|Annu. Rev. Astron. Astrophys. 1988. 26: Copyright © 1988 by .
All rights reserved 2.2. The Idea of Geometrical Experiments How
then are we to measure deviations from Euclidean predictions?
What rules concerning the properties of measuring rods do we
adopt, and by what rules do we assess whether an experiment has
given a non-Euclidean result? Early on, Poincaré denied the
reality of actual curved space by stating that in any
measurement that appeared to give a non-Euclidean result, one is
at liberty to redefine the properties of the measuring rods in
such a way as to recover a Euclidean prediction. A particularly
interesting example of this, involving nonuniformly heated metal
measuring rods, is given by Robertson (1949). Poincaré's point
has been variously debated (cf. Whittaker 1958, Reichenbach
1958) with the consensus opinion being that contrived
(unreasonable) explanations of changes in the measuring rods, if
they are required to save the Euclidean case, are less desirable
than a real Riemann-Lobachevski