Abstract The reconstruction of quantum physics has been connected with the interpretation of the quantum formalism, and has continued to be so with the recent deeper consideration of the relation of information to quantum states and processes. This recent form of reconstruction has mainly involved conceiving quantum theory on the basis of informational principles, providing new perspectives on physical correlations and entanglement that can be used to encode information. By contrast to the traditional, interpretational approach to the foundations of quantum mechanics, which attempts directly to establish the meaning of the elements of the theory and often touches on metaphysical issues, the newer, more purely reconstructive approach sometimes defers this task, focusing instead on the mathematical derivation of the theoretical apparatus from simple principles or axioms. In its most pure form, this sort of theory reconstruction is fundamentally the mathematical derivation of the elements of theory from explicitly presented, often operational principles involving a minimum of extra‐mathematical content. Here, a representative series of specifically information‐based treatments—from partial reconstructions that make connections with information to rigorous axiomatizations, including those involving the theories of generalized probability and abstract systems—is reviewed.Abstract The reconstruction of quantum physics has been connected with the interpretation of the quantum formalism, and has continued to be so with the recent deeper consideration of the relation of information to quantum states and processes. This recent form of reconstruction has mainly involved conceiving quantum theory on the basis of informational principles, providing new perspectives on physical correlations and entanglement that can be used to encode information. By contrast to the traditional, interpretational approach to the foundations of quantum mechanics, which attempts directly to establish the meaning of the elements of the theory and often touches on metaphysical issues, the newer, more purely reconstructive approach sometimes defers this task, focusing instead on the mathematical derivation of the theoretical apparatus from simple principles or axioms. In its most pure form, this sort of theory reconstruction is fundamentally the mathematical derivation of the elements of theory from explicitly presented, often operational principles involving a minimum of extra‐mathematical content. Here, a representative series of specifically information‐based treatments—from partial reconstructions that make connections with information to rigorous axiomatizations, including those involving the theories of generalized probability and abstract systems—is reviewed.

Annalen der PhysikSep 12, 201813 citations

Reconstruction of Quantum Mechanics

Peter Mittelstaedt

Springer eBooksOct 9, 20102 citations

The Role of Reconstruction in the Elucidation of Quantum Theory *

Philip Goyal

The quantum reconstruction program seeks to uncover the deeper physical meaning of the quantum formalism by distilling its content into a set of physically graspable postulates. Once reconstructed, one can further elucidate the theory by reflecting philosophically upon the postulates rather than the inscrutable formalism in which the theory is couched. Quantum reconstruction thereby opens up a two-step strategy for developing a quantum conceptual framework that reflects the full physical content of quantum theory and can be used to establish precisely what aspects of the classical conceptual framework are retained, modified, or abandoned. The chapter is organized as follows. Section 11.2 describes the tripartite structure of classical physics, whose coherency I argue underlies its intelligibility. Section 11.3 discusses the lack of intelligibility of quantum physics, analyses the limitations of the main traditional elucidative approaches, and describes how reconstruction can remove the fundamental interpretative bottleneck. Section 11.4 discusses the methodology of reconstruction per se , showing that it is part of the natural life-cycle of physical theories, and summarizes its use in the elucidation of the theories of classical physics. Finally, circling back to quantum theory, Section 11.5 summarizes the reconstruction of quantum theory, and Section 11.6 describes some of the interpretative insights obtained thus far through interpretation of reconstructions of the abstract quantum formalism and the quantum symmetrization postulate.The quantum reconstruction program seeks to uncover the deeper physical meaning of the quantum formalism by distilling its content into a set of physically graspable postulates. Once reconstructed, one can further elucidate the theory by reflecting philosophically upon the postulates rather than the inscrutable formalism in which the theory is couched. Quantum reconstruction thereby opens up a two-step strategy for developing a quantum conceptual framework that reflects the full physical content of quantum theory and can be used to establish precisely what aspects of the classical conceptual framework are retained, modified, or abandoned. The chapter is organized as follows. Section 11.2 describes the tripartite structure of classical physics, whose coherency I argue underlies its intelligibility. Section 11.3 discusses the lack of intelligibility of quantum physics, analyses the limitations of the main traditional elucidative approaches, and describes how reconstruction can remove the fundamental interpretative bottleneck. Section 11.4 discusses the methodology of reconstruction per se , showing that it is part of the natural life-cycle of physical theories, and summarizes its use in the elucidation of the theories of classical physics. Finally, circling back to quantum theory, Section 11.5 summarizes the reconstruction of quantum theory, and Section 11.6 describes some of the interpretative insights obtained thus far through interpretation of reconstructions of the abstract quantum formalism and the quantum symmetrization postulate.

Routledge eBooksNov 20, 20235 citations

A Reconstruction of Algebraic Quantum Theory

Bharath Ron

We obtain a condensed reconstruction of algebraic quantum theory, emphasizing its foundational aspects and algebraic structure. We obtain the $W^*$ -algebra structure from elementary assumptions about observers and how they can observe reality. This work highlights the need for the abstract algebraic approach by directly obtaining the mathematical axioms from simple thought experiments.We obtain a condensed reconstruction of algebraic quantum theory, emphasizing its foundational aspects and algebraic structure. We obtain the $W^*$-algebra structure from elementary assumptions about observers and how they can observe reality. This work highlights the need for the abstract algebraic approach by directly obtaining the mathematical axioms from simple thought experiments.

arXiv:2311.17739Nov 29, 20230 citations

Reconstruction of Quantum Mechanics

Peter Mittelstaedt

Springer eBooksOct 4, 20121 citation

We obtain a condensed reconstruction of algebraic quantum theory, emphasizing its foundational aspects and algebraic structure. We obtain the

W^*

-algebra structure from elementary assumptions about observers and how they can observe reality. This work highlights the need for the abstract algebraic approach by directly obtaining the mathematical axioms from simple thought experiments.