Basil Hiley
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Basil James Hiley (15 November 1935 – 25 January 2025) was a British physicist and
professor emeritus ''Emeritus/Emerita'' () is an honorary title granted to someone who retirement, retires from a position of distinction, most commonly an academic faculty position, but is allowed to continue using the previous title, as in "professor emeritus". ...
of the
University of London The University of London (UoL; abbreviated as Lond or more rarely Londin in Post-nominal letters, post-nominals) is a collegiate university, federal Public university, public research university located in London, England, United Kingdom. The ...
. Long-time colleague of
David Bohm David Joseph Bohm (; 20 December 1917 – 27 October 1992) was an American scientist who has been described as one of the most significant Theoretical physics, theoretical physicists of the 20th centuryDavid Peat Who's Afraid of Schrödinger' ...
, Hiley is known for his work with Bohm on implicate orders and for his work on algebraic descriptions of
quantum mechanics Quantum mechanics is the fundamental physical Scientific theory, theory that describes the behavior of matter and of light; its unusual characteristics typically occur at and below the scale of atoms. Reprinted, Addison-Wesley, 1989, It is ...
in terms of underlying symplectic and orthogonal
Clifford algebras In mathematics, a Clifford algebra is an algebra generated by a vector space with a quadratic form, and is a unital associative algebra with the additional structure of a distinguished subspace. As -algebras, they generalize the real numbers ...
. Hiley co-authored the book ''The Undivided Universe'' with David Bohm, which is considered the main reference for Bohmian mechanics. The work of Bohm and Hiley has been characterized as primarily addressing the question "whether we can have an adequate conception of the reality of a quantum system, be this causal or be it
stochastic Stochastic (; ) is the property of being well-described by a random probability distribution. ''Stochasticity'' and ''randomness'' are technically distinct concepts: the former refers to a modeling approach, while the latter describes phenomena; i ...
or be it of any other nature" and meeting the scientific challenge of providing a mathematical description of quantum systems that matches the idea of an implicate order.


Biography

Basil James Hiley was born November 15, 1935 in
Burma Myanmar, officially the Republic of the Union of Myanmar; and also referred to as Burma (the official English name until 1989), is a country in northwest Southeast Asia. It is the largest country by area in Mainland Southeast Asia and ha ...
, where his father, James Hiley, worked for the military of the
British Raj The British Raj ( ; from Hindustani language, Hindustani , 'reign', 'rule' or 'government') was the colonial rule of the British The Crown, Crown on the Indian subcontinent, * * lasting from 1858 to 1947. * * It is also called Crown rule ...
. He moved to
Hampshire Hampshire (, ; abbreviated to Hants.) is a Ceremonial counties of England, ceremonial county in South East England. It is bordered by Berkshire to the north, Surrey and West Sussex to the east, the Isle of Wight across the Solent to the south, ...
, England, at the age of twelve, where he attended secondary school. His interest in science was stimulated by his teachers at secondary school and by books, in particular '' The Mysterious Universe'' by James Hopwood Jeans and ''
Mr Tompkins in Wonderland Mr Tompkins is the title character in a series of four popular science books by the physicist George Gamow, which were published from 1940. The books are structured as a series of dreams in which Mr Tompkins enters alternative worlds where the ph ...
'' by
George Gamow George Gamow (sometimes Gammoff; born Georgiy Antonovich Gamov; ; 4 March 1904 – 19 August 1968) was a Soviet and American polymath, theoretical physicist and cosmologist. He was an early advocate and developer of Georges Lemaître's Big Ba ...
. Hiley performed undergraduate studies at
King's College London King's College London (informally King's or KCL) is a public university, public research university in London, England. King's was established by royal charter in 1829 under the patronage of George IV of the United Kingdom, King George IV ...
. In 1962 he obtained his PhD from King's College in
condensed matter physics Condensed matter physics is the field of physics that deals with the macroscopic and microscopic physical properties of matter, especially the solid and liquid State of matter, phases, that arise from electromagnetic forces between atoms and elec ...
, more specifically on cooperative phenomena in ferromagnets and long chain
polymer A polymer () is a chemical substance, substance or material that consists of very large molecules, or macromolecules, that are constituted by many repeat unit, repeating subunits derived from one or more species of monomers. Due to their br ...
models, under the supervision of Cyril Domb and
Michael Fisher Michael Ellis Fisher (3 September 1931 – 26 November 2021) was an English physicist, as well as chemist and mathematician, known for his many seminal contributions to statistical physics, including but not restricted to the theory of phase t ...
. Hiley first met David Bohm during a week-end meeting organized by the student society of King's College at
Cumberland Lodge Cumberland Lodge is a 17th-century Grade II listed country house in Windsor Great Park 3.5 miles south of Windsor Castle. Since 1947 it has been occupied by the charitable foundation known as Cumberland Lodge, an educational charity and social ...
, where Bohm held a lecture. In 1961 Hiley was appointed assistant lecturer at Birkbeck College, where Bohm had taken the chair of Theoretical Physics shortly before. Hiley wanted to investigate how physics could be based on a notion of ''process'', and he found that
David Bohm David Joseph Bohm (; 20 December 1917 – 27 October 1992) was an American scientist who has been described as one of the most significant Theoretical physics, theoretical physicists of the 20th centuryDavid Peat Who's Afraid of Schrödinger' ...
held similar ideas. He reports that during the seminars he held together with
Roger Penrose Sir Roger Penrose (born 8 August 1931) is an English mathematician, mathematical physicist, Philosophy of science, philosopher of science and Nobel Prize in Physics, Nobel Laureate in Physics. He is Emeritus Rouse Ball Professor of Mathematics i ...
he Hiley worked with David Bohm for many years on fundamental problems of
theoretical physics Theoretical physics is a branch of physics that employs mathematical models and abstractions of physical objects and systems to rationalize, explain, and predict List of natural phenomena, natural phenomena. This is in contrast to experimental p ...
. Initially Bohm's model of 1952 did not feature in their discussions; this changed when Hiley asked himself whether the " Einstein-Schrödinger equation", as Wheeler called it, might be found by studying the full implications of that model. They worked together closely for three decades. Together they wrote many publications, including the book ''The Undivided Universe: An Ontological Interpretation of Quantum Theory'', published 1993, which is now considered the major reference for Bohm's interpretation of quantum theory. In 1995, Basil Hiley was appointed to the chair in physics at
Birkbeck College Birkbeck, University of London (formally Birkbeck College, University of London), is a public research university located in London, England, and a member institution of the University of London. Established in 1823 as the London Mechanics' ...
at the
University of London The University of London (UoL; abbreviated as Lond or more rarely Londin in Post-nominal letters, post-nominals) is a collegiate university, federal Public university, public research university located in London, England, United Kingdom. The ...
. He was awarded the 2012 Majorana Prize in the category ''The Best Person in Physics'' for the algebraic approach to quantum mechanics and furthermore in recognition of "his paramount importance as natural philosopher, his critical and open minded attitude towards the role of science in contemporary culture". Hiley died on 25 January 2025.


