Physical Formulation of Our Theory

Satoru Yamamoto

Albert S. Schwarz

We show how to formulate physical theory taking as a starting point the set of states (geometric approach). We discuss the relation of this formulation to the conventional approach to classical and quantum mechanics and the theory of complex systems. The equations of motion and the formulas for probabilities of physical quantities are analyzed. A heuristic proof of decoherence in our setting is used to justify the formulas for probabilities. We show that any physical theory can be obtained from classical theory if we restrict the set of observables. This remark can be used to construct models with any prescribed group of symmetries; one can hope that this construction leads to new interesting models that cannot be build in the conventional framework. The geometric approach can be used to formulate quantum theory in terms of Jordan algebras, generalizing the algebraic approach to quantum theory. The scattering theory can be formulated in geometric approach.

Mario Bunge

The question is asked whether, as is often claimed, the Lagrangian formulation of a physical theory provides its mechanical interpretation. For purposes of this enquiry, an analysis of physical theories is performed, with special emphasis on classical mechanics, electromagnetism, and quantum mechanics. Three aspects are distinguished and defined: the formulation (statement), the representation (transformation properties), and the interpretation (meaning). Confusion of formalism with meaning is criticized, and is suggested as a source of some misunderstandings of recent reinterpretations of quantum mechanics. Properties and advantages of Lagrangian formulations are listed, and it is recalled that their chief usefulness lies in that they are the most helpful precisely when mechanisms are either ignored or absent. It is concluded that Lagrangian formulations contribute to the demechanization of physics and that the program of reduction to mechanics has not succeeded in physics.

Josh Roeloffs

Andrea Di Biagio, Pietro Donà, Carlo Rovelli C

The operational formulations of quantum theory are drastically time oriented. However, to the best of our knowledge, microscopic physics is time-symmetric. We address this tension by showing that the asymmetry of the operational formulations does not reflect a fundamental time-orientation of physics. Instead, it stems from built-in assumptions about the users of the theory. In particular, these formalisms are designed for predicting the future based on information about the past, and the main mathematical objects contain implicit assumption about the past, but not about the future. The main asymmetry in quantum theory is the difference between knowns and unknowns.

A. Lukš, Vlasta Peřinová