Elements for Physics Quantities, Qualities, and Intrinsic Theories

Content URL: Link To Content
While usual presentations of physical theories emphasize the notion of physical quantity, this book shows that there is much to gain when introducing the notion of physical quality. The usual physical quantities simply appear as coordinates over the manifolds representing the physical qualities. This allows to develop physical theories that have a degree of invariance much deeper than the usual one. It is shown that properly developed physical theories contain logarithms and exponentials of tensors: their conspicuous absence in usual theories suggests, in fact, that the fundamental invariance principle stated in this book is lacking in present-day mathematical physics. The book reviews and extends the theory of Lie groups, develops differential geometry, proposing compact definitions of torsion and of curvature, and adapts the usual notion of linear tangent application to the intrinsic point of view proposed for physics. As an illustration, two simple theories are studied with some detail, the theory of heat conduction and the theory of linear elastic media. The equations found differ quantitatively and qualitatively from those usually presented. 
Written for: 
Advanced students 
Keywords: 

* Invariance 
* Lie groups 
* Manifolds 
* Mathematical physics 
* Theoretical physics   

The Official String Theory Website

Content URL: Link To Content
What is theoretical physics? 

Theoretical physicists today still use a core technology that was developed in the 18th century out of the calculus pioneered by Isaac Newton and Gottfried von Leibniz. 

saac Newton derived his three Laws of Motion through close, almost obsessive observation and experimentation, as well as mathematical reasoning. The relationship he discovered between force and acceleration, which he expressed in his own arcane notation of fluxions, has had the most impact on the world in the differential notation used by his professional rival, Wilhelm von Leibniz, as the familiar differential equation from freshman physics: 

F = ma = m(d^2x/dt^2)   

The Second Superstring Revolution

 Author: Patricia Schwarz

 Content URL: Link To Content

Major advances in understanding of the physical world have been achieved during the past century by focusing on apparent contradictions between well-established theoretical structures. In each case the reconciliation required a better theory, often involving radical new concepts and striking experimental predictions. 
Four major advances of this type are indicated in Figure 1. [1] These advances were the discoveries of special relativity, quantum mechanics, general relativity, and quantum field theory. Let us briefly recall the contradictions that each of these resolved and some of the experimental confirmations that followed.