We develop a systematic approach to quantum probability as a theory of rational betting in quantum gambles. In these games of chance the agent is betting in advance on the outcomes of several incompatible measurements. One of the measurements is subsequently chosen and performed and the money placed on the other measurements is returned to the agent. We show how the rules of rational betting imply all the interesting features of quantum probability, even in such finite gambles. These include the (...) uncertainty principle and the violation of Bell's inequality among others. Quantum gambles are closely related to quantum logic and provide a new semantics to it. We conclude with a philosophical discussion on the interpretation of quantum mechanics. (shrink)

A paradigmatic shift in the foundations of quantum mechanics is recorded, from interpreting to reconstructing quantum theory. Examples of reconstruction are analyzed, and conceptual foundations of the information-theoretic reconstruction developed. A concept of intentionally incomplete reconstruction is introduced to mark the novel content of research in the foundation of quantum theory. ‡Many thanks to Lucien Hardy, Jeff Bub and Bill Demopoulos for their comments. This research was supported through the ANR grant ANR-06-BLAN-0348-01. Part of this research was held at the (...) Perimeter Institute for Theoretical Physics. Research at Perimeter Institute for Theoretical Physics is supported in part by the Government of Canada through NSERC and by the Province of Ontario through MRI. †To contact the author, please write to: CEA-Saclay, 91191 Gif-sur-Yvette, France; e-mail: [email protected]. (shrink)

What belongs to quantum theory is no more than what is needed for its derivation. Keeping to this maxim, we record a paradigmatic shift in the foundations of quantum mechanics, where the focus has recently moved from interpreting to reconstructing quantum theory. Several historic and contemporary reconstructions are analyzed, including the work of Hardy, Rovelli, and Clifton, Bub and Halvorson. We conclude by discussing the importance of a novel concept of intentionally incomplete reconstruction.

This is a review of those key thought experiments in physics from the late 19th century onward that seem to have played a particular role in the process of the discovery or advancement of theory. Among others the paper discusses Maxwell's demon, several of Einstein's thought experiments in relativity, Heisenberg's microscope, the Einstein-Schrödinger cat, and the EPR thought experiment.