Quantum Foundations

In June 1925 Heisenberg arrived at Helgoland/Heligoland island to escape a fit of hay fever. He returned with a sketch of a strange theory of the micro-world, which we now call quantum mechanics. This essay attempts to present a look at this theory, which tries to return to the original insight of Heisenberg on what should be the essence of a theory of atomic realm: it must be a theory of the observable events, in which fundamentally unobservable quantities have no place. No ontological status is given to elements of the mathematical formulation of the theory. The theory is about our description of events in laboratories, probabilities of which are given by the Born rule. Following Bohr, these events involve macroscopic measuring apparatuses, and the accessible final events are classically describable and "the unambiguous account of proper quantum phenomena must, in principle, include a description of all relevant features of experimental arrangement". . Information about the events is cloneable, as it is of a classical nature, The modern quantum theory of classicality is the decoherence theory. It treats "the pointer variable" of measuring apparatus as an open system interacting with an environment consisting of all other "zillions" of degrees of freedom of the device, and anything coupled to it. Because such environment is uncontrollable we have no possibility to reverse measurements. The quantum mechanical measurement theory based on decoherence theory is reproducing the probabilistic predictions of Born rule. There is no “measurement problem” in quantum mechanics, as it is a theory giving probabilistic predictions. “The quantum state only describes our knowledge” (Zeilinger). Notwithstanding, possibility of reversing measurements and of application of Born rule in situations other than these which lead to macroscopically observable events are features of a modification of quantum mechanics which is called by its adherents "unitary quantum mechanics". As its predictions, which go beyond quantum mechanics, are not testable - we claim that unitary quantum mechanics in an interpretation of quantum mechanics. As such it is metaphysics. The talk is based on arXiv:2003.07464 (PRL) and arXiv:2508.19207 co authored with M. Markiewicz.

In the early twentieth century, Alfred North Whitehead developed the most comprehensive metaphysical framework of process philosophy. Although he also applied his ideas to interpret quantum theory, his insights have remained largely unnoticed by the physics community, especially by today’s researchers in quantum foundations. In this talk, I will introduce the main ideas of process reality, with a special focus on Whitehead’s approach. The core idea is that the basic elements of reality are processes of becoming rather than static material substances. The picture of the world is one of a growing organism, where the individual parts are dynamic, relational units whose identity is defined by the network of interactions they participate in. I will argue that adopting a process-based ontology can offer the conceptual shift needed to resolve the main interpretational puzzles of quantum theory, in particular the ones associated with the no-go theorems (Bell, Kochen-Specker, etc.).

Quantum jumps pre-date the birth of modern quantum theory 100 years ago. But the modern understanding of these and other quantum stochastic processes emerged only in the early 1990s, via a process of convergence of surprisingly many different streams of research, in experimental and theoretical atomic physics and quantum optics, quantum foundations, mathematical physics, and control theory. Serendipitously, I began my PhD on this topic just as this was happening, so I played a small role in this development. My enduring fascination with the stochastic "unravellings" of the evolution of simple quantum systems also led to the formalisation of EPR-steering, to design experiments (yet to be done) to definitively disprove the idea that atoms undergo quantum jumps (or any other objective stochastic unravelling) independent of our observation.

The two postulates of orthodox quantum mechanics that jointly exhaust the change of the quantum state over time—process 1, the collapse postulate, and process 2, the unitary dynamics—evoke the question: why two postulates, and why these two? The scholarship on the foundations of quantum theory has been largely conditioned, to borrow from Quine’s apt expression, by two dogmas. One is that the collapse postulate was appended to the formalism ad hoc, merely to account for observations, and the other is that the two processes stand in hopeless contradiction. In this talk I will show—on the basis of Studies in History and Philosophy of Science 109 (2025): 89–105, co-authored with Ricardo Correa da Silva—that both dogmas are ill-founded. They are, I will argue, myths. Von Neumann postulated nothing arbitrarily: his basic constructive assumption—the equivalence between Matrix and Wave Mechanics—renders the “dual dynamics,” as he called his processes 1 and 2, a logical necessity. The true paradox lies in the nature of the equivalence: how can Matrix Mechanics—a theory of discontinuous jumps—and Wave Mechanics—a theory built from the ground up on the notion of continuity—be equivalent? They rather seem—here lies the root of the second dogma—self-contradictory. Von Neumann himself asked why the unified quantum-theoretical formalism requires a dual dynamics, but he could not articulate a proper answer within his static Hilbert space framework. A proper answer must be grounded on a dynamical principle—and I will argue that we have identified it. I will show the exact sense in which Matrix Mechanics implicitly contains Wave Mechanics and vice versa, the exact sense in which they are versions of the same theory: their dynamics, though different, are unified at a deep level—there is a single variational structure determining the dual dynamics. It is generally taken for granted in physics that the dynamics of a physical theory must follow from the action functional, and, in this talk, I will show that orthodox quantum mechanics is no exception to this golden rule. If the quantum-theoretical formalism requires “a peculiar dual dynamics,” as von Neumann called it, that is because the formalism is based on the deeper dynamical symmetry that entails the equivalence of Matrix and Wave Mechanics: the dual dynamics of the quantum-theoretical formalism is completely determined by the constraints of a dual action.

This talk will explore an underappreciated chapter in the history of the development of wave mechanics. It focuses upon the interactions between Einstein and Schrödinger in the wake of Einstein’s promotion of Bose’s new derivation of the Planck formula for the energy distribution of black-body radiation in 1924 and Einstein’s subsequent extension of Bose’s technique to material bodies. The main claim is that what Schrödinger was really attempting to do was to find a dynamical equation that would provide a bottom-up explanation for why bosons obeyed Bose-Einstein statistics.