Work


Quantum potential and active information

In the 1970s Bohm, Hiley and co-workers at Birkbeck College expanded further on the theory presented by David Bohm in 1952. They suggested to re-express the field equations of physics in a way that is independent of their spacetime description. They interpreted
Bell's theorem Bell's theorem is a term encompassing a number of closely related results in physics, all of which determine that quantum mechanics is incompatible with local hidden-variable theories, given some basic assumptions about the nature of measuremen ...
as a test of spontaneous localization, meaning a tendency of a
many-body system The many-body problem is a general name for a vast category of physical problems pertaining to the properties of microscopic systems made of many interacting particles. Terminology ''Microscopic'' here implies that quantum mechanics has to be ...
to factorize into a product of localized states of its constituent particles, pointing out that such spontaneous localization removes the need for a fundamental role of the measuring apparatus in quantum theory. They proposed that the fundamental new quality introduced by quantum physics is non-locality. In 1975, they presented how in the causal interpretation of the quantum theory introduced by Bohm in 1952 the concept of a '' quantum potential'' leads to the notion of an "unbroken wholeness of the entire universe", and they proposed possible routes to a generalization of the approach to relativity by means of a novel concept of time. By performing numeric computations on the basis of the quantum potential, Chris Philippidis, Chris Dewdney and Basil Hiley used
computer simulation Computer simulation is the running of a mathematical model on a computer, the model being designed to represent the behaviour of, or the outcome of, a real-world or physical system. The reliability of some mathematical models can be determin ...
s to deduce ensembles of particle trajectories that could account for the interference fringes in the
double-slit experiment In modern physics, the double-slit experiment demonstrates that light and matter can exhibit behavior of both classical particles and classical waves. This type of experiment was first performed by Thomas Young in 1801, as a demonstration of ...
and worked out descriptions of scattering processes. Their work renewed the interests of physicists in the Bohm interpretation of quantum physics. In 1979, Bohm and Hiley discussed the
Aharonov–Bohm effect The Aharonov–Bohm effect, sometimes called the Ehrenberg–Siday–Aharonov–Bohm effect, is a quantum mechanics, quantum-mechanical phenomenon in which an electric charge, electrically charged point particle, particle is affected by an elect ...
which had recently found experimental confirmation. They called attention to the importance of the early work of
Louis de Broglie Louis Victor Pierre Raymond, 7th Duc de Broglie (15 August 1892 – 19 March 1987) was a French theoretical physicist and aristocrat known for his contributions to quantum theory. In his 1924 PhD thesis, he postulated the wave nature of elec ...
on pilot waves, emphasizing his insight and physical intuition and stating that developments based on his ideas aimed at a better understanding than mathematical formalism alone. They offered ways of understanding quantum non-locality and the measurement process, the limit of classicality, interference and
quantum tunneling In physics, a quantum (: quanta) is the minimum amount of any physical entity (physical property) involved in an interaction. The fundamental notion that a property can be "quantized" is referred to as "the hypothesis of quantization". This me ...
. They showed how in the Bohm model, introducing the concept of ''active information'', the
measurement problem In quantum mechanics, the measurement problem is the ''problem of definite outcomes:'' quantum systems have superpositions but quantum measurements only give one definite result. The wave function in quantum mechanics evolves deterministically ...
and the
collapse of the wave function In various Interpretations of quantum mechanics, interpretations of quantum mechanics, wave function collapse, also called reduction of the state vector, occurs when a wave function—initially in a quantum superposition, superposition of seve ...
, could be understood in terms of the quantum potential approach, and that this approach could be extended to relativistic
quantum field theories In theoretical physics, quantum field theory (QFT) is a theoretical framework that combines field theory and the principle of relativity with ideas behind quantum mechanics. QFT is used in particle physics to construct physical models of subatom ...
. They described the measurement process and the impossibility of measuring position and momentum simultaneously as follows: "The ѱ field itself changes since it must satisfy the Schrödinger equation, which now contains the interaction between the particle and apparatus, and it is this change that makes it impossible to measure position and momentum together". The ''collapse of the wave function'' of the
Copenhagen interpretation The Copenhagen interpretation is a collection of views about the meaning of quantum mechanics, stemming from the work of Niels Bohr, Werner Heisenberg, Max Born, and others. While "Copenhagen" refers to the Danish city, the use as an "interpretat ...
of quantum theory is explained in the quantum potential approach by the demonstration that information can become ''inactive'' in the sense that from then on "all the packets of the multi-dimensional wave function that do not correspond to the actual result of measurement have no effect on the particle". Summarizing Bohm's and his own interpretation, Hiley has explained that the quantum potential "does not give rise to a ''mechanical'' force in the Newtonian sense. Thus while the Newtonian potential drives the particle along the trajectory, the quantum potential organises the form of the trajectories in response to the experimental conditions." The quantum potential can be understood as an aspect of "some kind of self-organising process" involving a basic underlying field.B. J. Hiley: ''Active Information and Teleportation'', In: Epistemological and Experimental Perspectives on Quantum Physics, D. Greenberger et al. (eds.), pages 113–126, Kluwer, Netherlands, 1999
p. 7
/ref> The quantum potential (or ''information potential'') links the quantum system under investigation to the measuring apparatus, thereby giving that system a ''significance'' within the context defined by the apparatus. It acts on each quantum particle individually, each particle influencing itself. Hiley cites the wording of
Paul Dirac Paul Adrien Maurice Dirac ( ; 8 August 1902 – 20 October 1984) was an English mathematician and Theoretical physics, theoretical physicist who is considered to be one of the founders of quantum mechanics. Dirac laid the foundations for bot ...
: "''Each electron only interferes with itself''" and adds: "Somehow the 'quantum force' is a 'private' force. It thus cannot be regarded as a distortion of some underlying sub-quantum medium as was originally suggested by de Broglie".B. J. Hiley: ''Nonlocality in microsystems'', in: Joseph S. King, Karl H. Pribram (eds.): ''Scale in Conscious Experience: Is the Brain Too Important to be Left to Specialists to Study?'', Psychology Press, 1995, pp. 318 ff., se
p. 326–327
/ref> It is independent of field intensity, thus fulfilling a precondition for non-locality, and it carries information about the whole experimental arrangement in which the particle finds itself. In processes of non-signalling transmission of
qubit In quantum computing, a qubit () or quantum bit is a basic unit of quantum information—the quantum version of the classic binary bit physically realized with a two-state device. A qubit is a two-state (or two-level) quantum-mechanical syste ...
s in a system consisting of multiple particles (a process that is generally called "
quantum teleportation Quantum teleportation is a technique for transferring quantum information from a sender at one location to a receiver some distance away. While teleportation is commonly portrayed in science fiction as a means to transfer physical objects from on ...
" by physicists), active information is transferred from one particle to another, and in the Bohm model this transfer is mediated by the non-local quantum potential.


Relativistic quantum field theory

With Pan N. Kaloyerou, Hiley extended the quantum potential approach to quantum field theory in
Minkowski space In physics, Minkowski space (or Minkowski spacetime) () is the main mathematical description of spacetime in the absence of gravitation. It combines inertial space and time manifolds into a four-dimensional model. The model helps show how a ...
time. Bohm and Hiley proposed a new interpretation of the
Lorentz transformation In physics, the Lorentz transformations are a six-parameter family of Linear transformation, linear coordinate transformation, transformations from a Frame of Reference, coordinate frame in spacetime to another frame that moves at a constant vel ...
and considered the relativistic invariance of a quantum theory based on the notion of ''be''ables, a term coined by John Bell to distinguish these variables from ''
observable In physics, an observable is a physical property or physical quantity that can be measured. In classical mechanics, an observable is a real-valued "function" on the set of all possible system states, e.g., position and momentum. In quantum ...
s''. Hiley and a co-worker later extended the work further to curved spacetime. Bohm and Hiley demonstrated that the non-locality of quantum theory can be understood as limit case of a purely local theory, provided the transmission of ''active information'' is allowed to be greater than the speed of light, and that this limit case yields approximations to both quantum theory and relativity. The Bohm–Hiley approach to relativistic quantum field theory (RQFT) as presented in Bohm and Hiley's book ''Undivided Universe'' and in the work of their co-worker Kaloyerou was reviewed and re-interpreted by Abel Miranda, who stated:


