Special Relativity Tensors And Energy Tensor With Worked Problems
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Special Relativity, Tensors, And Energy Tensor: With Worked Problems
This book takes the reader from the preliminary ideas of the Special Theory of Relativity (STR) to the doorsteps of the General Theory of Relativity (GTR).The first part explains the main concepts in a layman's language, including STR, the Lorentz transformation, relativistic mechanics. Thereafter the concept of tensors is built up in detail, especially Maxwell's stress tensor with illustrative examples, culminating in the energy-momentum conservation in electromagnetic fields. Mathematical structure of Minkowski's space-time is constructed and explained graphically. The equation of motion is formulated and then illustrated by the example of relativistic rocket. The principle of covariance is explained with the covariant equations of classical electrodynamics. Finally, the book constructs the energy tensor which constitutes the source term in Einstein's field equation, which clears the passage to the GTR.In the book, the concepts of tensors are developed carefully and a large number of numerical examples taken from atomic and nuclear physics. The graphs of important equations are included. This is suitable for studies in classical electrodynamics, modern physics, and relativity.
Relativity
The most important feature in this book is the simple presentation with details of calculations. It is very easy to follow. Fairly sophisticated calculations are developed very rapidly. The presentation is logical and the detailed coverage makes this book very readable and useful. The contents develop Relativity as a modern theory of motion, starting by placing it in historical perspective and proceeding to show its logical necessity. The development of the Lorentz transformation is given using only one assumption rather than two. Right away in Chapter 3, geometry as required in Special Relativity for extension to General Relativity is introduced. This enables the use of the four-vector formalism of Minkowski. By the end of Chapter 4, the general Lorentz transformations for three-dimensional motion and their relation to four-dimensional boosts have already been explained. In Chapter 5 applications of relevance in Physics are provided. After a brief introduction to elementary electromagnetic theory, it is reformulated as a theory in four-dimensions using tensors in Chapter 6. Finally in Chapter 7, the theory is extended to deal with accelerated motion as ?corrections? to Special Relativity.
What is Space-Time Made Of?
In the first part of this book, the author synthesizes the main results and formulas of physics-Albert Einstein's, with general relativity, gravitational waves involving elastic deformable space-time, quantum field theory, Heisenberg's principle, and Casimir's force implying that a vacuum is not nothingness. In the second part, based on these scientific facts, the author re-studies the fundamental equation of general relativity in a weak gravitational field by unifying it with the theory of elasticity. He considers the Ligo and Virgo interferometers as strain gauges. It follows from this approach that the gravitational constant G, Einstein's constant κ, can be expressed as a function of the physical, mechanical and elastic characteristics of space-time. He overlaps these results and in particular Young's modulus of space-time, with publications obtained by renowned scientists. By imposing to satisfy the set of universal constants G, c, κ, ħ and by taking into account the vacuum data, he proposes a new quantum expression of G which is still compatible with existing serious publications. It appears that time becomes the lapse of time necessary to transmit information from one elastic sheet of space to another. Time also becomes elastic. Thus, space becomes an elastic material, with a particle size of the order of the Planck scale, a new deformable ether, therefore different from the non-existent luminiferous ether. Finally, in the third part, in appendices, the author demonstrates the fundamentals of general relativity, cosmology and the theory of elasticity.