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Abstract

The Group\'s current focus is a universal

computational science of knowing based on

the semantic modality of computer rewrite

systems. Set out in Rowlands\' 2007 World

Scientific book Zero to Infinity investigations

under way show that this discovery not only

provides a fundamental semantic foundation

for universal quantum computation, but is the

likely keystone for a fundamental semantic

foundation for mathematics, quantum physics

the genetic code /molecular biology, neuro-

science and an evolutionary cosmology.

It provides well determined testable models,

some already in agreement with experiment,

which show that the structure of the cosmos,

the genetic code, the human brain and human

language correspond to quantum mechanics

as determined by the generalized nilpotent

Dirac equation see Chapters 19 Natures Code

& 20 Nature\'s Rules and a resolution of the

Bohr/Einstein Quantum/General Relativity

dichotomy, as outlined here

Were Bohr and Einstein both right?Peter Marcer

Cybernetics Machine specialist Group chairman

AGM Presentation 16th March 2009

The principal focus of the Group\'s programme concerns

- David Deutsch\'s 1985 discovery of the theory of the universal quantum computer where the physical Church Turing Principle replaces the Church Turing Hypothesis,
- see notes
- marks another giant step in the science of computation.
- It shows that computation is fundamentally a physical process,
- but leaves 3 fundamental questions unanswered

The unanswered, still unsettled questions

- 1. \'What is it a universal quantum computer can do that a universal digital computer cannot?\'
- For Deutsch showed, this new theory contains Turing computation as a sub-process,
- 2. \'Of just how such universal quantum computers might be constructed?\'
- 3. \'Of how biological brains/information processing and learning might work, so as explain why the architecture of the human brain, is quite different from any we understand?\'

a universal computational science of knowing

- The publication of Peter Rowlands’ 2007

World Scientific book

\'Zero to Infinity\'

defines a testable

- Semantic universal computational science (urs) of knowing which in principle provides answers to all these questions, see also Notes
- \'Are these the right answers?\'

For if not, the urs will be incomplete or even wrong.

How is such a universal computational science of knowing constructed?

- It takes the modality of the computational rewrite system where a fixed or finite alphabet specifies a grammar/semantics and generalizes it to a rewrite system with an universal grammar and semantics
- where from first principles and no assumptions whatsoever, an infinitely extensible alphabet can be shown to exist, such that any symbol of the alphabet may stand for itself, a sub-alphabet or the whole infinite alphabet

How is such a universal computational science of knowing constructed?

- its self consistent construction is emergent as each new symbol reveals itself, and
- the resulting construction defines a quantum thermodynamic field theory of measurement which concerns creation and annihilation operations.

The modality of this computational construction

- Rewrite systems concern the semantic language in which programs are rewritten as symbols of an alphabet for computer hardware to interpret.
- The universal rewrite system is of particular significance because
- its alphabets, emerge in minimal way,
- have a mathematical interpretation as algebra, and define
- a quantum physical order code specified by the nilpotent Dirac algebra.

The Quantum Code

- This code generalizes Dirac\'s now famous quantum mechanical equation, so as to include not only mass and electric charge but also the strong and weak forces charges, and implicitly the property of quantum spin, i.e. the Standard model of elementary particle physics :–
- showing that this science is indeed \'the right one\' at the fundamental level of quantum physics.

The Quantum Code

- The nilpotent generalization of Dirac’s famous equation D(N)

(1)where E, p, m, t and r are respectively energy, momentum, mass, time, space and the symbols 1, i, i, j, k, i, j, k, are used to represent the respective units required by the scalar, pseudo-scalar, quaternion and multivariate vector groups.

- The Table of the nilpotents D(N, Xi ), where the nilpotent operators

Xi2= 0, but Xi0 specify the quantizations of the experimentally validated particles of the Standard Model of elementary particle physics. To see these go to Group homepages www.bcs.org.uk/cybergroup.htm and at Keywords click on \'the nilpotent Dirac equation\' to see the particle quantizations D(N) defines or see Sheet A provided

Returning to the unanswered questions

- The urs alphabet requires additional computational primitives that correspond algebraically to commutation, anti commutation and non associativity where
- ab may not = ba ; nor abc = bca or cab.
- Others than that of the universal digital nand gate, those of the unit wire, signal exchange and signal fanout, are needed to design the signal processing hardware of a digital computer, as Feynman has shown

Returning to the unanswered questions

- Anti commutativity, which in quantum physics concerns fermion states, obeying the Pauli exclusion principle so these can never be the same, plays a fundamental role in defining the urs infinite alphabet
- It supplies the canonical labelling crucial to Deutsch\'s paper, that such a thing as universal quantum computation exists, and
- is entirely concerned with fermions and their interactions (bosons being generated by these) which are known to define physics at the fundamental level.

