Canonical science is based in the so-called canonical theory. A first version of the canonical theory was pioneered by and satisfactorily applied to several physical, chemical, and biological processes: hidrodynamics, nonlinear nonequilibrium thermodynamics, chemical reactions in surfaces, Egg metabolism, etc.
The modern version of the canonical theory is a unified scientific formulation that covers a much broader range of multidisciplinary phenomena from elementary particle physics to cosmology, through the dynamics of human populations. A modern Perspective –available to everyone through open access– is given in the report Canonical science: its history, goals, and future
[1].
Canonical science has the next interesting properties not found in any other field [2]:
The concept of unification as understood in canonical science goes beyond the traditional meaning in physics. This canonical unification is irreducible to the more 'poethic' concept of unification used in the speculative superstring and M theories.
Being a true unified discipline, it is not strange that canonical science contains, as special cases, the currently available disciplines of physics, chemistry, biology, ecology, and others. For instance, the quantum field theory that conforms the basis of elementary particle physics is obtained after applying a series of quantum approximations; mathematical ecology is obtained in a well-defined macroscopic regime, where the details of the underlying physico-chemical processes are ignored; the master equations used by the Nobel laureate in chemistry in nuclear magnetic resonance (NMR) are obtained when non-Markovian contributions are ignored in a theory where gravitation effects are absent too; classical thermodynamics is a subset of canonical theory for equilibrium regimes; general relativity is obtained in a geometrodynamics approximation to the classical version of canonical theory, etcetera.
Another advantage is that we can go beyond the limitations of the current disciplines and formalisms. For instance, we do not just obtain a quantum theory of fields, but we can derive now the mass, energy, and spin of field quanta as bosons from first principles. We can go beyond classical thermodynamics and even beyond linear nonequilibrium thermodynamics; for instance, providing a generalized set of -like relationships valid also for nonlinear regimes. We can consider the effect of different non-Markovian corrections to the usual master equations used by chemists and optics comunity. We can study galactic and cosmological phenomena that cannot be studied withing the framework of general relativity. Therefore, the unification through canonical science may be understood in the sense of an umbrella theory of broadest applicability.
Whereas some disciplines in modern science are almost unrelated, others are rather interrelated. Physical chemistry, as something at the border between 'pure' physics and 'pure' chemistry, is a nice example of a multidisciplinary subject in modern science. Still, if one explores physical chemistry, one discovers that the field is not unified. There is not strong links between the different formalisms; they are mainly unrelated except by some weak connections. Physical chemistry looks like a truly heterogeneous way of studying phenomena of common interest to physicists and chemists. The 'unification' is in the subject under study rather than in the formalism used.
Canonical science breaks the usual barriers between disciplines. The same theory and formal concepts can be applied to both thermodynamic systems and lions populations, to chemical reactions and quantum mechanics, to gravitation in distant galaxies and to electromagnetic phenomena in solids at laboratory, for instance. Disciplines traditionally unrelated –such as quantum field theory and epidemiology– receive a common framework in canonical science. No other discipline achieves this.
The complexity of an organized system involves three basic features: multiplicity, interaction between subunits, and integration of subunits into the whole. As is well-known, the traditional reductionist formulations by physicists cannot adequately describe the rich behavior we can observe in complex systems. Canonical science embraces both elementary and complex phenomena at once.
The Nobel laureate in chemistry writes:
The novel features that appear at each level of complexity [...] do not and even cannot conceptually exist at the level below [...] Such an attitude is not reductionist, it is not a reduction of a level to the lower one(s) but an integration, connecting a level to the other ones by integrating species and interactions to describe and explain increasing complexity of behavior.
Complex levels of organization of matter contain more information than elementary levels. Canonical science provides an adequate conceptual and mathematical foundation for the Nobel laureate in physics brilliant thought more is different
.
