Comparing theories: the dynamics of changing vocabulary. A casestudy in relativity theory
Abstract
There are several firstorder logic (FOL) axiomatizations of special relativity theory in the literature, all looking essentially different but claiming to axiomatize the same physical theory. In this paper, we elaborate a comparison, in the framework of mathematical logic, between these FOL theories for special relativity. For this comparison, we use a version of mathematical definability theory in which new entities can also be defined besides new relations over already available entities. In particular, we build an interpretation of the referenceframe oriented theory SpecRel into the observationally oriented Signalling theory of James Ax. This interpretation provides SpecRel with an operational/experimental semantics. Then we make precise, "quantitative" comparisons between these two theories via using the notion of definitional equivalence. This is an application of logic to the philosophy of science and physics in the spirit of Johan van Benthem's work.
 Publication:

arXiv eprints
 Pub Date:
 July 2013
 DOI:
 10.48550/arXiv.1307.1885
 arXiv:
 arXiv:1307.1885
 Bibcode:
 2013arXiv1307.1885A
 Keywords:

 Mathematics  Logic;
 Mathematical Physics;
 Physics  History and Philosophy of Physics;
 03B10 (Primary);
 03C40;
 03A10;
 83A05;
 51P05;
 03B80;
 03B30 (Secondary)
 EPrint:
 27 pages, 8 figures. To appear in Springer Book series Trends in Logic