# Peter RowlandsUniversity of Liverpool | UoL · Department of Physics

Peter Rowlands

PhD

## About

96

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Introduction

**Skills and Expertise**

## Publications

Publications (96)

The universal rewrite system (URS), first formulated by Rowlands and Diaz [2002], which may well be the meta-pattern driving the systems of the physical universe, has been realized, in the companion paper, in the deterministic Turing machine and other devices foundational to computational theory. Here, we show that we can extend the results to actu...

The meta-pattern of the universe, first formulated by Rowlands and Diaz [2002], is a universal rewrite system (URS). This universal pattern finds a formulation in formal language theory centred around the fundamental semantic unit of the zero word or the zero string: 0 = X o X # 0 . This is realized successively in the computational procedures of T...

July 5 - 8, 2021, Bauman Moscow State Technical University hosted the XXII International Conference on Modern Problems of the Theory of Relativity, Cosmology, and Astrophysics “Physical Interpretations of the Relativity Theory PIRT-2021”.
List of International Advisory Council, Conference Committee, Local Committee, Invited Speakers, Support to the...

Around the time of the completion of the Standard Model of particle physics in the 1970s, schemes were put forward for unifying the three gauge interactions (electric, strong and weak) using the renormalization equations at an energy approaching the Planck mass. Though these looked promising, the exact unification never materialised, and doubts hav...

The universal rewrite system (URS), first formulated by Rowlands and Diaz [2002], which may well be the meta-pattern driving the systems of the physical universe, has been realized, in the companion paper, in the deterministic Turing machine and other devices foundational to computational theory. Here, we show that we can extend the results to actu...

The meta-pattern of the universe, first formulated by Rowlands and Diaz [2002], is a universal rewrite system (URS). This universal pattern finds a formulation in formal language theory centred around the fundamental semantic unit of the zero word or the zero string: 0 = X0X#0. This is realized successively in the computational procedures of Turing...

We discuss the structure of the Dirac equation and how the nilpotent and the Majorana operators arise naturally in this context. This provides a link between Kauffman's work on discrete physics, iterants and Majorana Fermions and the work on nilpotent structures and the Dirac equation of Peter Rowlands. We give an expression in split quaternions fo...

While gravity is often imagined to have the characteristics of a local gauge theory, no such gauge theory has so far been constructed, with all attempts at quantum gravity leading to nonrenormalizable infinities. All known gauge theories, however, have both local and nonlocal aspects, and it is worth exploring how far we can describe gravity using...

Only a few exact solutions are known for quantum mechanical equations, and some of these tend to be complicated, requiring special mathematical techniques and multiple particular cases. The relativistic nilpotent Dirac equation has the virtue of allowing highly streamlined solutions for all the existing solvable problems and also adding others not...

There have been a number of claims, going back to the 1970s, that the Standard Model of particle physics, based on fermions and antifermions, might be derived from an octonion algebra. The emergence of SU (3), SU (2) and U (1) groups in octonion-based structures is suggestive of the symmetries of the Standard Model, but octonions themselves are an...

This autonomous self-governed explanation of the cosmological thermodynamics of entirely novel states of matter (as in a renormalization group approach) includes the currently accepted fundamentals of physics, chemical valence, the periodic table and the basic neuroscience architecture/Nature’s IT of the sentient evolution of intelligent life; with...

The Standard Model has three generations of fermions and antifermions, each with two states of isospin, and each of these has both a lepton and a quark in three possible colour states. In total there are 48 states. No known system exists for constructing these from first principles. Here, it is suggested that the number of degrees of freedom requir...

The Dirac algebra is widely recognized as a Clifford algebra and there have been numerous representations of the Dirac equation using a single Cl(3,0) for the momentum term while retaining the conventional gamma matrices to separate the various terms in the equation. It is suggested here, however, that a particularly powerful result occurs when we...

The VII International Symposium Honoring French Mathematical Physicist Jean‐Pierre Vigier
Conference date: 12–14 July 2010
Location: London
Volume number: 1316
Published: Dec 22, 2010

This volume, recording the 10th international symposium honoring noted French mathematical physicist Jean-Pierre Vigier surveys and continues to develop Unified Field Mechanics (UFM) from the perspective of Multiverse cosmology and Topological Field Theory. UFM represents a developing paradigm shift with many new parameters extending the Standard M...