Implicate orders, pre-space and algebraic structures

Much of Bohm and Hiley's work in the 1970s and 1980s has expanded on the notion of implicate, explicate and generative orders proposed by Bohm. This concept is described in the books '' Wholeness and the Implicate Order'' by Bohm and '' Science, Order, and Creativity'' by Bohm and F. David Peat. The theoretical framework underlying this approach has been developed by the Birkbeck group over the last decades. In 2013 the research group at Birkbeck summarized their over-all approach as follows: : "It is now quite clear that if gravity is to be quantised successfully, a radical change in our understanding of spacetime will be needed. We begin from a more fundamental level by taking the notion of process as our starting point. Rather than beginning with a spacetime continuum, we introduce a structure process which, in some suitable limit, approximates to the continuum. We are exploring the possibility of describing this process by some form of non-commutative algebra, an idea that fits into the general ideas of the implicate order. In such a structure, the non-locality of quantum theory can be understood as a specific feature of this more general a-local background and that locality, and indeed time, will emerge as a special feature of this deeper a-local structure." As of 1980, Hiley and his co-worker Fabio A. M. Frescura expanded on the notion of an ''implicate order'' by building on the work of Fritz Sauter and
Marcel Riesz Marcel Riesz ( ; 16 November 1886 – 4 September 1969) was a Hungarian mathematician, known for work on summation methods, potential theory, and other parts of analysis, as well as number theory, partial differential equations, and Clifford alg ...
who had identified
spinor In geometry and physics, spinors (pronounced "spinner" IPA ) are elements of a complex numbers, complex vector space that can be associated with Euclidean space. A spinor transforms linearly when the Euclidean space is subjected to a slight (infi ...
s with minimal left ideals of an algebra. The identification of ''algebraic spinors'' with minimal left ideals, which can be seen as a generalization of the ordinary spinorBasil Hiley: Algebraic quantum mechanics, algebraic spinors and Hilbert space, Boundaries, Scientific Aspects of ANPA, 2003
preprint
was to become central to the Birkbeck group's work on algebraic approaches to quantum mechanics and quantum field theory. Frescura and Hiley considered algebras that had been developed in the 19th century by the mathematicians
Hermann Grassmann Hermann Günther Grassmann (, ; 15 April 1809 – 26 September 1877) was a German polymath known in his day as a linguist and now also as a mathematician. He was also a physicist, general scholar, and publisher. His mathematical work was littl ...
,
William Rowan Hamilton Sir William Rowan Hamilton (4 August 1805 – 2 September 1865) was an Irish astronomer, mathematician, and physicist who made numerous major contributions to abstract algebra, classical mechanics, and optics. His theoretical works and mathema ...
, and
William Kingdon Clifford William Kingdon Clifford (4 May 18453 March 1879) was a British mathematician and philosopher. Building on the work of Hermann Grassmann, he introduced what is now termed geometric algebra, a special case of the Clifford algebra named in his ...
.F. A. M. Frescura, B. J. Hiley: ''Geometric interpretation of the Pauli spinor'', American Journal of Physics, February 1981, Volume 49, Issue 2, pp. 152
abstract
As Bohm and his colleagues emphasized, in such an algebraic approach operators and operands are of the same type: "there is no need for the disjoint features of the present mathematical formalism f quantum theory namely the
operators Operator may refer to: Mathematics * A symbol indicating a mathematical operation * Logical operator or logical connective in mathematical logic * Operator (mathematics), mapping that acts on elements of a space to produce elements of another ...
on the one hand and the state vectors on the other. Rather, one uses only a single type of object, the algebraic element"., and its introductory note More specifically, Frescura and Hiley showed how "the states of quantum theory become elements of the minimal ideals of the algebra and .the projection operators are just the idempotents which generate these ideals". In a 1981 preprint that remained unpublished for many years, Bohm, P. G. Davies and Hiley presented their algebraic approach in context with the work of Arthur Stanley Eddington. Hiley later pointed out that Eddington attributed to a particle not a metaphysical existence but a structural existence as an idempotent of an algebra, similarly as in
process philosophy Process philosophy (also ontology of becoming or processism) is an approach in philosophy that identifies processes, changes, or shifting relationships as the only real experience of everyday living. In opposition to the classical view of change ...
an object is a system which continuously transforms onto itself. With their approach based on algebraic idempotents, Bohm and Hiley "incorporate Bohr's notion of 'wholeness' and d'Espagnat's concept of 'non-separability' in a very basic way". In 1981, Bohm and Hiley introduced the "characteristic matrix", a non-Hermitian extension of the
density matrix In quantum mechanics, a density matrix (or density operator) is a matrix used in calculating the probabilities of the outcomes of measurements performed on physical systems. It is a generalization of the state vectors or wavefunctions: while th ...
. The Wigner and Moyal transformation of the characteristic matrix yields a complex function, for which the dynamics can be described in terms of a (generalized) Liouville equation with the aid of a matrix operating in
phase space The phase space of a physical system is the set of all possible physical states of the system when described by a given parameterization. Each possible state corresponds uniquely to a point in the phase space. For mechanical systems, the p ...
, leading to eigenvalues that can be identified with stationary states of motion. From the characteristic matrix, they constructed a further matrix that has only non-negative eigenvalues which can thus be interpreted as a quantum "statistical matrix". Bohm and Hiley thus demonstrated a relation between the Wigner–Moyal approach and Bohm's theory of an implicate order that allows to avoid the problem of negative probabilities. They noted that this work stands in close connection with
Ilya Prigogine Viscount Ilya Romanovich Prigogine (; ; 28 May 2003) was a Belgian physical chemist of Russian-Jewish origin, noted for his work on dissipative structures, complex systems, and irreversibility. Prigogine's work most notably earned him the 19 ...
's proposal of a Liouville space extension of quantum mechanics. They extended this approach further to relativistic phase space by applying the phase space interpretation of Mario Schönberg to the
Dirac algebra In mathematical physics, the Dirac algebra is the Clifford algebra \text_(\mathbb). This was introduced by the mathematical physicist P. A. M. Dirac in 1928 in developing the Dirac equation for spin- particles with a matrix representation of the ...
. Their approach was subsequently applied by Peter R. Holland to
fermion In particle physics, a fermion is a subatomic particle that follows Fermi–Dirac statistics. Fermions have a half-integer spin (spin 1/2, spin , Spin (physics)#Higher spins, spin , etc.) and obey the Pauli exclusion principle. These particles i ...
s and by Alves O. Bolivar to
boson In particle physics, a boson ( ) is a subatomic particle whose spin quantum number has an integer value (0, 1, 2, ...). Bosons form one of the two fundamental classes of subatomic particle, the other being fermions, which have half odd-intege ...
s. In 1984, Hiley and Frescura discussed an algebraic approach to Bohm's notion of implicate and explicit orders: the implicate order is carried by an algebra, the explicate order is contained in the various representations of this algebra, and the geometry of space and time appear at a higher level of abstraction of the algebra.F. A. M. Frescura, B. J. Hiley
Algebras, quantum theory and pre-space
p. 3–4 (published in Revista Brasileira de Fisica, Volume Especial, Julho 1984, Os 70 anos de Mario Schonberg, pp. 49–86)
Bohm and Hiley expanded on the concept that "relativistic quantum mechanics can be expressed completely through the interweaving of three basic algebras, the bosonic, the fermionic and the Clifford" and that in this manner "the whole of relativistic quantum mechanics can also be put into an implicate order" as suggested in earlier publications of David Bohm from 1973 and 1980.D. Bohm, B. J. Hiley: ''Generalisation of the twistor to Clifford algebras as a basis for geometry'', published in Revista Brasileira de Fisica, Volume Especial, Os 70 anos de Mario Schönberg, pp. 1–26, 1984
PDF
On this basis, they expressed the
twistor theory In theoretical physics, twistor theory was proposed by Roger Penrose in 1967 as a possible path to quantum gravity and has evolved into a widely studied branch of theoretical and mathematical physics. Penrose's idea was that twistor space should ...
of Penrose as a
Clifford algebra In mathematics, a Clifford algebra is an algebra generated by a vector space with a quadratic form, and is a unital associative algebra with the additional structure of a distinguished subspace. As -algebras, they generalize the real number ...
, thereby describing structure and forms of ordinary space as an explicit order that unfolds from an implicate order, the latter constituting a ''pre-space''. The spinor is described mathematically as an ideal in the Pauli Clifford algebra, the twistor as an ideal in the conformal Clifford algebra. The notion of another order underlying space was not new. Along similar lines, both
Gerard 't Hooft Gerardus "Gerard" 't Hooft (; born July 5, 1946) is a Dutch theoretical physicist and professor at Utrecht University, the Netherlands. He shared the 1999 Nobel Prize in Physics with his thesis advisor Martinus J. G. Veltman "for elucidating t ...
and John Archibald Wheeler, questioning whether space-time was the appropriate starting-point for describing physics, had called for a deeper structure as starting point. In particular, Wheeler had proposed a notion of pre-space which he called '' pregeometry'', from which spacetime geometry should emerge as a limiting case. Bohm and Hiley underlined Wheeler's view, yet pointed out that they did not build on the foam-like structure proposed by Wheeler and by
Stephen Hawking Stephen William Hawking (8January 194214March 2018) was an English theoretical physics, theoretical physicist, cosmologist, and author who was director of research at the Centre for Theoretical Cosmology at the University of Cambridge. Between ...
but rather worked towards a representation of the implicate order in form of an appropriate algebra or other pre-space, with
spacetime In physics, spacetime, also called the space-time continuum, is a mathematical model that fuses the three dimensions of space and the one dimension of time into a single four-dimensional continuum. Spacetime diagrams are useful in visualiz ...
itself considered part of an ''explicit order'' that is connected to pre-space as ''implicit order''. The spacetime manifold and properties of locality and non-locality then arise from an order in such pre-space. In the view of Bohm and Hiley, "things, such as particles, objects, and indeed subjects, are considered as semi-autonomous quasi-local features of this underlying activity". These features can be considered to be independent only up to a certain level of approximation in which certain criteria are fulfilled. In this picture, the
classical limit The classical limit or correspondence limit is the ability of a physical theory to approximate or "recover" classical mechanics when considered over special values of its parameters. The classical limit is used with physical theories that predict n ...
for quantum phenomena, in terms of a condition that the action function is not much greater than the
Planck constant The Planck constant, or Planck's constant, denoted by h, is a fundamental physical constant of foundational importance in quantum mechanics: a photon's energy is equal to its frequency multiplied by the Planck constant, and the wavelength of a ...
, indicates one such criterion. Bohm and Hiley used the word holomovement for the underlying activity in the various orders together. This term is intended to extend beyond the movement of objects in space and beyond the notion of process, covering movement in a wide context such as for instance the "movement" of a symphony: "a total ordering which involves the whole movement, past and anticipated, at any one moment". This concept, which avowedly has similarities with the notion of ''organic mechanism'' of
Alfred North Whitehead Alfred North Whitehead (15 February 1861 – 30 December 1947) was an English mathematician and philosopher. He created the philosophical school known as process philosophy, which has been applied in a wide variety of disciplines, inclu ...
, underlies Bohm and Hiley's efforts to establish algebraic structures that relate to quantum physics and to find an ordering that describes thought processes and the mind. They investigated non-locality of spacetime also in terms of the time dimension. In 1985, Bohm and Hiley showed that Wheeler's delayed-choice experiment does ''not'' require the existence of the past to be limited to its recording in the present. Hiley and R. E. Callaghan later confirmed this view, which stands in stark contrast to Wheeler's earlier statement that "the past has no existence except as it is recorded in the present", by a detailed trajectory analysis for delayed choice experiments and by an investigation into ''welcher Weg'' experiments. Hiley and Callaghan in fact showed that, an interpretation of Wheeler's delayed choice experiment based on Bohm's model, the past is an objective history that cannot be altered retroactively by delayed choice (''see also:'' Bohmian interpretation of Wheeler's delayed choice experiment). Bohm and Hiley sketched also how Bohm's model could be treated under the point of view of
statistical mechanics In physics, statistical mechanics is a mathematical framework that applies statistical methods and probability theory to large assemblies of microscopic entities. Sometimes called statistical physics or statistical thermodynamics, its applicati ...
, and their joint work on this was published in their book (1993) and a subsequent publication (1996). Hiley has pursued work on algebraic structures in quantum theory throughout his scientific career.B. J. Hiley
''A note on the role of idempotents in the extended Heisenberg algebra''
''Implications'', Scientific Aspects of ANPA 22, pp. 107–121, Cambridge, 2001
Basil J. Hiley: ''Towards a Dynamics of Moments: The Role of Algebraic Deformation and Inequivalent Vacuum States'', published in: Correlations ed. K. G. Bowden, Proc. ANPA 23, 104–134, 2001
PDF
B.J. Hiley: ''Non-Commutative Quantum Geometry: A Reappraisal of the Bohm Approach to Quantum Theory''. In: Avshalom C. Elitzur, Shahar Dolev, Nancy Kolenda (eds.): ''Quo Vadis Quantum Mechanics? The Frontiers Collection'', 2005
pp. 299–324

