Dualities in string theory relate different regions of the theory's moduli space where coupling constants may take on different values, potentially interchanging what is viewed as fundamental versus composite. These dualities do not provide unification or explanation according to the author, but may still reveal deeper underlying structures without requiring a single deeper theory. The document discusses various interpretations of string theory and issues regarding background dependence, structuralism, and the role of dualities.
This document discusses the concept of an ecumenical logic system that allows both classical and intuitionistic reasoning to coexist. It summarizes Dag Prawitz's approach to defining such a system, which uses different symbols for logical constants that have different meanings classically versus intuitionistically. However, the document raises the question of why Prawitz's system only includes one symbol for negation rather than separate classical and intuitionistic negation symbols. Possible answers discussed include the interderivability of the two notions of negation and the view that negation asserts a contradiction from assuming the negated proposition. The document does not conclude there is a definitive answer and suggests this as an interesting open problem area.
This document provides an outline for a course on category theory from a logician's perspective. It introduces the instructor, Valeria de Paiva, and their background in category theory through their PhD thesis on Dialectica categories. The course will cover categories, functors, natural transformations, adjunctions, deductive systems as categories, and a taste of glue semantics. It emphasizes viewing proofs as first-class objects and using category theory for proof semantics rather than set-based models. The goal is to represent proofs explicitly rather than just knowing if a proof exists. The course will take an intuitionistic and constructive perspective on logic.
This dissertation thesis investigates congruence lattices of algebras in locally finite, congruence-distributive varieties that have the congruence intersection property. It provides some general results and a complete characterization for certain types of varieties. The thesis describes congruence lattices in two ways: via direct limits and via Priestley duality. It addresses long-standing open problems in lattice theory regarding representing algebraic lattices and distributive lattices as congruence lattices of algebras.
Correspondence and Isomorphism Theorems for Intuitionistic fuzzy subgroupsjournal ijrtem
ABSTRACT:The aim of this paper is basically to study the First Isomorphism Theorem, Second Isomorphism Theorem, Third Isomorphism theorem, Correspondence Theorem etc. of intuitionistic fuzzy/vague sub groups of a crisp group.
KEY WORDS: Intutionistic fuzzy or Vague Subset, Intutionistic fuzzy Image, Intutionistic fuzzy Inverse Image, Intutionistic fuzzy/vague sub (normal) group, Correspondence Theorem, First (Second, Third) Isomorphism Theorem.
In this article we present a brief history and some applications of semirings, the structure of compact monothetic c semirings. The classification of these semirings be based on known description of discrete cyclic semirings and compact monothetic semirings. Boris Tanana "Compact Monothetic C-semirings" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-5 | Issue-2 , February 2021, URL: https://www.ijtsrd.com/papers/ijtsrd38612.pdf Paper Url: https://www.ijtsrd.com/mathemetics/algebra/38612/compact-monothetic-csemirings/boris-tanana
This document provides an introduction and overview of the theory of relations as presented in the book "Theory of Relations" by R. Fraisse. It discusses how relation theory originated from the study of order types and connects to fields like logic, combinatorics, and graph theory. The introduction outlines some of the key concepts and results covered in each chapter of the book, including work on partial orders, embeddability, scattered chains, barriers, and the classification of relations by age.
Conceptual Spaces for Cognitive Architectures: A Lingua Franca for Different ...Antonio Lieto
We claim that Conceptual Spaces offer a lingua franca that allows to unify and generalize many aspects of the symbolic, sub-symbolic and diagrammatic approaches (by overcoming some of their typical problems) and to integrate them on a common ground. In doing so we extend and detail some of the arguments explored by Gardenfors [23] for defending the need of a conceptual, intermediate, representation level between
the symbolic and the sub-symbolic one. Additionally, we argue that Conceptual Spaces could offer a unifying framework for interpreting many kinds of diagrammatic and analogical representations. As a consequence, their adoption could also favor the integration of diagrammatical representation and
reasoning in Cognitive Architectures
This document discusses the concept of an ecumenical logic system that allows both classical and intuitionistic reasoning to coexist. It summarizes Dag Prawitz's approach to defining such a system, which uses different symbols for logical constants that have different meanings classically versus intuitionistically. However, the document raises the question of why Prawitz's system only includes one symbol for negation rather than separate classical and intuitionistic negation symbols. Possible answers discussed include the interderivability of the two notions of negation and the view that negation asserts a contradiction from assuming the negated proposition. The document does not conclude there is a definitive answer and suggests this as an interesting open problem area.
This document provides an outline for a course on category theory from a logician's perspective. It introduces the instructor, Valeria de Paiva, and their background in category theory through their PhD thesis on Dialectica categories. The course will cover categories, functors, natural transformations, adjunctions, deductive systems as categories, and a taste of glue semantics. It emphasizes viewing proofs as first-class objects and using category theory for proof semantics rather than set-based models. The goal is to represent proofs explicitly rather than just knowing if a proof exists. The course will take an intuitionistic and constructive perspective on logic.
This dissertation thesis investigates congruence lattices of algebras in locally finite, congruence-distributive varieties that have the congruence intersection property. It provides some general results and a complete characterization for certain types of varieties. The thesis describes congruence lattices in two ways: via direct limits and via Priestley duality. It addresses long-standing open problems in lattice theory regarding representing algebraic lattices and distributive lattices as congruence lattices of algebras.
Correspondence and Isomorphism Theorems for Intuitionistic fuzzy subgroupsjournal ijrtem
ABSTRACT:The aim of this paper is basically to study the First Isomorphism Theorem, Second Isomorphism Theorem, Third Isomorphism theorem, Correspondence Theorem etc. of intuitionistic fuzzy/vague sub groups of a crisp group.
KEY WORDS: Intutionistic fuzzy or Vague Subset, Intutionistic fuzzy Image, Intutionistic fuzzy Inverse Image, Intutionistic fuzzy/vague sub (normal) group, Correspondence Theorem, First (Second, Third) Isomorphism Theorem.
In this article we present a brief history and some applications of semirings, the structure of compact monothetic c semirings. The classification of these semirings be based on known description of discrete cyclic semirings and compact monothetic semirings. Boris Tanana "Compact Monothetic C-semirings" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-5 | Issue-2 , February 2021, URL: https://www.ijtsrd.com/papers/ijtsrd38612.pdf Paper Url: https://www.ijtsrd.com/mathemetics/algebra/38612/compact-monothetic-csemirings/boris-tanana
This document provides an introduction and overview of the theory of relations as presented in the book "Theory of Relations" by R. Fraisse. It discusses how relation theory originated from the study of order types and connects to fields like logic, combinatorics, and graph theory. The introduction outlines some of the key concepts and results covered in each chapter of the book, including work on partial orders, embeddability, scattered chains, barriers, and the classification of relations by age.
