Quantum Physics

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.

The upheaval in quantum theory in the mid-1920s is often presented as a Kuhnian paradigm shift. The new quantum mechanics, to use a building metaphor, was erected on the ruins of the old quantum theory, brought down by an accumulation of anomalies. In our book Constructing Quantum Mechanics (2019/2023), Tony Duncan and I use a different building metaphor. As suggested by the subtitles of the two volumes of our book, The Scaffold: 1900–1923 and The Arch: 1923–1927, we see the architects of the new quantum mechanics using parts of the old quantum theory as scaffolds to build the arch of the new one. In this talk, after sketching the underlying alternative to Kuhn's account of scientific revolutions in general, I will give an overview, as non-technical as possible, of the genesis of quantum mechanics in the period 1900–1927.

I claim that the idea of "reconstructing" quantum mechanics along the lines of quantum probability was there from the beginning of the theory as we know it, in von Neumann's paper "Probabilistic construction of quantum mechanics". In this paper, von Neumann derives (and often introduces for the first time) a slew of now-familiar concepts in quantum mechanics, such as both pure and mixed states (respectively as wavefunctions and—generally unnormalized—density operators), the general form of the Born rule for expectation values, a rather general form of transition probabilities, and a recognisable version of the collapse postulate for the general case of maximal measurements and in a special case of non-maximal measurements. He does so axiomatically, starting from two probabilistic axioms that are neutral between classical and quantum probability and two axioms characterising quantum mechanical quantities in terms of a non-commutative algebra (that of self-adjoint operators in Hilbert space). The presentation of this material in von Neumann's 1932 book is usually understood as a "no-hidden-variables" theorem. However, the sense in which a "completion" of the theory is ruled out is merely that a theory with dispersion-free states would require a different algebraic structure. Grete Hermann pointed this out already in the 1930s (she later retracted the additional claim of "circularity"), and it is arguably also how von Neumann himself saw his result. The more fundamental disagreement between von Neumann and Hermann (and arguably between von Neumann and Bohr) turns out to be about the nature of the quantum state and the status of collapse.

We show that classical mechanics can be recovered as the high-entropy limit of quantum mechanics. The mathematical limit $\hbar \to 0$ can be recovered by decreasing entropy of pure states to minus infinity, in the same way that non-relativistic mechanics can be recovered mathematically by increasing the speed of light c to plus infinty. Physically, these limits are more appropriately understood as a high entropy limit and low speed limit respectively, representing approximations that are independent of underlying mechanism. With this approach, the classical limit is both formally and conceptually similar to the non-relativistic limit, and is independent of interpretation. It also gives an intuitive understanding to the Dirac correspondence principle: it is looking for a theory with lower entropy bound that, at high entropy, recovers classical mechanics. Given that the Moyal bracket is the unique one-parameter Lie-algebraic deformation of the Poisson bracket, quantum mechanics is the only theory that can provide such a lower bound on the entropy.

The Heisenberg microscope provides a powerful mental image of the measurement process of quantum mechanics (QM), attempting to explain the uncertainty relation through an uncontrollable back-action from the measurement device. However, Heisenberg's proposed back-action uses features that are not present in the QM description of the world, and according to Bohr not present in the world. Therefore, Bohr argues, the mental image proposed by Heisenberg should be avoided. Later developments by Bell and Kochen-Specker shows that a model that contains the features used for the Heisenberg microscope is in principle possible but must necessarily be nonlocal and contextual. In this paper we will re-examine the measurement process within a restriction of QM known as Stabilizer QM, that still exhibits for example Greenberger-Horne-Zeilinger nonlocality and Peres-Mermin contextuality. The re-examination will use a recent extension of stabilizer QM, the Contextual Ontological Model (COM), where the system state gives a complete description of future measurement outcomes reproducing the quantum predictions, including the mentioned phenomena. We will see that the resulting contextual Heisenberg microscope back-action can be completely described within COM, and that the associated randomness originates in the initial state of the pointer system, exactly as in the original description of the Heisenberg microscope. The presence of contextuality, usually seen as prohibiting ontological models, suggests that the contextual Heisenberg microscope picture could perhaps be enabled in general QM.

On March 27th, 1927, Heisenberg published the paper in which he introduced the uncertainty relations through his well-known $\gamma$-ray microscope thought experiment. Since then, the debates and commentaries over the origin of the uncertainty relations have continued for a century (see, for instance, Bacciagaluppi and Valentini 2009; Beller 1999; Brown and Redhead 1981; Busch 1990; Hilgevoord and Uffink 1985,2024; Jammer 1974; Uffink 1990). Going back to 1927 through a selection of letters -- including an unpublished letter from Jordan to Rosenfeld -- this talk aims to add a crucial piece to this century-old puzzle by shedding new light on the differences between Heisenberg and Bohr's conceptual basis of the uncertainty relations. According to the received view, Bohr derives the uncertainty relations from the \textit{wave-particle duality} of light. By contrast, it is commonly stated that Heisenberg based them on the \textit{discontinuity} in the interaction between the electron and the light quantum, i.e., the uncontrollable change resulting from the Compton effect (cf. Camilleri 2009). I will challenge the received view by arguing that: (i) Bohr’s derivation of the uncertainty relations fundamentally relies on the use of \textit{classical concepts}, consistent with their central role in his broader interpretation of quantum mechanics. (ii) The supposed contrast rooted in the wave-particle duality of light may stem from Heisenberg’s 1927 misrepresentation (or misinterpretation) of Bohr's ideas on the $\gamma$-ray microscope. This misrepresentation may have influenced the reception of Bohr’s interpretation, particularly regarding his ideas on the conceptual justification for the uncertainty relations, and contributed to obscuring the deeper significance of Bohr's complementarity principle - fully comprehensible only in light of (i).

We articulate a collection of desiderata for an account of the dynamical quantities of a physical theory, and we present a theory that meets these desiderata in the case of quantum mechanics. Our theory retains a distinction between the values of dynamical quantities and the truth values of sentences asserting that a system has a particular value of a particular quantity. This allows our theory to incorporate the phenomenon of quantum indeterminacy as a pattern in the properties instantiated by a system in a particular quantum state, while also retaining the semantics of classical logic. We contrast our theory with quantum logic, which flattens the distinction between quantity values and truth values. We discuss the historical origin of the assumptions leading to this feature of quantum logic, and we address a series of objections that have been raised to previous attempts to reconcile quantum indeterminacy with classical logic.