abstractpreprint
After Bohm's death in 1992, he published several papers on how different formulations of quantum physics, including Bohm's, can be brought in context. Hiley also pursued further work on the
thought experiment A thought experiment is an imaginary scenario that is meant to elucidate or test an argument or theory. It is often an experiment that would be hard, impossible, or unethical to actually perform. It can also be an abstract hypothetical that is ...
s set out by the
EPR paradox EPR may refer to: Science and technology * EPR (nuclear reactor), European Pressurised-Water Reactor * EPR paradox (Einstein–Podolsky–Rosen paradox), in physics * Earth potential rise, in electrical engineering * East Pacific Rise, a mid-ocea ...
of
Albert Einstein Albert Einstein (14 March 187918 April 1955) was a German-born theoretical physicist who is best known for developing the theory of relativity. Einstein also made important contributions to quantum mechanics. His mass–energy equivalence f ...
Boris Podolsky and
Nathan Rosen Nathan Rosen (; March 22, 1909 – December 18, 1995) was an American and Israeli physicist noted for his study on the structure of the hydrogen molecule and his collaboration with Albert Einstein and Boris Podolsky on entangled wave functions and ...
and by Hardy's paradox of Lucien Hardy, in particular considering the relation to
special relativity In physics, the special theory of relativity, or special relativity for short, is a scientific theory of the relationship between Spacetime, space and time. In Albert Einstein's 1905 paper, Annus Mirabilis papers#Special relativity, "On the Ele ...
. In the late 1990s, Hiley expanded further on the notion he had developed with Bohm on the description of quantum phenomena in terms of processes.Basil Hiley
''Mind and matter: aspects of the implicate order described through algebra''
published in:
Karl H. Pribram Karl H. Pribram ( �pr̝̊iːbram (February 25, 1919 – January 19, 2015) was a visionary pioneer in the fields of cognitive psychology, cognitive science, neuropsychology, holonomic brain theory, and holographic consciousness. He was describ ...
, J. King (eds.): ''Learning as Self-Organization'', pp. 569–586, Lawrence Erlbaum Associates, New Jersey, 1996,
Basil J. Hiley, Marco Fernandes: ''Process and time'', in: H. Atmanspacher, E. Ruhnau: ''Time, temporality, now: experiencing time and concepts of time in an interdisciplinary perspective'', pp. 365–383, Springer, 1997,
preprint
Hiley and his co-worker Marco Fernandes interpret time as an aspect of ''process'' that should be represented by a mathematically appropriate description in terms of an ''algebra of process''. For Hiley and Fernandes, time should be considered in terms of "moments" rather than extensionless points in time, in conventional terms implying an integration over time, recalling also that from the "characteristic matrix" of Bohm and Hiley a positive definite probability can be obtained. They model the unfolding of implicate and explicate orders and the evolution of such orders by a mathematical formalism which Hiley has termed the ''Clifford algebra of process''.


