Srinivasan, Radhakrishnan (2002) *Inertial frames, special relativity and consistency.* [Preprint]

| Postscript Download (106Kb) | Preview | |

Tex/LaTeX Download (21Kb) |

## Abstract

The theory of special relativity (SR) is considered in the framework of classical first-order logic. The four axioms of SR are: The existence of a flat four-dimensional spacetime continuum, the existence of global inertial frames of reference and Einstein's two postulates. The propositions permitted are those involving the kinematics and dynamics of SR as formulated from an inertial frame; these give a complete description of the evolution of the universe. Assuming SR as consistent, there must exist a model M for SR in which F is an inertial frame in a non-trivial universe U(IBC) of material objects, with appropriate initial-boundary conditions IBC specified. Let P be defined as ``F is an inertial frame in U(IBC)''. Using Goedel's second incompleteness theorem, it is argued that P is undecidable in SR. Let Q be any proposition such that (Q --> P) is not a theorem of SR. If, in addition, (P --> Q) is a theorem of SR then Q must necessarily be true in M. It follows that there must exist a model N for SR in which Q is true and P is false, i.e., F is an accelerated frame in U(IBC). The philosophical and mathematical implications of this result for the consistency of SR are discussed.

Export/Citation: | EndNote | BibTeX | Dublin Core | ASCII/Text Citation (Chicago) | HTML Citation | OpenURL |

Social Networking: |

Item Type: | Preprint |
---|---|

Commentary on: | Srinivasan, Radhakrishnan(2002) Quantum superposition justified in a new non-Aristotelian finitary logic. [Preprint] |

Keywords: | inertial frames, consistency, Goedel's incompleteness theorems, self-reference, classical logic |

Subjects: | Specific Sciences > Mathematics Specific Sciences > Physics Specific Sciences > Physics > Relativity Theory |

Depositing User: | Radhakrishnan Srinivasan |

Date Deposited: | 27 Jun 2002 |

Last Modified: | 07 Oct 2010 11:10 |

Item ID: | 666 |

URI: | http://philsci-archive.pitt.edu/id/eprint/666 |

### Commentary/Response Threads

- Srinivasan, RadhakrishnanQuantum superposition justified in a new non-Aristotelian finitary logic. (deposited 04 May 2002)
- Srinivasan, RadhakrishnanPlatonism in classical logic versus formalism in the proposed non-Aristotelian finitary logic. (deposited 21 May 2003)
- Srinivasan, RadhakrishnanInertial frames, special relativity and consistency. (deposited 27 Jun 2002)
**[Currently Displayed]**

### Actions (login required)

View Item |