Quantum physical constraints

- hardware signal processing theory demands that each signal / signal process have a measure / metric respectively ; for example, in terms of a energy function / Hamiltonian as in quantum theory, and in the urs arising from the fact that (E2 – p2 – m2) = 0 where E is the energy, p the momentum, m the mass; a relativistic equation which leads to Einstein\'s famous E = mc2 .
- for any measurement, there must exist a measurement standard, for without a common standard, measurements can have no meaning.
- But such a measurement standard is fundamental to quantum description, since quantum state vectors are defined only up to a fixed arbitrary quantum phase, so that only relative (gauge invariant) geometric phases can be measured.

Quantum physical constraints

- In the urs version of quantum field theory defined through the nilpotent Dirac equation,
- the quantum amplitude and quantum phase are linked through the criterion of nilpotence
- the quantum phase concerns relativistic 3D geometry,
- the arbitrary fixed phase serves to define both the measurement standard/reference phase/frame and the mechanism of quantum entanglement/quantum coherence, and

so, too, in relation to each newly emergent unique fermion state and its interactions, will an arbitrary relative fixed phase, for, by the criterion of nilpotence, this state corresponds to each newly emergent distinct urssymbol of the infinite alphabet during the urs\'s emergent construction.

Were Bohr and Einstein both right?

- Thus it is postulated, that the criterion of nilpotence linking quantum amplitude and phase resolves the dichotomy between quantum mechanics and Einstein\'s general relativity,
- i.e. quantum thermodynamically through the mechanism of quantum phase θ, where the universe is treated as a quantum thermodynamic Carnot engine (QCE), consisting of single heat bath in which the ensembles of elementary particles retain a small amount of quantum entanglement /coherence phase dθ, where each ensemble constitutes a new state of matter (called a phaseonium by Sully et al in relation to the QCE, see Keywords homepages) in the form of each novel emergent fermion state, as represented by the urs symbols.

Were Bohr and Einstein both right?

- That is to say, the role of initial arbitrary fixed phase in quantum mechanics is crucial to such an explanation and to understanding quantum physics, entanglement and quantum thermodynamics.
- And it provides the \'instantaneous action at a distance\' that is the apparent property of Newton\'s gravitational mass, and an explanation of why inertial mass (as a property of relativistic relative phase states) is only equivalent to it.

Summary and illustrations

- So not only do the initial arbitrary fixed phase and the corresponding nilpotent fixed relative phases permit measurement according to a common standard, they also ensure that each rewrite canonically labelled fermion system subject to measurement is fully quantum entangled with remainder of the whole quantum universe.
- And in the urs version of quantum field theory, but not in quantum mechanics (lacking creation/annihilation operation description), measurement results in not just \'the collapse of the wave function\' (annihilation), but also in its re-expansion (creation). As will now be show is the case, in relation to MRI

Magnetic Resonance Imaging (MRI).

- The control process (for the quantum preparation/input) of the MRI image production is specified algebraically in terms of the nilpotent Lie algebra g of the 3D Heisenberg Lie group G, see homepages http://www.bcs.org.uk/cybergroup.htm go to Keywords and click on \'3D nilpotent Heisenberg Lie group\' or see sheet B, where this algebra defines the Heisenberg uncertainty and remarkably its Lie dual / inverse! And as in elementary particle physics, it concerns a Lie algebra.
- This MRI process, where the controlled repeated collapse and re-expansion of the electromagnetic wave fields, so defined, is observed to take place, Figure 2.

Magnetic Resonance Imaging (MRI)

Fig. 2 illustrates how the encoding / decoding Fourier transform action (in accord with the Heisenberg uncertainty principle (defined by g the Lie algebra of G) actually happens in MRI. It shows the ‘frequency induced signal’ U(1,C) described by the Heisenberg helix of G off resonance losing amplitude (z axis), i.e. thermodynamically decaying due to a transverse relaxation effect, but, remarkably, simultaneously regaining energy due to longitudinal relaxation,

wave diffraction patterns in the form of quantum holograms

- It results in wave diffraction patterns in the form of quantum holograms as the thermodynamic consequence of the fermion spin quantum signal decay;
- where when these output signal patterns are subject to fast symplectic Fourier transform action, they produce the MRI medical 2D/3D images required, where no process of holography (as is appropriate to the patterns) is possible without the existence of a relative reference frame / measurement standard.

wave diffraction patterns in the form of quantum holograms

- Figure 4 – next – is an actual quantum hologram / wave diffraction pattern A and its brain image B as produced in Magnetic Resonance Imaging machines used in medical diagnosis.

