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**Trick or Truth: the Mysterious Connection Between Physics and Mathematics**

*Contest Partners: Nanotronics Imaging, The Peter and Patricia Gruber Foundation, and The John Templeton Foundation*

Media Partner: Scientific American

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**How Should Humanity Steer the Future?**

*January 9, 2014 - August 31, 2014*

*Contest Partners: Jaan Tallinn, The Peter and Patricia Gruber Foundation, The John Templeton Foundation, and Scientific American*

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**It From Bit or Bit From It**

*March 25 - June 28, 2013*

*Contest Partners: The Gruber Foundation, J. Templeton Foundation, and Scientific American*

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**Questioning the Foundations**

Which of Our Basic Physical Assumptions Are Wrong?

*May 24 - August 31, 2012*

*Contest Partners: The Peter and Patricia Gruber Foundation, SubMeta, and Scientific American*

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**Is Reality Digital or Analog?**

*November 2010 - February 2011*

*Contest Partners: The Peter and Patricia Gruber Foundation and Scientific American*

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**What's Ultimately Possible in Physics?**

*May - October 2009*

*Contest Partners: Astrid and Bruce McWilliams*

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**The Nature of Time**

*August - December 2008*

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Previous Contests

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Which of Our Basic Physical Assumptions Are Wrong?

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FQXi ESSAY CONTEST

September 30, 2016

2008

First Juried Prize

The Nature of Time

By Julian Barbour

By Julian Barbour

Essay Abstract

A review of some basic facts of classical dynamics shows that time, or precisely duration, is redundant as a fundamental concept. Duration and the behaviour of clocks emerge from a timeless law that governs change.

Author Bio

After completing a PhD in theoretical physics, I became an independent researcher. I wished to study fundamental issues and avoid the publish-or-perish syndrome. For forty years I have worked on the nature of time and motion and have published numerous papers (details on my website platonia.com). I have written two books: The Discovery of Dynamics and The End of Time. I was also the joint editor of the conference proceedings Mach's Principle: From Newton's Bucket to Quantum Gravity. I have recently been made a Visiting Professor in Physics at the University of Oxford.

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A review of some basic facts of classical dynamics shows that time, or precisely duration, is redundant as a fundamental concept. Duration and the behaviour of clocks emerge from a timeless law that governs change.

Author Bio

After completing a PhD in theoretical physics, I became an independent researcher. I wished to study fundamental issues and avoid the publish-or-perish syndrome. For forty years I have worked on the nature of time and motion and have published numerous papers (details on my website platonia.com). I have written two books: The Discovery of Dynamics and The End of Time. I was also the joint editor of the conference proceedings Mach's Principle: From Newton's Bucket to Quantum Gravity. I have recently been made a Visiting Professor in Physics at the University of Oxford.

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Second Juried Prizes

Does Time Exist in Quantum Gravity?

By Claus Kiefer

By Claus Kiefer

Essay Abstract

Time is absolute in standard quantum theory and dynamical in general relativity. The combination of both theories into a theory of quantum gravity leads therefore to a 'problem of time'. In my essay I shall investigate those consequences for the concept of time that may be drawn without a detailed knowledge of quantum gravity. The only assumptions are the experimentally supported universality of the linear structure of quantum theory and the recovery of general relativity in the classical limit. Among the consequences are the fundamental timelessness of quantum gravity, the approximate nature of a semiclassical time, and the correlation of entropy with the size of the Universe.

Author Bio

CLAUS KIEFER is a professor of theoretical physics at the University of Cologne, Germany. He has earned his PhD from Heidelberg University in 1988. He has held positions at the Universities of Heidelberg, Zurich, and Freiburg, and was an invited visitor to the Universities of Alberta, Bern, Cambridge, Montpellier, and others. His main interests are quantum gravity, cosmology, black holes, and the foundations of quantum theory. He has published several books including the monograph "Quantum Gravity" (second edition: Oxford 2007). He is a member of The Foundational Questions Institute since 2006.

