By Abhay Ashtekar
Ashtekar A. Lectures on nonperturbative canonical gravity (WS, 1991)(K)(T)(ISBN 9810205732)(177s)
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Extra resources for Lectures on non-perturbative canonical gravity
As Frappier notes, “Heisenberg’s claim that the relations existing between physical concepts are defined in systems of axioms and definitions … [might suggest] that he did not completely understand Hilbert’s idea that a theory’s axioms implicitly define its theoretical terms, and that consequently, a concept can change reference across interpretations” (Frappier 2004, p. 165). ”11 Despite the importance of axiomatic systems for Heisenberg’s account of closed theories, his account of such systems and its elements regrettably remains far from clear.
22) At the conclusion of their discussion of theory change, Kuhn agrees with Heisenberg that, “with regard to evolutionary views about the development of science, you and I say very much the same thing” (Kuhn 1963, February 28th, p. 3). Heisenberg explicitly connects up his revolutionary model of theory change with his belief that, in order to make progress in science, one must abandon the concepts of the predecessor theory. In the interview with Kuhn he goes on to criticize many of the other founders of quantum theory who “were not able to do the other step which would have been absolutely necessary to come further and that is, to throw away the old physics, that is throw away all the classical concepts and replace them with new ones” (Heisenberg 1963, February 28th, p.
Similarly, Ballentine demonstrates that Ehrenfest’s theorem is not a necessary condition for the classical limit by showing that there are several physical systems whose quantum states may behave classically, even when the Ehrenfest conditions do not apply. Ballentine notes that one of the difficulties with using Ehrenfest’s theorem to characterize the classical regime is that it assumes that the classical limit of a wavefunction is a single trajectory rather than an ensemble of classical trajectories.
Lectures on non-perturbative canonical gravity by Abhay Ashtekar