The most significant characteristic of nilpotent quantum mechanics is that the quantum system (fermion state) and its environment (vacuum) are, in mathematical terms, mirror images of each other. So a change in one automatically leads to corresponding changes in the other. We have used this characteristic as a model for self-organization, which has...

A fundamental problem in the theory of computing concerns whether descriptions of systems at all times remain tractable, that is whether the complexity that inevitably results can be reduced to a polynomial form (P) or whether some problems lead to a non-polynomial (NP) exponential growth in complexity. Here, we propose that the universal computati...

Dimensionality has been a much discussed subject since Minkowski formalized special relativity by extending 3D space to 4D space-time. However, there has never been any consensus on the number of dimensions that nature requires and there has been no explanation of why dimensions are needed at all. It is proposed here that dimensions originate in th...

Relativistic quantum mechanics and the properties of Dirac fermions can be generated in a particularly powerful way using two vector spaces which are commutative to each other and which contain identical information. The apparently broken symmetry between the two spaces ob- served through the quadratic geometry of ordinary space becomes a perfect a...

RobertFox (ed.), Thomas Harriot and His World: Mathematics, Exploration and Natural Philosophy in Early Modern England. Farnham: Ashgate, 2012. Pp. xviii+255. ISBN 978-0-7546-6960.9. £65.00 (hardback). - Volume 47 Issue 3 - Peter Rowlands

Space is the only quantity which can be directly observed. Its main characteristics, in its 3-dimensional Euclidean form, are describable by a Clifford algebra. There have been attempts to construct physics on the basis of this parameter alone, involving extensions to extra dimensions and non-Euclidean forms of geometry. However, it seems that addi...

The book originated in a series of lectures given at Liverpool in 2013 to a group that included postgraduate and undergraduate students and staff of the Physics Department. They followed from two very successful lectures given to the undergraduate Physical Society. It seemed that there was a very large interest among the students in investigating t...

Physics at the fundamental level can be effectively reduced to an
explanation of the structures and interactions of fermions. Fermions
appear to be singularities rather than extended objects, but there is no
obvious way of creating such structures within the 3-dimensional space
of observation. However, the algebra associated with the Dirac equation...

We make a preliminary exploratory study of higher dimensional (HD)
orthogonal forms of the quaternion algebra in order to explore putative
novel Nilpotent/Idempotent/Dirac symmetry properties. Stage-1 transforms
the dual quaternion algebra in a manner that extends the standard
anticommutative 3-form, i, j, k into a 5D/6D triplet. Each is a copy of...

The principal criteria Cn (n = 1 to 23) and grammatical production rules
are set out of a universal computational rewrite language spelling out a
semantic description of an emergent, self-organizing architecture for
the cosmos. These language productions already predicate: (1) Einstein's
conservation law of energy, momentum and mass and, subsequent...

Experimental evidence over a number of recent years has shown the density
parameter of the universe omega converging to the critical value of 1, which
defines a flat, Euclidean universe. No such calculations have defined a
critical value for the most significant component of omega, that for the dark
energy, omega lambda, but the new data provided b...

The eight Vigier Symposium held at a joint meeting with the British Computer Society - Cybernetics Machine Group (BCS-V8) at its national headquarters in Covent Garden, London, was very succesfull with about 50 delegates from dozen of countries. As the 52 chapters will reflect this symposium was a delightifull and erudite cornucopia of ideas.
The...

The maximal failure of the quantum prediction of the 'cosmological constant' creates difficulties for a quantum theory of gravity, and for gravity as a local force, as does the failure of quantum gravity to preserve locality. The attractive nature of the gravitational force and the negative sign of its energy may be indications that it is intrinsic...

The articles in your special issue marking the centenary of superconductivity were interesting and quite rightly included one that describes the neglected work of the London brothers ("The forgotten brothers" April 2010 pp26–29).

