Download Symposium 10+

Symposium 10+
8th BCSCMsG International Symposium
on
Computational Self-Organised Emergence
Organised by Peter J. Marcer
British Computer Society Cybernetic Machine specialist Group
Sessions 10.1 Tuesday 8.30 -12.30
10.2 Thursday 8.30 -12.30
10.3 Friday 8.30 -12.30
2)
plus Allied Sessions including
1) the Tuesday Plenary CASYS 11 Award Session
of Professor Louis H. Kauffman
'On the Halting Problem'
Workshop on the 'Laws of Form and its Ramifications'
Session 2.4
&
3) Session 3.2 Tuesday 14.00 – 18.00
CASYS’11
-
Symposium 10
+
___________________________________________________________________________________
The Computational Self-Organised Emergence of 3D Dynamic
Structural Complexity
Peter Marcer
55 rue Jean Jaures,
83600, Frejus
Var, France
email [email protected]
Keywords : no quantum enigma, no measurement observation/observer problem, no initial
matter/ antimatter initial state, a nilpotent trace zero universe, with non zero fermion states.
Abstract.
Scientific discovery has revealed a natural hierarchy of 3D dynamic structural complexity on
Earth from the families of the elementary particles of quantum physics, through the periodic
table of the elements which regulates their chemistry, upward to the molecular biology of life
governed by the DNA/RNA genetic code, culminating in the molecular complexity of the
neurophysiology of the human brain, the connectivity of which is only surpassed by that of
the Universe itself.
Increasingly substantive evidence of a single scientific process description which predicts this
hierarchy of 3D dynamic structural complexity in the form of the universal nilpotent
computational rewrite system will be presented. In particular this evidence says :1) there is no quantum enigma, only a self organisation with its own universal computational
unique fixed measurement standard, against which all subsequent measurement/observation is
ultimately made. This standard (as the preferred reference frame template) not only provides a
required explanation of quantum inseparability and entanglement, it puts all subsequent
observation (and implicitly observers) on the same footing, solving the so called
measurement/observation/observer problem.
2) there is no initial stage of the universe composed purely of matter & anti matter, for this
would leave the creation of the observed 3+1 space time plenum (within which Einstein's
conservation of Energy, Momentum and Mass holds) unexplained. There is only a self
organized universal quantum mechanical process of their joint evolution (as the emergence of
the 3D hierarchy from the primaeval dark energy), which explains and generates both
(Rowlands et al 2007)
These, it tells us, can be accomplished without any change to the standard quantum
mechanical formalism simply by choosing a nilpotent boundary condition such that the
quantum universe constitutes a dynamic zero totality at all times.
This condition not only predicts the required hierarchy of 3D dynamic structural complexity
predicated above, it tells us, that any arbitrary fixed phase θ of quantum formalism to which
the wave function remains undefined, can to be selected as the preferred measurement
standard. That is to say the nilpotent criterion defines a trace zero totality universal evolution,
where its emergent fermion states, which by Pauli exclusion are unique and non zero, are the
evolution's stable critical points, emergent from the initial dark energy as the initial unstable
critical point.
CASYS’11
-
Symposium 10
+
___________________________________________________________________________________
Information, Bifurcation and Entropy in the Universal Rewrite
System
Peter Marcer 1 and Peter Rowlands 2
1
rue Jean Jaurès, 83600, Fréjus, Var, France,
[email protected]
2
Department of Physics, University of Liverpool, Oliver Lodge
Laboratory, Liverpool, L69 7ZE, UK,
[email protected]
Keywords : universal rewrite system, self-organization, nilpotent quantum mechanics,
entropy, chaos, information, bifurcation
Abstract
The universal rewrite system, which has previously been applied especially to the generation
of the number system and to nilpotent quantum mechanics, not only provides a generalised
description for all natural processes but also creates a direct measure of entropy increase and
information transfer, which is especially significant for systems on the edge of chaos. Entropy
and information can be shown to have a direct connection with the concept of the generation
of the number field at a very fundamental level.
CASYS’11
-
Symposium 10
+
___________________________________________________________________________________
Frequency and Anticipation in Bio-Systems
Cyril W. Smith
Retired
36 Westminster Road,
Ellesmere Park,
Eccles,
Manchester M30 9EA,
England.
