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### Summary

### Summary

The concept of multiple unperceived dimensions in the universe is one of the hottest topics in contemporary physics. It is essential to current attempts to explain gravity and the underlying structure of the universe. The Great Beyond begins with Einstein's famous quarrel with Heisenberg and Bohr, whose theories of uncertainty threatened the order Einstein believed was essential to the universe, and it was his rejection of uncertainty that drove him to ponder the existence of a fifth dimension. Beginning with this famous disagreement and culminating with an explanation of the newest "brane" approach, author Paul Halpern shows how current debates about the nature of reality began as age-old controversies, and addresses how the possibility of higher dimensions has influenced culture over the past one hundred years.

### Author Notes

Paul Halpern is professor of physics and mathematics at the University of the Sciences in Philadelphia.

### Reviews 3

### Publisher's Weekly Review

Ever since Plato first told his students the allegory of the cave, people have wondered whether dimensions exist beyond the three we immediately perceive. An extra dimension-time-played a role in Einstein's work, although he saw it only as a necessary evil to get his equations to work. Other scientists were more receptive: mathematical physicists Oskar Klein and Theodor Kaluza made higher dimensions an integral part of their attempts to discover a "theory of everything" that would tie together strong and weak nuclear forces, electromagnetism and gravity. Halpern explains that over the past century gravity has been the shadow flickering on the walls of the cave hinting at other realms. Why is it so weak compared with electromagnetism? With string theory, and its successor, M-theory, physicists speculate that gravity "leaks" back and forth between our reality, an 11-dimensional "brane" (or membrane) and other branes, perhaps as close as a millimeter away. Halpern masterfully creates word pictures to illustrate mind-bending scientific theories, and he paints highly detailed sketches of the scientists involved-sometimes too detailed, leading readers to lose the thread of the narrative. Science buffs won't find much new here, but for average readers, this is an accessible account of the search for what lies behind our dim perception of reality. B&w photos. Agent, Giles Anderson. (July 16) (c) Copyright PWxyz, LLC. All rights reserved

### Library Journal Review

Many physicists are continuing to work toward the fabled goal of a "theory of everything." A successful theory would unify the four known physical forces-gravity, electromagnetism, and the nuclear strong and weak forces-and cast some light upon newly discovered cosmological phenomena and puzzles. Quite a few theoreticians are attempting to use postulated extra dimensions to come up with a workable product; fantastic as it may seem, a universe containing ten or 11 dimensions offers considerable promise. Halpern (physics & mathematics, Univ. of the Sciences, Philadelphia) takes a historical approach to examining the advancement of multidimensional theory. Kaluza, Klein, Einstein, and many other contributors over the past 100 years are discussed, and their work is described at a level appropriate for a general audience. Only Halpern's terminology and the pace of the discussion in the last few chapters will challenge nonspecialists. Recommended for academic and large public libraries.-Jack W. Weigel, Ann Arbor, MI (c) Copyright 2010. Library Journals LLC, a wholly owned subsidiary of Media Source, Inc. No redistribution permitted.

### Choice Review

Halpern (Univ. of the Sciences, Philadelphia), a cosmological theorist and successful popularizer, has here presented a readable history of the background of current M-theory, with an emphasis on the mathematical and theoretical developments leading to the clash between general relativity and particle theory, and the attempts by supersymmetry and string theorists to push on to quantum gravity theory. The seldom-told story of the mathematical rivals to Einstein, particularly of Kaluza and Klein, and the postrelativistic work of Bergmann and Bargmann is particularly well done. As with any popularization, the balance between simplification and distortion is precarious, and the use of metaphors, particularly visual, in describing mathematical strategies, is formidable. Halpern succeeds in many areas (e.g., renormalization and Minkowski space) and arguably falls short in others (e.g., gauge field theory and isospin); the result is far more accurate than the current competition. The final blitz on current research is probably too dense for a popular audience (that loves the terminology anyway), although professionals will appreciate the peek behind the curtain of brane theory. ^BSumming Up: Highly recommended. General readers; lower-division undergraduates through faculty; two-year technical program students. P. D. Skiff Bard College

### Table of Contents

Acknowledgments | p. vii |

Introduction: The Kaluza-Klein Miracle | p. 1 |

1 The Power of Geometry | p. 10 |

2 Visions of Hyperspace | p. 26 |

3 The Physicist's Stone: Uniting Electricity, Magnetism, and Light | p. 61 |

4 Getting Gravity in Shape | p. 84 |

5 Striking the Fifth Chord: Kaluza's Remarkable Discovery | p. 101 |

6 Klein's Quantum Odyssey | p. 114 |

7 Einstein's Dilemma | p. 139 |

8 Truth under Exile: Theorizing at Princeton | p. 158 |

9 Brave New World: Seeking Unity in an Age of Conflict | p. 179 |

10 Gauging the Weak and the Strong | p. 206 |

11 Hyperspace Packages Tied Up in Strings | p. 231 |

12 Brane Worlds and Parallel Universes | p. 267 |

Conclusion: Extra-dimensional Perception | p. 290 |

Notes | p. 299 |