Table of contents for issue 1, volume 3189, Journal of Physics: Conference Series

These proceedings are a collection of papers written by the contributors to the Memorial Symposium for Professor Basil Hiley held at University College London on the 30th of June 2025.

The symposium bought together collaborators of the late Basil Hiley to celebrate his contributions to the foundation of quantum theory and present work which relates closely to his interests. Basil Hiley was a key researcher in the field of the foundations of quantum mechanics. He worked for 30 years with David Bohm and together they developed an approach to quantum mechanics which emphasized an ontological foundation based on the concepts of implicate and explicate order. This led to many publications and the book “The Undivided Universe”.

They introduced concepts of structure processes which Basil developed further by establishing an algebraic approach to the study of the Schrödinger, Pauli and Dirac equations using Clifford algebras. This is discussed in the contributions of P. T. J. Bradshaw and C. Robson. Links between general relativity and quantum mechanics were of great interest to Basil for many years and are discussed in the contribution of R. Penrose and also of L. Neil et al.. The contribution of G. Dennis and M. de Gosson is a study of the invariance of quantum blobs under canonical transformations which they initiated in a previous publication with Basil. T. Palmer’s paper investigates counterfactuals and Bell’s theorem which goes to the essence of many of the investigations that Basil was interested in.

A very important aspect of Basil’s scientific research was his profound belief in the importance of the links between quantum physics, philosophy and the wider social and educational implications as discussed in the papers of his close collaborator P. Pylkkanen, B. Coecke et al. and S. F. Fischer. The importance of the role of the quantum potential in the understanding of quantum behaviour in a more intuitive manner, including allowing quantum trajectories or flow-lines to describe phenomena, is discussed in the contributions of F. Daems et al. and A. S. Sanz and that of his long time collaborator C. Dewdney. Basil was a theoretical physicist who had a profound understanding of the importance of experiments. In the last fifteen years he was instrumental in setting up an experimental group at University College London whose aim is to investigate the role of the quantum potential. The contribution of V. Monachello et al. describes how this could be achieved by measuring the local velocity of atoms in Stern-Gerlach and double-slit experiments.

All papers published in this volume have been reviewed through processes administered by the Editors. Reviews were conducted by expert referees to the professional and scientific standards expected of a proceedings journal published by IOP Publishing.

• Type of peer review: Single Anonymous

• Conference submission management system: Morressier

• Number of submissions received: 13

• Number of submissions sent for review: 13

• Number of submissions accepted: 13

• Acceptance Rate (Submissions Accepted / Submissions Received × 100): 100

• Average number of reviews per paper: 1

• Total number of reviewers involved: 12

• Contact person for queries:

Name: Dr Peter Van Reeth

Email: p.reeth@ucl.ac.uk

Affiliation: University College London

Professor Basil J. Hiley’s career in physics spanned more than six decades across myriad disciplines including condensed matter physics, Clifford algebras, and the foundations of quantum mechanics. He worked with some of the most well-known physicists of the 20th century and was himself known to, and influenced, countless others. His full legacy is impossible to estimate.

Despite this, as his last PhD student, I am keenly aware of the impact Basil’s ideas and mentorship have had on my own research. In this talk, I will walk through some of this work and highlight where Basil’s influence can most clearly be seen. This will allow us to not only explore Basil’s personal philosophies regarding physics and mathematics, but also see something of his character. In this manner, we will reveal some ways in which his ideas will live on.

Two key themes of Basil Hiley’s work were the development of David Bohm’s approach to Quantum Mechanics and the importance of Clifford Algebras in fundamental physics. In this paper I will combine these themes by beginning to examine the mathematics of Dirac operators within the Bohm-Hiley approach. I will begin by discussing the geometric interpretation of Dirac operators, and how this is made clearer by the use of Clifford algebras . Next, I will rewrite the Cl(2) Dirac wavefunction in Polar form, and show that new behaviour arises due to topological nonlocality. Finally, I discuss the relationship between the Dirac and Schroedinger equations.

It has been argued that quantum state reduction is a gravitational effect. However, to make sense of it one needs to distinguish “Quantum Reality” from the more familiar “Classical Reality”. This notion of quantum reality is developed here, indicating its curious relation to the normal flow of time, most strikingly in the Einstein-Podolski-Rosen type of phenomena.

In Bryce DeWitt’s 1952 paper Point Transformations in Quantum Mechanics, (Phys. Rev., (1952) 85 653-661) he constructs a new Hamiltonian operator for the Schrödinger equation on a pseudo-Riemannian configuration space. That Hamiltonian features an additional term which he refers to as a “quantum mechanical potential”, Q_DeWitt, which is required to make the equation covariant under a general point transformation in curved space. The current paper presents an outline of DeWitt’s derivation and a comparison between DeWitt’s version of the quantum potential and that which features in the work of David Bohm and Basil Hiley. The two quantum potentials are related to the kinetic energy term in the usual Schrödinger equation but they have different physical origins and properties.