Though 3‐D vector space has no mechanism within itself for creating fundamental particle singularities, this can be accomplished by a commutative combination of two 3‐D vector spaces, each of which is dual (in a physical sense) to the other. The resulting combination leads to a nilpotent quantum mechanics / quantum field theory, which incorporates...

Recent attempts to consider isolated particles and real constitutive wave elements as localized, extended spacetime structures (i.e., moving within time-like hypertubes or branes are developed within a causal extension of the Feynman-Gell-Mann electron model. These extended structures contain real internal motions, (i.e., internal hidden parameters...

Further evidence is presented in favour of the computational paradigm, conceived and constructed by Rowlands and Diaz, as detailed in Rowlands’ book Zero to Infinity (2007) [2], and in particular the authors’ paper ‘The Grammatical Universe: the Laws of Thermodynamics and Quantum Entanglement’ [1]. The paradigm, which has isomorphic group and algeb...

The universal nilpotent computational rewrite system (UNCRS) is shown to formalize an irreversible process of evolution in conformity with the First, Second and Third Laws of Thermodynamics, in terms of a single algebraic creation operator (ikE+ip+jm) which delivers the whole quantum mechanical language apparatus, where k, i, j are quaternions unit...

Nilpotent quantum mechanics provides a powerful method of making efficient calculations. More importantly, however, it provides insights into a number of fundamental physical problems through its use of a dual vector space and its explicit construction of vacuum. Physical interpretation of the nilpotent formalism is discussed with respect to boson...

A totally new computational grammatical structure has been developed which encompasses the general class of self-organizing systems. It is based on a universal rewrite system and the principle of nilpotency, where a system and its environment have a space-time variation defined by the phase, which preserves the dual mirror-image relationship betwee...

Our notions of what is physically 'real' have long been based on the idea that the real is what is immediately apprehended, that is the local or observable, the physically tangible, though there has always been an alternative philosophical notion that the 'real' is some kind of ontological structure beyond immediate apprehension, and so inaccessibl...

Assuming that Nature is described by a universal rewrite system and operates according to a process that we can refer to as Nature’s code, we define certain numbers as being crucial indicators of how the code operates, whether in biology, chemistry or physics. We also show how these numbers originate in the most extraordinarily simple way from two...

The question we are concerned with is: how can the highly ordered replicating state which we call ‘life’ form within a universe where the tendency of natural processes is towards a state of increasing disorder? The existence of a machine order code or driving process for life to emerge seems to be suggested by the generation of a universal rewrite...

Vacuum can be defined with exact mathematical precision as the state which remains when a fermion, with all its special characteristics, is created out of absolutely nothing. The definition leads to a special form of relativistic quantum mechanics, which only requires the construction of a creation operator. This form of quantum mechanics is especi...

We propose that the mathematical structures related to the 'universal rewrite system' define a universal process applicable to Nature, which we may describe as 'Nature's code'. We draw attention here to such concepts as 4 basic units, 64-and 20-unit structures, symmetry-breaking and 5-fold symmetry, chirality, double 3-dimensionality, the double he...

Your editorial in the July issue (p17) drew attention to the fact that there are many physicists who feel they have a contribution to make, and are fully qualified to do so, but who, for reasons of age, lack of status, lack of good connections or lack of previous publications in the most prestigious journals, are not given an adequate hearing. In t...

A variety of mathematical structures is explored, which relate to the algebra and geometry of a nilpotent universal rewrite system. The structures are shown to encode significant biological and physical information.

A definition of intelligence in terms of the computational principles by which a sentient being may make sense of a universe structured according to the nilpotent universal computational rewrite system (NUCRS), with an infinite universal alphabet as discovered by Rowlands and Diaz, is briefly set out. This alphabet defines the semantics of quantum...

The relative signs associated with the energy and momentum operators used in representing the nilpotent Dirac state vectors of fermions and antifermions are a direct indication of the interactions to which these particles are subject, and also of the processes by which mass is generated from the vacuum.

We present D, a symbol that can be used in the universal alphabet that provides a computational path to the nilpotent Dirac equation (Diaz & Rowlands, 2004) and which results in a tractable computer representation of the infinite square roots of –1. We outline how the representation is derived, the properties of the representation, and how the form...