Conceptual Spaces for Cognitive Architectures: A Lingua Franca for Different ...Antonio Lieto
We claim that Conceptual Spaces offer a lingua franca that allows to unify and generalize many aspects of the symbolic, sub-symbolic and diagrammatic approaches (by overcoming some of their typical problems) and to integrate them on a common ground. In doing so we extend and detail some of the arguments explored by Gardenfors [23] for defending the need of a conceptual, intermediate, representation level between
the symbolic and the sub-symbolic one. Additionally, we argue that Conceptual Spaces could offer a unifying framework for interpreting many kinds of diagrammatic and analogical representations. As a consequence, their adoption could also favor the integration of diagrammatical representation and
reasoning in Cognitive Architectures
Extending the knowledge level of cognitive architectures with Conceptual Spac...Antonio Lieto
Extending the knowledge level of cognitive architectures with Conceptual Spaces (+ a case study with Dual-PECCS: a hybrid knowledge representation system for common sense reasoning). Talk given at Stockholm, September 2016.
This document discusses constructive modal logics and open questions in the field. It describes two main families of constructive modal logics, CK and IK, which differ in their proof-theoretical properties. Developing satisfactory proof theories for these logics has been challenging, requiring augmentations to sequent systems. The document also notes that while IK logics have better model-theoretic properties, CK logics are better suited for lambda calculus interpretations. Overall, the document advocates for further work to develop a unified framework that can capture both families of logics along with categorical semantics.
This document summarizes Michael Kreisel's dissertation on the connection between Gabor frames for quasicrystals, the topology of the hull of a quasicrystal, and K-theory of an associated twisted groupoid algebra. The author constructs a finitely generated projective module over this algebra, where any multiwindow Gabor frame for the quasicrystal can be used to construct a projection representing this module in K-theory. As an application, results are obtained on the twisted version of Bellissard's gap labeling conjecture for quasicrystals.
What is Odd about Binary Parseval FramesMicah Bullock
This document examines the construction and properties of binary Parseval frames. It addresses when a binary Parseval frame has a complementary Parseval frame, and which binary symmetric idempotent matrices are Gram matrices of binary Parseval frames. Unlike real or complex Parseval frames, binary Parseval frames do not always have complements. A necessary condition for a binary Parseval frame to have a complement is that it contains at least one even vector. Certain symmetric idempotent matrices that are not Gram matrices of binary Parseval frames can exist if they only have even column vectors.
The document discusses the logic of informal proofs in mathematics. It makes 5 key claims:
1) Understanding informal proofs is important because most mathematical proofs are informal.
2) Informal proofs rely on both logical form and content.
3) Properly understanding informal proofs requires seeing logic as the study of inferential actions, where content plays a role.
4) This conception accommodates proofs involving actions on objects other than propositions.
5) It explains why mathematics relies on external representations, since representations can be manipulated.
The document argues this view connects logical questions about rigor to the cultural study of mathematical practices.
This document outlines the key points that will be covered in a presentation on dialectica categories as models of linear logic. It discusses four main theorems: 1) The original dialectica category DC is a model of intuitionistic linear logic without the exponential bang (!). 2) Adding a co-free monoidal comonad makes DC a model of full intuitionistic linear logic. 3) The simplified dialectica category GC is a model of classical linear logic without bang and question mark (?). 4) Adding a complicated monoidal comonad makes GC a model of full classical linear logic. The document provides brief motivations and outlines of the constructions and proofs involved in these main results. It also discusses some applications and areas for further development
The document discusses modalities in linear logic and dialectica categories. It motivates studying (co)monads and (co)algebras as constructive modalities in linear logic. It describes how the linear logic bang modality ! can be modeled as a comonad in dialectica categories. Specifically, in the dialectica category Dial2(C), ! is modeled as a cofree comonad. This provides a model of intuitionistic linear logic with both linear and non-linear connectives. In the simpler category DDial2(C), modeling the bang requires composing two comonads.
1. The document discusses the need for a positive account of informal proof in mathematics, as most mathematical proofs are informal. It argues against the view that informal proofs are recipes for formal derivations.
2. The document proposes that logic should be understood more broadly as the general study of inferential actions, as informal proofs often involve actions on mathematical objects beyond propositions. Examples of such actions include diagram manipulation in Euclidean geometry.
3. The document reviews work that may support this broader view of logic in informal proofs, such as studies of reasoning with diagrams in knot theory and using Cayley graphs to prove group theory results.
(1) The document discusses the concepts of emergence and reduction in physics, specifically arguing that they pose a false dichotomy as they are logically independent.
(2) It provides examples where emergence occurs alongside reduction, such as the emergence of classical behavior from quantum mechanics in certain limits, and the emergence of thermodynamic laws and properties from statistical mechanics.
(3) The key point is that reduction, viewed as deduction, allows for novelty through the choices made in taking limits, such as which symmetries to break or states to keep. So emergence and reduction can be compatible.
Jean-Yves Béziau the metalogical hexagon of opposition
The difference between truth and logical truth is a fundamental distinction of modern logic promoted by Wittgenstein. We show here how this distinction leads to a metalogical triangle of contrariety which can be naturally extended into a metalogical hexagon of oppositions, representing in a direct and simple
way the articulation of the six positions of a proposition vis-à-vis a theory. A particular case of this hexagon is a metalogical hexagon of propositions which can be interpreted in a modal way. We end by a semiotic hexagon emphasizing the value of true symbols, in particular the logic hexagon itself.
Talk given at Oxford Philosophy of Physics, LSE's Sigma Club, the Munich Center for Mathematical Philosophy, Carlo Rovelli's 60th birthday conference.
I construe dualities in physics as particular cases of theoretical equivalence. The question then naturally arises whether duality is compatible with emergence. For the the focus of emergence is on novelty rather than on equivalence.
In the first part of the talk, I review recent work dealing with this question. I exhibit two ways in which duality and equivalence can be made compatible, and I give an example of emergence in gauge/gravity dualities: dualities between a theory of gravity in (d+1) dimensions and a quantum field theory (QFT) in d dimensions.
In the second part of the talk, I present new results on the question whether diffeomorphisms in gravity theories emerge from QFTs. I critically assess the following idea, taken from the physics literature: given that (a) the QFT is not a diffeomorphism invariant theory, and that (b) there is a duality between the QFT and the gravity theory, are we entitled to (c) conclude that the diffeomorphisms of the gravity theory emerge from the QFT?
I argue that one must distinguish different kinds of diffeomorphisms: some diffeomorphisms are ‘invisible’ to the QFT: all of the QFT’s quantities are invariant under them, therefore the QFT does not ‘see’ them. But other diffeomorphisms are ‘visible’ to the QFT. The invisible diffeomorphisms prompt a ‘Bulk Argument’, in analogy with the Hole Argument. The analysis of emergence is different for these different kinds of diffeomorphisms, and I discuss the way in which we can speak of emergence of diffeomorphisms in gauge/gravity dualities.
