Patterns in Physics

CollectionNovathème ISBN9782553016332 EditorPresses internationales Polytechnique pages214 Published2012-06-28
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When various pattern analysis methods are applied to study the Universe, this leads to considering the four interactive forces of Nature as emerging blueprints, and the fundamental constants as numerical primitives. Starting from two basic premises, the principles of interdependence and of asymptotic congruence, and using a statistical pattern recognition paradigm based on Bayes' law and the central limit theorem, Einstein's global field equation is generalized to incorporate a factor that takes into account the probability of presence of a given matter-energy density and better reflects its interconnected role with space-time curvature. One key feature of the resulting metric is that it postulates the existence of an intrinsic physical constant , a star-specific proper length that scales measurements in its surroundings.
In this context, a weighted Newton's law of gravitation emerges from the slowly convergent process of massive object formation and the errors of convergence toward this Gaussian representation can be assimilated to three residual interactions that share common similarities with the Coulomb's law, the weak and strong forces.
It is also shown that the archetype static model is algebraically equivalent to an asymmetric metric that describes a massive body dragging its associated space-time, inducing rotation and expansion.
Furthermore, the whole paradigm highlights some basic relationships between many physical constants and the star proper length.


This book aims to lay out some groundworks from which a theory for bridging the gap between quantum mechanics and general relativity could be built. It should excite the curiosity of many scientists interested in the search for new patterns that could lead to the unification of physics, more specifically graduate and undergraduate students, postgraduates, researchers, engineers and academics working in the area of fundamental and theoretical physics, quantum mechanics, general relativity, astrophysics and cosmology.
Réjean Plamondon is a professor in the Electrical Engineering
Department at É cole Polytechnique de Montréal. His main
research interests deal with pattern recognition, human motor
control, neurocybernetics, biometry and theoretical physics. As
a full member of the Canadian Association of Physicists and the
Ordre des ingénieurs du Québec, Professor Plamondon is also a
lifetime Fellow of the NIAS , the IAPR and the IEEE .


The origin of Newton's law
Putting general relativity into a probabilistic context.
Principle of interdependence. The emergence of Newton's law
of gravitation. A symptotic congruence.

The intrinsic link between the speed of light, the gravitational
and the Boltzmann constants
The numerical value of c and the Pioneer 10/11 anomaly.
The numerical value of G, of the Boltzmann constant, the
electron and proton masses and the Avogadro number.

The symmetric metric, the Sun's mass, the Hubble constant
and the cosmic microwave background
The spherically symmetric metric. Investigating the solar
system. Modelling a general star. An extendable model.
The Hubble constant. Cosmic microwave background.
The black hole and gravitational collapse.

A detailed study of the symmetric metric
The symmetric metric and the field equations. The geodesics.
The motion of massive particles. The motion of photons.
Investigating a stellar system interior.

The axisymmetric metric, dark matter, dark energy
and the cosmological constant
An axisymmetric solution. Investigating the solar system. A galaxy model. Dark matter. A Universe model. Cosmological
constant and dark energy.

A detailed study of the axisymmetric metric
The axisymmetric metric. The geodesics. The equatorial orbits.
The circular equatorial orbits. The radial equatorial geodesics.

The Planck constant, the electric charge and the emergence
of Coulomb's law
The convergence error and the Planck constant. The electric
charge, the permittivity of the vacuum and a link with
Coulomb's law. The permeability of vacuum. The Heisenberg
principle. A potential pathway to quantum field theory.
The latent existence of magnetic monopoles.

The weak and strong interactions, the fine structure constant
and the neutrinos
The three residual interactions. The weak and strong fields
and potentials. The fine structure constant. Energy
conservation and neutrinos.

General conclusion

Appendix A Generalizing to other systems of units
Appendix B Christoffel symbols and Riemann tensor
for the symmetric metric
Appendix C Unsuccessful attempts at offset removal
Appendix D Axisymmetric energy equation