Some of the things you can do with the GrassmannAlgebra software. You can: * Set up your own space of any dimension and metric. The default is a 3D Euclidean * Work basis-free or with a basis * Declare your own scalar symbols * Declare your own vector symbols: * Apply Grassmann operations. A Grassmann operation is any of: the complement operation and the six product operations: the exterior, regressive, interior, generalized Grassmann, hypercomplex and Clifford products. * Manipulate Grassmann expressions and numbers. A Grassmann expression is either a scalar, a Grassmann variable, or the result of a sequence of Grassmann operations or sums on Grassmann expressions. A Grassmann number is a Grassmann expression expressed as a linear combination of basis elements. * Compute the grade of any Grassmann expression. * Query the attributes of any expression. * Extract components of different types
Review of Modern Physics 1986 The interpretational problems of quantum mechanics are considered. The way in which the standard Copenhagen Interpretation (CI) of quantum mechanics deals with these problems is reviewed. A new interpretation of the formalism of quantum mechanics, the Transactional Interpretation (TI), is presented. The basic element of TI is the transaction describing a quantum event as an exchange of advanced and retarded waves, as implied by the work of Wheeler and Feynman, Dirac, and others. The TI is explicitly nonlocal and thereby consistent with recent tests of the Bell Inequality, yet is relativistically invariant and fully causal. A detailed comparison of the TI and CI is made in the context of well known quantum mechanical gedanken experiments and "paradoxes". The TI permits quantum mechanical wave functions to be interpreted as real waves physically present in space rather than as "mathematical representations of knowledge" as in the CI.
Natural Science is an international journal dedicated to the latest advancement of natural sciences. The goal of this journal is to provide a platform for scientists and academicians all over the world to promote, share, and discuss various new issues and developments in different areas of natural sciences. All manuscripts must be prepared in English, and are subject to a rigorous and fair peer-review process.
Natural Science is an international journal dedicated to the latest advancement of natural sciences. The goal of this journal is to provide a platform for scientists and academicians all over the world to promote, share, and discuss various new issues and developments in different areas of natural sciences. All manuscripts must be prepared in English, and are subject to a rigorous and fair peer-review process. Accepted papers will immediately appear online followed by printed hard copy.
@ Cornell University, video shows six laboratory demonstrations of chaos and nonlinear phenomena, intended for use in a first course on nonlinear dynamics. Steven Strogatz explains the principles being illustrated and why they are important.