Proof-Theoretic Semantics: Point-free meaninig of first-order systemsMarco Benini
This document summarizes a talk on providing a semantics for first-order logical theories using logical categories. The semantics interprets formulae as objects in a category and proofs as morphisms, without assuming elements exist. Quantifiers are interpreted using stars and costars. A logical category is a prelogical category where stars and costars exist to interpret all formulae. This semantics is sound and complete - a formula is true if a proof morphism exists. The semantics can interpret many other approaches and inconsistent theories have "trivial" models.
This document discusses the topics of paracompact spaces and compact spaces in topology. It provides background on the historical development of these concepts, from Bolzano's work in the 19th century on limit points of sequences to the formalization of compactness by Frechet in 1906. Paracompactness was introduced in 1944 as a generalization of compactness, replacing the requirement that every open cover have a finite subcover with the weaker condition of having a locally finite open refinement. The document aims to analyze paracompactness and compare it to compactness, exploring how compactness implies paracompactness.
The document discusses graph theory and algorithms for finding shortest paths in graphs. It introduces concepts like paths, cycles, and connectedness in graphs. It then describes several important algorithms for solving shortest path problems, including Dijkstra's algorithm, Bellman-Ford algorithm, Floyd-Warshall algorithm, and Ford's algorithm. Dijkstra's algorithm finds the shortest path from a source vertex to all other vertices in a graph and works by iteratively labeling vertices with their shortest path distances from the source.
The Gödel incompleteness can be modeled on the alleged incompleteness of quantum mechanics
Then the proved and even experimentally confirmed completeness of quantum mechanics can be reversely interpreted as a strategy of completeness as to the foundation of mathematics
Infinity is equivalent to a second and independent finiteness
Two independent Peano arithmetics as well as one single Hilbert space as an unification of geometry and arithmetic are sufficient to the self-foundation of mathematics
Quantum mechanics is inseparable from the foundation of mathematics and thus from set theory particularly
2014 10 rotman mecnhanism and climate models Ioan Muntean
This document discusses the potential transition from climate models to mechanistic explanations in climate science. It argues that understanding climate change through mechanisms could provide several advantages over the current model-based approach, such as introducing new explanations, integrating causal stories, and facilitating communication. However, some challenges are also noted, such as the holistic nature of climate science and concerns about reductionism. The document explores topics like feedback mechanisms, mapping models to mechanisms, and assessing climate models based on their representation of mechanisms. Overall, it presents arguments both for and against adopting a more mechanistic view of climate science.
How to connect with your life purpose...againTasha Scott
This article discusses how to reconnect with your life purpose when you've lost your passion for it. It suggests connecting with your motivations, approaching your work with an open mind like a beginner, mentoring others, asking for help, setting new goals, avoiding comparisons to others, taking breaks, pursuing hobbies, and continuous learning. The author is a personal development coach who provides tips on her website for staying true to your purpose.
The document discusses the relationship between science and metaphysics. It examines several approaches to this relationship, including viewing them on a continuum, finding similarities in their methods of modeling, and emphasizing their differences. The key point is that while science and metaphysics may use similar language and concepts of modality, possibility, and necessity, the document argues that the modalities used in scientific modeling are fundamentally different than those used in metaphysical modeling. Specifically, fictional entities and idealizations in metaphysics are constrained only by conceivability, while in science they are constrained by theoretical and empirical factors. Emphasizing these differences, rather than similarities, can advance both fields.
Extending the knowledge level of cognitive architectures with Conceptual Spac...Antonio Lieto
Extending the knowledge level of cognitive architectures with Conceptual Spaces (+ a case study with Dual-PECCS: a hybrid knowledge representation system for common sense reasoning). Talk given at Stockholm, September 2016.
This document discusses constructive modal logics and open questions in the field. It describes two main families of constructive modal logics, CK and IK, which differ in their proof-theoretical properties. Developing satisfactory proof theories for these logics has been challenging, requiring augmentations to sequent systems. The document also notes that while IK logics have better model-theoretic properties, CK logics are better suited for lambda calculus interpretations. Overall, the document advocates for further work to develop a unified framework that can capture both families of logics along with categorical semantics.
This document summarizes Michael Kreisel's dissertation on the connection between Gabor frames for quasicrystals, the topology of the hull of a quasicrystal, and K-theory of an associated twisted groupoid algebra. The author constructs a finitely generated projective module over this algebra, where any multiwindow Gabor frame for the quasicrystal can be used to construct a projection representing this module in K-theory. As an application, results are obtained on the twisted version of Bellissard's gap labeling conjecture for quasicrystals.
What is Odd about Binary Parseval FramesMicah Bullock
This document examines the construction and properties of binary Parseval frames. It addresses when a binary Parseval frame has a complementary Parseval frame, and which binary symmetric idempotent matrices are Gram matrices of binary Parseval frames. Unlike real or complex Parseval frames, binary Parseval frames do not always have complements. A necessary condition for a binary Parseval frame to have a complement is that it contains at least one even vector. Certain symmetric idempotent matrices that are not Gram matrices of binary Parseval frames can exist if they only have even column vectors.
The document discusses the logic of informal proofs in mathematics. It makes 5 key claims:
1) Understanding informal proofs is important because most mathematical proofs are informal.
2) Informal proofs rely on both logical form and content.
3) Properly understanding informal proofs requires seeing logic as the study of inferential actions, where content plays a role.
4) This conception accommodates proofs involving actions on objects other than propositions.
5) It explains why mathematics relies on external representations, since representations can be manipulated.
The document argues this view connects logical questions about rigor to the cultural study of mathematical practices.
This document outlines the key points that will be covered in a presentation on dialectica categories as models of linear logic. It discusses four main theorems: 1) The original dialectica category DC is a model of intuitionistic linear logic without the exponential bang (!). 2) Adding a co-free monoidal comonad makes DC a model of full intuitionistic linear logic. 3) The simplified dialectica category GC is a model of classical linear logic without bang and question mark (?). 4) Adding a complicated monoidal comonad makes GC a model of full classical linear logic. The document provides brief motivations and outlines of the constructions and proofs involved in these main results. It also discusses some applications and areas for further development
The document discusses modalities in linear logic and dialectica categories. It motivates studying (co)monads and (co)algebras as constructive modalities in linear logic. It describes how the linear logic bang modality ! can be modeled as a comonad in dialectica categories. Specifically, in the dialectica category Dial2(C), ! is modeled as a cofree comonad. This provides a model of intuitionistic linear logic with both linear and non-linear connectives. In the simpler category DDial2(C), modeling the bang requires composing two comonads.
1. The document discusses the need for a positive account of informal proof in mathematics, as most mathematical proofs are informal. It argues against the view that informal proofs are recipes for formal derivations.
2. The document proposes that logic should be understood more broadly as the general study of inferential actions, as informal proofs often involve actions on mathematical objects beyond propositions. Examples of such actions include diagram manipulation in Euclidean geometry.
3. The document reviews work that may support this broader view of logic in informal proofs, such as studies of reasoning with diagrams in knot theory and using Cayley graphs to prove group theory results.