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Time is absolute in standard quantum theory and dynamical in general relativity. The combination of both theories into a theory of quantum gravity leads therefore to a 'problem of time'. In my essay I shall investigate those consequences for the concept of time that may be drawn without a detailed knowledge of quantum gravity. The only assumptions are the experimentally supported universality of the linear structure of quantum theory and the recovery of general relativity in the classical limit. Among the consequences are the fundamental timelessness of quantum gravity, the approximate nature of a semiclassical time, and the correlation of entropy with the size of the Universe.

Author Bio

CLAUS KIEFER is a professor of theoretical physics at the University of Cologne, Germany. He has earned his PhD from Heidelberg University in 1988. He has held positions at the Universities of Heidelberg, Zurich, and Freiburg, and was an invited visitor to the Universities of Alberta, Bern, Cambridge, Montpellier, and others. His main interests are quantum gravity, cosmology, black holes, and the foundations of quantum theory. He has published several books including the monograph "Quantum Gravity" (second edition: Oxford 2007). He is a member of The Foundational Questions Institute since 2006.

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What if Time Really Exists?

By Sean Carroll

By Sean Carroll

Essay Abstract

Despite the obvious utility of the concept, it has often been argued that time does not exist. I take the opposite perspective: let's imagine that time does exist, and the universe is described by a quantum state obeying ordinary time-dependent quantum mechanics. Reconciling this simple picture with the known facts about our universe turns out to be a non-trivial task, but by taking it seriously we can infer deep facts about the fundamental nature of reality. The arrow of time finds a plausible explanation in a "Heraclitean universe," described by a quantum state eternally evolving in an infinite-dimensional Hilbert space.

Author Bio

Sean Carroll is a Senior Research Associate in theoretical physics at the California Institute of Technology. He obtained his Ph.D. from Harvard University in 1993, and has held positions at MIT, the Institute for Theoretical Physics at UC Santa Barbara, and the University of Chicago. He is the author of Spacetime and Geometry, a graduate-level textbook on general relativity. His research interests include cosmology, field theory, particle physics, general relativity, quantum gravity, quantum mechanics, and thermodynamics.

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Despite the obvious utility of the concept, it has often been argued that time does not exist. I take the opposite perspective: let's imagine that time does exist, and the universe is described by a quantum state obeying ordinary time-dependent quantum mechanics. Reconciling this simple picture with the known facts about our universe turns out to be a non-trivial task, but by taking it seriously we can infer deep facts about the fundamental nature of reality. The arrow of time finds a plausible explanation in a "Heraclitean universe," described by a quantum state eternally evolving in an infinite-dimensional Hilbert space.

Author Bio

Sean Carroll is a Senior Research Associate in theoretical physics at the California Institute of Technology. He obtained his Ph.D. from Harvard University in 1993, and has held positions at MIT, the Institute for Theoretical Physics at UC Santa Barbara, and the University of Chicago. He is the author of Spacetime and Geometry, a graduate-level textbook on general relativity. His research interests include cosmology, field theory, particle physics, general relativity, quantum gravity, quantum mechanics, and thermodynamics.

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First Community Prize

Forget Time*

By Carlo Rovelli

By Carlo Rovelli

Essay Abstract

Following a line of research that I have developed for several years, I argue that the best strategy for understanding quantum gravity is to build a picture of the physical world where the notion of time plays no role at all. I summarize here this point of view, explaining why I think that in a fundamental description of nature we must "forget time", and how this can be done in the classical and in the quantum theory. The idea is to develop a formalism that treats dependent and independent variables on the same footing. In short, I propose to interpret mechanics as a theory of relations between variables, rather than the theory of the evolution of variables in time.

Author Bio

Carlo Rovelli is professor of Physics at the University of Marseille, France and member of the Institut Universitaire de France. His main research interests are in quantum gravity, where he has contributed to the definition and the development of Loop Quantum Gravity. He is particularly interested in the foundations of the physics of space and time. He has written the books: "Quantum Gravity" (2004), "What is Time? What is Space" (2004), and "Anaximander of Miletus" (2008). He has received the 1995 Xanthopoulos Award for his contributions to gravitational and spacetime physics.