+44 161 789 4768
[email protected]
Keywords: Bio-Systems, Frequencies, Computing, Anticipation, Control
Abstract
Bio-systems have a computing function at many levels of biological activity and the problem
is how does it work? Frequency is the language of this bio-computing activity and these
frequencies may be as coherent as is theoretically possible. Frequency has a duality with
chemical structure. Frequency as an expression of energy level change may provide a control
function. All bio-systems are water based and the properties of water in respect of frequencies
have been discussed by the writer previously in CASYS ‘05,’07,’09 including the possibility
of implementing the basic arithmetic operations and the three basic reversible logic gates in
respect of frequencies imprinted into water. Strong anticipation is imbedded chemically in the
nucleotides and in the chemical frequency signatures arising from interaction with vicinal
water in the whole chemistry of the bio-system itself including structure and isomerism. Weak
anticipation derives from the bio-system’s need for future chemicals and activities predicted
from within the bio-system’s model of itself.
CASYS’11
-
Symposium 10
+
___________________________________________________________________________________
The Contravariancy of Anticipatory Systems
Dimitrios Sisiaridis, Michael Heather & Nick Rossiter
Northumbria University,
Newcastle NE2 1XE, UK,
[email protected];
[email protected];
[email protected] ;
http://www.computing.unn.ac.uk/staff/CGNR1/
Keywords : Contravariancy, Duality, Type changing, System theory, Topos
Abstract
Where does anticipation come from? By definition strong anticipation resides in the
anticipatory system itself. If this is so, anticipation is of the nature of the system and forms
part of the Universe. Anticipation must therefore reside in nature and arise from relationships
in nature. Likewise from no more than its definition, the Universe consists of entities related
one to the other. Thus each entity affects every other. Existence is not therefore just a first
order effect but needs an inherent higher order formalism to represent such multi-body
interdependence. The relationship between any pair of entities depends on every possible
path between them. In category theory this is the property of cartesian closure found in the
highest structure possible-- the identity natural transformation designated as the ‘topos’.
However if every entity is related to every other it follows that the relationship is both ways
but not just a simple inverse relationship as appears from the laws of physics. A category C
of objects and arrows between the objects will have a dual Cop with arrows reversed. The
whole universal structure of both-ways relationships will then be represented by the product
Cop x C. This gives rise to the principle of duality throughout the Universe.
Duality is a common enough concept in mathematics, philosophy and most of the sciences
with some renowned examples like the mind-body duality. It also appears in other versions of
contrast as between the dynamic and the static and between global and local. To capture the
full effect and subtleties of opposing views and relationships a single view of the duality is
needed as a process. Duality is not a closed Boolean view. Rather it encapsulates opposite
orderings within a single (functorial) concept of variancy. These may be conveniently labelled
covariant and contravariant but only relative one to the other and not as absolute descriptions.
Systems theory is a case in point where these different views need to be integrated. Thus for
anticipatory systems, anticipation is an instantaneous, local static instantiation of a dynamic
global feature that looks either forward or back. The natural categories of process as advanced
by Whitehead encompass this contravariancy found in reality.
A three-level structure is sufficient to provide complete closure with internal contravariant
logic providing a generalisation of negation. Contravariancy across levels provides more
sophisticated reversals such as reverse engineering.
The ultimate contravariancy is to be found in the universal adjointness between any pair of
functors contravariant one to the other to provide both the quantitative and qualitative
semantics of intension-extension logic. A topical example may be found in quantum
information processing where the simple ‘qubit’ is now recognised to be a dual package
(described as ‘discord’) containing both covariancy and contravariancy. This Heyting
negation sacrifices the principle of tertium non datur but recovers associativity in quantum
mechanics.
An anticipatory system is but the structured ordering of adjointness between the systems as a
whole and every locality within it. Thus in the special case of time, the present is the
particular locality of interest as a reductionist self-duality. The past and the present is a
CASYS’11
-
Symposium 10
+
___________________________________________________________________________________
contravariant view of the past from the present while the present access to future states is also
a contravariant arrow from the future to the present.
CASYS’11
-
Symposium 10
+
___________________________________________________________________________________
Is the Human Brain Quantum Mechanical?
