Were Bohr and Einstein both
Peter Marcer
Cybernetics Machine
specialist Group
AGM Presentation 16th
March 2009
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, neuroscience 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
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
• but leaves 3 fundamental questions unanswered
The unanswered, still unsettled
• 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
• 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
• 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
• 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)
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 Xi  0 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
• 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
• 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
• 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 urs
symbol 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
• 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
Magnetic Resonance Imaging
• 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
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
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
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
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
• 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.
The End

Quaternions Multivariate Ve