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Ian Durham

Saint Anselm College, Physics, Associate Professor

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I’m a mathematician and physicist whose research focus is on quantum information, quantum foundations, quantum gravity, the foundations of mathematics and physics, and whatever else happens to interest me at a given moment. Lately I have been focused on resource theory in quantum information, particularly from a relativistic quantum information standpoint. In terms of foundations, I am interested in the limits of physical knowledge, specifically where does physics "end" and philosophy "begin?" In relation to that, I've always been interested in the work of Arthur Eddington (my PhD was a study of his Fundamental Theory) and have recently become interested in some of Wheeler's ideas, and I've begun to delve into this stuff a bit more recently.
Phone: 603-222-4073
Address: Department of Physics
Saint Anselm College
100 Saint Anselm Drive, Box 1759
Manchester, NH 03102

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University of Salamanca

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Observatoire de Paris

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Shanghai Jiao Tong University

David Mattingly

University of New Hampshire

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Books by Ian Durham

The Biographical Encyclopedia of Astronomers

My contributions included: Autolycus J.J. Balmer George Birkhoff Vilhelm Bjerknes Niels Bohr Ger... more My contributions included:

Autolycus
J.J. Balmer
George Birkhoff
Vilhelm Bjerknes
Niels Bohr
Gerbert d'Aurillac
Robert Emden
Euctemon
Geminus
Hicetus
Theodor Kaluza
Nicolaus Kauffman
Joseph Larmor
J-D. Maraldi
B.E. Markarian
Metrodorus of Chios
Rudolph Minkowski
Henry Plummer
Posidonius
Simplicius of Cilicia
Johannes Stark
William of Saint-Cloud
Xenophanes of Colophon

Papers by Ian Durham

Measuring acceleration using the Purcell effect

Quantum

We show that a two-level atom resonantly coupled to one of the modes of a cavity field can be use... more We show that a two-level atom resonantly coupled to one of the modes of a cavity field can be used as a sensitive tool to measure the proper acceleration of a combined atom-cavity system. To achieve it we investigate the relation between the transition probability of a two-level atom placed within an ideal cavity and study how it is affected by the acceleration of the whole. We indicate how to choose the position of the atom as well as its characteristic frequency in order to maximize the sensitivity to acceleration.

Limitations on entropic Bell inequalities

The derivation of Bell inequalities in terms of quantum statistical (thermodynamic) entropies is ... more The derivation of Bell inequalities in terms of quantum statistical (thermodynamic) entropies is considered. Inequalities of the Wigner form are derived but shown to be extremely limiting in their applicability due to the nature of the density matrices involved. This also helps to identify a limitation in the Cerf-Adami inequalities.

Quantum Puzzles in the Metaworld of Heisenberg, Clauser, and Horne

This paper follows up on a recent pre-print (Durham [2005]) by first deriving a set theoretic rel... more This paper follows up on a recent pre-print (Durham [2005]) by first deriving a set theoretic relationship between the generalized uncertainty relations and the Clauser-Horne inequalities. The physical, metaphysical, and metamathematical implications and problems are then explored. The discussion builds on previous work by Pitowsky [1994] and suggests that there is a fundamental problem in quantum correlation that could potentially lead to a paradox. It leaves open the question of whether the problem is in experiment, theory, or phenomena. 1 Introduction 2 Preliminaries 3 A Meta Challenge 3.1 Metamathematics 3.2 Metaphysics 4 Implications and Interpretation 5 Conclusion and further suggestions

Entanglement and the second law

Aps Meeting Abstracts, Mar 1, 2007

The second law of thermodynamics is, in reality, a strong argument about the nature of probabilit... more The second law of thermodynamics is, in reality, a strong argument about the nature of probabilities. In essence, the same can be said of Bell&#39;s inequalities, of which thermodynamic variations have been found. The tantalizingly close nature of these two arguments has potentially profound implications for quantum theory and, in particular, practical quantum computing. This presentation explores this relationship and

