Philosophy 426 Notes

Philosophy 426 Notes - Philosophy 426 Notes Minkowski...

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Philosophy 426 Notes Minkowski Spacetime: o The points of spacetime will be all the locations of possible ideal events o Spacetime is the set of all events o Pre-relativistic: An event is specified by where and when it took place o Structure radically different from Newtonian spacetime: It is not meaningful to ask for the temporal separation between two events or the spatial separation o Minkowski spacetime has four dimensions o Do no discuss the distances between events but rather the interval between them o Interval is not a distance o Fundamental assumption of relativistic theories is that there are no such faster-than-light signals, spacelike-seperated events have no possible causal signal connecting them at all Gauss – All an empirical question which geometry to use; empirical not a priori o Geometry is only an empirical matter once we’ve chosen our convention Riemann’s Spherical Geometry – no parallels to a single line; a triangle will always be greater than two right triangles, maximum 3 straight lines Hyperbolic Geometry – also that of constant curvature; through a point outside a line there is an infinity of lines that are parallel to a given line Relative Consistence Proof – To show a set of axioms are consistent, must prove you can’t derive a contradiction Lobachevskian Geometry: o ‘point’ – point inside the bounding circle o ‘line’ – chord of this circle excluding endpoints o ‘parallel lines’ – chords of the circle that don’t intersect o All Euclidean theorems come out true, so Lobachevskian geometry is consistant o Each axiom of Lobachevskian plane geometry translates into a theorem of Euclidean geometry Poincare – Empirical observations can be wrong o The choice of the geometry to describe the world is simply a matter of convenience; is true by convention and not by how the world is
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o Geometries are true by convention but are meaningless empirically o Geometry is analytic a priori o Euclidean geometry is intrinsically simpler than other geometries Though sometimes better to use more complex geometry and simpler physics Richenbach – Considered himself an empiricist against Poincare’s conventionalism (knew about Riemannian geometry) Reichenbach’s a conventionalist o Discussed Riemannian geometry; said finding out the true geometry is an empirical question o Can use the earth to find out geometries of the earth, you should therefore be able to do the
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Philosophy 426 Notes - Philosophy 426 Notes Minkowski...

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