(1) The document discusses the concepts of emergence and reduction in physics, specifically arguing that they pose a false dichotomy as they are logically independent.
(2) It provides examples where emergence occurs alongside reduction, such as the emergence of classical behavior from quantum mechanics in certain limits, and the emergence of thermodynamic laws and properties from statistical mechanics.
(3) The key point is that reduction, viewed as deduction, allows for novelty through the choices made in taking limits, such as which symmetries to break or states to keep. So emergence and reduction can be compatible.
Jean-Yves Béziau the metalogical hexagon of opposition
The difference between truth and logical truth is a fundamental distinction of modern logic promoted by Wittgenstein. We show here how this distinction leads to a metalogical triangle of contrariety which can be naturally extended into a metalogical hexagon of oppositions, representing in a direct and simple
way the articulation of the six positions of a proposition vis-à-vis a theory. A particular case of this hexagon is a metalogical hexagon of propositions which can be interpreted in a modal way. We end by a semiotic hexagon emphasizing the value of true symbols, in particular the logic hexagon itself.
Talk given at Oxford Philosophy of Physics, LSE's Sigma Club, the Munich Center for Mathematical Philosophy, Carlo Rovelli's 60th birthday conference.
I construe dualities in physics as particular cases of theoretical equivalence. The question then naturally arises whether duality is compatible with emergence. For the the focus of emergence is on novelty rather than on equivalence.
In the first part of the talk, I review recent work dealing with this question. I exhibit two ways in which duality and equivalence can be made compatible, and I give an example of emergence in gauge/gravity dualities: dualities between a theory of gravity in (d+1) dimensions and a quantum field theory (QFT) in d dimensions.
In the second part of the talk, I present new results on the question whether diffeomorphisms in gravity theories emerge from QFTs. I critically assess the following idea, taken from the physics literature: given that (a) the QFT is not a diffeomorphism invariant theory, and that (b) there is a duality between the QFT and the gravity theory, are we entitled to (c) conclude that the diffeomorphisms of the gravity theory emerge from the QFT?
I argue that one must distinguish different kinds of diffeomorphisms: some diffeomorphisms are ‘invisible’ to the QFT: all of the QFT’s quantities are invariant under them, therefore the QFT does not ‘see’ them. But other diffeomorphisms are ‘visible’ to the QFT. The invisible diffeomorphisms prompt a ‘Bulk Argument’, in analogy with the Hole Argument. The analysis of emergence is different for these different kinds of diffeomorphisms, and I discuss the way in which we can speak of emergence of diffeomorphisms in gauge/gravity dualities.
Proof-Theoretic Semantics: Point-free meaninig of first-order systemsMarco Benini
This document summarizes a talk on providing a semantics for first-order logical theories using logical categories. The semantics interprets formulae as objects in a category and proofs as morphisms, without assuming elements exist. Quantifiers are interpreted using stars and costars. A logical category is a prelogical category where stars and costars exist to interpret all formulae. This semantics is sound and complete - a formula is true if a proof morphism exists. The semantics can interpret many other approaches and inconsistent theories have "trivial" models.
This document discusses the topics of paracompact spaces and compact spaces in topology. It provides background on the historical development of these concepts, from Bolzano's work in the 19th century on limit points of sequences to the formalization of compactness by Frechet in 1906. Paracompactness was introduced in 1944 as a generalization of compactness, replacing the requirement that every open cover have a finite subcover with the weaker condition of having a locally finite open refinement. The document aims to analyze paracompactness and compare it to compactness, exploring how compactness implies paracompactness.
The document discusses graph theory and algorithms for finding shortest paths in graphs. It introduces concepts like paths, cycles, and connectedness in graphs. It then describes several important algorithms for solving shortest path problems, including Dijkstra's algorithm, Bellman-Ford algorithm, Floyd-Warshall algorithm, and Ford's algorithm. Dijkstra's algorithm finds the shortest path from a source vertex to all other vertices in a graph and works by iteratively labeling vertices with their shortest path distances from the source.
The Gödel incompleteness can be modeled on the alleged incompleteness of quantum mechanics
Then the proved and even experimentally confirmed completeness of quantum mechanics can be reversely interpreted as a strategy of completeness as to the foundation of mathematics
Infinity is equivalent to a second and independent finiteness
Two independent Peano arithmetics as well as one single Hilbert space as an unification of geometry and arithmetic are sufficient to the self-foundation of mathematics
Quantum mechanics is inseparable from the foundation of mathematics and thus from set theory particularly
2014 10 rotman mecnhanism and climate models Ioan Muntean
This document discusses the potential transition from climate models to mechanistic explanations in climate science. It argues that understanding climate change through mechanisms could provide several advantages over the current model-based approach, such as introducing new explanations, integrating causal stories, and facilitating communication. However, some challenges are also noted, such as the holistic nature of climate science and concerns about reductionism. The document explores topics like feedback mechanisms, mapping models to mechanisms, and assessing climate models based on their representation of mechanisms. Overall, it presents arguments both for and against adopting a more mechanistic view of climate science.
How to connect with your life purpose...againTasha Scott
This article discusses how to reconnect with your life purpose when you've lost your passion for it. It suggests connecting with your motivations, approaching your work with an open mind like a beginner, mentoring others, asking for help, setting new goals, avoiding comparisons to others, taking breaks, pursuing hobbies, and continuous learning. The author is a personal development coach who provides tips on her website for staying true to your purpose.
The document discusses the relationship between science and metaphysics. It examines several approaches to this relationship, including viewing them on a continuum, finding similarities in their methods of modeling, and emphasizing their differences. The key point is that while science and metaphysics may use similar language and concepts of modality, possibility, and necessity, the document argues that the modalities used in scientific modeling are fundamentally different than those used in metaphysical modeling. Specifically, fictional entities and idealizations in metaphysics are constrained only by conceivability, while in science they are constrained by theoretical and empirical factors. Emphasizing these differences, rather than similarities, can advance both fields.
The document summarizes a talk on string geometry given by Johar M. Ashfaque at a postgraduate conference in complex geometry. The talk aimed to show how geometry has played a key role in string theory and highlight various connections. It covered topics like Calabi-Yau manifolds, orbifolds, heterotic strings, and how internal geometry in string compactification determines the 4D effective field theory.
A 3D Model to a Purpose-filled life is designed for high school and college students embarking on the bigger journey we call life. It provides practical advice beyond the classroom that's designed to remind students of the power of personal choice.
The document discusses Eastern perspectives on consciousness from various Hindu scriptures and philosophies.
It describes consciousness as being described in the Upanishads as Brahman or the universal self, and as being the power or source behind our senses and mind. The Kena Upanishad tells the story of gods realizing they have no power without Brahman.
The Mandukya Upanishad analyzes the three states of consciousness - waking, dreaming, and dreamless sleep - and relates them to the syllable sounds of "Om." It establishes a fourth state of consciousness, Turiya, as the highest reality beyond the other three states.