Long-range spin-coupled interactions: a Gedankenexperiment on the nature of spin

What is intrinsic spin? It is at the heart of the quantum information revolution and yet it defie... more What is intrinsic spin? It is at the heart of the quantum information revolution and yet it defies many of the efforts to better understand it, even to the point of pushing particle physics beyond the Standard Model. Long assumed to require the relativistic theory of Dirac, in 1967 L'evy-Lablond demonstrated that this was not the case: it is not necessarily a relativistic effect. In this article, we apply the L'evy-Lablond model to a simple Gedankenexperiment that suggests the existence of a quasi-fundamental long-range spin-coupled interaction. Calculations of the eigenfunctions of a test particle and the coupling constant of the force gives insight into the behavior of the potential that gives rise to this interaction. For large separation distances the potential looks like a simple potential well while for very small separation distances it exhibits a more complex nature. This, in turn, sheds additional light on the nature of intrinsic spin and a suggests a path for future research.

A Historical Perspective on the Topology and Physics of Hyperspace

n 1 a … (2) : one of a group of properties whose number is necessary and sufficient to determine ... more n 1 a … (2) : one of a group of properties whose number is necessary and sufficient to determine uniquely each element of a system of usu. mathematical entities (as an aggregate of points in real or abstract space) <the surface of a sphere has two ~s>; also : a parameter or coordinate variable assigned to such a property <the three ~s of momentum> … 1

In search of continuity: thoughts of an epistemic empiricist

Eprint Arxiv 1106 1124, Jun 6, 2011

Is the universe digital or analog? In this essay I argue that both classical and quantum physics ... more Is the universe digital or analog? In this essay I argue that both classical and quantum physics include limits that prevent us from definitively answering that question. That quantum physics does so is no surprise. That classical physics does so is rather unexpected. In fact, I argue that classical physics is itself really nothing more than a convenient approximation. Either way, it turns out that our knowledge of the universe is discrete and so it is extraordinarily difficult, perhaps even impossible, to determine the underlying continuity of the universe itself.

Context Rich Consent Controlled Food Purchase Management

Bell's Theorem, Uncertainty, and Conditional Events

This article explores a relationship between the generalized form of Heisenberg's uncertainty rel... more This article explores a relationship between the generalized form of Heisenberg's uncertainty relations and Bell-type inequalities in the context of their associated algebras. I begin by exploring the algebraic and logical background for each, drawing parallels and a noticeable symmetry. In addition I describe a thought experiment linking the conceptual foundation of one to a mathematical representation of the other. Finally, I explore the requirements for a more inscrutable relationship between the two pointing out the tantalizing questions this suggestion raises as well as potential answers. The purpose of this article is to show that there is more to this relationship than meets the eye and suggests that a very general Bell-like theorem can be interpreted as a limiting case of the broader generalized uncertainty principle. 1 Introduction 2 Foundations 2.1 Matrix algebra, operators, and uncertainty 2.2 Boolean algebra and Bell's theorem 3 Can position and momentum satisfy a Bell-type inequality? 4 Symmetry…or not? 4.1 To commute or to not commute 4.2 Origins of observables in the commutation relation 5 Conclusion and further suggestions

Food Management Services

Quantum frameness for charge-parity-time inversion symmetry

ABSTRACT Physical laws are invariant under simultaneous charge-parity-time (CPT) inversion, which... more ABSTRACT Physical laws are invariant under simultaneous charge-parity-time (CPT) inversion, which is due to relativistic Lorentz covariance and the linearity of quantum mechanics. We show that CPT-superselection can be circumvented by employing a system that possesses CPT frameness, and we construct such resources in two cases: for massive spin-zero particles and for Dirac-spinors. In the case of spin-zero particles, we explicitly construct and quantify all resourceful pure states. Our approach is to treat CPT inversion unitarily by considering the aggregate action of the CPT transformation, rather than sequentially composing a unitary and two anti-unitary transformations, thereby overcoming a major drawback of circumventing time-inversion symmetry alone using an anti-unitary transformation [G. Gour, P. S. Turner and B. C. Sanders, J. Math. Phys. 50, 102105 (2009)]. We discuss an explicit example using pionic communication to overcome CPT superselection.

