## Gravity and Quantum Non-LinearityFor many years Maxwell's equations were mute testimony to the Lorentz coordinate transformations of special relativity, but the significance of this transformation was not fully understood until relativity itself had been discovered. The author of this book claims that an oversight has once again occurred in fundamental physics. A direct link between Quantum Mechanics and Gravity - perhaps the biggest scientific enigma of all time - has been overlooked. In an entirely novel approach to Quantum-Gravity, this book suggests that Gravity is the manifestation of a very weak non-linearity in Quantum Mechanics; a non-linearity only apparent in the presence of large quantities of matter or very condensed wave functions. The reader will discover how this non-linearity is a natural consequence of a particular interpretation of the Quantum Equations. This book however, does not share the same genre of totalising theories that emphatically and triumphantly declare a new dawn. Instead its thesis can only present itself as a fascinating hypothesis submitted for consideration. Should the theory presented here prove its mettle, then it would provide the key to opening up new vistas of theoretical and experimental research, thus helping to clear the conceptual log jam in which contemporary fundamental physics finds itself. |

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### Contents

The Diffusion Equation | 1 |

Imaginary Diffusion | 10 |

The Imaginary Biased Diffusion Equation | 16 |

Special Relativity | 24 |

Relativistic Masking in Kinematic Relativity | 33 |

The Gravitational Effect of Wave Functions | 41 |

Macroscopic Gravity I | 49 |

Relationship with Einsteins Equation | 65 |

Derivation of Real and Imaginary Diffusion Equations | 92 |

Derivation of Real and Imaginary Biased Diffusion Equations | 103 |

Currents Caused by Drift and Diffusion | 108 |

Deriving the Imaginary Biased Diffusion Equation | 112 |

A Solution to the Imaginary Biased Diffusion Equation | 116 |

Clock Synchronisation in Special Relativity | 118 |

Wave Number Approximation | 121 |

Drift in Real Diffusion | 124 |

Extensive Matter | 70 |

Epilogue | 83 |

Spatial Transition Rates and Gaussian Envelopes | 90 |

Elementary Quantum Gas | 126 |

Equilibrium Gravitational Field Equation | 127 |

### Common terms and phrases

absolute frame Appendix approximation assume Biased Diffusion Equation clocks complex components constant coordinate system Copenhagen interpretation defined derive differential distribution drift term effect Einstein's equation epsilon distance equation 4.1 equilibrium expression extensive matter fact factor finite flow Gaussian envelope given gives gravitational field gravitational wave function group velocity heat energy Imaginary Biased Diffusion imaginary diffusion intensive isotropic last chapter linear Lorentz transformation magnitude mean square step measured moving frame moving observer multiverse node non-linearity number of steps one-dimensional ordinary random walk particle wave function physical probability density probability envelopes proportional quantity quantum gravity quantum mechanics quantum waves real diffusion reality represent right hand side root mean square Schroedinger equation simulation slope solution space contraction space-time curvature special relativity speed of light standards of length stationary frame stationary observer stationary with respect step probability step velocity test particle theory being proposed three-dimensional underlying vector wave number