CollectionNovathème
ISBN9782553016332
EditorPresses internationales Polytechnique
pages214
Published2012-06-28

AuthorRéjean Plamondon

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.

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 .

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 .

Foreword

Acknowledgements

CHAPTER 1

Introduction

CHAPTER 2

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.

CHAPTER 3

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.

CHAPTER 4

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.

CHAPTER 5

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.

CHAPTER 6

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.

CHAPTER 7

A detailed study of the axisymmetric metric

The axisymmetric metric. The geodesics. The equatorial orbits.

The circular equatorial orbits. The radial equatorial geodesics.

CHAPTER 8

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.

CHAPTER 9

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.

CHAPTER 10

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

References

Biography

Index

Acknowledgements

CHAPTER 1

Introduction

CHAPTER 2

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.

CHAPTER 3

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.

CHAPTER 4

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.

CHAPTER 5

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.

CHAPTER 6

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.

CHAPTER 7

A detailed study of the axisymmetric metric

The axisymmetric metric. The geodesics. The equatorial orbits.

The circular equatorial orbits. The radial equatorial geodesics.

CHAPTER 8

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.

CHAPTER 9

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.

CHAPTER 10

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

References

Biography

Index