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B. J. Hiley

Publications and source records attributed to B. J. Hiley.

At least 19 recordsLinked to original sources
arXiv2021

Characterising a tunable, pulsed atomic beam using matter-wave interferometry

We describe the creation and characterisation of a velocity tunable, spin-polarized beam of slow metastable argon atoms. We show that beam velocity can be determined with a precision below 1 \% using matter-wave interferometry. The profile of the interference pattern was also used to determine the velocity spread of the beam, as well as Van der Waals co-efficient for the interaction between the metastable atoms and the multi-slit silicon nitride grating. The Van der Waals co-efficient was determined to be $C_3$=1.84$\pm$0.17\,a.u., in good agreement with values derived from spectroscopic data. Finally, the spin polarization of the beam produced during acceleration of the beam was also measured, demonstrating a spatially uniform spin polarization of 96 \% in the m=+2 state.

physics.atom-ph↗
arXiv2019

Dirac, Bohm and the Algebraic Approach

In this paper we show how Dirac, in 1947, anticipated the Bohm approach using an argument based on what is now called the Heisenberg picture. From a detailed examination of these ideas, we show that the role played by the Dirac standard ket is equivalent to the introduction and use of the idempotent in the orthogonal and symplectic Clifford algebras. This formalism is then used to show that the so-called `Bohm trajectories' are the average of an ensemble of individual stochastic Feynman paths. Since the Bohm approach can be simply reduced to classical mechanics, the algebraic formalism presented here provides a natural way to relate quantum mechanics to classical mechanics without the need for decoherence. We show that this approach suggests an underlying fractal space-time of the type discussed by Nottale.

quant-ph↗
arXiv2018

The Dirac-Bohm Picture

We examine Dirac's early algebraic approach which introduces the {\em standard} ket and show that it emerges more clearly from a unitary transformation of the operators based on the action. This establishes a new picture that is unitarily equivalent to both the Schrödinger and Heisenberg pictures. We will call this the Dirac-Bohm picture for the reasons we discuss in the paper. This picture forms the basis of the Feynman path theory and allows us to show that the so-called `Bohm trajectories' are averages of an ensemble of Feynman paths.

quant-ph↗
arXiv2018

Stapp, Bohm and the Algebra of Process

Henry Stapp has made many significant contributions in quantum physics and its use in trying to understand the mind-matter relationship. I have been influenced by his use of the notion of {\em process} to bring more clarity to understand quantum phenomena. In this paper I want to summarise the latest ideas on the time development of quantum processes that relate the transformation theory of Dirac, Feynman and Schwinger to the notion of weak values which has triggered experimental investigations of the nature of a deeper underlying stochastic structure of quantum processes.

quant-ph↗
arXiv2017

A method for measuring the real part of the weak value of spin using non-zero rest mass particles

A method for measuring the real part of the weak (local) value of spin is presented using a variant on the original Stern-Gerlach apparatus. The experiment utilises metastable helium in the $\rm 2^{3}S_{1}$ state. A full simulation using the impulsive approximation has been carried out and it predicts a displacement of the beam by $\rm Δ_{w} = 17 - 33\,μm$. This is on the limit of our detector resolution and we will discuss ways of increasing $\rm Δ_{w}$. The simulation also indicates how we might observe the imaginary part of the weak value.

quant-ph↗
arXiv2016

Weak Values of Momentum of the Electromagnetic Field: Average Momentum Flow Lines, Not Photon Trajectories

In a recent paper Mahler {\em et al.} have argued that the experiments of Kocsis {\em et al.} provide experimental evidence for Bohmian mechanics. Unfortunately these experiments used relativistic, zero rest mass photons whereas Bohmian mechanics is based on non-relativistic Schrödinger particles having non-zero rest mass. The experimental results can be accounted for in terms of a different approach based on the electromagnetic field that was already outlined by Bohm in an appendix of the second of his 1952 papers. A subsequent development of this approach by Bohm, Hiley, Holland, Kaloyerou, Lam and Dewdney, shows in detail how this theory accounts for experimental quantum phenomena in general. Using this theory, we are led to the conclusion that the experiments have constructed mean momentum flow lines by measuring the real part of what we term the weak Poynting vector. These results support and clarify the analysis of Bliokh {\em et al}. The experimental flow lines can be constructed independently of the number of photons in the beam leading to the conclusion that flow lines cannot be interpreted as `photon trajectories'. We discuss exactly how the notion of a photon arises in the field approach in the light of weak values.

