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

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Abstract
The theory of special relativity (SR) is considered in the framework of classical firstorder logic. The four axioms of SR are: The existence of a flat fourdimensional 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 nontrivial universe U(IBC) of material objects, with appropriate initialboundary 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.
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Item Type:  Preprint  

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Commentary on:  Srinivasan, Radhakrishnan (2002) Quantum superposition justified in a new nonAristotelian finitary logic. [Preprint]  
Keywords:  inertial frames, consistency, Goedel's incompleteness theorems, selfreference, 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 15:10  
Item ID:  666  
URI:  http://philsciarchive.pitt.edu/id/eprint/666 
Commentary/Response Threads

Srinivasan, Radhakrishnan
Quantum superposition justified in a new nonAristotelian finitary logic. (deposited 04 May 2002)
 Srinivasan, Radhakrishnan Platonism in classical logic versus formalism in the proposed nonAristotelian finitary logic. (deposited 21 May 2003)
 Srinivasan, Radhakrishnan Inertial frames, special relativity and consistency. (deposited 27 Jun 2002) [Currently Displayed]
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