Peter Marcer 1 and Peter Rowlands 2
rue Jean Jaurès, 83600, Fréjus, Var, France,
[email protected]
2
Department of Physics, University of Liverpool, Oliver Lodge
Laboratory, Liverpool, L69 7ZE, UK,
[email protected]
1
Keywords : quantum explanation of the brain's signal processing, the computer constructor
universal unit wire, Wittgenstein's principle, Photosynthetic harvesting of photons by
chlorophyll Nature, Extracting Work from a single heat bath via vanishing quantum coherence,
Science
Abstract
Da Vinci mooted that the relative proportions of the human body contained in the unit disk
were those of the golden number G. Computationally the unit disk with metric I 2 +1 = 0, an
equation for chaos, character G, fractal dimension 2, has the desired qubit logic √(NOT = –1 =
False) It also describes Feynman’s computer constructor universal primitive, the unit wire and
ensures signals in the plane (x, y) are a Fourier duality pair. Quantum Anticipatory Erat
Demonstrandum, the human body and brain may indeed have a quantum mechanical
explanation, since the human genome is to known to specify both; and evidentially the genetic
code is computer constructor universal in the Von Neumann (1966) sense – a conclusion
confirmed in Science 330 (Miller, 19/11/2010, pp 1059-60) where three distantly related
mammals are shown to share a self organized visual cortex brain architecture characterised by
density π, for from the Euler identity exp i(θ = π) = –1, i as a parameter, has characters π, –1
and exponential constant e. The unit disk has infinitely many unit vectors (each of unique
relative phase θ) all of which are roots of the metric, which from exp i(θ = π/2) = i are all
orthogonal and so specify the Hilbert space in which all the solutions /roots of the quantum
formalism are known to lie. These Hilbert space unit vectors satisfy Wittgenstein’s (1975)
semantic language principle that ‘there is only one proposition to each fact θ that answers to it,
and the sense of the proposition cannot be expressed except by repeating it’. Its unitary (U)
symmetries are the well known behaviours U(1), SU(2), SU(3) of Standard Model Elementary
particle physics and SU(4) / SU(5) of Einstein’s General Relativity / Klein Kaluza
respectively. Examples of the U(1) unit wire are the chemical bond, the neural axon and 1
dimensional Fourier transform action. Recent impeccable supporting evidence from Science
(2003) and Nature (2010) is cited.
CASYS’11
-
Symposium 10
+
___________________________________________________________________________________
The Hard Problem of Consciousness
Peter Marcer
55 rue Jean Jaures,
83600, Frejus
Var, France
email [email protected]
Keywords: self organisation, the observer problem, third party objectivity, first person
subjectivity, the nilpotent universal computational rewrite system, quantum mechanics
Abstract
Further to the accompanying paper 'Is the Human Brain Quantum Mechanical?' the nature of
the human observer, observation in relation to the human brain/mind, and in particular a
central aspect of the hard problem of consciousness - 'how third party objectivity relates to
first person subjectivity' is briefly explained, in the context of self organization as defined by
universal nilpotent computational rewrite system.
CASYS’11
-
Symposium 10
+
___________________________________________________________________________________
The Projective Self-Organization of the Visual Cortex Cerebri
with Application to Avian Magnetic Compass Navigation
Walter Schempp (Germany)
Lehrstuhl fuer Mathematik I
University of Siegen
57068 Siegen, Germany
[email protected]
Keywords: Projective organization of the Retina and the primary visual Cortex cerebri,
Heisenberg unipotent Lie group, Heisenberg nilpotent Lie algebra, double metaplectic
representation, stabilizing pinwheel arrangements, distributional Fourier filter, spatial
orientation columns of neurons, Tusi couple, libration theory, self-organization of the primary
Cortex cerebri
Abstract
Research on the applications of the mathematical discipline of nilpotent harmonic analysis has
branched out in many different directions.
Among the various applications such as photonics, the areas of theoretical biology and
computational neuroscience are particularly promising.
Specifically, the field of non-invasive diagnostic imaging ([1], [6], [11]) belongs to the most
powerful photonic applications.
It needs to be combined with projective geometry, because the geometry of projective spaces
provides the basic model of vision and imaging ([14]), and the contact geometry of projective
spaces provides a Dupin cyclide approach ([3]) to the Huygens principle of wave optics ([4]).