The construction of a nilpotent Dirac equation leads to the definition of a nilpotent state as a creation operator acting on a vacuum with which it is self-dual. The nilpotent structure leads to a unique formulation for the hadronic state, with both the required SU(3) symmetry, and an automatic generation of hadronic mass. Gauge invariance between...

It is proposed that the Dirac equation, as normally interpreted, incorporates intrinsic redundancies whose removal necessarily leads to an enormous gain in calculating power and physical interpretation. Streamlined versions of the Dirac equation can be developed which remove the redundancies and singularities from many areas of quantum physics whil...

On 6th February 1672, the 29 year old Issac Newton confidently dispatched his first paper to the Royal Society of London. Newton was totally unprepared for anything other than full acceptance, and the Royal Society's reaction left him aghast. Newton gradually lost interest in science and finally threw in the towel in the year 1678, and for the next...

Mathematical structures apparently underlying different aspects of physics and biology are examined in relation to their possible common origin in a universal system of process applicable to Nature.

The structures of fermionic and bosonic states can be determined in an axiomatic way starting from a symmetrical representation of the parameters space, time, mass and charge, with an algebra determined by a combination of multivariate 4-vector and quaternion units. The combination leads to a nilpotent representation of the Dirac state, that appear...

A multivariate 4‐vector representation for space‐time and a quaternion representation for mass and the electric, strong and weak charges leads to a nilpotent form of the Dirac equation, which packages the entire physical information available about a fermion state. The nilpotent state vector breaks the symmetry between the strong, electric and weak...

The nilpotent Dirac formalism has been shown, in previous publications, to generate new physical explanations for aspects of particle physics, with the additional possibility of calculating some of the parameters involved in the Standard Model. The applications so far obtained are summarised, with an outline of some more recent developments.

A model of quarks, based on integral charges, suggests a value of sin2θw=0.25, with a consequent prediction of Grand Unification at the Planck mass, and a value of 1/α=118 at 14 TeV.

We present two ways in which an infinite universal alphabet may be generated using a novel rewrite system that conserves zero (a special character of the alphabet and the symbol for that character) at every step. The recursive method delivers the entire alphabet in one step when invoked with the zero character as the initial subset alphabet. The it...

Based on a fundamental symmetry between space, time, mass and charge, a series of group structures of physical interest is generated, ranging from C2 to E8. The most significant result of this analysis is a version of the Dirac equation combining quaternions and multivariate vectors, which is already second quantized and intrinsically supersymmetri...

A brief history is given of the factor 2, starting in the most elementary considerations of geometry and kinematics of uniform acceleration, and moving to relativity, quantum mechanics and particle physics. The basic argument is that in all the significant cases in which the factor 2 or 1/2 occurs in fundamental physics, whether classical, quantum...

The nilpotent formalism for the Dirac equation, outlined in previous papers,is applied to QED. It is shown that what is usually described as 'renormalization' is effectively a statement of the fact that the nilpotent formulation is automatically second quantized and constrains the field into producing finite values for fundamental quantities.

It seems unlikely that we will ever lose our fascination for the man whom David Berlinski calls "the largest figure in the history of Western science" and the author of "the greatest of scientific theories". Indeed, there have been many biographies of Isaac Newton over the last two decades. What is important for Berlinski, however, are not the deta...

A core level of basic information for physics is identified, based on an analysis of the characteristics of the parameters space, time, mass and charge. At this level, it is found that certain symmetries operate, which can be used to explain certain physical facts and even to derive new mathematical theorems. Applications are made to classical mech...

A representation of the Dirac algebra, derived from first principles, can be related to the combinations of unit charges which determine particle structures. The algebraic structure derives from a broken symmetry between 4-vectors and quaternions which can be applied to the broken symmetry between the three nongravitational interactions. The signif...

The nilpotent version of the Dirac equation is applied to the baryon wavefunction, the strong interaction potential, electroweak mixing, and Dirac and Klein-Gordon propagators. The results are used to interpret a quaternion-vector model of particle structures.