Overall the document presents consciousness in Eastern thought as being the fundamental eternal reality, the source of
String theory began as an attempt to understand nuclear forces but emerged as a promising theory of quantum gravity and particle physics. It posits that fundamental particles are vibrational states of tiny strings. The theory unexpectedly revealed a unique 11-dimensional framework underlying 10-dimensional superstring theories. While this provides a path to unification, challenges remain in explaining experimental observations, identifying the specific string vacuum that describes our universe, understanding dark energy and formulating a complete and compelling description of the theory.
String theory proposes that fundamental particles are not point-like but vibrations of tiny filaments called strings. It seeks to address problems in theoretical physics like quantizing gravity and explaining mass hierarchies. String theory requires 10 dimensions but extra dimensions are hypothesized to be compactified at the Planck scale. While early formulations included competing theories, M-theory incorporating an 11th dimension aims to unify them through membranes interacting in a multiverse. Observational evidence could come from detecting supersymmetric particles at the LHC or imprints of string physics on cosmological phenomena like gravitational waves or the CMB.
2012 10 phi ipfw science and metaphysicsIoan Muntean
This document discusses the relationship between metaphysics and science. It presents several views on this relationship, including:
1) A divorce between metaphysics and science, with no common ground between them.
2) A possible convergence or reconciliatory relationship where metaphysics can help interpret science and vice versa. However, full convergence is unlikely.
3) A "division of labor" view where metaphysics explores possibilities through reason and science explores actual reality through evidence. Metaphysics deals with modal truths rather than empirical truths.
The document also discusses similarities and differences between metaphysics and science, such as their use of modeling and concepts like causation. However, it argues the
Berlin Slides Dualities and Emergence of Space-Time and GravitySebastian De Haro
Holographic relations between theories have become an important theme in quantum gravity research. These relations entail that a theory without gravity is equivalent to a gravitational theory with an extra spatial dimension. The idea of holography was first proposed in 1993 by ‘t Hooft on the basis of his studies of evaporating black holes. Soon afterwards the holographic AdS/CFT duality was introduced, which since has been intensively studied in the string theory community and beyond. Recently, Verlinde has proposed that Newton’s law of gravitation can be related holographically to the ‘thermodynamics of information’ on screens. I discuss the last two scenarios, with special attention to the status of the holographic relation in them and to the question of whether they make gravity and spacetime emergent. I conclude that only Verlinde’s scheme instantiates emergence in a clear and uncontroversial way. I suggest that a reinterpretation of AdS/CFT may create room for the emergence of spacetime and gravity there as well.
The logic(s) of informal proofs (tyumen, western siberia 2019)Brendan Larvor
The document discusses the difference between formal mathematical proofs and actual mathematical practice. It notes that while a formal proof is an unbroken chain of logical inferences from axioms, in practice mathematicians use informal proofs that are sketches which could be routinely translated into formal proofs. It argues that many mathematical proofs involve actions on mathematical objects other than propositions, and that a full understanding of mathematical reasoning requires acknowledging the role of content and representations in inferences.
This document provides an overview of torus knots and links and discusses computing their bracket polynomial. It begins with background on knots and links, including their history, applications, and classifications. It then introduces knot polynomials and focuses on the bracket polynomial, describing how it is developed using skein relations and proofs of invariance under Reidemeister moves. The document examines properties of torus knots and links and describes computing the bracket polynomial for (n,2) torus links through finding a recurrence relation. It includes appendices with Maple code and tables of bracket polynomials.
1. The study of chaos analyzes nonlinear dynamical systems that are highly sensitive to initial conditions. While a universal definition of chaos is still lacking, mathematicians generally agree that chaos involves sensitive dependence on initial conditions, mixing, and dense periodic points.
2. This paper formulates a new approach to studying chaos in discrete dynamical systems based on concepts from inverse problems, set-valued mappings, graphical convergence theory, and topology. The author argues that order, chaos and complexity can be viewed as parts of a unified mathematical structure applying topological convergence theory to increasingly nonlinear mappings.
3. By applying concepts from spectral approximation theory and introducing "latent chaotic states", the author aims to develop a theory of chaos and interpret how nature
String theory is a theoretical framework that models particles as vibrating strings instead of point-like objects. It seeks to unite quantum mechanics and general relativity by incorporating gravity at small scales. In string theory, strings exist in 10 or 11 dimensions and vibrate in different ways. Their vibrational patterns determine properties like mass and charge, allowing strings to represent all known particles. String theory remains unproven, but efforts using machine learning may help explore its vast theoretical landscape.
Albert Einstein (2) Relativity Special And General TheoryKukuasu
This document provides instructions for classifying ebooks based on their file format and subject matter. It specifies that:
1) Ebooks should be in Adobe PDF or Tomeraider format, with txt files not considered ebooks.
2) The file name should include the classification in parenthesis - (ebook - File Format - Subject Matter).
3) The subject matter classification should be one of: Biography, Children, Fiction, Food, Games, Government, Health, Internet, Martial-Arts, Mathematics, Other, Programming, Reference, Religious, Science, Sci-Fi, Sex, or Software.
This standardization of ebook file names helps groups like Fink Crew
The architectural metaphor of foundations in mathematics is dead among mathematicians for several reasons:
1) Mathematics has become more specialized with the rise of abstract algebra, moving away from thinking of operations on elements to relations between subsets and homomorphisms.
2) Developments in logic and set theory brought "roots" and "branches" of mathematics together rather than viewing them as separate, undermining the tree analogy.
3) Mathematicians by the 1920s took for granted the use of set theory for basic definitions and reasoning rather than viewing it as providing foundations in an architectural sense.
The metaphor died sometime between the wars as mathematics ceased requiring foundations in the architectural sense due to its changing nature and methods becoming
This document summarizes Einstein's seminal work "Relativity: The Special and General Theory", published in 1916. It begins with a preface by Einstein explaining his goal to make the key ideas of relativity theory accessible to a broad scientific audience, despite the mathematical complexity. The work is divided into three parts, with Part I covering Einstein's Special Theory of Relativity and how it revolutionized concepts of space and time. Part II then introduces Einstein's General Theory of Relativity and how it geometrized gravity. The document provides summaries of each chapter to concisely outline Einstein's monumental theories that transformed modern physics.
Introduction to set theory by william a r weiss professormanrak
This chapter introduces a formal language for describing sets using variables, logical connectives, quantifiers, and the membership symbol. Formulas in this language are constructed recursively from atomic formulas using negation, conjunction, disjunction, implication, biconditional, universal quantification, and existential quantification. The key concepts of subformula and bound variable are also defined. This language will allow precise discussion of sets without ambiguities like those found in natural languages.
The document summarizes a talk on Dirac lattices and emergent Lorentz symmetry. It discusses how Lorentz symmetry could emerge at low energies from an underlying non-relativistic model, motivated by examples like graphene. It proposes studying a tight-binding Hamiltonian on a lattice that may admit a continuum limit with Dirac fermions. The goal is to understand if a microscopic theory could flow to existing particle models in the infrared regime.
