From Linearity to Nonlinearity: Reconstructing the Physical and Philosophical Foundations of Quantum Theory

NORMAN R. CAMPBELL

Philipp Berghofer

The program of reconstructing quantum theory based on information-theoretic principles enjoys much popularity in the foundations of physics. Surprisingly, this endeavor has only received very little attention in philosophy. Here I argue that this should change. This is because, on the one hand, reconstructions can help us to better understand quantum mechanics, and, on the other hand, reconstructions are themselves in need of interpretation. My overall objective, thus, is to motivate the reconstruction program and to show why philosophers should care. My specific aims are threefold. (i) Clarify the relationship between reconstructing and interpreting quantum mechanics, (ii) show how the informational reconstruction of quantum theory puts pressure on standard realist interpretations, (iii) defend the quantum reconstruction program against possible objections.

Holger Lyre

Carl Friedrich von Weizsaecker's thinking has always crossed the borders between physics and philosophy. Being a physicist by training he still feels at home in the physics community, as a philosopher by passion, however, his mind cannot stop thinking at the limits of physics. His physical ideas are based on the general conceptual and methodological preconditions of physical theories. Such a line of reasoning about the foundations of physics has brought Weizsaecker into an abstract program of a possible reconstruction of physics in terms of yes-no-alternatives, which he called "ur-theory." I shall start this paper with a review of the basic ideas of ur-theory: the definition of an ur and the connection between ur-spinors and spacetime. I then go over to some of ur-theory's present borders: the construction of quantized spacetime tetrads and the difficulties to incorporate gravity and gauge theories. Finally, I shall discuss the possible prospects of ur-theory -- partly with a view to modern quantum gravity approaches, but mainly in connection with its philosophical implications. Here, one of the crucial questions is, whether form, or, modern, information is an entity per se and what particular consequences this may have.

Carl Friedrich von Weizsäcker

Yurii Vladimirovich Brezhnev

Clarifying the nature of the quantum state |Ψ⟩ is at the root of the problems with insight into counter-intuitive quantum postulates. We provide a direct—and math-axiom free—empirical derivation of this object as an element of a vector space. Establishing the linearity of this structure—quantum superposition—is based on a set-theoretic creation of ensemble formations and invokes the following three principia: (I) quantum statics, (II) doctrine of the number in the physical theory, and (III) mathematization of matching the two observations with each other (quantum covariance). All of the constructs rest upon a formalization of the minimal experimental entity—the registered micro-event, detector click. This is sufficient for producing the ℂ-numbers, axioms of linear vector space (superposition principle), statistical mixtures of states, eigenstates and their spectra, and non-commutativity of observables. No use is required of the spatio-temporal concepts. As a result, the foundations of theory are liberated to a significant extent from the issues associated with physical interpretations, philosophical exegeses, and mathematical reconstruction of the entire quantum edifice.