books:

	Hyperspace: A Scientific Odyssey through Parallel Universes, Time Warps, and the Tenth Dimension Michio Kaku Oxford University Press, USA, 1994 - 384 pages average customer review:based on 213 reviews view larger image
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highly recommended

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.

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Modern Mathematics and Modern Physics

The central challenge of theoretical physics today is to unify the four fundamental forces--the electromagnetic force (electricity, magnetism, and light), the strong nuclear force (provides the energy that fuels the star, fusion), the weak nuclear force (governs certain form of radioactive decay), the gravitational force (keeps the earth and the planets in their orbits)--into a single force. Beginning with Einstein, the giants of physics have tried and failed to find such a unified mathematical model. However, the answer that eluded Einstein for the last 30 years of his life may lie in the hyperspace theory. In short, Einstein has three major ideas. The first one is the special relativity, which time can covert into space and vice versa. The second one is the general relativity, which matter (energy) can bent space (time). In other words, forces do not exist; force is a consequence of geometry due to curved space. The third one is the unified field theory. The goal is to describe matter by geometry. But the quantum theory dominates theoretical physics in the next 60 years until 1980s.

Quantum theory is the opposite of Einstein's theory. Einstein's general relativity is a theory of the cosmos (stars and galaxies). Quantum theory is a theory of the microcosm (subatomic particles).

In essence, the key differences between Einstein's geometric theory and quantum theory are: (1) Forces are created by the exchange of discrete packets of energy, called quanta. (2) Different forces are caused by the exchange of different quanta. (3) We can never know simultaneously the velocity and positions of a subatomic particle. (4) There is a finite probability that particles may "tunnel" through or make a quantum leap through impenetrable barriers.

After 50 years of research, we have the following picture of subatomic matter: All matter consists of quarks and leptons, which interact by exchanging different types of quanta, described by the Maxwell and Yang-Mills field. The Yang-Mills field makes the theory of matter--the Standard Model--possible. The Standard Model is based on symmetry. Symmetry is the preservation of the shape of an object even after we deform or rotate it. The first type of symmetry is rotations and reflections. The second type of symmetry is reshuffling a series of objects. The Standard Model unifies the three fundamental forces by one large symmetry: SU(3) (strong force, shuffle of three colored quarks) x SU(2) (weak force, interchange of electron and neutrino) x U(1) (electromagnetic force, rotates the components of the Maxwell field into itself), which is just the product of the symmetries of the individual forces. SU stands for special unitary matrix. The determinant of the matrix is one. The Standard Model is incomplete, because it does not describe gravity. Second, it is ugly (complicated), because there are 36 quarks, 8 Yang-Mills fields to describe the gluons, 4 Yang-Mills fields to describe the weak and electromagnetic forces, 6 types of leptons, a large number of Higgs particles, and at least 19 arbitrary constants.

In 1980s, the Einstein type theory (higher dimensional space theory) returns to the mainstream of research in the name of string theory. Superstring theory is probably the most advanced higher dimensional space theory. It postulates that all the matter consists of tiny vibrating strings. The theory predicts the dimensions for space and time is ten. The corresponding mathematics for the dimensions is called Ramanujan function, a modular function. The matter in the universe and the four forces may be different vibrations of hyperspace. The required mathematics to understand superstring theory reached the deepest level ever. Any unified field theory must first absorb the Riemannian geometry from Einstein's theories and the Lie groups from quantum field theory. Then a new branch of mathematics--topology--merges them together. In fact, Gauss, Riemann, and Poincare all considered physics to be the most important source of new mathematics, because mathematics is the language of physics.

A ten-dimensional matrix (space) has enough room to accommodate all four fundamental forces. Furthermore, the ten-dimensional matrix has room to explain the subatomic particles produced by atomic smashers. Thus the matrix, a mathematical object, consists of both forces (consequence of bent space-time) and matter (energy).

The hyperspace theory reopens the question of whether the extra dimensions can be used for traveling. The shortest path between two points in higher dimensional space is not a straight line but a wormhole. The Poincare Conjecture could be used to determine whether a hyper-surface consist a wormhole or not. Our world is simply connected because a lasso of rope can always be shrunk to a point. If the lasso is placed around the entrance of the wormhole, then it cannot be shrunk to a point. Such spaces are called multiple connected. Although the bending of our universe has been experimentally measured, it is still a controversy on whether warmhole exists or whether our universe is multiply connected.

A field is a collection of numbers at every point in space. The numbers describes a force at that point. Field theory allows us to calculate the required energy to form wormhole in space-time. The required energy to form a wormhole is centuries ahead of our current technology. Hence, time travel is not testable.

Michio Kaku's "Hyperspace: A Scientific Odyssey through Parallel Universes, Time Warps, and the Tenth Dimension" is a must have for whom would like to understand the latest and the greatest of theoretical physics.

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Great read

I have enjoyed all of his books and his attitude in science as far as he doesn't come across as feeling we know it all as scientists so often have.
Simply put even with no idea about higher dimensions /quantum mechanics or string theory you can still get what it means, so easy a child can start to understand it but indepth enough to get a real feel where science is at today in theory


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Interesting fairly-simple read

A littler out of date with newer theoretical developments in string theory, but still an interesting and fascinating read. I found it to be a fairly simple and smooth read for the average reader, however, I felt like some statements/facts he presented could've used more background and explanation. It's much harder to understand and remember concepts when you're expected to accept them as is without an explanation of why they hold true.

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reviews: page 1, 2, 3, 4, 5, 6, 7, 8, 9, 10

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