Is Mass at Rest One and the Same? A Philosophical Comment: on the Quantum I...Vasil Penchev
The way, in which quantum information can unify quantum mechanics (and therefore the standard
model) and general relativity, is investigated. Quantum information is defined as the generalization
of the concept of information as to the choice among infinite sets of alternatives. Relevantly, the
axiom of choice is necessary in general. The unit of quantum information, a qubit is interpreted
as a relevant elementary choice among an infinite set of alternatives generalizing that of a bit.
The invariance to the axiom of choice shared by quantum mechanics is introduced: It constitutes
quantum information as the relation of any state unorderable in principle (e.g. any coherent quantum
state before measurement) and the same state already well-ordered (e.g. the well-ordered statistical
ensemble of the measurement of the quantum system at issue). This allows of equating the classical and
quantum time correspondingly as the well-ordering of any physical quantity or quantities and their
coherent superposition. That equating is interpretable as the isomorphism of Minkowski space and
Hilbert space. Quantum information is the structure interpretable in both ways and thus underlying
their unification. Its deformation is representable correspondingly as gravitation in the deformed
pseudo-Riemannian space of general relativity and the entanglement of two or more quantum
systems. The standard model studies a single quantum system and thus privileges a single reference
frame turning out to be inertial for the generalized symmetry [U(1)]X[SU(2)]X[SU(3)] “gauging” the
standard model. As the standard model refers to a single quantum system, it is necessarily linear
and thus the corresponding privileged reference frame is necessary inertial. The Higgs mechanism
U(1) → [U(1)]X[SU(2)] confirmed enough already experimentally describes exactly the choice of the
initial position of a privileged reference frame as the corresponding breaking of the symmetry. The
standard model defines ‘mass at rest’ linearly and absolutely, but general relativity non-linearly
and relatively. The “Big Bang” hypothesis is additional interpreting that position as that of the
“Big Bang”. It serves also in order to reconcile the linear standard model in the singularity of the
“Big Bang” with the observed nonlinearity of the further expansion of the universe described very
well by general relativity. Quantum information links the standard model and general relativity in
another way by mediation of entanglement. The linearity and absoluteness of the former and the
nonlinearity and relativeness of the latter can be considered as the relation of a whole and the same
whole divided into parts entangled in general.
Unlikely bedfellows or unholy alliance.pptxBrendan Larvor
Lakatos demonstrates the possibility of philosophical hybridism by combining influences from Hegel, Pólya and Popper in his philosophy of mathematics, which seems unlikely but points to the eclectic nature of the philosophy of mathematical practice. The talk will discuss the tensions and synergies in Lakatos’s thought from his intellectual influences and migration, and illustrate the benefits of philosophical hybridism, including a robustness criterion. It will also discuss prospects for collaboration among various projects under the philosophy of mathematical practices.
Gravity: Superstrings or Entropy? A Modest Proffer from an Amateur ScientistJohn47Wind
This essay evaluates the promise that superstring theory will culminate in a quantum theory of gravity that unifies all the forces of nature into one package. In particular, the proponents of superstring theory promise that it will show how all forces of nature are “unified” at high energies. The essay traces the history of string theory from its humble beginnings in the 1960s, to explain the scattering of sub-atomic particles, to its culmination as five different string theories that supposedly comprise a yet-to-be defined theory named M-theory. In contrast, this essay presents a simple theory of gravity based on entropy that is distributed throughout space. A surprising consequence of entropic gravity is that Newton’s constant, G, has been decreasing over the life of universe, which fulfills the unfulfilled promise made by string theorists. Moreover, this consequence can be tested experimentally, unlike string theory, which makes no testable predictions.
Gravity as entanglement, and entanglement as gravityVasil Penchev
1) The document discusses the relationship between gravity and quantum entanglement, exploring the possibility that they are equivalent or closely connected concepts.
2) It outlines an approach to interpret gravity in terms of a generalized quantum field theory that includes entanglement, which could explain why gravity cannot be quantized.
3) The key idea is that entanglement expressed "outside" of space-time points looks like gravity "inside", and vice versa, with gravity representing a smooth constraint on the quantum behavior of entities imposed by all others.
2. Motivations for this talk
I. Underdetermination
II. Unification and explanation
Do structures unify? Do they explain?
III. Fundamentalism
IV. Emergence of spacetime structures
In this talk I will focus especially on II-IV, but add:
Dualities
Does duality unveil a “deeper structure” beyond the two
theories? What is a structure?
2
3. Assumptions of my argument
A. “String theory” is a collection of mathematical
models, not a theory (or a collection of theories)
B. Dualities play a role in the structural interpretation
of string theory
C. Reality and structures are not scale invariant.
3
4. Prospective results
D. Dualities are not unificatory or explanatory (pace
Rickles)
E. Dualities unveil a deeper structure, with or without
a deeper theory.
F. Dualities act as corrective relations to string models.
They may predict and accommodate/integrate facts
about the dual model.
I take accommodation / integration as weaker than
unification and explanation.
4
5. A. String Theory as a quantum
gravity program
String theory:
Is a “particle physics” programme (cf. a “relativity”
programme )
Uses additional structures: supersymmetry, geometrical
objects (branes), unnatural fields (“the dilaton”)
It is mainly perturbative, although a non-perturbative
formulation is sought for
(French, Rickles 2006)
5
6. Structural realism and string theory
Quantum gravity is a natural framework to discuss structural realism (Rickles,
French Saatsi, 2006); (Rickles 2010, 2011, 2012).
a metaphysics of relations is suggested by quantum gravity (Smolin, Baez)
This relationalism is easily and best construed as a variety of structuralism
(French, Rickles 2006)
String theory is a “main contender” in the search for quantum gravity
Does it reveal relationism? Or structuralism?
String theory is a quantum field program
hence its benefits and sins : although it solves UV divergences, it is background
dependent
String theory is an ever-changing, paradigm-shifting, self-inventing “theory”
It constitutes a good playground for ESR
It is natural to investigate “a the structural interpretation of string theory”.
6
7. Structural realism and background
dependence
“in general, string theory, and other background-dependent
approaches, are […] examples of how not to go about
constructing a theory of quantum gravity” (Rickles French 2006)
background independence and structuralism are “well-matched
bedfellows”
Can we interpret string theory as a structural metaphysics even if
it is not (yet) background independent?
Alternatives:
talk about the promises of a background independent string theory
The concept of background independence needs more
philosophical work.
Dualities may play the central role
7
8. Spanked by the GR community
“What is very frustrating is that […] string theory does
not seem to fully incorporate the basic lesson of GR,
which is that space and time are dynamical rather than
fixed, and relational rather than absolute […] all that
happens is that some strings move against this fixed
background and interact with one another.” (Smolin
2001, 159)
Penrose, Stachel, Woit and others would agree.
