Fotini Markopoulou-Kalamara
Encyclopedia
Fotini G. Markopoulou-Kalamara (Greek
: Φωτεινή Μαρκοπούλου-Καλαμαρά; born April 3, 1971) is a Greek
theoretical physicist interested in foundational mathematics
and quantum mechanics
. She is a faculty member at Perimeter Institute for Theoretical Physics
and is an adjunct professor at the University of Waterloo
.
Markopoulou received her Ph.D.
from Imperial College London
in 1998 and held postdoctoral positions at the Albert Einstein Institute, Imperial College, and Penn State University. She shared First Prize in the Young Researchers competition at the Ultimate Reality Symposium in Princeton
, New Jersey
.
She has been influenced by researchers such as Christopher Isham
who call attention to the unstated assumption in most modern physics that physical properties are most naturally calibrated by a real-number continuum. She, and others, attempt to make explicit some of the implicit mathematical assumptions underpinning modern theoretical physics and cosmology.
In her interdisciplinary paper "The Internal Description of a Causal Set: What the Universe Looks Like from the Inside", Markopoulou instantiates some abstract terms from mathematical category theory
to develop straightforward models of space-time. It proposes simple quantum models of space-time based on category-theoretic notions of a topos
and its subobject classifier
(which has a Heyting algebra
structure, but not necessarily a Boolean algebra structure).
For example, hard-to-picture category-theoretic "presheaves" from topos theory become easy-to-picture "evolving (or varying) sets" in her discussions of quantum spacetime
. The diagrams in Markopoulou's papers (including hand-drawn diagrams in one of the earlier versions of "The Internal Description of a Causal Set") are straightforward presentations of possible models of space-time. They are intended as meaningful and provocative, not just for specialists but also for newcomers.
In May 2006, Markopoulou published a paper with Lee Smolin
that further popularized this Causal Dynamical Triangulation (CDT) Theory by explaining time slicing of the Ambjorn-Loll CDT model as result of gauge fixing. Their approach relaxed the definition of the Ambjorn-Loll CDT model in 1 + 1 dimensions to allow for a varying lapse.
In 2008, Markopoulou, Tomasz Konopka and Simone Severini initiated the study of a new background independent model of evolutionary space called quantum graphity.
In the quantum graphity model, points in spacetime are represented by nodes on a graph connected by links that can be on or off. This indicates whether or not the two points are directly connected as if they are next to each other in spacetime. When they are on the links have additional state variables which are used to define the random dynamics of the graph under the influence of quantum fluctuations and temperature. At high temperature the graph is in Phase I where all the points are randomly connected to each other and no concept of spacetime as we know it exists. As the temperature drops and the graph cools, it is conjectured to undergo a phase transition to a Phase II where spacetime forms. It will then look like a spacetime manifold on large scales with only near-neighbour points being connected in the graph. The hypothesis of quantum graphity is that this geometrogenesis models the condensation of spacetime in the big bang. Recently a second model, related to quantum gravity, has been published.
Greek language
Greek is an independent branch of the Indo-European family of languages. Native to the southern Balkans, it has the longest documented history of any Indo-European language, spanning 34 centuries of written records. Its writing system has been the Greek alphabet for the majority of its history;...
: Φωτεινή Μαρκοπούλου-Καλαμαρά; born April 3, 1971) is a Greek
Greece
Greece , officially the Hellenic Republic , and historically Hellas or the Republic of Greece in English, is a country in southeastern Europe....
theoretical physicist interested in foundational mathematics
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
and quantum mechanics
Quantum mechanics
Quantum mechanics, also known as quantum physics or quantum theory, is a branch of physics providing a mathematical description of much of the dual particle-like and wave-like behavior and interactions of energy and matter. It departs from classical mechanics primarily at the atomic and subatomic...
. She is a faculty member at Perimeter Institute for Theoretical Physics
Perimeter Institute for Theoretical Physics
Perimeter Institute for Theoretical Physics is an independent, resident-based research institute devoted to foundational issues in theoretical physics located in Waterloo, Ontario, Canada. Perimeter Institute was founded in 1999 by Mike Lazaridis...
and is an adjunct professor at the University of Waterloo
University of Waterloo
The University of Waterloo is a comprehensive public university in the city of Waterloo, Ontario, Canada. The school was founded in 1957 by Drs. Gerry Hagey and Ira G. Needles, and has since grown to an institution of more than 30,000 students, faculty, and staff...
.
Markopoulou received her Ph.D.
Ph.D.
A Ph.D. is a Doctor of Philosophy, an academic degree.Ph.D. may also refer to:* Ph.D. , a 1980s British group*Piled Higher and Deeper, a web comic strip*PhD: Phantasy Degree, a Korean comic series* PhD Docbook renderer, an XML renderer...
from Imperial College London
Imperial College London
Imperial College London is a public research university located in London, United Kingdom, specialising in science, engineering, business and medicine...
in 1998 and held postdoctoral positions at the Albert Einstein Institute, Imperial College, and Penn State University. She shared First Prize in the Young Researchers competition at the Ultimate Reality Symposium in Princeton
Princeton, New Jersey
Princeton is a community located in Mercer County, New Jersey, United States. It is best known as the location of Princeton University, which has been sited in the community since 1756...