Our universe is multi-hierarchical. The canonical theory has the same formal structure for the description of phenomena at each level of description: microscopic, mesoscopic, macroscopic, cosmological. This multi-hierarchical formal structure is not available in any other formulation. These features from canonical theory override the basic premises of the reductionism.
The formal structure of the canonical theory is very elegant and based in four main principles.
(i) A vector n represents the state of the natural system at any instant.
(ii) Canonical processes represented as
change the state n according to the stoichometric vector w = n(\sup +) – n(\sup –).
(iii) The average rate of change of state follows from
This equation is very general and describes phenomena cannot be described by the usual laws of physics, chemistry, or biology. For instance when all terms on the right-hand-side but S can be neglected and the state of the system n is well described by a pure quantum state, then the above equation reduces to the equation of quantum mechanics
(iv) Small fluctuations around the average follow the rate
where f is a generalization of random force.
The following table contains a heterogeneous sample of canonical processes. The range of processes selected –from particle physics to cosmology, through chemistry, heat science, biology, astrophysics, or epidemiology– illustrates the broad applicability of the canonical theory.
| 2 H(\sub 2)O (\larr ←)(\rarr →) H(\sub 3)O(\sup +) + OH(\sup –) | Autoionization of water |
 (\larr ←)(\rarr →) |
Keto-enol tautomerization |
| Zn + Cu(\sup 2+) (\larr ←)(\rarr →) Zn(\sup 2+) + Cu | Electron transfer |
| e(\sup +) + e(\sup –) (\larr ←)(\rarr →) 2 γ | Electron-positron annihilation |
| (\mi (\de (\sup 235)U\(III\) + (\sup 238)U\(IV\) ) (\de (\larr ←)(\rarr →)) (\de (\sup 238)U\(III\) + (\sup 235)U\(IV\))) | Uranium exchange with nuclear spin effect† |
| ε(\sub S) + ε(\sub B) (\larr ←)(\rarr →) ε'(\sub S) + ε'(\sub B) | System-bath heat transfer |
 (\larr ←)(\rarr →) |
electronic resonance† |
| B–C (\larr ←)(\rarr →) B + C | Breaking-formation process |
| (\mi (\de hydrophilic-surface + HMDS) (\de (\larr ←)(\rarr →)) (\de hydrophobic-surface + NH(\sub 3))) | HMDS dip-pen nanolitography writing on semiconductor surface |
| S + I (\larr ←)(\rarr →) 2 I | SIR spread of a disease in epidemiology |
| ρ(\sub A) + ρ(\sub B) (\larr ←)(\rarr →) ρ(\sub C) + ρ(\sub D) | ensemble process |
| M(\sup *) (\larr ←)(\rarr →) M + ћν | Emission-absorption of microwaves |
| vacuum (\sub j) (\larr ←)(\rarr →) vacuum (\sub k) + universe | Big Bang†† |
| D(\sup +·) + A(\sup −·) (\larr ←)(\rarr →) D(\sup ··) + A(\sup 0) | 's stabilization of a triplet state |
| C(x) + M(x(\sub m)) (\larr ←)(\rarr →) C(x + x(\sub m)) | Homogeneous nucleation by clustering |
| (\mi (\de customer–p€ + business–item) (\de (\larr ←)(\rarr →)) (\de customer–item + business–p€)) | Purchase-sale of item by p Eurs†† |
| C + X(\sub inside) (\larr ←)(\rarr →) C + X(\sub outside) | Two-state channel biomembrane transport |
| v(\sub 1) + v(\sub 2) (\larr ←)(\rarr →) v(\sub 1) + v(\sub 2) | Atomic elastic scattering |
| Prey + Lion (\larr ←)(\rarr →) 2 Lion | L/V predator-prey ecology |
Go to the index for scientific details on each program or contact with the Center for more information.
[1] Canonical science: its history, goals, and future 2008: Can. Sci. Rep. 20083v1.
[2] Including modern but outdated attempts as superstring or M-theory.