BASIL HILEY (1935-2025) A MEMORIAL SYMPOSIUM

Order of talks

0915h 

Speaker:  Peter Van REETH / Mathematics, University College London

“Conversations with Basil Hiley concerning The Quantum Potential and more”

The quantum potential as derived in David Bohm’s 1952 papers was for Basil Hiley the very cornerstone of the Bohmian approach to quantum mechanics.

To Basil’s regret, the fact that the quantum potential is already embedded in the Schrödinger equation has often been overlooked or misunderstood and this has led to some deep misconceptions concerning the Bohmian approach.  In this talk I will discuss both fundamental and also more practical aspects of the quantum potential based on the many conversations on this topic which I had with Basil.  I will also present some of his ideas linking the quantum potential to the Coriolis effect and to both the local and osmotic/amplitude momentum.

1015h 

Speaker:  P Calum ROBSON / Mathematics, LSE

“Clifford Algebras as Phase Spaces”

One of Basil Hiley’s principal insights concerned the role of Clifford Algebras in modern physics, especially as the framework for a revision of the formalism of Quantum Theory in which he sought to implement the radical process ontology he developed in  collaboration with David Bohm. In the last 15 years of his research Basil made important advances in this program for the use of Clifford algebras to study quantum mechanics, returning to and building on work he had begun in the 1970s and 80s. In this talk I shall discuss these advances, describing how Basil showed that we could interpret multivector functions on Clifford algebras as quantum wavefunctions, and  I will link this work to the more standard Hilbert space approach. 

In the second part of the talk, I will discuss my own research in this area. I will argue that we can put a Kahler structure on any Clifford algebra, and show that this gives these algebras a phase space structure, which also allows us to define a Hamiltonian dynamics on them. Finally, I shall present some recent work on Dirac operators on the  Clifford Algebra Cl(2),  and how this can extend some concepts from Bohmian mechanics to the relativistic case.

11.15h 

Coffee Break

11.30h 

Speaker:  Tim PALMER FRS / Department of Physics, Oxford

“Four reasons for discretising Hilbert Space”

In this talk I want to give four quite compelling reasons why the continuum of Hilbert Space (the absolute bedrock of quantum mechanics) is an idealised approximation for something inherently discrete. Firstly, as John Wheeler predicted, discrete Hilbert Space reveals the information-theoretic nature of the wavefunction, concealed by the continuum approximation. This is because there are inherently discrete ways of representing complex numbers, quaternions and hence Pauli matrices (the bedrock of qubit physics), as permutation/negation operators acting on bit strings. Secondly, the concept of measurement-induced state reduction can be formulated, in a very precise way, as a decrease in the information content of the wavefunction at a minimal rate of one bit per Planck time. Thirdly, the introduction of the gravitational constant above allows a precise estimate of the degree of discreteness in the state space of qubits of a quantum computer. This leads to a predicted consequence of discrete Hilbert Space structure, that should be testable in the coming 5 years (if quantum tech companies are to be believed): the exponential speed up of algorithms like Shor’s will saturate (‘max out’) in quantum computers that use more than about 500-1,000 logical qubits. Finally, the gappy nature of discrete Hilbert Space allows a novel interpretation of complementarity and Bell inequality violation in terms of a failure of simultaneous counterfactual definiteness (a concept first proposed by Henry Stapp). Mathematically, this interpretation arises because properties that in quantum mechanics are associated with non-commuting observables, are instead, in discrete Hilbert Space, associated with incommensurate number-theoretic properties of trigonometric functions. I will conclude my talk by discussing links to Basil’s work: where he and I agreed, and where we disagreed. 

12.30h 

Lunch at nearby Restaurant (Speakers covered)

14.15h 

Speaker:  Lindon NEIL / Physics, UCL

Title: 1952 – DeWitt and Bohm: A tale of two potentials

In the summer of 2021, Bryce Seligman DeWitt’s 1952 paper “Point transformations in quantum mechanics” became a focus of discussion in the work of Basil Hiley and his research group at UCL. In that paper DeWitt showed that an additional “quantum mechanical potential” was required alongside the classical potential in the Hamiltonian of the Schrodinger equation to make it applicable in the setting of a pseudo Riemannian space. Earlier in 1952,  in the very same volume of Physical Review as DeWitt’s paper, David Bohm published his derivation of what has become known as the de Broglie-Bohm quantum potential. This quantum potential is a feature of the Hamilton-Jacobi equation which arises from applying the Schrodinger equation to a polar decomposition of the wave function. DeWitt’s derivation of his notion of a quantum potential naturally raised issues in connection with two of the main pillars of Basil’s research: firstly, his exploration of Bohm’s notion of the quantum potential in all its aspects and secondly, the pursuit of an algebraic approach to quantum mechanics and its associated geometry. This talk explores and seeks to clarify the intricate and far-from-straightforward relationship  between the quantum potentials of DeWitt and Bohm.

15.00h 

Speaker:  Peter BRADSHAW / Physics, UCL

 “The Algebraic Legacy of Basil Hiley”

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.

As his last PhD student, I am keenly aware of the impact Basil’s ideas and mentorship have had on my own research, particularly his work on algebraic approaches to physics. In this talk, we will walk through some of his most significant work in this area, allowing us to explore Basil’s personal philosophies regarding physics and mathematics, and gain an appreciation for his character. We will also consider some ways in which his ideas will live on.

15.45

Coffee Break

16.00h 

Speaker:  Bob COECKE

“Quantum picturalism, and some interpretable AI, and some music”

Over some 20 years we have developed a diagrammatic quantum formalism, sometimes referred to as quantum picturalism [1, 2].  We showed that this formalism enabled secondary school students to perform exceptionally well on an Oxford University post-grad quantum exam [3].  It was in fact John von Neumann himself who denounced `his own’ quantum formalism, that relies on Hilbert space.  Alternatives had been proposed, including by von Neumann himself, but none play a role in quantum theory today.  Quantum picturalism on the other hand, is not widespread in quantum industry.  The same formalism has been used as the basis for interpretable AI [4], and even music [5].  

[1] Bob Coecke and Aleks Kissinger (2017) Picturing Quantum Processes.  Cambridge University Press.
[2] Bob Coecke and Stefano Gogioso (2022) Quantum in Pictures.
[3] https://www.theguardian.com/science/2023/dec/16/physicist-bob-coecke-its-easier-to-convince-kids-than-adults-about-quantum-mechanics
[4] https://thequantuminsider.com/2024/09/18/quantinuum-unveils-first-contribution-toward-responsible-ai-uniting-power-of-its-quantum-processors-with-experimental-work-on-integrating-classical-quantum-computing/
[5] https://qspace.fqxi.org/articles/264/quanthovens-fifth  

16.45h 

Speaker: Roger PENROSE / Oxford University

“On the Curiously Retro-causal Effects of Quantum State Reduction on Quantum Reality”

In the late 1960s and early 1970s, I used to have weekly discussions with Basil Hiley, in Birkbeck College, these being also attended by students and frequently by David Bohm. These discussions were on the foundations of quantum mechanics, most frequently on the mysterious phenomenon of wave-function collapse upon measurement. Eventually, after I had left Birkbeck to join the University of Oxford, Basil developed his own ideas in relation to those of Bohm, as finally presented in a very substantial book.

My own ideas developed very differently, under the belief that quantum state reduction had to be a gravitational effect, where one needs to distinguish a “Quantum Reality” from the more familiar “Classical Reality”. In this talk I shall develop the ideas of quantum reality, indicating its curious relation to the normal flow of time, most strikingly in Einstein-Podolski-Rosen types of phenomena.