Projections into shadow manifolds

Around the same time, in 1997, Hiley's co-worker Melvin Brown showed that the Bohm interpretation of quantum physics need not rely on a formulation in terms of ordinary space (x-space), but can be formulated, alternatively, in terms of momentum space (p-space). Ignazio Licata: ''Emergence and computation at the edge of classical and quantum systems'', in: Ignazio Licata, Ammar Sakaji (eds.): ''Physics of Emergence and Organization'', World Scientific, 2008
pp. 1–26
,
In 2000, Brown and Hiley showed that the Schrödinger equation can be written in a purely algebraic form that is independent of any representation in a Hilbert space. This algebraic description is formulated in terms of two operator equations. The first of these (formulated in terms of the
commutator In mathematics, the commutator gives an indication of the extent to which a certain binary operation fails to be commutative. There are different definitions used in group theory and ring theory. Group theory The commutator of two elements, ...
) represents an alternative form of the quantum Liouville equation, which is well known to describe the conservation of probability, the second (formulated in terms of the anticommutator), which they dubbed the "quantum phase equation", describes the conservation of energy. This algebraic description in turn gives rise to descriptions in terms of multiple vector spaces, which Brown and Hiley call "shadow phase spaces" (adopting the term "shadow" from Michał Heller). These shadow phase space descriptions include the descriptions in terms of the ''x''-space of the Bohm trajectory description, of the quantum phase space, and of the ''p''-space. In the
classical limit The classical limit or correspondence limit is the ability of a physical theory to approximate or "recover" classical mechanics when considered over special values of its parameters. The classical limit is used with physical theories that predict n ...
, the shadow phase spaces converge to one unique
phase space The phase space of a physical system is the set of all possible physical states of the system when described by a given parameterization. Each possible state corresponds uniquely to a point in the phase space. For mechanical systems, the p ...
. In their algebraic formulation of quantum mechanics the equation of motion takes on the same form as in the
Heisenberg picture In physics, the Heisenberg picture or Heisenberg representation is a Dynamical pictures, formulation (largely due to Werner Heisenberg in 1925) of quantum mechanics in which observables incorporate a dependency on time, but the quantum state, st ...
, except that the ''bra'' and ''ket'' in the
bra–ket notation Bra–ket notation, also called Dirac notation, is a notation for linear algebra and linear operators on complex vector spaces together with their dual space both in the finite-dimensional and infinite-dimensional case. It is specifically de ...
each stand for an element of the algebra and that the Heisenberg time evolution is an inner automorphism in the algebra. In 2001, Hiley proposed to extend the Heisenberg Lie algebra, which is defined by the pair (\hat,\hat) satisfying the commutator bracket hat,\hati\hbar and which is nilpotent, by additionally introducing an idempotent into the algebra to yield a symplectic Clifford algebra. This algebra makes it possible to discuss the Heisenberg equation and Schrödinger equation in a representation-free manner. He later noted that the idempotent can be the
projection Projection or projections may refer to: Physics * Projection (physics), the action/process of light, heat, or sound reflecting from a surface to another in a different direction * The display of images by a projector Optics, graphics, and carto ...
formed by the outer product of the ''standard ket'' and the ''standard bra'', which had been presented by Paul Dirac in his work '' The Principles of Quantum Mechanics''.B. J. Hiley: ''Non-commutative quantum geometry: A Reappraisal of the Bohm approach to Quantum Theory''. In:
p. 316
The set of two operator equations, first derived and published by Brown and Hiley in 2000, was re-derived and expanded upon in Hiley's later publications. Hiley also pointed out that the two operator equations are analogous to the two equations that involve the sine and cosine bracket, and that the quantum phase equation has apparently not been published prior to his work with Brown, except that such an equation was hinted at by P. Carruthers and F. Zachariasen. Hiley has emphasized that quantum processes cannot be displayed in phase space for reason of lacking
commutativity In mathematics, a binary operation is commutative if changing the order of the operands does not change the result. It is a fundamental property of many binary operations, and many mathematical proofs depend on it. Perhaps most familiar as a p ...
. As
Israel Gelfand Israel Moiseevich Gelfand, also written Israïl Moyseyovich Gel'fand, or Izrail M. Gelfand (, , ; – 5 October 2009) was a prominent Soviet and American mathematician, one of the greatest mathematicians of the 20th century, biologist, teache ...
had shown, commutative algebras allow a unique manifold to be constructed as a sub-space which is dual to the algebra; non-commutative algebras in contrast cannot be associated with a unique underlying manifold. Instead, a non-commutative algebra requires a multiplicity of shadow manifolds. These shadow manifolds can be constructed from the algebra by means of projections into subspaces; however, the projections inevitably lead to distortions, in similar manner as Mercator projections inevitably result in distortions in geographical maps. The algebraic structure of the quantum formalism can be interpreted as Bohm's implicate order, and shadow manifolds are its necessary consequence: "The order of process by its very essence cannot be displayed in one unique manifest (explicate) order. ..we can only display some aspects of the process at the expense of others. We are inside looking out."


