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## 74. Theory Identity

### FREDERICK SUPPE

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In 1925 the old quantum mechanics of Planck, Einstein, and Bohr was replaced by the new (matrix) quantum mechanics of Born, Heisenberg, Jordan, and Dirac. In 1926 Schrödinger developed wave mechanics , which proved to be equivalent to matrix mechanics in the sense that they led to the same energy levels. Dirac and Jordan joined the two theories into one transformation quantum theory . In 1932 von Neumann presented his Hilbert space formulation of quantum mechanics and proved a representation theorem showing that sequences in transformation theory were isomorphic to sequences in the Hilbert space formulation (see quantum mechanics ). Three different notions of theory identity are involved here: theory individuation, theoretical equivalence, and empirical equivalence. What determines whether theories T 1 and T 2 are instances of the same theory or distinct theories? By construing scientific theories as partially interpreted syntactical axiom systems TC , positivism made specifics of the axiomatization individuating features of the theory. Thus different choices of axioms T or alterations in the correspondence rules - say, to accommodate a new measurement procedure - resulted in a new scientific theory. Positivists also held that axioms and correspondence rules implicitly defined the meanings of the theory's descriptive terms τ. Thus significant alterations in the axiomatization ... log in or subscribe to read full text

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