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Following a line of research that I have developed for several years, I argue that the best strategy for understanding quantum gravity is to build a picture of the physical world where the notion of time plays no role at all. I summarize here this point of view, explaining why I think that in a fundamental description of nature we must "forget time", and how this can be done in the classical and in the quantum theory. The idea is to develop a formalism that treats dependent and independent variables on the same footing. In short, I propose to interpret mechanics as a theory of relations between variables, rather than the theory of the evolution of variables in time.

Author Bio

Carlo Rovelli is professor of Physics at the University of Marseille, France and member of the Institut Universitaire de France. His main research interests are in quantum gravity, where he has contributed to the definition and the development of Loop Quantum Gravity. He is particularly interested in the foundations of the physics of space and time. He has written the books: "Quantum Gravity" (2004), "What is Time? What is Space" (2004), and "Anaximander of Miletus" (2008). He has received the 1995 Xanthopoulos Award for his contributions to gravitational and spacetime physics.

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Second Community Prizes

The Flow of Time*

By George F. R. Ellis

By George F. R. Ellis

Essay Abstract

Current theoretical physics suggests the flow of time is an illusion: the entire universe just is, with no special meaning attached to the present time. This paper points out that this view, in essence represented by usual space-time diagrams, is based on time-reversible microphysical laws, which fail to capture essential features of the time-irreversible nature of decoherence and the quantum measurement process, as well as macro-physical behaviour and the development of emergent complex systems, including life, which exist in the real universe. When these are taken into account, the unchanging block universe view of spacetime is best replaced by an evolving block universe which extends as time evolves, with the potential of the future continually becoming the certainty of the past; spacetime itself evolves, as do the entities within it. However this time evolution is not related to any preferred surfaces in spacetime; rather it is associated with the evolution of proper time along families of world lines. The default state of fundamental physics should not be taken to be a time irreversible evolution of physical states: it is an ongoing irreversible development of time itself.

Author Bio

George Ellis is Professor Emeritus of applied mathematics at the University of Cape Town. He has written or co-authored many books and papers on relativity theory and cosmology, including On the Large Scale Structure of Space Time with Stephen Hawking.

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Current theoretical physics suggests the flow of time is an illusion: the entire universe just is, with no special meaning attached to the present time. This paper points out that this view, in essence represented by usual space-time diagrams, is based on time-reversible microphysical laws, which fail to capture essential features of the time-irreversible nature of decoherence and the quantum measurement process, as well as macro-physical behaviour and the development of emergent complex systems, including life, which exist in the real universe. When these are taken into account, the unchanging block universe view of spacetime is best replaced by an evolving block universe which extends as time evolves, with the potential of the future continually becoming the certainty of the past; spacetime itself evolves, as do the entities within it. However this time evolution is not related to any preferred surfaces in spacetime; rather it is associated with the evolution of proper time along families of world lines. The default state of fundamental physics should not be taken to be a time irreversible evolution of physical states: it is an ongoing irreversible development of time itself.

Author Bio

George Ellis is Professor Emeritus of applied mathematics at the University of Cape Town. He has written or co-authored many books and papers on relativity theory and cosmology, including On the Large Scale Structure of Space Time with Stephen Hawking.

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Free will, undecidability, and the problem of time in quantum gravity*

By Rodolfo Gambini & Jorge Pullin

By Rodolfo Gambini & Jorge Pullin

Essay Abstract

In quantum gravity there is no notion of absolute time. Like all other quantities in the theory, the notion of time has to be introduced "relationally", by studying the behavior of some physical quantities in terms of others chosen as a "clock". We have recently introduced a consistent way of defining time relationally in general relativity. When quantum mechanics is formulated in terms of this new notion of time the resolution of the em measurement problem can be implemented via decoherence without the usual pitfalls. The resulting theory has the same experimental results of ordinary quantum mechanics, but every time an event is produced or a measurement happens two alternatives are possible: a) the state collapses; b) the system evolves without changing the state. One therefore has two possible behaviors of the quantum mechanical system and physical observations cannot decide between them, not just as a matter of experimental limitations but as an issue of principle. This first-ever example of fundamental undecidability in physics suggests that nature may behave sometimes as described by one alternative and sometimes as described by another. This in particular may give new vistas on the issue of free will.