Relation of the de Broglie–Bohm theory to quantum phase space and Wigner–Moyal

In 2001, picking up on the "characteristic matrix" developed with Bohm in 1981 and the notion of a "moment" introduced with Fernandes in 1997, Hiley proposed to use a moment as "an extended structure in both space and time" as a basis for a quantum dynamics, to take the place of the notion of a
point particle A point particle, ideal particle or point-like particle (often spelled pointlike particle) is an idealization of particles heavily used in physics. Its defining feature is that it lacks spatial extension; being dimensionless, it does not take ...
. Hiley demonstrated the equivalence between Moyal's
characteristic function In mathematics, the term "characteristic function" can refer to any of several distinct concepts: * The indicator function of a subset, that is the function \mathbf_A\colon X \to \, which for a given subset ''A'' of ''X'', has value 1 at points ...
for the Wigner quasi-probability distribution ''F(x,p,t)'' and von Neumann's
idempotent Idempotence (, ) is the property of certain operations in mathematics and computer science whereby they can be applied multiple times without changing the result beyond the initial application. The concept of idempotence arises in a number of pl ...
within the proof of the Stone–von Neumann theorem, concluding: "In consequence, ''F(x,p,t)'' is ''not'' a probability density function but a specific representation of the quantum mechanical
density operator In quantum mechanics, a density matrix (or density operator) is a matrix used in calculating the probabilities of the outcomes of measurements performed on physical systems. It is a generalization of the state vectors or wavefunctions: while thos ...
", thus the Wigner–Moyal formalism exactly reproduces the results of quantum mechanics. This confirmed an earlier result by George A. Baker that the quasi-probability distribution can be understood as the density matrix re-expressed in terms of a mean position and momentum of a "cell" in phase space, and furthermore revealed that the
Bohm interpretation Bohm may refer to: Physics * David Bohm, 20th century theoretical physicist who lent his name to several concepts in physics: ** Aharonov–Bohm effect of electromagnetic potential on a particle ** Bohm sheath criterion for a Debye sheath plasma ...
arises from the dynamics of these "cells" if the particle is considered to be at the center of the cell. Hiley pointed out that the equations defining the Bohm approach can be taken to be implicit in certain equations of the 1949 publication by José Enrique Moyal on the phase space formulation of quantum mechanics; he emphasized that this link between the two approaches could be of relevance for constructing a
quantum geometry In quantum gravity, quantum geometry is the set of mathematical concepts that generalize geometry to describe physical phenomena at distance scales comparable to the Planck length. Each theory of quantum gravity uses the term "quantum geometry" ...
. In 2005, building on his work with Brown, Hiley showed that the construction of subspaces allows the Bohm interpretation to be understood in terms of the choice of the ''x''-representation as shadow phase space as ''one particular choice'' among an infinite number of possible shadow phase spaces. Hiley noted a conceptual parallel in the demonstration given by mathematician Maurice A. de Gosson that "''the Schrödinger equation can be shown rigorously to exist in the
covering group In mathematics, a covering group of a topological group ''H'' is a covering space ''G'' of ''H'' such that ''G'' is a topological group and the covering map is a continuous (topology), continuous group homomorphism. The map ''p'' is called the c ...
s of the
symplectic group In mathematics, the name symplectic group can refer to two different, but closely related, collections of mathematical groups, denoted and for positive integer ''n'' and field F (usually C or R). The latter is called the compact symplectic gr ...
of classical physics and the quantum potential arises by projecting down onto the underlying group''". More succinctly yet, Hiley and Gosson later stated: ''The classical world lives in a symplectic space, while the quantum world unfolds in the covering space.'' In mathematical terms, the covering group of the symplectic group is the
metaplectic group In mathematics, the metaplectic group Mp2''n'' is a double cover of the symplectic group Sp2''n''. It can be defined over either real or ''p''-adic numbers. The construction covers more generally the case of an arbitrary local or finite field, ...
, and De Gosson summarizes the mathematical reasons for the impossibility of constructing simultaneous position and momentum representations as follows: "''Hiley's 'shadow phase space' approach is a reflection of the fact that we cannot construct a global chart for the metaplectic group, when it is viewed as a
Lie group In mathematics, a Lie group (pronounced ) is a group (mathematics), group that is also a differentiable manifold, such that group multiplication and taking inverses are both differentiable. A manifold is a space that locally resembles Eucli ...
, that is, as a manifold equipped with a continuous algebraic structure''". In Hiley's framework, the quantum potential arises as "a direct consequence of projecting the non-commutative algebraic structure onto a shadow manifold" and as a necessary feature which ensures that both energy and momentum are conserved.B.J. Hiley: ''Phase space description of quantum mechanics and non-commutative geometry: Wigner–Moyal and Bohm in a wider context'', In: Theo M. Nieuwenhuizen et al. (eds.): ''Beyond the quantum'', World Scientific Publishing, 2007, , pp. 203–211, therein p. 204
preprint
Similarly, the Bohm and the Wigner approach are shown to be two different shadow phase space representations.B. J. Hiley: ''Phase space descriptions of quantum phenomena'', in: A. Khrennikov (ed.): ''Quantum Theory: Re-consideration of Foundations–2'', pp. 267–286, Växjö University Press, Sweden, 2003
PDF
With these results, Hiley gave evidence to the notion that the ontology of implicate and explicate orders could be understood as a process described in terms of an underlying non-commutative algebra, from which spacetime could be abstracted as one possible representation. The non-commutative
algebraic structure In mathematics, an algebraic structure or algebraic system consists of a nonempty set ''A'' (called the underlying set, carrier set or domain), a collection of operations on ''A'' (typically binary operations such as addition and multiplicatio ...
is identified with an implicate order, and its ''shadow manifolds'' with the sets of explicate orders that are consistent with that implicate order. Here emerges, in Hiley's words, "a radically new way of looking at the way quantum processes enfold in time", built on the work of Bohm and Hiley in the 1980s: in this school of thought, processes of movement can be seen as automorphisms ''within'' and ''between'' inequivalent representations of the algebra. In the first case, the transformation is an
inner automorphism In abstract algebra, an inner automorphism is an automorphism of a group, ring, or algebra Algebra is a branch of mathematics that deals with abstract systems, known as algebraic structures, and the manipulation of expressions within thos ...
, which is a way of expressing the enfolding and unfolding movement in terms of ''potentialities'' of the process; in the second case it is an
outer automorphism In mathematics, the outer automorphism group of a group, , is the quotient, , where is the automorphism group of and ) is the subgroup consisting of inner automorphisms. The outer automorphism group is usually denoted . If is trivial and has a ...
, or transformation to a new Hilbert space, which is a way of expressing an ''actual change''.