Unification and Emergence in Physics: the Problem of Articulation

Eprint Arxiv 1001 4304, Jan 24, 2010

What is physics? What are the limits of what physics can say about the world? In seeking ever-bro... more What is physics? What are the limits of what physics can say about the world? In seeking ever-broader theoretical `umbrellas' for physical phenomena, we are seeking unifying principles. Emergent phenomena have turned out to be some of the most difficult to explain, causing a `clash of umbrellas' so-to-speak, at the interface between the quantum and classical domains. This essay explores the role of articulation in this particularly vexing problem and ultimately addresses the question of whether the language and mathematics we use to describe the universe is sufficient in its present form and application.

Quantum mechanics and the nature of the second law of thermodynamics

APS Bulletin of the American Physical Society. 2008 APS March Meeting Volume 53, Number 2. Monday... more

Quantum channel convexity and Birkhoff's theorem

Aps Meeting Abstracts, Mar 1, 2010

Birkhoff&#x27;s Theorem states that doubly stochastic matrices are convex combinations of per... more

A category theoretic approach to asymptotic quantum channel approximation and Birkhoff's Theorem

Birkhoff's Theorem states that doubly stochastic matrices are convex combinations of permutation ... more Birkhoff's Theorem states that doubly stochastic matrices are convex combinations of permutation matrices. Quantum mechanically these matrices are doubly stochastic channels, i.e. they are completely positive maps preserving both the trace and the identity. We expect these channels to be convex combinations of unitary channels and yet it is known that some channels cannot be written that way. Recent work has suggested that n copies of a single channel might approximate a mixture (convex combination) of unitaries. In this paper we show that n(n + 1)/2 copies of a symmetric unital quantum channel may be arbitrarily-well approximated by a mixture (convex combination) of unitarily implemented channels. In addition, we prove that any extremal properties of a channel are preserved over n (and thus n(n + 1)/2) copies. The result has the potential to be completely generalized to include non-symmetric channels. I. INTRODUCTION AND BACKGROUND There is a famous theorem attributed to Garrett Birkhoff that states that doubly stochastic matrices are convex combinations of permutation matrices. In the quantum context, doubly stochastic matrices become doubly stochastic channels, i.e. completely positive maps preserving both the trace and the identity. Quantum mechanically we understand the permutations to be the unitarily implemented channels. That is, we expect doubly stochastic quantum channels to be convex combinations of unitary channels. Unfortunately it is wellknown that some quantum channels cannot be written that way [1, 2]. Recent work has suggested that n copies of a single channel might approximate a mixture (convex combina-*

Distance Learning Programs to Inspire Students in the Sciences

Inspiring students to enter the sciences, in particular more traditional hard sciences and certai... more Inspiring students to enter the sciences, in particular more traditional hard sciences and certain engineering disciplines, has become a greater challenge in the days of high tech computer jobs that pay far higher wages. In addition maintaining student interest in the classroom has also become more difficult with the increasing complexity and sophistication of home computer technology. Often students have

Static environments in open quantum systems

An open quantum system is one that interacts in some way with another quantum system external to ... more

Ordering relations for quantum states

Bulletin of the American Physical Society, Mar 4, 2015

Cosmonumerology, Cosmophysics, and the Large Numbers Hypothesis: British Cosmology in the 1930s

A number of unorthodox cosmological models were developed in the 1930s, many by British theoretic... more A number of unorthodox cosmological models were developed in the 1930s, many by British theoreticians. Three of the most notable of these theories included Eddington's cosmonumerology, Milne's cosmophysics, and Dirac's large numbers hypothesis (LNH). Dirac's LNH was based partly on the other two and it has been argued that modern steady-state theories are based partly on Milne's cosmophysics. But what influenced Eddington and Milne? Both were products of the late Victorian education system in Britain and could conceivably have been influenced by Victorian thought which, in addition to its strict (though technically unoffical) social caste system, had a flair for the unusual. Victorianism was filled with a fascination for the occult and the supernatural, and science was not insulated from this trend (witness the Henry Slade trial in 1877). It is conceivable that the normally strict mentality of the scientific process in the minds of Eddington and Milne was affecte...

