SCIENCE AND TECHNOLOGY XXI: New Physica, Physics X.0 & Technology X.0

The fundamentality of discovery implies if there is the Faraday effect, Lorentz-Zeeman effects, Doppler effect, Einstein’s photoelectric effect, Compton effect, Cherenkov effect, M?ssbauer effect, Hall effects…., there MUST be the Inverse Faraday effect, Lorentz-Zeeman effects, Doppler effect, Einstein’s photoelectric effect, Compton effect, Cherenkov effect, M?ssbauer effect, Hall effects,…, by LAW, of Reversibility of Effects and Convertibility of Forces and Energies.

In brief, we proposed a model of Nature, with the Force, Reversibility, Convertibility and Unity as its essential constructs, integrating the natural phenomena, causes, forces, processes and effects, and bringing forth a single strategy of physical science.

We showed the universality of reversibility properties of nature as the Principle of Reversibility, being correlative with the Principle of Symmetry and the Law of Conservation, and stating “if there is a physical process or effect in nature, there must be its inverse, converse or reversed process”. Otherwise it is hardly a real effect.

THE LAW OF GLOBAL REVERSIBILITY strictly implies that there MUST be the inverse effects, as of the above-mentioned, just by LAW, of Reversibility of Processes and Effects and Convertibility of Forces and Energies, and that Matter, Energy or Force can be neither created nor destroyed, but reversed and converted.

The discovery involves all the key features of universal laws of nature, being illustrated by an increasing number of inverse effects, as discovered or under discovery, experimental studies or innovative applications.

As such, the Law of Reversal combines all the key attributes of universal laws:

asserting the interdependence between varying quantities of physical properties;

stating that physical events occur an invariant order;

dealing with cause and effect relationships;

stating a constant regularity in the relations or order of physical phenomena in the world, thus embracing all empirical regularities of numerous physical effects.

In sum, an “outstanding scientific importance” of the Principle of Process Reversal and its Effect Conversion Laws consists in enabling the prediction of physical processes and actions of physical forces and effects as well as the nonlinear interactions and macroscopic behavior of complex systems in the systematic and consistent ways without having to consider the details of the courses of physical processes and systems (Abdoullaev, A. (2008). What Determines the World. IGI Global; http://www.igi-global.com/bookstore/chapter.aspx?titleid=28314).

Mathematics of Nature: A Categorical Theory of Everything: the Principle of Reversibility or the Laws of Convertibility

Mathematics of Nature is the key theme of Mathematical Physics X.0, which involves physics, experimental and theoretical, and general ontology of the universe (the first, as its key subject, and the second, as the guiding discipline) and pure mathematics, like as partial differential equations, geometry and topology, abstract algebra and category theory (Abdoullaev A., Reality, Universal Ontology and Knowledge Systems: Toward the Intelligent World, IGI Global, USA, 2008).

As such, it has to generate a complete and consistent representation of Nature as the total sum of material entities, changes, forces and interactive relationships, ideally, in terms of mathematical systems of definitions and axioms, rules, principles, and theorems, as deduced laws. As it was published in a famous list of mathematical problems, in Hilbert's sixth problem, challenging researchers to find an axiomatic basis to all of physics.

In brief, New Physics X.0 is about creating the ToE as a Final Theory, Ultimate Theory, or Master Theory, as a single, all-encompassing, consistent and complete theoretical framework of physics interrelating together all the physical properties and phenomena of the universe.

A Theory of Everything: the Universe as a Pre-Ordered Category of Change Sets

The algebraic language of relations, categories and functors looks the effective mathematical instruments for a formal unified description of interactions of all physical phenomena in nature. All is in terms of force (cause-effect) relationships as the force-interactions and the productive interrelationships of force, energy or power, activity and efficiency, represented by the state-change-variables, or varying quantities of physical changes, or causal sets of events. For the interactive forces of relations are the interrelationships among specific kinds of entity variables, neither object variables nor state variables, but change variables, presented in the material world as physical forces involving changes in quantity (state) variables.

The Reversibility Principle and Convertibility Laws being deduced from the mathematical physics of universal forcible relationship have a close analogy to the duality principle, an essential property of mathematical structures having a lattice order, as set theory, symbolic logic or projective geometry. It states that one true statement, operation, function or effect can be obtained from another by converting, transposing, or interchanging its correlatives. The dual formulation in the natural science of physics is as true as in mathematics.

Bearing in the mind that the nature of force-relations R

is described by the mathematics of relations, relation algebras and abstract algebra of categories, a formal definition of a category of R

is to be obtained by the standard axioms and postulates of Causal Category Theory (CCT):

There is a class of disjoint change sets C

, C

, C

…of a universal change set C;

There is a class of transformations R

, R

, R

, … of a universal force-interrelationship set R

, named functions describing the forcible relationships between change sets, namely from the domain change sets to the change range sets;

There exists an identity force-relationship of interactions I

= = R

(C, C) which may be associated with each change set

= I

: C

? C

;

To each ordered couple of change sets C

, C

in R

, it is assigned the set of one-to-one transformations R

(correspondences, morphisms, or maps) from C

to C

, as well as the set of inverse morphisms R

from C

to C

;

To each ordered triple of change sets C

, C

, C