Author Bio

Rodolfo Gambini is professor of physics at the University of the Republic in Montevideo, Uruguay. He is a member of the Academy of Sciencies of Latin America, the Argentine Academy of Exact Sciences and the Third World Academy of Sciences. He is a fellow of the American Physical Society. Jorge Pullin is the Horace Hearne Chair in theoretical physics at the Louisiana State University. A Fulbright, Guggenheim and Sloan fellow, he is a member of the National Academies of Science of Argentina, Mexico and the Latin American Academy. He received the Bouchet award of the American Physical Society.

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In quantum gravity there is no notion of absolute time. Like all other quantities in the theory, the notion of time has to be introduced "relationally", by studying the behavior of some physical quantities in terms of others chosen as a "clock". We have recently introduced a consistent way of defining time relationally in general relativity. When quantum mechanics is formulated in terms of this new notion of time the resolution of the em measurement problem can be implemented via decoherence without the usual pitfalls. The resulting theory has the same experimental results of ordinary quantum mechanics, but every time an event is produced or a measurement happens two alternatives are possible: a) the state collapses; b) the system evolves without changing the state. One therefore has two possible behaviors of the quantum mechanical system and physical observations cannot decide between them, not just as a matter of experimental limitations but as an issue of principle. This first-ever example of fundamental undecidability in physics suggests that nature may behave sometimes as described by one alternative and sometimes as described by another. This in particular may give new vistas on the issue of free will.

Author Bio

Rodolfo Gambini is professor of physics at the University of the Republic in Montevideo, Uruguay. He is a member of the Academy of Sciencies of Latin America, the Argentine Academy of Exact Sciences and the Third World Academy of Sciences. He is a fellow of the American Physical Society. Jorge Pullin is the Horace Hearne Chair in theoretical physics at the Louisiana State University. A Fulbright, Guggenheim and Sloan fellow, he is a member of the National Academies of Science of Argentina, Mexico and the Latin American Academy. He received the Bouchet award of the American Physical Society.

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Electron time, mass and zitter

By David Hestenes

By David Hestenes

Essay Abstract

de Broglie's original idea that the electron has an internal clock has recently received experimental confirmation by measuring the period of the clock in an electron channeling experiment. This result has been explained by a new model of the electron, called the zitter model because it incorporates Schroedinger's qualitative zitterbewegung concept into a fully specified interacting particle model. The zitter electron is a lightlike charged particle with intrinsic spin that maintains it in a helical spacetime path, with curvature and frequency determined by the electron mass. Thus, electron mass is fully reduced to clock frequency in electron motion. This essay discusses details of the model and its implications.

Author Bio

David Hestenes is Emeritus Professor of Physics at Arizona State University, APS Fellow, Overseas Fellow of Churchill College, Cambridge. Formerly UCLA University Fellow, NSF Postdoctoral Fellow, NASA Faculty Fellow and Senior Fulbright Fellow. His main line of research is development and application of Geometric Algebra as a unified mathematical language for physics. In recognition of this work he was designated Foundations of Physics Honoree in 1993. For contributions to physics education he was awarded the 2002 Oersted Medal by the AAPT and the 2003 Education Research Award by the National Council of Scientific Society Presidents.

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de Broglie's original idea that the electron has an internal clock has recently received experimental confirmation by measuring the period of the clock in an electron channeling experiment. This result has been explained by a new model of the electron, called the zitter model because it incorporates Schroedinger's qualitative zitterbewegung concept into a fully specified interacting particle model. The zitter electron is a lightlike charged particle with intrinsic spin that maintains it in a helical spacetime path, with curvature and frequency determined by the electron mass. Thus, electron mass is fully reduced to clock frequency in electron motion. This essay discusses details of the model and its implications.

