Heisenberg’s 1925 Paper and the Need for a Reinterpretation of the Concept of Trajectory

9 Dec 2025, 15:10
40m

Speakers

Marco Giliberti Luisa Lovisetti

Description

In the abstract of his “Umdeutung” paper—traditionally regarded as the founding act of quantum mechanics—Heisenberg declares that the purpose of his work “is to attempt to establish the foundations for a quantum-theoretical mechanics that is based exclusively on relationships between quantities that are, in principle, observable”. This statement has often drawn readers’ attention to the philosophical aspects of Heisenberg’s approach. However, after having noted that the trajectory of an electron within an atom is not observable, Heisenberg proceeds—on the basis of precise physical and mathematical arguments—to show the impossibility of identifying a classical trajectory capable of generating the observed electromagnetic spectrum. This reflection marks the beginning of the “reinterpretation” announced in the title of the paper and forms the basis of his new formulation of quantum theory. Thus, the need to reinterpret the concept of trajectory, as indicated in the title itself, is not for Heisenberg merely or primarily a philosophical issue (inspired by positivism), but rather an essential element of the emerging theory. The nonexistence of a well-defined trajectory would continue to concern Heisenberg and ultimately lead him to formulate the uncertainty principle in 1927—although in that later context the argument is extended to show the general impossibility of defining a trajectory in quantum mechanics. Heisenberg’s early “philosophy”, therefore, seems mainly grounded in profoundly physical considerations. In this presentation, we will focus on this important aspect of the 1925 paper, which, in our view, has often been insufficiently appreciated and discussed.

Authors

Marco Giliberti Luisa Lovisetti

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