## On the Emergence Theme of PhysicsThe book surveys mathematical relations between classical and quantum mechanics, gravity, time and thermodynamics from various points of view and many sources (with appropriate attribution). The emergence theme is developed with an emphasis on the meaning via mathematics. A background theme of Bohemian mechanics and connections to the quantum equivalence principle of Matone et al. is also developed in great detail. Some original work relating the quantum potential and Ricci flow is also included. |

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### Contents

Chapter 1 SOME QUANTUM BACKGROUND | 1 |

Chapter 2 SOME GEOMETRIC ASPECTS | 37 |

Chapter 3 ASPECTS OF EMERGENCE | 75 |

Chapter 4 KALUZAKLEIN AND COSMOLOGY | 95 |

Chapter 5 REMARKS ON THERMODYNAMICS AND GRAVITY | 121 |

Chapter 6 GEOMETRY AND MECHANICS | 167 |

### Common terms and phrases

action algebra apparent horizon assumes automorphisms black hole Bohmian canonical classical conformal factor connection consider constant coordinates corresponding cosmological constant covariant curvature deﬁned denotes density derivative determined diffeomorphism Dirac dynamics eigenvalues Einstein equations energy entropy equations of motion equivalent ﬁnds ﬁrst Fisher information ﬁxed ﬂat ﬂuctuations Fock space Friedman equations gauge given gr-qc gravity Hamiltonian hence hep-th Hilbert space implies integral invariant involves Jour Lagrangian leads Lett manifold math-ph matrix metaplectic metric momentum Note obtains operator parameter particle phase space Phys physics QSHJE quant-ph quantization quantum mass quantum mechanics quantum potential recall REMARK Ricci flow Riemannian satisﬁes scalar scalar curvature Schwarzian derivative solution spacetime symmetric symplectic tensor term theorem theory thermal thermodynamics trajectories transformation vector wave function Weyl geometry Weyl vector write zero