with the squeezing parameter playing a relevant role. Ubiquity of fractals in Nature and relevance of coherent states and electromagnetic interaction point to a unified, integrated vision of Nature.

Water Bridging Dynamics of Polymerase Chain Reaction in the Gauge Theory Paradigm of Quantum Fields

“…Moreover, a fundamental role is played by the (fractal-like) self-similarity (Figure 2) of the EMS emitted by the DNA-{water dipole wave} interaction vertex, which has been shown [20][21][22][23] to be the manifestation of coherent microscopic dynamics, as indeed our discussion in this paper has suggested. These (fractal-like) self-similarity properties of the EMS in turn induce self-similar organization in the irradiated water.…”

“…The decimal dilutions of original concentration of 2 ng/ml HIV-1 emitting EMS are between 10 −6 and 10 −10 (the first of the serial dilutions do not emit detectable signals) [3][4][5][6]. In the range between about 100 and 2000 Hz the signal shows fluctuations densely distributed around the linear fit with negative slope coefficient d = 0.80794, thus exhibiting scale-free, self-similar behavior in that frequency range with self-similarity (fractal) dimension d. It is known [20][21][22][23] that such a fractal-like self-similarity structure is the manifestation of coherent dynamics active at a microscopic level, as we indeed find in the following sections. This first step can be followed in different conditions of space and time by a second step, consisting in transformation of the signal into an analog form and sending its electric vector to a solenoid which will generate a magnetic field in a test tube of water.…”

On the coherent behavior of pancreatic beta cell clusters

“…In each of the linearity intervals, the constancy of the angular coefficient d and its independence of n express the scale free nature and the self-similarity properties of the phenomenon. Indeed, d is called the self-similarity or fractal dimension [15] and q is called the deformation or squeezing parameter [16,17,18]. We recall that, self-similarity is properly defined only in the n → ∞ limit (cf.…”

“…As observed in Refs. [17,18,21,20], the n-th power component u n,q (α) of the self-similarity Eq. (2) is obtained by applying (a) n to |qα and restricting to real qα qα|(a) n |qα = (qα) n = u n,q (α), qα → Re(qα).…”

“…(2), and the n-th term in the q-deformed coherent state series. In other words, they provide the isomorphism relation between selfsimilarity properties of the observed phenomenology and the q-deformed algebra of the squeezed coherent states [17,18,21,20].…”