## The Riddle of GravitationIn this thought-provoking book, written for the layman, a noted physicist offers a fresh, nonmathematical introduction to the conceptual foundations of both Newton's and Einstein's theories of gravitation. Since Einstein's general relativity theory, which deals with gravitation, requires some acquaintance with the ideas of the special theory of relativity (not in itself concerned with gravitation), the first part of the book is devoted primarily to the special theory. This section ranges from Newtonian physics through Einstein's discovery of the relativity of time and space, to the fusion of time and space into a four-dimensional whole by Hermann Minkowski. Part Two is concerned with the general theory of relativity proper. General relativity is based on the hypothesis that, under the influence of gravity, space and time are curved, rather than flat, and that all aspects of gravity can be understood in terms of geometry. Part Three is devoted to recent developments, including the search for gravitational waves, the quantum theory of gravitation, particle motion, and other topics. Five appendixes contain mathematical derivations for the reader who desires a more technical treatment of the subject. For this new edition, Professor Bergmann has also added updated material on gravitational radiation detectors, current problems in cosmology, the significance of singularities of the gravitational field, and more. The result is a fascinating excursion into the rarefied world of theoretical physics, yet one that is well within the grasp of the nonphysicist. Indeed, any intelligent layman, curious about relativity theory and its relation to current astronomical knowledge, will welcome this eloquent and cogent presentation of the subject. |

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### Contents

Two Inertial Frames according to Einstein | 32 |

Components of a Vector in Two Lorentz Frames 80 | 43 |

The EnergyMomentum Vector in Minkowski SpaceTime | 44 |

Great Circles | 50 |

Relativity and Gravitation | 57 |

Ambiguity of Distance | 59 |

Gravitational Lens Action | 67 |

The Principle of General Covariance | 70 |

RECENT DEVELOPMENTS | 129 |

Gravitational Collapse | 131 |

Gravitational Radiation | 136 |

A Gravitational Wave | 137 |

Polarization of a Gravitational Wave Produced by a Double Star | 138 |

The Search for Gravitational Waves | 141 |

Michelson Interferometer I 44 | 143 |

I9 Cosmology | 146 |

Curvature of the Earths Gravitational Field | 77 |

Gravitation in the SpaceTime Continuum | 79 |

Lines of Force | 83 |

Schwarzschilds Solution | 87 |

Curvature of Schwarzschilds Field | 88 |

The Escape Velocity as a Function of Distance from a large Point Mass Newtonian Mechanics | 89 |

Schwarzschild Radius versus Actual Radius of Density Taken as Constant and Equal to That of Water | 90 |

Density versus Mass if the Schwarzschild Radius Is to Equal the Actual Radius | 91 |

Elliptic Orbit with Perihelion Advance | 92 |

Circles and Their Radii on a Sphere | 94 |

Velocity of a Freefalling Particle | 95 |

Freefall Velocity in Terms of Proper Time | 96 |

Inside the Schwarzschild Radius | 97 |

Redshift Dependence on Distance | 98 |

Curves of Constant Acceleration | 100 |

Curves of Constant Acceleration as Straight Lines | 101 |

Geometry near the Schwarzschild Radius | 102 |

Event Horizons | 106 |

Two Accelerated Observers | 107 |

Two Observers One Accelerated the Other Inertial I08 61 Past Light Cones of an Inertial Observer I 09 | 109 |

Newton | 113 |

Pages from Principia | 120 |

Linearly Expanding Universe | 148 |

Expanding Universe with Constant Hubble Coefficient I48 68 Oscillating Universe I 49 | 150 |

Astronomical Observations Lead Billions of Years Back into the History of the Universe | 151 |

Current Observational Programs | 156 |

Particle Motion | 163 |

Quantum Theory of Gravitation | 167 |

What Is an Observable? | 171 |

SpaceTime Today and Tomorrow | 174 |

APPENDIXES | 179 |

The EqualAreas law of Kepler | 181 |

Two Coordinate Systems That Coincide for Part of the Time I64 72 EqualAreas law I82 73 Unaccelerated Motion | 182 |

Detail of Fig 72 | 183 |

Derivation of the InverseSquare Law of Force | 185 |

Acceleration on a Circular Trajectory I86 76 Two Events on a Line Perpendicular to the Relative Motion | 186 |

The Lorentz Transformation | 187 |

The SCl1waI7_Cl1lld Radius I93 V Gravitational Radiation | 197 |

Glossary | 203 |

Suggestions for Further Reading | 223 |

A Small Segment of M 82 Further Enlarged | 225 |

227 | |

### Common terms and phrases

astronomical atoms axis called components conﬁrmed continuum coordinate system cosmological covariance curvature curved deﬁned deﬁnite depends direction distance double star earth eﬂects Einstein electric charge electromagnetic ﬁeld energy equal ﬁgure ﬁnd ﬁnite ﬁrst ﬁxed ﬂat ﬂux force ﬁelds four-dimensional frame of reference free-falling frame galaxies geometry gravitational ﬁeld gravitational radiation gravitational waves hence identiﬁed inertial frame inﬁnity inﬂuence instance interactions interior large mass law of continuity light cone light signal lightlike linear momentum Lorentz frame magnitude manifold mathematical matter Minkowski universe motion Newton's objects observer orbit parallel transport path planet principle of equivalence propagation pulsars quantities quasars redshift region relationship relativistic represent respect result right angles rotation Schwarzschild radius shear space space-time spacelike spatial special theory speed of light sphere spherical straight lines suﬂiciently surface tensor test bodies theory of gravitation theory of relativity timelike trajectory transformation values vector velocity world points