Conspansive Duality, Intertheoretic Relations, Guage Symmetry

Images (Kleinian movies): http://www.math.harvard.edu/~ctm/gallery/menu.html

"Conspansive duality, the role of which in the CTMU is somewhat analogous to that of the Principle of Equivalence in General Relativity, is the only escape from an infinite ectomorphic “tower of turtles”. Were the perceptual geometry of reality to lack a conspansive dual representation, motion of any kind would require a fixed spatial array or ectomorphic “background space” requiring an explanation of its own, and so on down the tower. Conspansion permits the universe to self-configure through temporal feedback. Each conspanding circle represents an event-potential corresponding to a certain combination of law and state; even after one of these intrinsically atemporal circles has “inner-expanded” across vast reaches of space and time, its source event is still current for anything that interacts with it, e.g. an eye catching one of its photons. At the same time, conspansion gives the quantum wave function of objects a new home: inside the conspanding objects themselves. Without it, the wave function not only has no home, but fails to coincide with any logically evolving system of predicates or “laws of physics”. Eliminate conspansion, and reality becomes an inexplicable space full of deterministic worldlines and the weighty load of problems that can be expected when geometry is divorced from logic.

Where reality is characterized by dual-aspect infocognitive monism (read on), it consists of units of infocognition reflecting a distributed coupling of transductive syntax and informational content. Conspansion describes the “alternation” of these units between the dual (generalized-cognitive and informational) aspects of reality, and thus between syntax and state. This alternation, which permits localized mutual refinements of cognitive syntax and informational state, is essential to an evolutionary process called telic recursion. Telic recursion requires a further principle based on conspansive duality, the Extended Superposition Principle, according to which operators can be simultaneously acquired by multiple telons, or spatiotemporally-extensive syntax-state relationships implicating generic operators in potential events and opportunistically guiding their decoherence.

Note that conspansion explains the “arrow of time” in the sense that it is not symmetric under reversal. On the other hand, the conspansive nesting of atemporal events puts all of time in “simultaneous self-contact” without compromising ordinality. Conspansive duality can be viewed as the consequence of a type of gauge (measure) symmetry by which only the relative dimensions of the universe and its contents are important."
http://www.megafoundation.org/CTMU/Articles/Langan_CTMU_092902.pdf

Unity from duality: gravity, gauge theory and strings

"In a distilled and pedagogical fashion, the contributions to this volume of the famous summer school in Les Houches cover the recent developments in supersymmetric string theory, the gauge theory/string theory correspondence and string duality. Further chapters deal with quantum gravity and D-brane geometry. Black hole mechanics and cosmology are treated too, as well as the AdS-CFT correspondence. The book is a comprehensive introduction to the recent developments in string/M-theory and quantum gravity. It addresses graduate students in physics and astrophysics."
http://books.google.com/books?id=q4512ZO2JAUC&dq=unity+from+duality&source=gbs_navlinks_s

String Theory and Duality:
http://www.slimy.com/~steuard/research/StringDuality/StringDuality.001.html

In Search of Symmetry Lost:
http://www.frankwilczek.com/Wilczek_Easy_Pieces/366_In_Search_of_Symmetry_Lost.pdf

"In gauge symmetry, 'gauge' means 'measure', and symmetry means 'stays the same'. Geometry is the study of the properties of objects that do not change when they move around. An object is symmetric if some motion leaves it looking the same, for instance, rotating an equilateral triangle through 120 degrees. Many physical properties are invariant under translation and rotation. When there are transformations of a physical system that do not change the laws of physics governing the system, such transformations are called "symmetries" of the physical system. For example, the results of many experiments will not change if the apparatus is moved, or faces a different direction, or if the experiment is performed at a later date. [1]

Gravity is a gauge theory because its predictions stay the same when measurements are taken from different baselines. For instance, a ball on a staircase has gravitational potential energy. If it moves down a step its loss in energy depends only on the strength of the gravitational field and the height dropped. You can measure its gravitational potential energy from anywhere (earth's surface, another step, Alpha Centauri...) and the difference in energy between the two steps 'stays the same'. This global invariance in the measurement procedure makes gravity a gauge theory, that is, a field theory showing gauge symmetry.