The Biographical Encyclopedia of Astronomers

My contributions included: Autolycus J.J. Balmer George Birkhoff Vilhelm Bjerknes Niels Bohr Ger... more My contributions included:

Autolycus
J.J. Balmer
George Birkhoff
Vilhelm Bjerknes
Niels Bohr
Gerbert d'Aurillac
Robert Emden
Euctemon
Geminus
Hicetus
Theodor Kaluza
Nicolaus Kauffman
Joseph Larmor
J-D. Maraldi
B.E. Markarian
Metrodorus of Chios
Rudolph Minkowski
Henry Plummer
Posidonius
Simplicius of Cilicia
Johannes Stark
William of Saint-Cloud
Xenophanes of Colophon

Measuring acceleration using the Purcell effect

Quantum

We show that a two-level atom resonantly coupled to one of the modes of a cavity field can be use... more We show that a two-level atom resonantly coupled to one of the modes of a cavity field can be used as a sensitive tool to measure the proper acceleration of a combined atom-cavity system. To achieve it we investigate the relation between the transition probability of a two-level atom placed within an ideal cavity and study how it is affected by the acceleration of the whole. We indicate how to choose the position of the atom as well as its characteristic frequency in order to maximize the sensitivity to acceleration.

Limitations on entropic Bell inequalities

The derivation of Bell inequalities in terms of quantum statistical (thermodynamic) entropies is ... more The derivation of Bell inequalities in terms of quantum statistical (thermodynamic) entropies is considered. Inequalities of the Wigner form are derived but shown to be extremely limiting in their applicability due to the nature of the density matrices involved. This also helps to identify a limitation in the Cerf-Adami inequalities.

Quantum Puzzles in the Metaworld of Heisenberg, Clauser, and Horne

This paper follows up on a recent pre-print (Durham [2005]) by first deriving a set theoretic rel... more This paper follows up on a recent pre-print (Durham [2005]) by first deriving a set theoretic relationship between the generalized uncertainty relations and the Clauser-Horne inequalities. The physical, metaphysical, and metamathematical implications and problems are then explored. The discussion builds on previous work by Pitowsky [1994] and suggests that there is a fundamental problem in quantum correlation that could potentially lead to a paradox. It leaves open the question of whether the problem is in experiment, theory, or phenomena. 1 Introduction 2 Preliminaries 3 A Meta Challenge 3.1 Metamathematics 3.2 Metaphysics 4 Implications and Interpretation 5 Conclusion and further suggestions

Entanglement and the second law

Aps Meeting Abstracts, Mar 1, 2007

The second law of thermodynamics is, in reality, a strong argument about the nature of probabilit... more The second law of thermodynamics is, in reality, a strong argument about the nature of probabilities. In essence, the same can be said of Bell&#39;s inequalities, of which thermodynamic variations have been found. The tantalizingly close nature of these two arguments has potentially profound implications for quantum theory and, in particular, practical quantum computing. This presentation explores this relationship and

Long-range spin-coupled interactions: a Gedankenexperiment on the nature of spin

What is intrinsic spin? It is at the heart of the quantum information revolution and yet it defie... more What is intrinsic spin? It is at the heart of the quantum information revolution and yet it defies many of the efforts to better understand it, even to the point of pushing particle physics beyond the Standard Model. Long assumed to require the relativistic theory of Dirac, in 1967 L'evy-Lablond demonstrated that this was not the case: it is not necessarily a relativistic effect. In this article, we apply the L'evy-Lablond model to a simple Gedankenexperiment that suggests the existence of a quasi-fundamental long-range spin-coupled interaction. Calculations of the eigenfunctions of a test particle and the coupling constant of the force gives insight into the behavior of the potential that gives rise to this interaction. For large separation distances the potential looks like a simple potential well while for very small separation distances it exhibits a more complex nature. This, in turn, sheds additional light on the nature of intrinsic spin and a suggests a path for future research.

