The dilemma concerning the meaning of the wave function is perhaps one of the most controversial and overlooked in contemporary physics. There is widespread disagreement in the scientific community as to whether the wave function should be viewed as a representative of a real physical object or whether it corresponds to a state of incomplete knowledge about the underlying system, such as a probability density. These views are respectively called ψ-ontic and ψ-epistemic. This article aims to give a clear insight into the problem and features of both views. After some clarifying preliminaries, I will give an overview of how the question was perceived and interpreted by the pioneers of quantum theory, such as Bohr and Einstein, and then move on to more modern days with the likes of Bell, Kochen, and Specker. Then I will focus on the contemporary literature and try to give a comprehensive account of the pros and cons of each view. Finally, I will discuss some of the questions that the question of the wave function raises for us, such as our relationship to reality.
The dilemma concerning the meaning of the wave function is perhaps one of the most controversial and overlooked in contemporary physics. There is widespread disagreement in the scientific community as to whether the wave function should be viewed as a representative of a real physical object or whether it corresponds to a state of incomplete knowledge about the underlying system, such as a probability density. These views are respectively called ψ-ontic and ψ-epistemic. This article aims to give a clear insight into the problem and features of both views. After some clarifying preliminaries, I will give an overview of how the question was perceived and interpreted by the pioneers of quantum theory, such as Bohr and Einstein, and then move on to more modern days with the likes of Bell, Kochen, and Specker. Then I will focus on the contemporary literature and try to give a comprehensive account of the pros and cons of each view. Finally, I will discuss some of the questions that the question of the wave function raises for us, such as our relationship to reality.
The meaning of the wave function has been a hot topic of debate since the early days of quantum mechanics. Recent years have witnessed a growing interest in this long-standing question. Is the wave function ontic, directly representing a state of reality, or epistemic, merely representing a state of (incomplete) knowledge, or something else? If the wave function is not ontic, then what, if any, is the underlying state of reality? If the wave function is indeed ontic, then exactly what physical state does it represent? In this book, I aim to make sense of the wave function in quantum mechanics and find the ontological content of the theory. The book can be divided into three parts. The first part addresses the question of the nature of the wave function (Chapters 1-5). After giving a comprehensive and critical review of the competing views of the wave function, I present a new argument for the ontic view in terms of protective measurements. In addition, I also analyze the origin of the wave function by deriving the free Schroedinger equation. The second part analyzes the ontological meaning of the wave function (Chapters 6, 7). I propose a new ontological interpretation of the wave function in terms of random discontinuous motion of particles, and give two main arguments supporting this interpretation. The third part investigates whether the suggested quantum ontology is complete in accounting for our definite experience and whether it needs to be revised in the relativistic domain (Chapters 8, 9).
The wave function gives probabilities, but is it a real physical quantity, as in the ontic interpretation of quantum mechanics, or just a measure of human belief about a physical system, as in an epistemic interpretation? These questions are introduced by treating Schrödinger’s cat and Wigner’s friend. An important question is whether quantum mechanics applies to macroscopic objects, for example, cats. SQUID experiments have been performed that see quantum interference in very large objects, whereas with most macroscopic objects quantum interference disappears because of decoherence. Various views of the meaning of quantum mechanics are discussed: the Copenhagen interpretation, continuous spontaneous localization, Everett’s many-worlds interpretation, Bohm’s hidden-variable model, and quantum Bayesianism. The latter holds that the wave function represents one’s best belief about the state of a quantum system, rather than an actual physical property. This leads to discussions of recent theories and experiments explicitly designed to test wave function reality.
The ontological status of the quantum wavefunction remains one of the most debated questions in quantum theory. While epistemic interpretations regard the wavefunction as a reflection of our knowledge or beliefs, ontic interpretations treat it as a real physical object. In this paper, we argue that epistemic approaches struggle to explain the universality and precision of the uncertainty principle, a core feature of quantum mechanics. By contrast, treating the wave-function as ontic allows a consistent and natural derivation of quantum uncertainty from the mathematical structure of Hilbert space. We examine key interpretations on both sides and highlight why the epistemic view falls short in addressing constraints that appear to be intrinsic to nature.
Even after a hundred years of quantum theory, the true meaning of the quantum state has not yet been clearly understood. Does a pure quantum state, described by a wave function φ, represent a real physical quantity, comparable to position and momentum in classical mechanics, or does it, even as a pure state, only have a statistical significance, similar to a probability distribution? In this paper, we show that there is no contradiction between these two interpretations. Two concepts must be distinguished here: on the one hand, physical objects, which have a finite lifetime, and on the other hand, subsystems (i.e., tensor factors) of the Hilbert space of the universe. A complete description of an object at a point in time t is given by a linear subspace A of its Hilbert space, which, in the case of dim A = 1, can be specified by a wave function φ as A = [φ]. However, for every subsystem Q, for each point in time t, and for every condition B, the conditional quantum state W = W(Q,t|B) can be defined as a statistical operator on the Hilbert space of Q. Using W, certain (conditional) probabilities can be calculated. In the case of rank W = 1, the operator W can also be specified by a wave function φ, namely as W = |φ><φ|. It is the subsystems of the Hilbert space that play the role of "quantum systems" in the Copenhagen formalism, and the quantum states defined for them behave exactly as described by this formalism. If a wave function φ represents the description of a (quantum) object, then we are dealing with a real physical property, that is, φ plays an "ontic" role. However, if φ represents a quantum state, then its role is merely "statistical". If, in this case, condition B corresponds to the knowledge of a subject, φ plays an "epistemic" role. Additional Remarks The reasoning in this paper is largely based on a new systematic approach to solving the interpretation problem of quantum theory, which was originally published in 2018 (in German) under the title "Realistische Quantentheorie". A comprehensive account of this approach (in English) was published in February 2026 under the title "Realistic Quantum Theory: Solving the Interpretation Problem". It is available in the Zenodo repository (zenodo.18644694, see link below under "Related works" / "References"). The present document provides an English version of an earlier paper in German under the same title, which is also available in the Zenodo repository (zenodo.10694813, see link below).
Abstract The ontological models framework distinguishes ψ-ontic from ψ-epistemic wave-functions. It is, in general, quite straightforward to categorize the wave-function of a certain quantum theory. Nevertheless, there has been a debate about the ontological status of the wave-function in the statistical interpretation of quantum mechanics: is it ψ-epistemic and incomplete or ψ-ontic and complete? I will argue that the wave-function in this interpretation is best regarded as ψ-ontic and incomplete.