CASYS’11
-
Symposium 10
+
___________________________________________________________________________________
Unifying the Sciences - Collapsing the Vector of State
O#o van Nieuwenhuijze, MSc, MD
Independent Research Scientist
17-II Gerard Doustraat, Amsterdam, NL-1072 VJ, The Netherlands
[email protected]
http://ottovannieuwenhuijze.googlepages.com
Keywords: Soliton, Phase Coupling, Freedom of Choice, Collapse of the Vector of State,
Realisation, Science
Abstract
Science is the art and act of creating mental constructs, of shared understanding. From the
perspective of Quantum Theory, our creation of realisation is determined by one factor: the
collapse of the vector of state. This paper explores the nature of this process; and how it
operates within us; in our body. It leads to the conclusion that we operate this in the interface,
between ourselves and our context. We find this in detail in the dynamics of cell division by
which our body unfolds; and is integrated. The Vrobel Time Fractal helps understand how
unity and integrity is therein always maintained. This needs to be linked to the concept of total
system inversion, by which a part is integrated with the whole. This requires a holographic
perspective, for which the Soliton can serve as model.
This can be used to formulate how we use Freedom of choice. That again can be used to see
how we can unify the sciences as we now know them; and more.
CASYS’11
-
Symposium 10
+
___________________________________________________________________________________
Geometrical Constraints in an N-Dimensional Topology in
Quantum Mechanics and Cosmology
Elizabeth A. Rauscher
Tecnic Research Laboratory
3500 S. Tomahawk Rd., Bldg #188
Apache Junction, AZ 85219
[email protected]
(480) 982-2285
Michael T. Hyson
The Resonance Project Foundation
PO Box 764
Holualoa, Hi 96725
and
Sirius Institute
PO Box 1979
Pahoa, HI 96778
[email protected]
(808) 896-8518
Keywords: cosmology, quantum mechanics, n-dimensional spaces, n-dimensional topological
spaces
Abstract
Geometrical constraints in general relativity and quantum mechanics are formulated in a
multidimensional Descarte space. A fundamental relationship between these correspondence
and complementarity constraints directs us towards a new understanding of the fundamental
relationship between relativity and quantum theory. The set of geometrical constraints of this
n-dimensional topology are expressed in terms of a hyper-dimensional Minkowski metric, Mn
for n > 4 which yields naturally closed cosmological solutions to Einstein’s field equations
which yields compatibility between Einstein’s field equations and the current big bang model
without Guth's inflationary model and its possible 10100 solutions as related to the string
theory. A comprehensive group theoretical approach to the model of the Descarte space
incorporates dark energy and dark matter which results from the model in a natural manner. A
lemma is formulated for the relationship of the maximum invariance for an n-dimensional
Descarte space and the dimensions of that space. Group multiplication tables for the Mn
geometry are formulated for the Descarte 10 and 11 dimensional spaces.
CASYS’11
-
Symposium 10
+
___________________________________________________________________________________
CASYS AWARD
The International Scientific and Program Committees of
CASYS’11
The Tenth International Conference on
Computing Anticipatory Systems
Bestowed the CASYS Award to
Louis H. Kauffman
For his outstanding scientific works on
Mathematics, Statistics and Computer Science
Liège, Belgium, August 2011
CASYS’11
-
Symposium 10
+
___________________________________________________________________________________
PHOTO © 2011 Louis H. Kauffman
Professor Louis H. Kauffman
University of Illinois at Chicago (USA)
CASYS’11
-
Symposium 10
+
___________________________________________________________________________________
Short Biography
Louis H. Kauffman
Louis Kauffman was born in Potsdam, New York on Feb. 3, 1945.
He graduated from Norwood-Norfolk Central High School in 1962 as
valedictorian.
He received the degree of B.S. in Mathematics from MIT in 1966.
Kauffman was awarded a PhD. in Mathematics by Princeton
University in 1972.
He has been teaching at the University of Illinois at Chicago since
January 1971, with visiting appointments at the University of
Michigan, Universidad de Zaragoza, Spain, Universita di Bologna,
Bologna, Italy and the Institute des Hautes Etudes Scientifiques in
Bures Sur Yvette, France, and others.
Kauffman's research is in algebraic topology and particularly in low
dimensional topology (knot theory) and its relationships with
algorithms, logic, combinatorics, mathematical physics and natural
science.
He discovered a state summation model for the Conway polynomial in
1980 and the bracket polynomial state model for the Jones polynomial
in 1985.
Kauffman showed that this state summation generalizes the Potts
model in statistical mechanics - translated to knot diagrams.