quant-ph↗
arXiv2016

Quantum Trajectories: Dirac, Moyal and Bohm

We recall Dirac's early proposals to develop a description of quantum phenomena in terms of a non-commutative algebra in which he suggested a way to construct what he called `quantum trajectories'. Generalising these ideas, we show how they are related to weak values and explore their use in the experimental construction of quantum trajectories. We discuss covering spaces which play an essential role in accounting for the `wave' properties of quantum particles. We briefly point out how new mathematical techniques take us beyond Hilbert space and into a deeper structure which connects with the algebras originally introduced by Born, Heisenberg and Jordan. This enables us to bring out the geometric aspects of quantum phenomena.

quant-ph↗
arXiv2016

Aspects of Algebraic Quantum Theory: a Tribute to Hans Primas

This paper outlines the common ground between the motivations lying behind Hans Primas' algebraic approach to quantum phenomena and those lying behind David Bohm's approach which led to his notion of implicate/explicate order. This connection has been made possible by the recent application of orthogonal Clifford algebraic techniques to the de Broglie-Bohm approach for relativistic systems with spin.

quant-ph↗
arXiv2016

Delayed Choice Experiments and the Bohm Approach

The delayed choice experiments of the type introduced by Wheeler and extended by Englert, Scully, Süssmann and Walther [ESSW], and others, have formed a rich area for investigating the puzzling behaviour of particles undergoing quantum interference. The surprise provided by the original delayed choice experiment, led Wheeler to the conclusion that "no phenomenon is a phenomenon until it is an observed phenomenon", a radical explanation which implied that "the past has no existence except as it is recorded in the present". However Bohm, Dewdney and Hiley have shown that the Bohm interpretation gives a straightforward account of the behaviour of the particle without resorting to such a radical explanation. The subsequent modifications of this experiment led both Aharonov and Vaidman and [ESSW] to conclude that the resulting Bohm-type trajectories in these new situations produce unacceptable properties. For example, if a cavity is placed in one arm of the interferometer, it will be excited by a particle travelling down the {\em other} arm. In other words it is the particle that does {\em not} go through the cavity that gives up its energy! If this analysis is correct, this behaviour would be truly bizarre and could only be explained by an extreme non-local transfer of energy that is even stronger than that required in an EPR-type processes. In this paper we show that this conclusion is not correct and that if the Bohm interpretation is used correctly, it gives a {\em local} explanation, which actually corresponds exactly to the standard quantum mechanics explanation offered by Englert, Scully, Süssmann and Walther [ESSW].

quant-ph↗
arXiv2016

The Algebraic Way

In this paper we examine in detail the non-commutative symplectic algebra underlying quantum dynamics. We show that this algebra contains both the Weyl-von Neumann algebra and the Moyal algebra. The latter contains the Wigner distribution as the kernel of the density matrix. The underlying non-commutative geometry can be projected into either of two Abelian spaces, so-called `shadow phase spaces'. One of these is the phase space of Bohmian mechanics, showing that it is a fragment of the basic underlying algebra. The algebraic approach is much richer, giving rise to two fundamental dynamical time development equations which reduce to the Liouville equation and the Hamilton-Jacobi equation in the classical limit. They also include the Schrödinger equation and its wave function, showing that these features are a partial aspect of the more general non-commutative structure. We discuss briefly the properties of this more general mathematical background from which the non-commutative symplectic algebra emerges.

quant-ph↗
arXiv2014

Bohm's approach and Individuality

Ladyman and Ross (LR) argue that quantum objects are not individuals (or are at most weakly discernible individuals) and use this idea to ground their metaphysical view, ontic structural realism, according to which relational structures are primary to things. LR acknowledge that there is a version of quantum theory, namely the Bohm theory (BT), according to which particles do have definite trajectories at all times. However, LR interpret the research by Brown {\em et al.} as implying that "raw stuff" or {\em haecceities} are needed for the individuality of particles of BT, and LR dismiss this as idle metaphysics. In this paper we note that Brown {\em et al.}'s research does not imply that {\em haecceities} are needed. Thus BT remains as a genuine option for those who seek to understand quantum particles as individuals. However, we go on to discuss some problems with BT which led Bohm and Hiley to modify it. This modified version underlines that, due to features such as context-dependence and non-locality, Bohmian particles have a very limited autonomy in situations where quantum effects are non-negligible. So while BT restores the possibility of quantum individuals, it also underlines the primacy of the whole over the autonomy of the parts. The later sections of the paper also examine the Bohm theory in the general mathematical context of symplectic geometry. This provides yet another way of understanding the subtle, holistic and dynamic nature of Bohmian individuals. We finally briefly consider Bohm's other main line of research, the "implicate order", which is in some ways similar to LR's structural realism.