A version of the Dirac equation is derived from first principles using a combination of quaternions and multivariate 4-vectors. The nilpotent form of the operators used allows us to derive explicit expressions for the wavefunctions of free fermions, vector bosons, scalar bosons; Bose-Einstein condensates, and baryons;annihilation, creation and vacu...

The history, and some of the later developments, of Sir Edward Appleton’s researches into the properties of the triode valve are discussed. These began in 1918, and continued until late 1924. Following an overview of his earliest work on the physics of the device, which he carried out both independently and with other research scientists, notably V...

It is often assumed that the three classic tests of general relativity require the full mathematical apparatus of that theory for their derivation. In fact, it is possible to derive them from Newtonian gravity and special relativity in a form at least partly accessible to pre-university students.

The representation of the 32-part Dirac algebra by a combination of 4-vectors and quaternions allows the Dirac equation to be represented in various simplified forms, including a fully symmetrical version involving all five gamma matrices. The symmetrical version can be used to identify the Dirac spinor wavefunction as containing the square root of...

The nature of quantum uncertainty and the origin of wave-particle duality can be linked to fundamental symmetries between the parameters space, time, mass and charge, which determine that conservation and nonconservation, and continuity and discontinuity, remain exactly opposite properties, with precisely defined meanings. The built-in physical opp...

The interpretation of last year's examination results in your news story "Exam results reveal ups and downs" (Physics World, September p5) cannot be left unchallenged. As an A-level teacher for the last 12 years and one of the people involved in the Institute of Physics initiative to the examining boards, it seems clear to me that the steady drop i...

Using a rewrite approach we introduce a computational path to a nilpotent form of the Dirac equation. The system is novel in allowing new symbols to be added to the initial alphabet and starts with just one symbol, representing 'nothing', and two fundamental rules: create, a process which adds news symbols, and conserve, a process which examines th...

Evidence is presented in support of the hypothesis that Diaz and Rowlands' remarkable discovery of a universal grammar for semantic quantum mechanical mathematical language description, is a candidate for 'alternative (a)' in Leggett's incisive Einstein's Legacy viewpoint in Science, 307, 2005, 871-872 on 'The Quantum Measurement (QM) Problem'. 'Al...

A novel approach to a proof of the Riemann Hypothesis (that all the zeros of the Zeta function lie on the line x = ½) is presented. It is based on the universal nilpotent computational rewrite system (NUCRS), derived in the World Scientific book Zero to Infinity, from a single nilpotent Dirac operator (Rowlands, 2007), establishing an entirely nove...

Various implications of Rowlands and Diaz" (R&D") discovery of a universal nilpotent computational rewrite system, are described. Evidence is presented that this discovery not only provides a new semantic fundamental foundation for universal quantum computation, but is the keystone of a fundamental computational foundation for mathematics, quantum...

To incorporate thermodynamic, quantum and classical dynamical laws, the Universe is treated as a quantum Carnot engine (QCE) or single heat bath in which the ensemble of elementary particles retains a small amount of quantum coherence, so as to constitute new states of matter known as "phaseonia", the first being its Zenergy, the empty ensemble of...

In order to address the central question at the heart of the concluding debate at the AAAI 07 Spring quantum interaction symposium, where it was proposed that other probabilistic and nondeterministic theories might replace quantum mechanics, even in relation to quantum physics, and in further explanation of our AAAI Spring 2007 paper 'How Intellige...

The fermionic state is the foundation for the whole of physics. Physics is entirely concerned with fermions and their interactions, and nothing else. It is possible to derive a mathematical expression for the fermionic state, which is an operator only, not an equation, or wavefunction. This operator appears to contain within it all the information...

One of the most successful components of the Standard Model of particle physics is the theory of the strong interaction, which is explained as a force between 'coloured' quarks mediated by massless gluons and described by the non-Abelian gauge theory of quantum chromodynamics (QCD). There is no doubt that this theory has stood the test of experimen...

Many ideas relating to gravity in the author's previous work have led to predictions and anticipations whose significance is only now becoming apparent, for example the dark energy and the holographic principle. The fact that these predictions have proved startlingly successful, and in some cases directly related to calculations now considered 'mai...

## Projects

Projects (2)