CASYS’11
-
Symposium 10
+
___________________________________________________________________________________
He discovered a two variable generalization of the original Jones
polynomial that is called the semi-oriented or Kauffman polynomial.
The bracket model led Kauffman, Murasugi and Thistlethwaite to
proofs of the Tait conjectures about the topological invariance of
number of crossings for reduced alternating link projections.
His recent research in Virtual Knot Theory has opened up a new field
of knot theory and has resulted in the discovery of many new
invariants of knots and links.
He is the author of four books on knot theory (three in Princeton
University Press and one in World Scientific Press), a book on map
coloring and the reformulation of mathematical problems, Map
Reformulation (Princelet Editions; London and Zurich (1986)) and is
the editor of the World-Scientific 'Book Series On Knots and
Everything'.
He is the Editor in Chief and founding editor of the Journal of Knot
Theory and Its Ramifications.
He is the co-editor of the review volume (with R. Baadhio) Quantum
Topology and editor of the review volume Knots and Applications,
both published by World Scientific Press.
Kauffman is the recipient of a 1993 University Scholar Award by the
University of Illinois at Chicago and he is the 1993 recipient of the
1993 Warren McCulloch Memorial Award of the American Society for
Cybernetics for significant contributions to the field of Cybernetics
and the 1996 award of the Alternative Natural Philosophy Association
for his contribution to the understanding of discrete physics.
He was Polya lecturer for the Mathematical Association of America
from 2008 to 2010 and President of the American Society for
Cybernetics from 2005 to 2008.
CASYS’11
-
Symposium 10
+
___________________________________________________________________________________
On the Halting Problem
Louis H Kauffman
Mathematics Department
University of Illinois at Chicago
851 South Morgan Street
Chicago, Illinois 60607-7045
USA
Keywords: Algorithm, halt, paradox, hypergame, cybernetics
Abstract
This paper discusses the presence of undecideable problems in mathematics, with reference to
the halting problem for algorithms, the hypergame paradox and the paradox of the wellfounded sets.
All these results are curiously related to self-reference and the strange loop by which a selfobserving system can indicate its own operations to itself.
CASYS’11
-
Symposium 10
+
___________________________________________________________________________________
WORKSHOP
on "Laws of Form and Its Ramifications"
organized by Louis Kaufmann and Matt Alpert
CASYS’11
-
Symposium 10
+
___________________________________________________________________________________
Laws of Form and Discrete Physics
Louis H. Kauffman
Mathematics Department
University of Illinois at Chicago
851 South Morgan Street
Chicago, Illinois 60607-7045
Keywords: form, distinction, indication, cross, order, non-commutativity, discrete
Abstract
This talk will trace how the worlds we represent arise from the making of a distinction, and
how when we take time and recursion into account a remarkable body of mathematics
emerges that is in direct parallel to the patterns of physical laws.
CASYS’11
-
Symposium 10
+
___________________________________________________________________________________
Universal Rewrite and Self-Organization
Peter Marcer 1 and Peter Rowlands 2
rue Jean Jaurès, 83600, Fréjus, Var, France,
[email protected]
2
Department of Physics, University of Liverpool, Oliver Lodge
Laboratory, Liverpool, L69 7ZE, UK,
[email protected]
1
Keywords: universal rewrite system, self-organization, nilpotent quantum mechanics,
renormalization group, Berry phase
Abstract.
The conventional approach to computer programming using rewrite or production systems
can be extended to create a universal rewrite system, which provides a computational
approach to both physics and mathematics, based on the idea of a zero totality alphabet.
Mathematics emerges from the system in the form of a Clifford-type algebra, while physics
takes the form of nilpotent quantum mechanics. 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 applications well beyond quantum physics. The
nilpotent structure has also been identified as being constructed from two commutative vector
spaces. This construction has a number of identifiable characteristics which we can expect to
find in systems where self-organization is dominant; a recent case involves the organization of
the neurons in the visual cortex. We expect to find many more complex systems where our
general principles, based, by analogy, on
nilpotent quantum mechanics, will apply.
CASYS’11
-
Symposium 10
+
___________________________________________________________________________________
Local and NonLocal
Peter Rowlands
Department of Physics,
University of Liverpool, Oliver Lodge Laboratory,
Oxford Street, Liverpool, L69 7ZE, UK.
e-mail [email protected]
Keywords: Nonlocality, nilpotent quantum mechanics, local interactions, vacuum, gravity
Abstract.