By contrast relative speed is not a gauge symmetry: if two objects pass us, one at 9% of the speed of light and the other at 20% of the speed of light, we will notice a difference in their speeds of 11% of the speed of light; however, an observer traveling at 50% of the speed of light, head-on with the same two objects, will observe the difference of the speed of those two objects to be only 7% of the speed of light (because of the effect of special relativity)."
http://en.wikipedia.org/wiki/Gauge_symmetry

"Summing up, physical dualities pose a dilemma to the philosophers of science: either the physicists’s ‘received view’ that dualities relate different formulations of the same theory is accepted, but this implies a notion of what is a ‘physical theory’ which is quite different from the common idea that a theory is identified on the basis of its fundamental dynamical equations and ontology; or, on the contrary, dualities are understood as relations between different physical theories, but then it is difficult to understand the real meaning of such inter-theory relations and to see in which sense they can be considered ‘symmetries’."
http://philsci-archive.pitt.edu/4679/1/dualities_epsa07.pdf

The Interpretation of String Dualities

"Many of the advances in string theory have been generated by the discovery of new duality symmetries connecting what were once thought to be distinct theories, solutions, processes, backgrounds, and more. Indeed, duality has played an enormously important role in the creation and development of numerous theories in physics and numerous fields of mathematics. Dualities often lie at those fruitful intersections at which mathematics and physics are especially strongly intertwined. In this paper I describe some of these dualities and unpack some of their philosophical consequences, focusing primarily on string-theoretic dualities. I argue that dualities fall uncomfortably between symmetries and gauge redundancies, but that they differ in that they point to genuinely new deeper structures."
http://philsci-archive.pitt.edu/5079/

"Background independence, also called universality, is the concept or assumption, fundamental to all physical sciences, that the nature of reality is consistent throughout all of space and time. More specifically, no observer can, under any circumstances, perform a measurement that yields a result logically inconsistent with a previous measurement, under a set of rules that are independent of where and when the observations are made.

This is not a suggestion that spacetime is uniform, merely that the fundamental rules governing the measurable characteristics of the physical universe are the same everywhere, at all times."
http://en.wikipedia.org/wiki/Background_independence

"We describe the definition and the role background independence and the closely related notion of diffeomorphism invariance play in modern string theory. These important concepts are transformed by a new understanding of gauge redundancies and their implementation in non-perturbative quantum field theory and quantum gravity. This new understanding also suggests a new role for the so-called background-independent approaches to directly quantize the gravitational field. This article is intended for a general audience, and is based on a plenary talk given in the Loops 2007 conference in Morelia, Mexico."
http://arxiv.org/abs/0809.3962

Zee in QFT in nut shell says
"The most unsatisfying feature of field theory is the present formulation of gauge theories. Gauge symmetry does not relate 2 different physical states but the same physical state. We have this strange language with redundancy which we cannot live without"

He also says "We even know how to avoid this redundancy from the start at the price of a discrete space time"
(closing words pg 456)

Dear Colleagues,

There are several differences between classical and quantum theories that have an impact on the possible symmetries:

Physical states represented in Hilbert space rather than phase space.
Quantum mechanics defines symmetries as mappings between physical states that preserve transition amplitudes. (As Wigner proved, these symmetries can be represented in Hilbert space by unitary and anti-unitary operators.)
Quantum mechanics assigns complex numbers to these transition amplitudes.
The algebra of observables in quantum mechanics is non-commutative.
Quantum particles are indistinguishable.
Composite quantum systems are not represented by a Cartesian product structure, but by a linear tensor structure.

Quantum symmetries may also include gauge redundancies and dualities. Gauge redundancies can be understood as multiple representations of the same physical state. Dualities can be understood as isomorphisms holding between pairs of Hilbert spaces together with (canonical) operators. The possibilities for quantum symmetries are tightly constrained by the number of spacetime dimensions and by the dimensionality of the objects of the theory (including whether they are extensionless or structured). Quantum symmetries also refer to quantum groups, which aren't groups as such but algebras that reduce to groups in the limit as a deformation parameter (playing the part of Planck's constant) goes to 1 (returning multiplication to normal).

Contributions are invited on all aspects of quantum symmetries. Those that involve foundational issues or the intersection of theoretical physics and pure mathematics are especially welcomed. Possible themes (not ranked in order preference) include:

2D Conformal Field Theory, Modular Invariance, Statistical Mechanics.
Dualities in Quantum Theories.
Mirror Symmetry in String Theory.
Emergent Quantum Symmetries, Symmetry Breaking, Effective Field Theory, Renormalization Group.
Hopf Algebras, Quantum Groups and Low Dimensional Physics.
Quantum Geometry (including Non-Commutative Geometry).
Spin-Statistics, Anyons, Fractional Quantum Hall Effect.
Connections between Quantum Symmetries and Spacetime/Object Dimensionality.
Quantum Symmetries in Computation.
Relationship between Classical and Quantum Symmetries.

Deadline for manuscript submissions: 31 January 2011

http://www.mdpi.com/journal/symmetry/special_issues/quantum/