A Historical Perspective on the Topology and Physics of Hyperspace

n 1 a … (2) : one of a group of properties whose number is necessary and sufficient to determine ... more n 1 a … (2) : one of a group of properties whose number is necessary and sufficient to determine uniquely each element of a system of usu. mathematical entities (as an aggregate of points in real or abstract space) <the surface of a sphere has two ~s>; also : a parameter or coordinate variable assigned to such a property <the three ~s of momentum> … 1

In search of continuity: thoughts of an epistemic empiricist

Eprint Arxiv 1106 1124, Jun 6, 2011

Is the universe digital or analog? In this essay I argue that both classical and quantum physics ... more Is the universe digital or analog? In this essay I argue that both classical and quantum physics include limits that prevent us from definitively answering that question. That quantum physics does so is no surprise. That classical physics does so is rather unexpected. In fact, I argue that classical physics is itself really nothing more than a convenient approximation. Either way, it turns out that our knowledge of the universe is discrete and so it is extraordinarily difficult, perhaps even impossible, to determine the underlying continuity of the universe itself.

Context Rich Consent Controlled Food Purchase Management

Bell's Theorem, Uncertainty, and Conditional Events

This article explores a relationship between the generalized form of Heisenberg's uncertainty rel... more This article explores a relationship between the generalized form of Heisenberg's uncertainty relations and Bell-type inequalities in the context of their associated algebras. I begin by exploring the algebraic and logical background for each, drawing parallels and a noticeable symmetry. In addition I describe a thought experiment linking the conceptual foundation of one to a mathematical representation of the other. Finally, I explore the requirements for a more inscrutable relationship between the two pointing out the tantalizing questions this suggestion raises as well as potential answers. The purpose of this article is to show that there is more to this relationship than meets the eye and suggests that a very general Bell-like theorem can be interpreted as a limiting case of the broader generalized uncertainty principle. 1 Introduction 2 Foundations 2.1 Matrix algebra, operators, and uncertainty 2.2 Boolean algebra and Bell's theorem 3 Can position and momentum satisfy a Bell-type inequality? 4 Symmetry…or not? 4.1 To commute or to not commute 4.2 Origins of observables in the commutation relation 5 Conclusion and further suggestions

Food Management Services

Quantum frameness for charge-parity-time inversion symmetry

ABSTRACT Physical laws are invariant under simultaneous charge-parity-time (CPT) inversion, which... more ABSTRACT Physical laws are invariant under simultaneous charge-parity-time (CPT) inversion, which is due to relativistic Lorentz covariance and the linearity of quantum mechanics. We show that CPT-superselection can be circumvented by employing a system that possesses CPT frameness, and we construct such resources in two cases: for massive spin-zero particles and for Dirac-spinors. In the case of spin-zero particles, we explicitly construct and quantify all resourceful pure states. Our approach is to treat CPT inversion unitarily by considering the aggregate action of the CPT transformation, rather than sequentially composing a unitary and two anti-unitary transformations, thereby overcoming a major drawback of circumventing time-inversion symmetry alone using an anti-unitary transformation [G. Gour, P. S. Turner and B. C. Sanders, J. Math. Phys. 50, 102105 (2009)]. We discuss an explicit example using pionic communication to overcome CPT superselection.

