Reciprocity as an Ever-Present Dual Property of Everything

Abstract

Reciprocity may be understood as relation of action and reaction in the sense of Hegel's philosophical definition. Quoting Kant, freedom and ethical necessities are reciprocally limited. In this contribution, a more mathematical than philosophical reflection about reciprocity as an ever-present dual property of everything was given. As a crystallographer, the author is familiar with the action of Fourier transforms and the relation between a crystal lattice and its reciprocal lattice, already pointing to the duality between particles and waves. A generalization of the reciprocity term was stimulated by results of the famous Information Relativity (IR) theory of Suleiman with its proven physical manifestation of matter-wave duality, compared to the set-theoretical E-Infinity theory developed by El Naschie, where the zero set represents the pre-quantum particle, and the pre-quantum wave is assigned to the empty set boundary surrounding the pre-particle. Expectedly, the most irrational number ( ) 5 1 2 ϕ = − of the golden mean is involved in these thoughts, because this number is intimately connected with its inverse. An important role plays further Hardy's maximum quantum entanglement probability as the fifth power of φ and its connection to the dark matter. Remembering, the eleven dimensions in Witten's M-theory may be decomposed into the Lucas number L 5 = 11 = φ −5 -φ 5 . Reciprocity is indeed omnipresent in our world as piloting waves that accompany all observable earthen and cosmic matter. As a side effect of the IR theory some fundamental constants such as the gyromagnetic factor of the electron, Sommerfeld's fine-structure constant as well as the charge of the electron must be marginally changed caused by altered relativistic corrections. Consequences also arise for our vision about the evolution of life and consciousness.

Crystal chemistry criteria of the existence of spin liquids on the kagome lattice

“…Duality is a fundamental phenomenon in nature producing equilibrium for contradictions. In physics, the term 'duality' has a rather broad concept [110][111][112][113]. In this case, duality-magnetic nonequivalence (weakness and strength) of crystallographically equivalent interactions-serves as a reason for creating the forces destructing the spin liquid and resulting in the magnetic ordering of frustrated AFM systems.…”

Phase Transitions Governed by the Fifth Power of the Golden Mean and Beyond

“…Essential suggestions of Irvin and scientific fellows about the golden ratio as a fundamental constant of nature could be ennobled by considering the IRT theory [8] [61]. The author wants to encourage "down-to-earth" physicists to follow and complete these suggestions and the perspective views of the present author, including the proposed change of some important physical constants [19] [62].…”

“…The maximum of this energy density relation at a recession velocity of φ yielded exactly φ 5 and was attributed to criticality of a transition at cosmic scale [9]. Another phase transition of economic relevance, the superconducting transition, also indicates a φ 5 relation [17] [18] [19]. After this a further topic is included, namely Tammes problem of the largest diameter of N non-overlapping circles on the surface of a sphere with its connection to viral morphology and crystallography [20].…”

Reciprocity Relation between Alternative Gravity Formulas

“…Reciprocity relations are frequently observed in physics. Most important is the reciprocal duality between particles and waves [9]. The reciprocity relation between Sommerfeld's structure constant [10] and Guynn's galactic velocity is another prominent example [11] [12] [13].…”