8
9. String Theory and spacetime
String models depend on a background
Unlike other QG programs, in ST the structure of
spacetime is more complicated:
Dimensionality D>4
Exotic topologies
Compactification
The dynamics of spacetime is codified by the “dilaton”
field
The GR physicists would insist:
So what? What determines the structure of the
convoluted spacetime?
9
10. The naïve solution
Curved spacetime is reducible to a collection of
gravitons
Given the Witten-Weiberg (no-go result), gravitons
cannot be reduced to any known bosons,
gravitation is simply not “yet another quantum field
theory”
Therefore you need something like strings.
As gravitons are states of strings, the covariant part of
the M space in string theory is in itself dynamical.
10
11. Four interpretations
[1] A collection of theories in quantum gravity, all being aspects of
a more fundamental theory (“M-theory”) which is ultimately the
theory of everything (TOE) of our reality. Other theories in
physics can/will be reduced to the TOE.
[2] string theory is a model of different aspects of reality. Most
plausibly, string theory is a model of Hadrons.
[3] A collection of string models which are mathematical models
of strings and branes vibrating in various types of spaces, having
different symmetries and geometries.
[4] A collection of conjectures about the relations among the
string models (interpreted as in [3])
[5] A collection of conjectures about the relations between string
models (as in [3]) and other theories in physics: gauge theories,
gravitation, thermodynamics of black hole, information theory,
etc.
11
12. What is the perturbative
approach?
An idealization
As in “a collection of models” some based on this
idealization, some presumably not.
12
13. Five string models
There are five string models of interest in D=10
1. I: SUSY, open and closed strings, group symmetry SO(32)
2. IIA: SUSY, open and closed strings, non-chiral fermions. D-branes
are the boundaries of open strings
3. IIB: SUSY, open and closed strings, chiral fermions. D-branes are the
boundaries of open strings
4. HO: Heterotic model: SUSY, closed strings only, right moving strings
and left moving strings differ, symmetry group SO(32)
5. HE: Heterotic model: SUSY, as above, but symmetry group is E8xE8
Dualities:
1/4: I and HO
2/5: IIA and HE
Witten’s conjecture (1995): all string models are related to each other
by dualities.
13
14. B. Interpretation of string models
1 Empiricist: If this string model were true, what
physics would look like?
2. What are the realist commitments of these models?
I choose here 2.
14
15. Structural questions about string
models
Is string theory object-oriented?
If not, what plays the role of the structure?
What is fundamental? What is non-fundamental?
Is the structural interpretation better off than object
oriented interpretations?
They need to be addressed within each string model.
15
16. Object-oriented string realism
Strings are fundamental entities
They are objects, not structures
They have 2D features, not intrinsic properties as
particles
They have individuation and individuality
Their excitations are other particles (gravitons,
photons, some gluons etc.)
Therefore the individuation of particles depends on
the individuation of strings.
16
17. Against the OO string realism
“Acceptable in the 80s” perhaps
Now we are past the brane revolution
Branes are as fundamental as strings
Are branes objects?
No, they are structures
Yes, they are.
Strings are “‘intersections’ of branes” cf Cassirer: “electrons
are points of intersection”
17
18. D-branes
“We start with strings in a flat background and discover that a
massless closed string state corresponds to fluctuations of the
geometry. Here we found first a flat hyperplane, and then
discovered that a certain open string state corresponds to
fluctuations of its shape. We should not be surprised that the
hyperplane has become dynamical.”
“Thus the hyperplane is indeed a dynamical object, a Dirichlet
membrane, or D-brane for short. The p-dimensional D-brane,
from dualizing 25-p dimensions, is a Dp-brane. In this
terminology, the original U(n) open string theory contains n
D25-branes.”
A D25-brane fills space, so the string endpoint can be anywhere:
it just corresponds to an ordinary Chan-Paton factor.
Polchinski, vol I, 269
18
19. Dualities symmetries and their
interpretations
Dualities are present in logic, mathematics, physics
In general, they are not philosophically appealing
Should structural realists pay more attention to dualities?
Some dualities for philosophers:
E/M duality (Castellani 2009, Rickles 2011,2012)
Bosonization of fermions in 1D
s-channel/t-channel duality of the dual model of hadrons
S-dualities in string theory
AdS/CFT duality
My claim is that the structural realist should pay attention
to some of these.
19
20. Dualities
Dualities are not:
Approximations of a theory by another theory
Correspondences (as in “theory correspondence”)
Notation variants of the same theory
It is not (always) a symptom of a gauge freedom
But
There is representational ambiguity in dualities
“Dualities can highlight which features of our ontological
picture are not fundamental”. Rickles 2011
Can be related to the symmetries of a theory
Hence their importance to underdetermination and scientific
realism
20
21. A definition of dualities (Vafa)
A theory is characterized by a moduli space M of the
coupling constants
In this space we have several regions conventionally
designated as weak coupling and strong coupling.
A physical system can be represented in various places of
the moduli space with various observables:
Q[ M , Oα ]
Two physical systems Q and Q’ are dual if:
M ↔ M '; Oα ↔ Oα '
i.e. there is an isomorphism between their moduli spaces
and one between their observables
21
22. Triviality and non-triviality
Dualities can relate two completely different theories of the same
physical system
Or two completely different systems described by two different
theories
The classical and the quantum theory of a system
A classical system to a quantum system
A gauge theory to a gravitational theory
A string theory to another string theory
The weak coupling regime of a theory to its strong regime
Claims in this talk:
some dualities are not philosophically trivial,
Some dualities in string theory are important to the structural
interpretation of quantum gravity
22
23. E/M duality (Dirac)
A dual theory is obtained by a “duality
transformation”:
E → B; B → − E
It is a rotation duality in the complex vector field E+iB
In QED, this symmetry signals the existence of
magnetic monopoles (g). They attract each other with
a force of (2/137)^2 greater than the force between two
electrons
Duality explanation: If there are magnetic poles, the
electric charge is quantized, because: eg = 2n;
23
24. The E/M duality in particle
parlance
EM duality relates weak and strong coupling of the same theory.
In one regime, α small, the electron charge is weak, i.e. it does
not interact with its own field (fine structure constant).
Electrons barely radiate photons. The electric field is weak. They
are hard to excite (can we excite an electron?)
There are poles, but they have large fields around them, they are
heavy. The poles are hard to separate, spread out, composite,
solitonic excitations. Structurally they are very rich.
At α large, the poles are fundamental and charges are heavy and
rich.
Either the charge is elementary and the poles are composite, OR
the poles are elementary and charges are composite.
All depends on the coupling constant α.
Castellani 2009, Rickles 2011.
24
25. Bosonization of fermions in 1D
For some range of the coupling constant, bosons are
more useful as fundamental particle than fermions
For some range of constants, fermions are
fundamental.
By turning the couple constants, one becomes more
fundamental than the other.
Does this show a common structure?
In 1+D this does not happen
25
26. Duality symmetries
In string theory, the moduli space is very rich. Each model is
characterized by a “moduli space” formed by the constants of the
theory.
The string coupling constant gs
The topology of the manifold
Other fields in the background
Everything (?)