quant-ph↗
arXiv2014

Quantum Processes and Energy-Momentum Flow

In this paper we focus on energy flows in simple quantum systems. This is achieved by concentrating on the quantum Hamilton-Jacobi equation. We show how this equation appears in the standard quantum formalism in essentially three different but related ways, from the standard Schrödingier equation, from Lagrangian field theory and from the von Neumann-Moyal algebra. This equation allows us to track the energy flow using the energy-momentum tensor, the components of which are related to weak values of the four-momentum operator. This opens up a new way to explore these components empirically. The algebraic approach enables us to discuss the physical significance of the underlying non-commutative symplectic geometry, raising questions as to the structure of particles in quantum systems.

quant-ph↗
arXiv2014

Some Personal Reflections on Quantum Non-locality and the Contributions of John Bell

I present the background of the Bohm approach that led John Bell to a study of quantum non-locality from which his famous inequalities emerged. I recall the early experiments done at Birkbeck with an aim to explore the possibility of `spontaneous collapse', a way suggested by Schrödinger to avoid the conclusion that quantum mechanics was grossly non-local. I also review some of the work that John did which directly impinged on my own investigations into the foundations of quantum mechanics and report some new investigations towards a more fundamental theory.

physics.hist-ph↗
arXiv2014

Weak Measurement and its Experimental Realisation

The relationship between the real part of the weak value of the momentum operator at a post selected position is discussed and the meaning of the experimentally determined stream-lines in the Toronto experiment of Kocsis {\em et al} is re-examined. We argue against interpreting the energy flow lines as photon trajectories. The possibility of performing an analogous experiment using atoms is proposed in order that a direct comparison can be made with the trajectories calculated by Philippidis, Dewdney and Hiley using the Bohm approach.

quant-ph↗
arXiv2013

The Metaplectic Group, the Symplectic Spinor and the Gouy Phase

In this paper we discuss a simplified approach to the symplectic Clifford algebra, the symplectic Clifford group and the symplectic spinor by first extending the Heisenberg algebra. We do this by adding a new idempotent element to the algebra. It turns out that this element is the projection operator onto the Dirac standard ket. When this algebra is transformed into the Fock algebra, the corresponding idempotent is the projector onto the vacuum. These additional elements give a very simple way to write down expressions for symplectic spinors as elements of the symplectic Clifford algebra. When this algebra structure is applied to an optical system we find a new way to understand the Gouy effect. It is seen to arise from the covering group, which in this case is the symplectic Clifford group, also known as the metaplectic group. We relate our approach to that of Simon and Mukunda who have shown the relation of the Gouy phase to the Berry phase.

math-ph↗
arXiv2013

Bohmian Non-commutative Dynamics: History and New Developments

The reality of Bohm's intellectual journey is very different from what is often claimed by the proponents of "Bohmian Mechanics" and others as we will explain in this paper. He did not believe a mechanical explanation of quantum phenomena was possible. Central to his thinking, and incidentally to Bohr's also, was the notion of 'unbroken wholeness', a notion that is crucial for understanding quantum properties like quantum nonlocality. His proposals were based on a primitive notion of `process' or `activity', producing a more 'organic' approach to quantum phenomena. He published many papers outlining these new ideas, some plausible, some less so, but was not able to develop a coherent mathematical structure to support the work. Over the last ten years much of that missing mathematics has been put in place. This paper will report this new work, concentrating on providing a coherent overview of the whole programme.

quant-ph↗
arXiv2012

On the Relationship between the Moyal Algebra and the Quantum Operator Algebra of von Neumann

The primary motivation for Moyal's approach to quantum mechanics was to develop a phase space formalism for quantum phenomena by generalising the techniques of classical probability theory. To this end, Moyal introduced a quantum version of the characteristic function which immediately provides a probability distribution. The approach is sometimes perceived negatively merely as an attempt to return to classical notions, but the mathematics Moyal develops is simply a re-expression of what is at the heart of quantum mechanics, namely the non-commutative algebraic structure first introduced by von Neumann in 1931. In this paper we will establish this relation and show that the "distribution function", F(P,X,t) is simply the quantum mechanical density matrix for a single particle. The coordinates, X and P, are not the coordinates of the particle but the mean co-ordinates of a cell structure (a `blob') in phase space, giving an intrinsically non-local description of each individual particle, which becomes a point in the limit to order $\hbar^2$. We discuss the significance of this non-commutative structure on the symplectic geometry of the phase space for quantum processes.

quant-ph↗