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
Prerelativistic: 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 fasterthanlight
signals, spacelikeseperated 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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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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 Spring '08
 Heary
 Philosophy, General Relativity, Riemannian geometry, galilean spacetime

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