The flow of theories is important but more complicated than in QFT
In this moduli space a duality symmetry can relate:
The weak coupling region of T1 with the strong coupling region of T2
The weak coupling region of T to the weak coupling region of the same
T
Interchange elementary quanta with solitons (collective excitations)
Exchange what is fundamental with what is composite
26
27. S-duality, informally
gs is the coupling constant in string theory. But in string theory
gs is a field, has its equation, changes from place to place
A string can split into two strings. The probability if this process
is ≈ gs.
The D0-brane and “strings” can interchange the role of
fundamental entity.
When gs is small f-strings are fundamental, light, hard to split.
D0-branes or D-1 are complicated and heavy. Their excitations
are the particles (photons, gravitons)
When D0 branes are light, f-string are heavier
When gs=1 , f-strings and D-branes look the same.
And topology is part of the moduli space. We can change
dimensionality or topology as we walk in the moduli space.
See (Sen 2002) for details
27
28. T-dualities
T1 and T2 can be different (different symmetries,
gauge invariants, topologies), or can be the same
theory (self-duality)!
Weak Weak
T1 T2
28
29. A standard S-duality map
This is not a “self-duality”.
T1 and T2 are structurally different (different
symmetries, gauge invariants, topologies)
They can be string models or other models in QCD
etc.
Weak Weak
T1 T2
Strong
Strong
29
30. D. Dualities and unification
Rickles 2011: “the dualities point to the fact that the
five consistent superstring theories, that were believed
to be distinct entities, are better understood as
different perturbative expansions of some single,
deeper theory.” (aka M theory)
For Rickles, the five points in moduli space are
representations of a single M-theory.
This is the received view in the community.
But….
30
31. Dualities without unification
“the duality relationships between the points in moduli space
will hold independently of the existence of an M-theory” Rickles
2012
but
“in order to achieve a computable scheme for the whole of the
moduli space (including regions away from the distinguished
'perturbation-friendly' points) such an underlying theory is
required” Rickles 2011, my emphasis
My argument is that we do not need M-theory to see the deep
structure of the S-dualities
One on my assumptions is to analyze these as models, not as
theories
Conceptually I separate the discussion on dualities from the
discussion on unification
31
32. Non-perturbative string theory and
S-duality
If we knew how to relate the weak coupling to the
strong coupling we would relate the non-perturbative
physics to the perturbative physics.
In the ADS/CFT duality this is the path to a
background independent theory.
32
33. Dive in AdS/CFT duality
We start from a IIB theory (D=10, SUSY with N=4, open
and closed strings)
(Maldacena 1998) but esp (Klebanov 2002)
This theory has a 16 supersymmetric group, the smallest
algebra in D=10.
If Ncgs ≪ 1, the low coupling regime, closed strings live in
We take Nc parallel D3-branes close one to the other.
empty space and the open strings end on the D-branes and
describe excitations of the D-branes.
Open and closed strings are decoupled from each
other.
33
34. Strong coupling and the YM
When Ncgs ≫ 1 the gravitational effect of the D-branes
on the spacetime metric is important, leading to a
curved geometry and to a “black brane”.
But near the horizon the strings are redshifted and
have low energy.
Gauge theory exists and the physics on the D-branes is
nothing else than a gauge theory
The physics is now described by a Yang-Mills CFT with
gYM=4πgs
34
35. Maldacena’s duality conjecture
The 4D, N=4 SUSY SU(Nc) gauge theory (Yang Mills)
is dual to a IIB string theory with the AdS/CFT
boundary.
35
36. Current research (post 2003)
People try to falsify the AdS/CFT. No success yet
More opportunistically, others try to understand black
holes through the duality as hot gases of fermions
Others try to look for more realistic dualities:
dS/CFT
Dualities with no SUSY, but with holographic principle
(T. Banks).
Understand hadrons with the IIB theory (“the
boomerang kid”)
36
37. E. The structure in the AdS/CFT
1. Is the Yang-Mills CFT the hidden structure of a string IIB
theory (which has gravitation in it)?
2. Is string structure of IIB model the hidden structure of the
Yang-Mills CFT?
3. Are they both aspects of a hidden structure?
A. M theory
B. SUSY
C. Other hidden structural assumption
4. Or perhaps we deal here with a loopy dependence relation?
3. B, 4, 3.A., 2, 1.
Physicists believe 1.
In this order of preference
37
38. Explanation/unification/prediction
in AdS/CFT?
Explanation? I do not see it
Unification? Not directly, without the M-theory.
Prediction? Perhaps, if we relate it to the Higgs
mechanism
Computational advantages? Yes, definitely!
Is the holographic principle doing any
explanatory/unification/predictive work?
38
39. F. Emergence? No,
accommodation!
May solve the problem of emergence in this case
People believe spacetime emerges in AdS/CFT (Seiberg, Koch
Murugan)
Some believe the curved spacetime of general relativity is a
holographic emergent construct from a quantum gauge field
without gravity rather than a fundamental feature of reality.
Strong emergence
Any spacetime emerges from any gauge theory
Weak emergence:
A special type of spacetime (the IIB gravitation) emerges from a
special type of gauge theory (SUSY YM in D=4)
Witness we assume here that:
“If a theory does not have general covariance, then the theory lacks
an underlying spacetime”
39
40. Spacetime structuralism in
AdS/CFT
We ignore the bulk fapp.
We focus on the boundary
We achieve a sort of background independence from
the bulk
Not independence on the boundary.
We may be OO realist on the boundary but we do not
need to be OO realists in the bulk
40
41. The OSR answer
Weak dependence
A structure of spacetime depend on a non-spacetime
structure
I take the CFT YM structure as determined by SUSY.
AdS/CFT: The AdS covariance (therefore the graviton
field) depends on the gauge symmetries of CFT
There is SUSY in both!!!
41
42. Ex SUSY quodlibet sequitur
SUSY can be a great candidate for the deeper structure
underlying S-dualities and the AdS/CFT duality.
SUGR is also present in the string sector
This is a an argument from symmetry
There are dS/CFT dualities but no non-SUSY dualities.
SUSY is part of the CFT Yang-Mills story because it is
the limit of a IIB theory.
I am not pluralist about SUSY, but I am
pluralist/functionalist about spacetime (and
background independence)
42
43. But symmetry is not enough
In AdS/CFT we do not have a symmetry in the moduli
space.
It is not like a gauge orbifold in the moduli space
There is something else than symmetry here.
43
44. Back to realism?
Nothing look even slightly related to reality:
SUSY?
SUGR?
D=10?
Large NC?
BUT:
In string theory spacetime is in fact a field that can be
traded with strings and branes.
We can trade in NC and D=10 with other assumptions
Give up the OO string realism because all these are
mathematical models
44
45. Conclusion
Dive-in in dualities
Interpret them as a stay-in feature of QG
They entail a decent OSR interpretation
There is also some conventionalism/antirealism fronts
to fight on.
45