Inspired by our work with Basil Hiley, we continue the exploration of Fermi’s Ansatz. Back in 1930, Fermi showed that a wavefunction could be associated with a hypersurface in phase space. Fermi’s approach therefore leads to a geometric picture of quantum states that is based on Fermi ellipsoids. Our investigations with Basil Hiley revealed that the internal energy provided by Bohm’s quantum potential sustains these Fermi blobs whenever a quantum process is unfolding. Moreover, this internal energy is associated with a noncommutative quantum phase space (coarse-grained by quantum blobs - minimum uncertainty phase-space cells that are in a bijective correspondence with the squeezed coherent states familiar from quantum optics). In this paper, we use Fermi’s method in order to gain further insights into the invariance of quantum blobs under canonical transformations. Starting with a real Gaussian, we multiply it by a complex exponential (“chirp”) and thereby obtain a generalized coherent state. The associated change of gauge enables us to make contact with Fermi’s approach. As in de Broglie-Bohm theory, the phase and magnitude of the wavefunction feature explicitly here and are revealed to play a key role. Subsequently, we find the Fermi Hamiltonian operator and associated eigenvalue equation which the generalized coherent state satisfies. Considering Hamilton’s equations written in compact form, we show that the Hamiltonian flow determined by the Fermi Hamiltonian consists of symplectic matrices that belong to a one-parameter subgroup of Sp(n) - we call this subgroup the canonical group of the generalized coherent state. The lift of this canonical group to the metaplectic group is found to leave the generalized Gaussian invariant; whereas the canonical group itself leaves the associated phase-space quantum blob invariant. We conclude that Fermi’s Ansatz provides an instructive method for proving these invariance results. It sheds light on subtle aspects of quantum processes that other approaches might miss.

Negating the Measurement Independence assumption (MI) is often referred to as the ‘third way’ to account for the experimental violation of Bell’s inequality. However, this route is generally viewed as ludicrously contrived, implying some implausible conspiracy where experimenters are denied the freedom to choose measurement settings as they like. Here, a locally realistic model of quantum physics is developed (Rational Mechanics - RaQM - based on a gravitational discretisation of Hilbert Space) which violates MI without denying free will. Crucially, RaQM distinguishes experimenters’ ability to freely choose measurement settings to some nominal accuracy, from an inability to choose exact settings, which were never under their control anyway. In RaQM, Hilbert states are necessarily undefined in bases where squared amplitudes and/or complex phases are irrational numbers. Such ‘irrational’ bases correspond to conceivable but necessarily impossible counterfactual measurements, and are shown to play a ubiquitous role in the analysis of both single- and entangled-particle quantum physics. It is concluded that violation of Bell inequalities can be understood with none of the strange processes historically associated with it. Instead, using concepts from (non-classical) p-adic number theory, we relate RaQM to Bohm and Hiley’s concept of a holistic Machian-like Undivided Universe. If this interpretation of Bell’s Theorem is correct, building more and more energetic particle accelerators to probe smaller and smaller scales, in the search for a theory which synthesises quantum and gravitational physics and hence a Theory of Everything, may be a fruitless exercise.

David Bohm’s notion of implicate order, while relatively well-known, is often said to be difficult to understand, and is almost completely absent in contemporary discussions in philosophy of quantum theory and relativity. Yet one can argue that it is a key part of Bohm’s and Basil Hiley’s research programme which anticipates currently fashionable topics, such as the idea of space-time as emergent. In this paper my aim is to briefly review the origin of Bohm’s focus on the notion of order, and the related notion that continuous space-time is an abstraction from a discrete structural process.

We are at the dawn of the second quantum revolution, where our ability to create and control individual quantum systems is poised to drive transformative advancements in basic science, computation, and everyday life. However, quantum theory has long been conceived as notoriously hard to learn, creating a significant barrier to workforce development, informed decision-making by stakeholders and policymakers, and broader public understanding.

This paper is concerned with Quantum Picturalism [15], a novel visual mathematical language for quantum physics. Originally developed over two decades ago to explore the foundational structure of quantum theory [2], this rigorous diagrammatic framework has since been adopted in both academia and industry as a powerful tool for quantum computing research and software development. Here, we demonstrate its potential as a transformative educational methodology.

We report the findings from a pilot study involving 54 UK high school students [27], randomly selected from a pool of 734 volunteers across the UK. Despite the absence of advanced mathematical prerequisites, these students demonstrated a strong conceptual grasp of key quantum principles and operations. On an assessment comprising university graduate-level exam questions, participants achieved an 82% pass rate, with 48% obtaining a distinction-level grade.

