July 4; rev. July 24, 2003 Must Evidence Underdetermine Theory?

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Natural Pairs

These are those that have arisen in the real development of science. The best know examples are these. In Newton's original version of mechanics, there was an absolute state of rest which transcended observational specification. We form an observationally equivalent pair by taking versions of Newtonian mechanics with different absolute states of rest. Einstein's special theory of relativity and a suitably adjusted version of Lorentz's ether theory agree on all that can be observed about the slowing of moving clocks and shrinking of moving rods, yet they disagree on the theoretical account behind it.9 In the 1920s, Cartan and Friedrichs showed how to construct a spacetime theory that returned all the same motions as Newton's theory of gravitation. Yet their theory did not represent gravitation as a field, but as a curvature of spacetime, modeled after Einstein's general theory of relativity. Finally it is a standard part of the lore of quantum mechanics, that two distinct quantum theories emerged in the 1920s, the matrix mechanics of Heisenberg, Born and Jordan, and the wave mechanics of de Broglie and Schrödinger. They were soon shown to be equivalent.10

Another pair that is often mentioned in this context is the non-relativistic quantum mechanics of particles and Bohm's (1952) hidden variable theory, although they are not strictly observationally equivalent. The former theory assigns no definite position to a quantum particle in most of its states; the position is brought to be by the act of measurement. The latter theory always assigns a position to the particle and it just becomes manifested on measurement. In both cases there is a probability distribution associated with the resulting positions and they will agree in all ordinary circumstances.11

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