The paper starts examining some ideas of Einstein and Rovelli about space and spacetime in the context of the general theory of relativity and identifying a connection among them.I continue drawing a parallel between ...The paper starts examining some ideas of Einstein and Rovelli about space and spacetime in the context of the general theory of relativity and identifying a connection among them.I continue drawing a parallel between those ideas in the field of physics and the conception of space in mathematics according to Riemann’s revolutionary view,basis of the elaboration of the mathematical structures used in general relativity.In analogy with Einstein’s and Rovelli’s ideas about physical space,I come to formulate the idea that it is not appropriate to think that,in forming a riemannian manifold(the mathematical object representing spacetime),the metric field places itself in a space pre-existing to it and it may do this differently.According to this idea,I formulate a critical remark about Earman and Norton’s famous hole argument focused on the rejection of the active interpretation of general covariance.I compare then my critical remark about the hole argument with the position of Weatherall on it.I conclude with some critical remarks on moderate structural realism about spacetime and proposing an interpretation of Einstein’s assertion that spacetime“does not claim existence on its own,but only as a structural quality of the field”.展开更多
文摘The paper starts examining some ideas of Einstein and Rovelli about space and spacetime in the context of the general theory of relativity and identifying a connection among them.I continue drawing a parallel between those ideas in the field of physics and the conception of space in mathematics according to Riemann’s revolutionary view,basis of the elaboration of the mathematical structures used in general relativity.In analogy with Einstein’s and Rovelli’s ideas about physical space,I come to formulate the idea that it is not appropriate to think that,in forming a riemannian manifold(the mathematical object representing spacetime),the metric field places itself in a space pre-existing to it and it may do this differently.According to this idea,I formulate a critical remark about Earman and Norton’s famous hole argument focused on the rejection of the active interpretation of general covariance.I compare then my critical remark about the hole argument with the position of Weatherall on it.I conclude with some critical remarks on moderate structural realism about spacetime and proposing an interpretation of Einstein’s assertion that spacetime“does not claim existence on its own,but only as a structural quality of the field”.