These MRI output wave diffraction patterns illustrate how the encoding / decoding Fourier transform action Figure 2 (in accord with the Heisenberg uncertainty principle defined by g the Lie algebra of G) actual happens in MRI. Heisenberg uncertainty is thus not the obstacle to the computation of this output but its actual means.

wave diffraction patterns in the form of quantum holograms

- In A (middle, and bottom) the outside and inside of the pattern A (top) has been removed to show B the reduced resolution of the whole brain slice compared to B (top) to illustrate A’s holographic nature.

Universal Semantic Computation is Quantum Mechanical and must be nilpotent

- Thus it can be concluded that universal quantum computers compute semantically (as per the nilpotent Dirac algebra order code) and not just syntactically (as per the universal digital machine order code). And since the urs semantic sub-alphabets emerge in a minimum way, this computational semantic encoding is geodesic in a minimum number of steps.
- A not unsurprising conclusion in view of the fact that physical systems of all kinds behave according to \'principles of least actions\' of which Feynman\'s sum of histories approach to quantum physics is an example.

Universal Semantic Computation is Quantum Mechanical and must be nilpotent

It thus appears that the syntactic correctness of a programming language is a necessary but not sufficient condition, which may only guarantee a combinatorial explosion of possible histories/ solutions, where these are in Pauli\'s famous phrase \'not even wrong\' and a sum over histories remains to be calculated as is necessary in quantum renormalization.

And it guarantees, the computation will be canonically labelled as Zuse knew to be crucial, as long ago as the late 1930s, if it is not to be subject to error. A fact Deutsch pointed out in his paper.

Universal Semantic Computation is Quantum Mechanical and must be nilpotent

- And so in the urs, where the Pauli exclusion principle applies ensuring that each urs symbol is unique, ie canonically labelled, Pauli exclusion constitutes an entirely new computational principle of calculation based on the criterion of nilpotent, where for each such state, an operator X ≠ 0 exists, such that X2 = 0. And this tells us that these quantum states are described in terms of creation and annihilation operators. For example such as exist in the quantum vacuum, where virtual particles are envisaged to appear and disappear to correctly model phenomena like the Lamb shift (in atomic spectroscopy) or the Casimir effect (in relation to two charged plates) both of which have no explanation in classical physics or quantum mechanics as distinct from quantum field theory.

Universal Semantic Computation is Quantum Mechanical and must be nilpotent

- Moreover this phenomena of the quantum vacuum, which cannot itself be measured, is now explained, because in the urs it constitutes the measurement standard for the whole universe and so quite logically there is nothing further to measure it against!
- And so is the fact of quantum holographic encoding and decoding for which it is the ultimate reference phase/frame and of the nilpotent Dirac algebra which not only predicts the Standard Model of elementary particles physics in the form of their quantizations and relative masses, but also the complementary emergence of 3+1 relativistic space time too!
- That is, 3+1 relativistic space time is itself a basic consequence of the original quantum vacuum, where this can be envisaged as an \'infinitely degenerate\' zero energy state, empty of all matter, space and time, from which these emerge to produce its non degenerate energy states (comparable to those atomic spectroscopy)

Dark Matter?

- thus the residual degenerate quantum vacuum from which all further new fermion states of matter ( each of which will be entirely composed of entangled Standard Model elementary particle matter which retains a small amount of quantum coherence) remain to emerge, constitutes the urs quantum universe\'s dark matter/energy.
- And where the key discoveries of Rowlands &coworker Hill and Marcer with coworkers Rowlands, Schempp and Mitchell, are already well advanced in respect of the DNA/RNA genetic code and the workings of the conscious human brain as published respectively in Chapters 19 Nature\'s Code and 20 Nature\'s Rules, of Rowland\'s book.

How the laws of physics become the laws of life

- That is to say, that within the urs these laws respectively, are found to concern, with a very significant degree of certainty, a new emergent urs symbol which corresponds to the whole urs infinite alphabet ie each is a complete rewrite of the urs at a higher degree of Standard Model elementary particle complexity, the molecular.
- See Notes
- And this is the focus and title of the 7th International BCSCMsG Symposium from August 3 – 8 in Liege, Belgium at the HEC School of Management in the University of Liege, within the 9th International Conference on Computing Anticipatory Systems, CASYS 09, Director, Professor Dubois. Department Head, Liege University organized under the auspices of the Belgium charity CHAOS, established to run these CASYS events.

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