While nonlocality has been considered by some to be a problem for quantum physics, it is, in
fact, an essential component of understanding how local interactions actually operate.
Locality and nonlocality are fundamental components of a dual system in which each
determines the behaviour of the other. The exact characteristics of the different local
interactions (weak, strong and electric) can be shown to be completely determined by the
nonlocal vacuum structures with which they are associated. At the same time, gravity
provides a nonlocal dual to the combined interactions, which has inertia as its local
manifestation. A completely integrated description of local interactions and nonlocal vacuum
structures is proposed, based on nilpotent quantum mechanics and its unique algebraic
structure.
CASYS’11
-
Symposium 10
+
___________________________________________________________________________________
Relativistic Perihelion of the Mercury Planet from an
Anticipatory Retarded Newtonian Gravity
Daniel M. Dubois
CHAOS ASBL, B37, Grande Traverse 12, B-4000 LIEGE 1, Belgium,
http://www.ulg.ac.be/mathgen/CHAOS
and Department of Applied Informatics and Artificial Intelligence,
HEC-ULg, N1, rue Louvrex 14, B-4000 LIEGE, Belgium
http://www.sia.hec.ulg.ac.be
[email protected]
Keywords: Newton, Schwarzschild, Mercury, Naked Singularities, Black Hole
Abstract
The Newton law of gravitation, based on an instantaneous propagation of gravity, for the solar
system works rather well, except that it does not show the advance of the perihelia of the
planets.
The case of the Mercury planet is taken as example because its precession is the most
important aberration in the solar system. This aberration is a relativistic effect as explained by
Einstein with the General Relativity, but it was shown that the Newton law of gravitation can
be corrected to obtain an equivalent effective potential as in General Relativity (Dubois,
2005). The correction was obtained from the Schwarzschild relativistic gravitational potential,
which is the solution of the Einstein equation for the geometry outside of a spherical star.
In this paper, we will present a new mathematical demonstration of the Newtonian law of
gravitation with a corrected relativistic term, given by an anticipatory retarded gravity. This
Relativistic correction corresponds to a natural physical strong anticipation to compensate the
finite speed of the radial propagation of gravity, which is the Newtonian instantaneous gravity,
while the tangential retarded gravity is responsible of the relativistic perihelion effect.
CASYS’11
-
Symposium 10
+
___________________________________________________________________________________
The Compact Manifold of Stellar Objects Spinning around the
Supermassive Black Hole in the Galactic Center
Walter Schempp
Lehrstuhl fuer Mathematik I
University of Siegen
57068 Siegen, Germany
[email protected]
Keywords: Black hole astrophyscs, astrometry, non-commutative geometry, the cylindrical
Dupin cyclide approach to the third Kepplerian law, spin structure and spin dynamics, the
Schwarzschild-Keppler proportions
Abstract
The purpose of the paper is to demonstrate how the Kepplerian astrophysics of planetary
motion can be extended to the manifold of stellar objects spinning around the supermassive
black hole in the center of the Galaxis.
The contact geometry of this compact manifold is determined by means of the phase sensitive
Hopf fibration of the Schwarzschild sphere over the heavenly sphere with circular fiber.
The direction of the cylindrical Dupin cyclide arising from non-commutative harmonic
analysis is determined by the laser pointer facility of the Very Large Telescope (VLT)
operated in the near-infrared by the European Southern Observatory.
A series of high-resolution images illustrates the spin dynamics of the stellar objects which
are spinning around the supermassive black hole Sgr A* in the galactic center within the
constellation Sagittarius.
CASYS’11
-
Symposium 10
+
___________________________________________________________________________________
Minkowski Space: Tick Here
Garnet N. Ord
Mathematics Department,
Ryerson University,
Toronto
Canada,
[email protected]
Keywords: Relativity, Quantum Mechanics, Statistical Mechanics
Abstract
We explore a two-photon model of a digital clock. The model implicates the use of spacetime
algebra to describe Minkowski space but suggests that the common use of Minkowski space
in special relativity presupposes reference frames of infinite mass. A close look at the digital
clock indicates that both classical special relativity and Dirac propagation emerge from the
clock depending on how many ticks are heard between the initial and final state.