Hierarchy of Clifford algebras

Hiley expanded on the notion of a ''process algebra'' as proposed by Hermann Grassmann and the ideas of ''distinction'' of Louis H. Kauffman. He took reference to the vector operators introduced by Mário Schönberg in 1957 and by Marco Fernandes in his PhD thesis of 1995, who had constructed orthogonal Clifford algebras for certain pairs of dual Grassmann algebras. Adopting a similar approach, Hiley constructed algebraic spinors as minimal left ideals of a process algebra built on the Kauffman's notion of distinction. By nature of their construction, these algebraic spinors are both spinors and elements of that algebra. Whereas they can be mapped (projected) into an external Hilbert space of ordinary spinors of the quantum formalism in order to recover the conventional quantum dynamics, Hiley emphasizes that the dynamic algebraic structure can be exploited more fully with the algebraic spinors than with the ordinary spinors. In this aim, Hiley introduced a ''Clifford density element'' expressed in terms of left and right minimal ideals of a Clifford algebra, analogous to the density matrix expressed as an outer product in bra–ket notation in conventional quantum mechanics. On this basis Hiley showed how three Clifford algebras Cl0,1, Cl3,0, Cl1,3 form a hierarchy of Clifford algebras over the real numbers that describe the dynamics of the Schrödinger, Pauli and Dirac particles, respectively. Using this approach to describe relativistic particle quantum mechanics, Hiley and R. E. Callaghan presented a complete relativistic version of the Bohm model for the Dirac particle in analogy to Bohm's approach to the non-relativistic Schrödinger equation, thereby refuting the long-standing misconception that the Bohm model could not be applied in the relativistic domain. Hiley pointed out that the Dirac particle has a 'quantum potential' which is the exact relativistic generalisation of the quantum potential found originally by de Broglie and Bohm. Within the same hierarchy, the twistor of Roger Penrose links to the conformal Clifford algebra Cl4,2 over the reals, and what Hiley calls the ''Bohm energy'' and the ''Bohm momentum'' arises directly from the standard energy-momentum tensor. The technique developed by Hiley and his co-workers demonstrates :"that quantum phenomena ''per se'' can be entirely described in terms of Clifford algebras taken over the reals without the need to appeal to specific representation in terms of wave functions in a Hilbert space. This removes the ''necessity'' of using
Hilbert space In mathematics, a Hilbert space is a real number, real or complex number, complex inner product space that is also a complete metric space with respect to the metric induced by the inner product. It generalizes the notion of Euclidean space. The ...
and all the physical imagery that goes with the use of the
wave function In quantum physics, a wave function (or wavefunction) is a mathematical description of the quantum state of an isolated quantum system. The most common symbols for a wave function are the Greek letters and (lower-case and capital psi (letter) ...
". This result is in line with Hiley's striving for a purely algebraic approach to quantum mechanics that is not a priori defined on any external vector space. In this purely algebraic approach, the information normally contained in the wave function is encoded in an element of a minimal left ideal of the algebra. Hiley refers to Bohm's ink droplet analogy for a rather easily understandable analogy of the notion of implicate and explicate order. Regarding the algebraic formulation of the implicate order, he has stated: "An important new general feature that emerges from these considerations is the possibility that not everything can be made explicit at a given time" and adding: 'Within the Cartesian order, complementarity seems totally mysterious. There exists no structural reason as to why these incompatibilities exist. Within the notion of the implicate order, a structural reason emerges and provides a new way of searching for explanations." Hiley has worked with Maurice A. de Gosson on the relation between classical and quantum physics, presenting a mathematical derivation of the Schrödinger equation from Hamiltonian mechanics. Together with mathematicians Ernst Binz and Maurice A. de Gosson, Hiley showed how "a characteristic Clifford algebra emerges from each (''2n-dimensional'')
phase space The phase space of a physical system is the set of all possible physical states of the system when described by a given parameterization. Each possible state corresponds uniquely to a point in the phase space. For mechanical systems, the p ...
" and discussed relations of quaternion algebra,
symplectic geometry Symplectic geometry is a branch of differential geometry and differential topology that studies symplectic manifolds; that is, differentiable manifolds equipped with a closed, nondegenerate 2-form. Symplectic geometry has its origins in the ...
and quantum mechanics.


Observed trajectories and their algebraic description

In 2011, de Gosson and Hiley showed that when in Bohm's model a continuous observation of a trajectory is performed, the observed trajectory is identical to the classical particle trajectory. This finding puts the Bohm model in connection to the well-known
quantum Zeno effect In quantum mechanics, frequent measurements cause the quantum Zeno effect, a reduction in transitions away from the systems initial state, slowing a systems time evolution. Sometimes this effect is interpreted as "a system cannot change while you ...
. They confirmed this finding when they showed that the quantum potential enters into the approximation for the quantum propagator only on time scales of the order of O(\Delta t^2), which means that a continuously observed particle behaves classically and furthermore that the quantum trajectory converges to a classical trajectory if the quantum potential decreases with time. Later in 2011, for the first time experimental results were published that showed paths that display the properties expected for Bohm trajectories. More specifically, photon trajectories were observed by means of weak measurements in a double-slit interferometer, and these trajectories displayed the qualitative features that had been predicted ten years earlier by Partha Ghose for Bohm trajectories. The same year, Hiley showed that a description of weak processes – "weak" in the sense of weak measurements – can be included in his framework of an algebraic description of quantum processes by extending the framework to include not only (orthogonal) Clifford algebras but also the ''Moyal algebra'', a symplectic Clifford algebra. Glen Dennis, de Gosson and Hiley, expanding further on de Gosson's notion of quantum blobs, emphasized the relevance of a quantum particle's internal energy – in terms of its kinetic energy as well as its quantum potential – with regard to the particle's extension in phase space. In 2018, Hiley showed that the Bohm trajectories are to be interpreted as the mean momentum flow of a set of individual quantum processes, not as the path of an individual particle, and related the Bohm trajectories to
Richard Feynman Richard Phillips Feynman (; May 11, 1918 – February 15, 1988) was an American theoretical physicist. He is best known for his work in the path integral formulation of quantum mechanics, the theory of quantum electrodynamics, the physics of t ...
's
path integral formulation The path integral formulation is a description in quantum mechanics that generalizes the stationary action principle of classical mechanics. It replaces the classical notion of a single, unique classical trajectory for a system with a sum, or ...
as an average of an ensemble of Feynman paths.


Relations to other work

Hiley has repeatedly discussed the reasons for which the Bohm interpretation has met resistance, these reasons relating for instance to the role of the quantum potential term and to assumptions on particle trajectories. He has shown how the energy–momentum-relations in the Bohm model can be obtained directly from the energy–momentum tensor of quantum field theory. He has referred to this as "a remarkable discovery, so obvious that I am surprised we didn't spot it sooner", pointing out that on this basis the quantum potential constitutes the missing energy term that is required for local energy–momentum conservation.B. J. Hiley: ''The Bohm approach re-assessed''
2010 preprint

p. 6
/ref> In Hiley's view the Bohm model and Bell's inequalities allowed a debate on the notion of non-locality in quantum physics or, in
Niels Bohr Niels Henrik David Bohr (, ; ; 7 October 1885 – 18 November 1962) was a Danish theoretical physicist who made foundational contributions to understanding atomic structure and old quantum theory, quantum theory, for which he received the No ...
's words, ''wholeness'' to surface. For his purely algebraic approach, Hiley takes reference to foundations in the work of Gérard Emch, the work of
Rudolf Haag Rudolf Haag (17 August 1922 – 5 January 2016) was a German theoretical physicist, who mainly dealt with fundamental questions of quantum field theory. He was one of the founders of the modern formulation of quantum field theory and he identifie ...
on local quantum field theory, and the work of Ola Bratteli and D.W. Robertson. He points out that the algebraic representation allows to establish a connection to the thermo field dynamics of Hiroomi Umezawa, using a
bialgebra In mathematics, a bialgebra over a Field (mathematics), field ''K'' is a vector space over ''K'' which is both a unital algebra, unital associative algebra and a coalgebra, counital coassociative coalgebra. The algebraic and coalgebraic structure ...
constructed from a two-time quantum theory. Hiley has stated that his recent focus on noncommutative geometry appears to be very much in line with the work of Fred van Oystaeyen on noncommutative topology. Ignazio Licata cites Bohm and Hiley's approach as formulating "a ''quantum event'' as the expression of a deeper ''quantum process''" that connects a description in terms of space-time with a description in non-local, quantum mechanical terms. Hiley is cited, together with Whitehead, Bohr and Bohm, for the "stance of elevating processes to a privileged role in theories of physics". His view of process as fundamental has been seen as similar to the approach taken by the physicist
Lee Smolin Lee Smolin (; born June 6, 1955) is an American theoretical physicist, a faculty member at the Perimeter Institute for Theoretical Physics, an adjunct professor of physics at the University of Waterloo, and a member of the graduate faculty of th ...
. This stands quite in contrast to other approaches, in particular to the blockworld approach in which spacetime is static. Philosopher Paavo Pylkkänen, Ilkka Pättiniemi and Hiley are of the view that Bohm's emphasis on notions such as "structural process", "order" and "movement" as fundamental in physics point to some form of scientific structuralism, and that Hiley's work on symplectic geometry, which is in line with the algebraic approach initiated by Bohm and Hiley, "can be seen as bringing Bohm's 1952 approach closer to scientific structuralism".


