## Neutrosophic Methods in General Relativity (Google eBook)Dmitri Rabounski, Dmitri Rabounski, Florentin Smarandache, Larissa Borissova, Florentin Smarandache, Larissa Borissova Neutrosophy is a theory developed by Florentin Smarandache in 1995 as a generalization of dialectics, which studies the origin, nature and properties of neutralities. This book applies neutrosophic method to the General Theory of Relativity, aiming to discover new effects hidden before.Studying Einstein's basic space-time, neutrosophic method displays new trajectories and particles never considered before. Such trajectories/particles are of two "mixed" kinds, which are (1) common for sub-light mass-bearing particles and massless photons (non-isotropic/isotropic trajectories) and (2) common for massless photons and super-light mass-bearing tachyons (isotropic/non-isotropic trajectories). As it is shown, such mass-bearing/light-like particles are accessible for observing, we can see them in different phenomena of nature.Solutions of Einstein's equations (evolution scenarios for the Universe) are collected in a table in this book. Each cell of the table is a cosmological model. Neutrosophic method, analyzing this cosmological table, displays new possible models of the evolution of the Universe.The foundation of Smarandache geometries is based on S-denying an axiom, i.e. in the same space an axiom is false in at least two different ways, or is false and also true. S-denying each of 4 signature conditions in Einstein's basic space-time we arrive to 4 kinds of expanded space-time for the General Theory of Relativity. The 4th expanded space-time type permits photon teleportation, well-known from the recent experiments, but which failed in the basic space-time, and also where virtual photons are permitted --- predicted by Quantum Electrodynamics instant-moving mediators between entangled regular particles. |

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### Contents

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13 Neutrosophic subjects | 13 |

14 Neutrosophic logic The origin of neutrosophy | 14 |

15 Definitions of neutrosophics | 16 |

TRAJECTORIES AND PARTICLES | 18 |

22 Standard set of trajectories and particles A way to expand the set | 22 |

23 Introducing trajectories of mixed isotropicnonisotropic kind | 28 |

26 More on an expanded spacetime of kind IV | 45 |

a home space for virtual photons | 52 |

nonquantum teleportation of photons | 55 |

29 Conclusions | 59 |

ENTANGLED STATES AND QUANTUM CAUSALITY THRESHOLD | 61 |

32 Incorporating entangled states into General Relativity | 64 |

33 Quantum Causality Threshold in General Relativity | 69 |

34 Conclusions | 72 |

24 Particles moving along mixed isotropicnonisotropic trajectories | 31 |

25 Sdenying the signature conditions Classification of the expanded spaces | 35 |

Bibliography | 73 |

### Common terms and phrases

Anti-A basic space-time basis vectors Borissova chronometrically invariant common conditions of degeneration coordinate velocity eikonal equation Einstein entanglement condition equation Euclidean expanded space-time expanded spaces formula four-dimensional impulse vector four-dimensional pseudo-Riemannian space fully degenerate fundamental metric tensor Fuzzy Set gikdxidxk gravitational potential infinitesimal inside the zero-space intersection isotropic cone isotropic trajectory light velocity mass-bearing particles massless light-like particles massless particles mathematical mirror Universe mixed Neut-A neutrosophic logic Neutrosophic method neutrosophic probability Non-A non-geodesic non-standard non-standard analysis non-zero observable metric tensor particle located particle moving problem statement Quantum Causality Threshold Quantum Electrodynamics quantum teleportation Rabounski regular observer relativistic masses Riemann geometry Riemannian geometry Riemannian space S-denied sign-alternating Smarandache geometries space rotation space-time interval space-time of kind spaces of kind spatial section sub-light subsets substantial particles super-light tachyons tangential Theorem Theory of Relativity three-dimensional space true viewpoint virtual particles viui world-line world-trajectories zero-particles zero-space