## The End of CertaintyTime, the fundamental dimension of our existence, has fascinated artists, philosophers, and scientists of every culture and every century. All of us can remember a moment as a child when time became a personal reality, when we realized what a "year" was, or asked ourselves when "now" happened. Common sense says time moves forward, never backward, from cradle to grave. Nevertheless, Einstein said that time is an illusion. Nature's laws, as he and Newton defined them, describe a timeless, deterministic universe within which we can make predictions with complete certainty. In effect, these great physicists contended that time is reversible and thus meaningless. |

### Contents

Only an Illusion? | 57 |

From Probability to Irreversibility | 73 |

The Laws of Chaos | 89 |

Beyond Newtons Laws | 107 |

A Unified Formulation of Quantum Theory | 129 |

Our Dialogue with Nature | 153 |

A Narrow Path | 183 |

### Common terms and phrases

arrow associated atoms baker transformation basic Bernoulli map bifurcation big bang Boltzmann Chapter classical and quantum classical dynamics classical mechanics concept consider coordinates correlations corresponds cosmology defined delocalized described deterministic chaos diffusion dissipative structures distribution function dynamical systems eigenfunctions eigenvalues Einstein energy ensembles entropy Epicurus equations of motion equilibrium evolution exponential expressed Figure formulation frequency fundamental gravitational Hamiltonian Hilbert space human initial conditions introduce irreversible processes laws of nature leads Liouville operator Lyapunov exponent macroscopic matter molecules momenta namics Newton's laws Newtonian nonequilibrium nonintegrability number of particles observe obtain Perron-Frobenius operator persistent interactions Petrosky phase space Phys physicists Poincaré resonances Prigogine probabilistic probability distribution problem quantum mechanics quantum paradox quantum theory result role Schrödinger equation scription second law Section singular functions situation space-time statistical description statistical level terms of trajectories thermodynamics time-reversible tion trajectory description universe unstable velocity versible wave function wave vectors