Author Bio

David Hestenes is Emeritus Professor of Physics at Arizona State University, APS Fellow, Overseas Fellow of Churchill College, Cambridge. Formerly UCLA University Fellow, NSF Postdoctoral Fellow, NASA Faculty Fellow and Senior Fulbright Fellow. His main line of research is development and application of Geometric Algebra as a unified mathematical language for physics. In recognition of this work he was designated Foundations of Physics Honoree in 1993. For contributions to physics education he was awarded the 2002 Oersted Medal by the AAPT and the 2003 Education Research Award by the National Council of Scientific Society Presidents.

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* The essays by Rovelli, Ellis and Gambini & Pullin were also selected for a less—and hence unawarded—juried prize.

Third Juried Prizes

What Makes Time Special

By Craig Adam Callender

By Craig Adam Callender

Essay Abstract

What is the difference between time and space? This paper proposes a novel answer: the temporal direction is that direction on the manifold of events in which our best theories can tell the strongest, most informative "stories." Put another way, time is that direction in which our theories can obtain as much determinism as possible. I make two arguments. The first is a general one based on an empiricist theory of laws. I argue that according to this theory time is distinguished as the direction of informative strength. The second argument is a more specific illustration of the first: understanding informative strength as having a well-posed Cauchy problem, I show that for a wide class of equations (i.e., second-order linear partial differential equations) the desire for strength does indeed distinguish the temporal direction. Not only that, but the argument rigorously connects three otherwise mysterious connections among temporal features to one another.

Author Bio

Craig Callender is Professor of Philosophy at the University of California, San Diego. He works in the foundations of physics, especially on statistical mechanics, the interpretation of quantum mechanics, and topics in quantum gravity. Much of his work focuses on the nature of time in modern physics. He has published extensively in philosophy and physics journals. In addition, he has edited two books "Philosophy Meets Physics at the Planck Scale" (CUP) and "Time, Reality and Experience" (CUP), and authored the popular science book "Introducing Time" (Icon/Totem).

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What is the difference between time and space? This paper proposes a novel answer: the temporal direction is that direction on the manifold of events in which our best theories can tell the strongest, most informative "stories." Put another way, time is that direction in which our theories can obtain as much determinism as possible. I make two arguments. The first is a general one based on an empiricist theory of laws. I argue that according to this theory time is distinguished as the direction of informative strength. The second argument is a more specific illustration of the first: understanding informative strength as having a well-posed Cauchy problem, I show that for a wide class of equations (i.e., second-order linear partial differential equations) the desire for strength does indeed distinguish the temporal direction. Not only that, but the argument rigorously connects three otherwise mysterious connections among temporal features to one another.

Author Bio

Craig Callender is Professor of Philosophy at the University of California, San Diego. He works in the foundations of physics, especially on statistical mechanics, the interpretation of quantum mechanics, and topics in quantum gravity. Much of his work focuses on the nature of time in modern physics. He has published extensively in philosophy and physics journals. In addition, he has edited two books "Philosophy Meets Physics at the Planck Scale" (CUP) and "Time, Reality and Experience" (CUP), and authored the popular science book "Introducing Time" (Icon/Totem).

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Space does not exist, so time can.

By Fotini Markopoulou

By Fotini Markopoulou

Essay Abstract

It is often said that in general relativity time does not exist. This is because the Einstein equations generate motion in time that is a symmetry of the theory, not true time evolution. In quantum gravity, the timelessness of general relativity clashes with time in quantum theory and leads to the "problem of time" which, in its various forms, is the main obstacle to a successful quantum theory of gravity. I argue that the problem of time is a paradox, stemming from an unstated faulty premise. Our faulty assumption is that space is real. I propose that what does not fundamentally exist is not time but space, geometry and gravity. The quantum theory of gravity will be spaceless, not timeless. If we are willing to throw out space, we can keep time and the trade is worth it.

