The first book devoted to black holes in more than four dimensions, for graduate students and researchers.

Are there other dimensions beyond our own? Is time travel possible? Can we change the past? Are there gateways to parallel universes? All of us have pondered such questions, but there was a time when scientists dismissed these notions as outlandish speculations. Not any more. Today, they are the focus of the most intense scientific activity in recent memory. In Hyperspace, Michio Kaku, author of the widely acclaimed Beyond Einstein and a leading theoretical physicist, offers the first book-length tour of the most exciting (and perhaps most bizarre) work in modern physics, work which includes research on the tenth dimension, time warps, black holes, and multiple universes. The theory of hyperspace (or higher dimensional space)--and its newest wrinkle, superstring theory--stand at the center of this revolution, with adherents in every major research laboratory in the world, including several Nobel laureates. Beginning where Hawking's Brief History of Time left off, Kaku paints a vivid portrayal of the breakthroughs now rocking the physics establishment. Why all the excitement? As the author points out, for over half a century, scientists have puzzled over why the basic forces of the cosmos--gravity, electromagnetism, and the strong and weak nuclear forces--require markedly different mathematical descriptions. But if we see these forces as vibrations in a higher dimensional space, their field equations suddenly fit together like pieces in a jigsaw puzzle, perfectly snug, in an elegant, astonishingly simple form. This may thus be our leading candidate for the Theory of Everything. If so, it would be the crowning achievement of 2,000 years of scientific investigation into matter and its forces. Already, the theory has inspired several thousand research papers, and has been the focus of over 200 international conferences. Michio Kaku is one of the leading pioneers in superstring theory and has been at the forefront of this revolution in modern physics. With Hyperspace, he has produced a book for general readers which conveys the vitality of the field and the excitement as scientists grapple with the meaning of space and time. It is an exhilarating look at physics today and an eye-opening glimpse into the ultimate nature of the universe.

One of the most talented contemporary authors of cutting-edge math and science books conducts a fascinating tour of a higher reality, the Fourth Dimension. Includes problems, puzzles, and 200 drawings. "Informative and mind-dazzling." — Martin Gardner.

Higher dimensional theories have attracted much attention because they make it possible to reduce much of physics in a concise, elegant fashion that unifies the two great theories of the 20th century: Quantum Theory and Relativity. This book provides an elementary description of quantum wave equations in higher dimensions at an advanced level so as to put all current mathematical and physical concepts and techniques at the reader’s disposal. A comprehensive description of quantum wave equations in higher dimensions and their broad range of applications in quantum mechanics is provided, which complements the traditional coverage found in the existing quantum mechanics textbooks and gives scientists a fresh outlook on quantum systems in all branches of physics. In Parts I and II the basic properties of the SO(n) group are reviewed and basic theories and techniques related to wave equations in higher dimensions are introduced. Parts III and IV cover important quantum systems in the framework of non-relativistic and relativistic quantum mechanics in terms of the theories presented in Part II. In particular, the Levinson theorem and the generalized hypervirial theorem in higher dimensions, the Schrödinger equation with position-dependent mass and the Kaluza-Klein theory in higher dimensions are investigated. In this context, the dependence of the energy levels on the dimension is shown. Finally, Part V contains conclusions, outlooks and an extensive bibliography.

A detailed description of what the fourth dimension would be like.

Foremost book available on polytopes, incorporating ancient Greek and most modern work. Discusses polygons, polyhedrons, and multi-dimensional polytopes. Definitions of symbols. Includes 8 tables plus many diagrams and examples. 1963 edition.