Essential physics

Physical Systems, 2012

The reconstruction of classical physics in previous chapters unveiled a conceptual relation between Galilean spacetime and Newtonian mass. Once the Galilean geometry of PUMs was assumed, the basic structure of Galilean spacetime was derived. The parameter μ 0 , which was later used to reconstruct mass, was derived from an implicit spacetime symmetry. The full meaning of mass was captured when the reconstruction introduced the "classical" Criterion of Isolation and the Rule of Composition governing motions.

2016

The incompatibility between the Lorentz invariance of classical electromagnetism and the Galilean invariance of continuum mechanics is one of the major barriers to prevent two theories from merging. In this note, a systematic approach of obtaining Galilean invariant field variables and equations of electromagnetism within the semirelativistic limit is reviewed and extended. In particular, the Galilean invariant forms of Poynting's theorem and the momentum identity, two most important electromagnetic identities in the thermomechanical theory of continua, are presented. In this note, we also introduce two frequently used stronger limits, namely the magnetic and the electric limit. The reduction of Galilean invariant variables and equations within these stronger limits are discussed.

2019

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Physics Today, 1963

Major revisions of the pillars of physics, Maxwell's equations and relativity theory, are proposed, based on imposing the requirement of true formal invariance. This theme is further exploited through length invariance and an application of GPS time that permits restoration of a meaningful concept of now. The consequence is a physics from which covariance has been consistently banished in favor of invariance. A crucial experiment is proposed.

The aim of this review is highlighting the common aspects between Symmetry in Physics and the Relativity Theory, particularly Special Relativity. After a brief historical introduction, emphasis is put on the physical foundations of Relativity Theory and its essential role in the clarification of many issues related to fundamental symmetries. Their different connections will be shown from Classical Mechanics to Modern Particle Physics.

Spacetime & Substance, Vol. 5, No. 4 (24), pp. 154-161, 2004

In this paper, we show that hν and all expressions for energy which are equivalent to it represent kinetic energy rather than total energy. The object velocity, u, is found to be relativistically invariant, along with the frequency of an object's de Broglie wave. Using the mathematics of indeterminancy (a term coined by the author to describe the introduction of an exponential scale or phase factor), we are able to derive a form of γ which emphasizes the underlying physics of the Galilean Transformation (GAL), the Lorentz Transformation (LT), and the general Einstein-Lorentz Transformation (GLT) , rather than the details of each particular transformation. By requiring symmetry between the transformation properties of kinematic and dynamic variables, we find a more general transformation (MGT). For the condition V ≥ c, in our spacetime, the (MGT) continues to describe a unique correspondence between the coordinates of two inertial frames of reference. We conclude by explaining how the logical necessity for zero rest mass in special relativity can be reconciled with physical observations of nonzero rest mass. In this way, it is also possible to show that the mass of an object does not become infinite if it were to move at the speed of light. Future theories may increase our understanding by providing more general representations of Nature. The various theories may be distinguished by the corresponding values of γ, the indeterminate part of which arises as the solution of an ordinary differential equation.

2013

In this article, by using fundamental concepts in classical mechanics, we derive equations describing gravitational red shift and Doppler effect for light as well as equations describing the relations among mass, momentum, and energy including mass-energy equivalence. Although our equations are different than those in Newtonian mechanics or special relativity, they yield results that are approximate results calculated with Newton mechanics or special relativity for values of velocity, which are much less than speed of light. Since the concepts in classical mechanics are not separated from the perspective of absolute space and time, this theory is named the theory of invariance.

Geometry, Symmetries, and Classical Physics: A Mosaic, 2021

This book provides advanced physics and mathematics students with an accessible yet detailed understanding of the fundamentals of differential geometry and symmetries in classical physics. Most of the topics covered in this book have previously only been scattered across many different sources of literature, therefore this is the first book to coherently present this treatment of topics in one comprehensive volume. - - Key features: -> Contains a modern, streamlined presentation of classical topics, which are normally taught separately. -> Includes several advanced topics, such as the Belinfante energy-momentum tensor, the Weyl-Schouten theorem, the derivation of Noether currents for diffeomorphisms, and the definition of conserved integrals in general relativity. -> Focuses on the clear presentation of the mathematical notions and calculational technique. - - - Table of Contents: - Chapter 1. Manifolds and Tensors. - Chapter 2. Geometry and Integration on Manifolds. - Chapter 3. Symmetries of Manifolds. - Chapter 4. Newtonian Mechanics. - Chapter 5. Lagrangian Methods and Symmetry. - Chapter 6. Relativistic Mechanics. - Chapter 7. Lie Groups. - Chapter 8. Lie Algebras. - Chapter 9. Representations. - Chapter 10. Rotations and Euclidean Symmetry. - Chapter 11. Boosts and Galilei Symmetry. - Chapter 12. Lorentz Symmetry. - Chapter 13. Poincare Symmetry. - Chapter 14. Conformal Symmetry. - Chapter 15. Lagrangians and Noether's Theorem. - Chapter 16. Spacetime Symmetries of Fields. - Chapter 17. Gauge Symmetry. - Chapter 18. Connection and Geodesics. - Chapter 19. Riemannian Curvature. - Chapter 20. Symmetries of Riemannian Manifolds. - Chapter 21. Einstein's Gravitation. - Chapter 22. Lagrangian Formulation. - Chapter 23. Conservation Laws and Further Symmetries. - - Appendices - A) Notation and Conventions. - Physical Units and Dimensions. - Mathematical Conventions. - Abbreviations. - B) Mathematical Tools. - Tensor Algebra. - Matrix Exponential. - Pauli and Dirac Matrices. - Dirac Delta Distribution. - Poisson and Wave Equation. - Variational Calculus. - Volume Element and Hyperspheres. - Hypersurface Elements. - C) Weyl Rescaling Formulae. - D) Spaces and Symmetry Groups. - - Bibliography. - - Index.