, New Jersey
New Jersey
New Jersey is a state in the Northeastern and Middle Atlantic regions of the United States. , its population was 8,791,894. It is bordered on the north and east by the state of New York, on the southeast and south by the Atlantic Ocean, on the west by Pennsylvania and on the southwest by Delaware...
.
She has been influenced by researchers such as Christopher Isham
Christopher Isham
Christopher Isham is a theoretical physicist at Imperial College London. His main research interests are quantum gravity and foundational studies in quantum theory. He was the inventor of an approach to temporal quantum logic called the HPO formalism, and has worked on loop quantum gravity and...
who call attention to the unstated assumption in most modern physics that physical properties are most naturally calibrated by a real-number continuum. She, and others, attempt to make explicit some of the implicit mathematical assumptions underpinning modern theoretical physics and cosmology.
In her interdisciplinary paper "The Internal Description of a Causal Set: What the Universe Looks Like from the Inside", Markopoulou instantiates some abstract terms from mathematical category theory
Category theory
Category theory is an area of study in mathematics that examines in an abstract way the properties of particular mathematical concepts, by formalising them as collections of objects and arrows , where these collections satisfy certain basic conditions...
to develop straightforward models of space-time. It proposes simple quantum models of space-time based on category-theoretic notions of a topos
Topos
In mathematics, a topos is a type of category that behaves like the category of sheaves of sets on a topological space...
and its subobject classifier
Subobject classifier
In category theory, a subobject classifier is a special object Ω of a category; intuitively, the subobjects of an object X correspond to the morphisms from X to Ω. As the name suggests, what a subobject classifier does is to identify/classify subobjects of a given object according to which elements...
(which has a Heyting algebra
Heyting algebra
In mathematics, a Heyting algebra, named after Arend Heyting, is a bounded lattice equipped with a binary operation a→b of implication such that ∧a ≤ b, and moreover a→b is the greatest such in the sense that if c∧a ≤ b then c ≤ a→b...
structure, but not necessarily a Boolean algebra structure).
For example, hard-to-picture category-theoretic "presheaves" from topos theory become easy-to-picture "evolving (or varying) sets" in her discussions of quantum spacetime
Quantum spacetime
In mathematical physics, the concept of quantum spacetime is a generalization of the usual concept of spacetime in which some variables that ordinarily commute are assumed not to commute and form a different Lie algebra...
. The diagrams in Markopoulou's papers (including hand-drawn diagrams in one of the earlier versions of "The Internal Description of a Causal Set") are straightforward presentations of possible models of space-time. They are intended as meaningful and provocative, not just for specialists but also for newcomers.
In May 2006, Markopoulou published a paper with Lee Smolin
Lee Smolin
Lee Smolin is an American theoretical physicist, a researcher at the Perimeter Institute for Theoretical Physics, and an adjunct professor of physics at the University of Waterloo. He is married to Dina Graser, a communications lawyer in Toronto. His brother is David M...
that further popularized this Causal Dynamical Triangulation (CDT) Theory by explaining time slicing of the Ambjorn-Loll CDT model as result of gauge fixing. Their approach relaxed the definition of the Ambjorn-Loll CDT model in 1 + 1 dimensions to allow for a varying lapse.
In 2008, Markopoulou, Tomasz Konopka and Simone Severini initiated the study of a new background independent model of evolutionary space called quantum graphity.
In the quantum graphity model, points in spacetime are represented by nodes on a graph connected by links that can be on or off. This indicates whether or not the two points are directly connected as if they are next to each other in spacetime. When they are on the links have additional state variables which are used to define the random dynamics of the graph under the influence of quantum fluctuations and temperature. At high temperature the graph is in Phase I where all the points are randomly connected to each other and no concept of spacetime as we know it exists. As the temperature drops and the graph cools, it is conjectured to undergo a phase transition to a Phase II where spacetime forms. It will then look like a spacetime manifold on large scales with only near-neighbour points being connected in the graph. The hypothesis of quantum graphity is that this geometrogenesis models the condensation of spacetime in the big bang. Recently a second model, related to quantum gravity, has been published.
External links
- Fotini Markopoulou, The Internal Description of a Causal Set: What the Universe Looks Like from the Inside (1999)
- Related seminar (1998)
- Biography at the Perimeter Institute
- Profile in Scientific AmericanScientific AmericanScientific American is a popular science magazine. It is notable for its long history of presenting science monthly to an educated but not necessarily scientific public, through its careful attention to the clarity of its text as well as the quality of its specially commissioned color graphics...
(2002) - Creating Spacetime - a lecture presented by Fotini Markopoulou at the Quantum to Cosmos festival.