These results pave the way for making quantum more inclusive, lowering traditional cognitive and demographic barriers to quantum learning. This approach has the potential to broaden participation in the field and provide a promising new entry point for stakeholders, future experts, and the general public.

Research and design of novel materials have advanced the development of humanity throughout its history. Todate, the methods of materials fabrication is ranging from the atomic to macroscopic scales which is enabled by application of fundamental principles of quantum physics. The research on electronic materials regarding the control of current flow of electrical charges, spin and heat lead to electronic applications. Here, fundamental principles of such transport phenomena in the quantum regime are exemplified. Further it is outlined that the usage of electronic materials in existing and emerging technologies, including quantum technologies, enhance processes of communication and industrialization, of which three with global impact and uncertain developments are identified as on-going ‘world experiments’. It is argued that these circumstances have the potential to change evolutionary processes. To meet future demands the way scientific disciplines, technologies and societies interact may require substantial change. In particular, the way science is performed may need to be developed further. Therefore, novel standardized formats allowing for universal interdisciplinary research including all sciences and the arts are called for.

From “surreal” trajectories to which-way measurements, Basil Hiley had a lesson: claims of falsifying the Bohmian model do not withstand scrutiny provided the model is applied correctly. In this work we compute de Broglie-Bohm trajectories for particles tunneling in coupled waveguides relevant to a recent experiment having claimed to challenge the Bohmian model. We show that the Bohmian model – correctly applied – gives results identical to the standard quantum approach, first by working out a simple one-dimensional model, and then by computing Bohmian trajectories for the full two-dimensional problem representing a quantum particle propagating inside coupled waveguides. We further recall the contextual nature of the Bohmian trajectories whereby the trajectories of a closed system differ from the ones observed when an interaction with a measurement apparatus takes places.

Since its inception, Bohmian mechanics has been surrounded by a halo of controversy. Originally proposed to bypass the limitations imposed by von Neumann’s theorem on the impossibility of hidden-variable models in quantum mechanics, it faced strong opposition from the outset. Over time, however, its use in tackling specific problems across various branches of physics has led to a gradual shift in attitude, turning the early resistance into a more moderate acceptance. A plausible explanation for this change may be that, since the late 1990s and early 2000s, Bohmian mechanics has been taking on a more operational and practical role. The original hidden-variable idea has gradually faded from its framework, giving way to a more pragmatic approach that treats it as a suitable analytical and computational tool. This discussion explores how and why such a shift in perspective has occurred and, therefore, answers questions such as whether Bohmian mechanics should be considered once and for all a legitimate quantum representation (i.e., worth being taught in elementary quantum mechanics courses) or, by extension, whether these ideas can be transferred to and benefit other fields. Here, the Schrödinger equation and several specific numerical examples are re-examined in the light of a less restrictive view than the standard one usually adopted in quantum mechanics.

This paper examines how quantum mechanics, interpreted through the de Broglie–Bohm (deBB) framework, can reveal a deeper underlying reality in configuration space. Rather than proposing new predictions, the aim is to clarify how deBB theory provides a coherent, realist account of massive particle, Hong–Ou–Mandel (HOM)-type correlations—often regarded as uniquely quantum. It is suggested that in this interpretation, configuration space is not simply a mathematical convenience but the fundamental arena in which quantum processes unfold. Observable non local behaviour in space and time arises as a projection of local configuration-space dynamics. The analysis illustrates the explanatory power of the deBB approach and supports the view that the configuration-space wave function carries ontological significance.

At University College London (UCL), our group had the great privilege of working closely with Professor Basil Hiley in the pursuit of experiments exploring the foundations of quantum theory. Among the many projects we undertook with Basil, one held particular significance for all of us: the experimental observation of the Bohm velocity. It was a long-standing ambition of Basil’s to see the ideas he and David Bohm had developed put to the test in the laboratory. The experimental techniques used to obtain the results presented in this paper form the foundation of an ongoing theoretical and early-stage experimental investigation at UCL, in which a velocity-sensitive Raman population transfer scheme is employed to encode the Bohm velocity into an atomic system by coherently transferring populations between two quantum states using a pair of laser beams.

In my talk, I briefly discussed several of the theoretical and experimental approaches that the group had developed together over the years. One such approach involves a subset of weak measurements, in which phase information that is normally inaccessible or lost in a strong projective measurement can instead be encoded into the transition amplitude probability density (TAPD). This paper focuses on this aspect of weak measurement theory and its experimental realisation. At UCL, the Quantum Foundations Group has demonstrated that such measurements can be implemented using atomic systems, specifically for metastable helium. These efforts represent a significant part of our time with Basil, and our ongoing attempt to bring foundational quantum ideas into the laboratory.