Unification and Emergence in Physics: the Problem of Articulation

Eprint Arxiv 1001 4304, Jan 24, 2010

What is physics? What are the limits of what physics can say about the world? In seeking ever-bro... more What is physics? What are the limits of what physics can say about the world? In seeking ever-broader theoretical `umbrellas' for physical phenomena, we are seeking unifying principles. Emergent phenomena have turned out to be some of the most difficult to explain, causing a `clash of umbrellas' so-to-speak, at the interface between the quantum and classical domains. This essay explores the role of articulation in this particularly vexing problem and ultimately addresses the question of whether the language and mathematics we use to describe the universe is sufficient in its present form and application.

Quantum mechanics and the nature of the second law of thermodynamics

APS Bulletin of the American Physical Society. 2008 APS March Meeting Volume 53, Number 2. Monday... more

Quantum channel convexity and Birkhoff's theorem

Aps Meeting Abstracts, Mar 1, 2010

Birkhoff&#x27;s Theorem states that doubly stochastic matrices are convex combinations of per... more

A category theoretic approach to asymptotic quantum channel approximation and Birkhoff's Theorem

Birkhoff's Theorem states that doubly stochastic matrices are convex combinations of permutation ... more Birkhoff's Theorem states that doubly stochastic matrices are convex combinations of permutation matrices. Quantum mechanically these matrices are doubly stochastic channels, i.e. they are completely positive maps preserving both the trace and the identity. We expect these channels to be convex combinations of unitary channels and yet it is known that some channels cannot be written that way. Recent work has suggested that n copies of a single channel might approximate a mixture (convex combination) of unitaries. In this paper we show that n(n + 1)/2 copies of a symmetric unital quantum channel may be arbitrarily-well approximated by a mixture (convex combination) of unitarily implemented channels. In addition, we prove that any extremal properties of a channel are preserved over n (and thus n(n + 1)/2) copies. The result has the potential to be completely generalized to include non-symmetric channels. I. INTRODUCTION AND BACKGROUND There is a famous theorem attributed to Garrett Birkhoff that states that doubly stochastic matrices are convex combinations of permutation matrices. In the quantum context, doubly stochastic matrices become doubly stochastic channels, i.e. completely positive maps preserving both the trace and the identity. Quantum mechanically we understand the permutations to be the unitarily implemented channels. That is, we expect doubly stochastic quantum channels to be convex combinations of unitary channels. Unfortunately it is wellknown that some quantum channels cannot be written that way [1, 2]. Recent work has suggested that n copies of a single channel might approximate a mixture (convex combina-*

Distance Learning Programs to Inspire Students in the Sciences

Inspiring students to enter the sciences, in particular more traditional hard sciences and certai... more Inspiring students to enter the sciences, in particular more traditional hard sciences and certain engineering disciplines, has become a greater challenge in the days of high tech computer jobs that pay far higher wages. In addition maintaining student interest in the classroom has also become more difficult with the increasing complexity and sophistication of home computer technology. Often students have

Static environments in open quantum systems

An open quantum system is one that interacts in some way with another quantum system external to ... more

Ordering relations for quantum states

Bulletin of the American Physical Society, Mar 4, 2015

Cosmonumerology, Cosmophysics, and the Large Numbers Hypothesis: British Cosmology in the 1930s

A number of unorthodox cosmological models were developed in the 1930s, many by British theoretic... more A number of unorthodox cosmological models were developed in the 1930s, many by British theoreticians. Three of the most notable of these theories included Eddington's cosmonumerology, Milne's cosmophysics, and Dirac's large numbers hypothesis (LNH). Dirac's LNH was based partly on the other two and it has been argued that modern steady-state theories are based partly on Milne's cosmophysics. But what influenced Eddington and Milne? Both were products of the late Victorian education system in Britain and could conceivably have been influenced by Victorian thought which, in addition to its strict (though technically unoffical) social caste system, had a flair for the unusual. Victorianism was filled with a fascination for the occult and the supernatural, and science was not insulated from this trend (witness the Henry Slade trial in 1877). It is conceivable that the normally strict mentality of the scientific process in the minds of Eddington and Milne was affecte...

Numerology and the cosmos: alternative cosmologies in 1930s Britain