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Author: E. J. Post Publisher: ISBN: Category : Differential equations Languages : en Pages : 38
Book Description
A mathematical procedure is given for singling out the causal solutions from the general set of solutions of self-adjoint differential equations. It consists in splitting the self-adjoint equation into a pair of adjoint equations whose solutions are purely causal and purely anti-causal, respectively. A subsequent merging of the equations then generates in full detail, including singularities, the causal and anti-causal :olutions of the original self -adjoint equation. As an important example, it is shown that the d'Alembertian with point source has a legitimate causal solution involving both retarded and advanced potentials at the source point itself, while at all other points, the retarded potential alone satisfies causality. Within the context of the formalism some recent attempts at modifying classical radiation theory can now be reassessed and more clearly categorized. In particular, the Dirac and Wheeler-Feynman approaches are examined in this light.
Author: E. J. Post Publisher: ISBN: Category : Differential equations Languages : en Pages : 38
Book Description
A mathematical procedure is given for singling out the causal solutions from the general set of solutions of self-adjoint differential equations. It consists in splitting the self-adjoint equation into a pair of adjoint equations whose solutions are purely causal and purely anti-causal, respectively. A subsequent merging of the equations then generates in full detail, including singularities, the causal and anti-causal :olutions of the original self -adjoint equation. As an important example, it is shown that the d'Alembertian with point source has a legitimate causal solution involving both retarded and advanced potentials at the source point itself, while at all other points, the retarded potential alone satisfies causality. Within the context of the formalism some recent attempts at modifying classical radiation theory can now be reassessed and more clearly categorized. In particular, the Dirac and Wheeler-Feynman approaches are examined in this light.
Author: Vyacheslav S. Stepin Publisher: Springer Science & Business Media ISBN: 1402030460 Category : Philosophy Languages : en Pages : 424
Book Description
In Theoretical Knowledge an original conception of a structure and dynamics of scientific knowledge is proposed. A detailed analysis of the foundations of science performed by the author allowed him to develop new ideas and approaches, to demonstrate how sociocultural factors are incorporated in the process of yielding of new theories. He shows direct and inverse links between foundations of science and new theories and empirical facts evolved from those, how among many potentially possible histories of science a culture selects just those directions which become a real history of science. The author analyses mechanisms of the generation of scientific theories and shows that those are changed in the process of historical development of science. He displays three historical types of scientific rationality (classical, non-classical and post-non-classical, which appears in modern science) and shows features of their coexistence and interplay. It is shown that along with the emerging of post-non-classical rationality science increases the sphere of its worldview applications. Science begins to correlate not only with the basic values of technogenic civilization but also with some values and patterns of traditional cultures. The investigation is based on the extensive literature on the history of natural and social sciences. The reader will find in the book authentic historical reconstructions of the processes of the development of classical and quantum electrodynamics, relativity, and conceptions of evolution in biology.
Author: E. J. Post
Author: E. J. Post
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Author: United States. Air Force. Office of Aerospace Research
Author: Vyacheslav S. Stepin
Author: B. L. Van Der Waerden
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Author: Air Force Cambridge Research Laboratories (U.S.)