Mind and matter

Hiley and Pylkkänen addressed the question of the relation between mind and matter by the hypothesis of an ''active information'' contributing to quantum potential.Basil J. Hiley, Paavo Pylkkänen: ''Active information and cognitive science – A reply to Kieseppä'', Brain, Mind and Physics, P. Pylkkänen et al. (Eds.), IOS Press, 1997,
p. 64 ff.
/ref> Recalling notions underlying Bohm's approach, Hiley emphasises that ''active information'' "informs" in the sense of a literal meaning of the word: it "induces a change of ''form from within''", and "this active side of the notion of information ..seems to be relevant both to material processes and to thought". He emphasizes: "even though the quantum level may be analogous to the human mind only in a rather limited way, it does help to understand the interlevel relationships if there are some common features, such as the activity of information, shared by the different levels. The idea is not to reduce everything to the quantum level but rather to propose a hierarchy of levels, which makes room for a more subtle notion of determinism and chance". Referring to two fundamental notions of
René Descartes René Descartes ( , ; ; 31 March 1596 – 11 February 1650) was a French philosopher, scientist, and mathematician, widely considered a seminal figure in the emergence of modern philosophy and Modern science, science. Mathematics was paramou ...
, Hiley states that "if we can give up the assumption that space-time is absolutely necessary for describing physical processes, then it is possible to bring the two apparently separate domains of ''
res extensa ''Res extensa'' is one of the two substances described by René Descartes in his Cartesian ontology (often referred to as "radical dualism"), alongside '' res cogitans''. Translated from Latin, "''res extensa''" means "extended thing" while th ...
'' and '' res cogitans'' into one common domain", and he adds that "by using the notion of process and its description by an algebraic structure, we have the beginnings of a descriptive form that will enable us to understand quantum processes and will also enable us to explore the relation between mind and matter in new ways". In Bohm and Hiley's work on implicate and explicate order, mind and matter are considered to be different aspects of the same process. : "Our proposal is that in the brain there is a manifest (or physical) side and a subtle (or mental) side acting at various levels. At each level, we can regard one side the manifest or material side, while the other is regarded as subtle or mental side. The material side involves electrochemical processes of various kinds, it involves neuron activity and so on. The mental side involves the subtle or virtual activities that can be actualised by active information mediating between the two sides. : These sides ..are two aspects of the ''same'' process. ..what is subtle at one level can become what is manifest at the next level and so on. In other words if we look at the mental side, this too can be divided into a relatively stable and manifest side and a yet more subtle side. Thus there is no real division between what is manifest and what is subtle and in consequence there is no real division between mind and matter". In this context, Hiley spoke of his aim of finding "an algebraic description of those aspects of this implicate order where mind and matter have their origins". Hiley also worked with biologist Brian Goodwin on a process view of biological life, with an alternate view on Darwinism.


Honors and awards

Hiley received the Majorana Prize by the
Electronic Journal of Theoretical Physics The ''Electronic Journal of Theoretical Physics'' is a quarterly Peer review, peer-reviewed open access scientific journal that was established in 2003. It covers all aspects of theoretical physics. The editors-in-chief are Ammar Sakaji (Internatio ...
for "Best person in physics" in 2012.


Publications

; Overview articles : * * * * * * B. J. Hiley: Particles, fields, and observers. In: Baltimore, D., Dulbecco, R., Jacob, F., Levi-Montalcini, R. (eds.) Frontiers of Life, vol. 1, pp. 89–106. Academic Press, New York (2002) ; Books : * David Bohm, Basil Hiley: ''The Undivided Universe: An Ontological Interpretation of Quantum Theory'', Routledge, 1993, * F. David Peat (Editor) and Basil Hiley (Editor): ''Quantum Implications: Essays in Honour of David Bohm'', Routledge & Kegan Paul Ltd, London & New York, 1987 (edition of 1991 ) ; Other : * Foreword to: ''"The Principles of Newtonian and Quantum Mechanics – The Need for Planck's Constant, h"'' by Maurice A. de Gosson, Imperial College Press, World Scientific Publishing, 2001, * Foreword to the 1996 edition of: ''"The Special Theory of Relativity"'' by David Bohm, Routledge, *


References


Further reading

* William Seager
Classical Levels, Russellian Monism and the Implicate Order
Foundations of Physics, April 2013, Volume 43, Issue 4, pp. 548–567.


External links



Birkbeck College �




find a hiley, basil – Search Results
High-Energy Physics Literature Database (
INSPIRE-HEP INSPIRE-HEP is an open access digital library for the field of high energy physics (HEP). It is the successor of the Stanford Physics Information Retrieval System (SPIRES) database, the main literature database for high energy physics since the 1 ...
) * Daniel M. Greenberger, Klaus Hentschel, Friedel Weinert (eds.): ''Compendium of Quantum Physics: Concepts, Experiments, History and Philosophy'',
Springer Springer or springers may refer to: Publishers * Springer Science+Business Media, aka Springer International Publishing, a worldwide publishing group founded in 1842 in Germany formerly known as Springer-Verlag. ** Springer Nature, a multinationa ...
, 2009, : *
Basil J. Hiley & authors bios
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*
Hidden variables
*
Pilot waves
* Interviews with Basil Hiley: *
The measurement problem in physics
'' In Our Time'',
BBC Radio 4 BBC Radio 4 is a British national radio station owned and operated by the BBC. The station replaced the BBC Home Service on 30 September 1967 and broadcasts a wide variety of spoken-word programmes from the BBC's headquarters at Broadcasti ...
, a discussion with
Melvyn Bragg Melvyn Bragg, Baron Bragg (born 6 October 1939) is an English broadcaster, author and parliamentarian. He is the editor and presenter of ''The South Bank Show'' (1978–2010, 2012–2023), and the presenter of the BBC Radio 4 documentary series ...
and guests Basil Hiley, Simon Saunders and
Roger Penrose Sir Roger Penrose (born 8 August 1931) is an English mathematician, mathematical physicist, Philosophy of science, philosopher of science and Nobel Prize in Physics, Nobel Laureate in Physics. He is Emeritus Rouse Ball Professor of Mathematics i ...
, 5 March 2009 *
Interview with Basil Hiley
conducted by Alexei Kojevnikov on December 5, 2000, Oral History Transcript, Niels Bohr Library & Archives,
American Institute of Physics The American Institute of Physics (AIP) promotes science and the profession of physics, publishes physics journals, and produces publications for scientific and engineering societies. The AIP is made up of various member societies. Its corpora ...
*
Interview with Basil Hiley
conducted by Olival Freire on January 11, 2008, Oral History Transcript, Niels Bohr Library & Archives, American Institute of Physics ** George Musser
The Wholeness of Quantum Reality: An Interview with Physicist Basil Hiley
Scientific American Blogs, November 4, 2013 *

conducted by M. Perus ** ** ** (part 1) ** , further interview (part 1) * Lecture slides by Basil Hiley: *
Weak measurements: A new type of quantum measurement and its experimental implications
(slides) ** Moyal and Clifford algebras in the Bohm approach
slides
) *
Weak measurements: Wigner–Moyal in a new light

slides
, ) *
Towards a quantum geometry: Groupoids, Clifford algebras and shadow manifolds
May 2008
slides
) *Lectures by Basil Hiley recorded at th
Åskloster Symposia
*
7-7-200410-7-200429-6-20059-7-20065-7-200725-7-200827-7-200823-7-200926-7-2009
{{DEFAULTSORT:Hiley, Basil 1935 births 2025 deaths British physicists British theoretical physicists British quantum physicists Academics of Birkbeck, University of London Alumni of King's College London