Author Bio

Fotini Markopoulou works on the problem of quantum gravity. Her work explores the microscopic structure of spacetime and the role of causality at very high energies. Born in Athens, Greece, she received her Ph.D. in theoretical physics from Imperial College, London. She held postdoctoral positions at Pennsylvania State University, Imperial College, and the Albert Einstein/Max Planck Institute for Gravitational Physics, Berlin, before moving to Canada in 2001 as a founding member and faculty at the Perimeter Institute for Theoretical Physics in Canada, a research institute devoted to foundational issues in theoretical physics.

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It is often said that in general relativity time does not exist. This is because the Einstein equations generate motion in time that is a symmetry of the theory, not true time evolution. In quantum gravity, the timelessness of general relativity clashes with time in quantum theory and leads to the "problem of time" which, in its various forms, is the main obstacle to a successful quantum theory of gravity. I argue that the problem of time is a paradox, stemming from an unstated faulty premise. Our faulty assumption is that space is real. I propose that what does not fundamentally exist is not time but space, geometry and gravity. The quantum theory of gravity will be spaceless, not timeless. If we are willing to throw out space, we can keep time and the trade is worth it.

Author Bio

Fotini Markopoulou works on the problem of quantum gravity. Her work explores the microscopic structure of spacetime and the role of causality at very high energies. Born in Athens, Greece, she received her Ph.D. in theoretical physics from Imperial College, London. She held postdoctoral positions at Pennsylvania State University, Imperial College, and the Albert Einstein/Max Planck Institute for Gravitational Physics, Berlin, before moving to Canada in 2001 as a founding member and faculty at the Perimeter Institute for Theoretical Physics in Canada, a research institute devoted to foundational issues in theoretical physics.

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On the global existence of time

By Ettore Minguzzi

By Ettore Minguzzi

Essay Abstract

The existence of a global time is often taken for granted but should instead be considered as a matter of investigation. By using the tools of global Lorentzian geometry I prove that, under physically reasonable conditions, the impossibility of finding a global time implies the singularity of spacetime.

Author Bio

Ettore Minguzzi is researcher of mathematical physics at the University of Florence, Italy. He has earned his PhD from Milano University in 2002. His main research interests are in general relativity and applied gauge theories. In the last years he has contributed to global Lorentzian geometry and causality theory in particular with the study of the "causal ladder of spacetimes". He is a member of SIGRAV "Societa Italiana di Relativita Generale e Fisica della Gravitazione", SEGRE "Spanish Society on Relativity and Gravitation" and ISGRG "International Society on General Relativity and Gravitation".

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The existence of a global time is often taken for granted but should instead be considered as a matter of investigation. By using the tools of global Lorentzian geometry I prove that, under physically reasonable conditions, the impossibility of finding a global time implies the singularity of spacetime.

Author Bio

Ettore Minguzzi is researcher of mathematical physics at the University of Florence, Italy. He has earned his PhD from Milano University in 2002. His main research interests are in general relativity and applied gauge theories. In the last years he has contributed to global Lorentzian geometry and causality theory in particular with the study of the "causal ladder of spacetimes". He is a member of SIGRAV "Societa Italiana di Relativita Generale e Fisica della Gravitazione", SEGRE "Spanish Society on Relativity and Gravitation" and ISGRG "International Society on General Relativity and Gravitation".

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Time, TOEs, and UltraStructuralism

By Dean Rickles

By Dean Rickles

Essay Abstract

The 'frozen' character of general relativity (and background independent theories) is usually considered to be a problem for the theory. However, the most obvious resolution of this problem, involving correlations between dynamical variables, can be shown to provide a natural explanation of the appearance of time in timeless mathematical structures. I argue that this response can resolve a problem with Tegmark's extreme structuralist position, namely how to account for the appearance of time and change given that the structures in question are taken to be mathematical and, therefore, timeless.

Author Bio

Dean Rickles is a lecturer in History and Philosophy of Science at the University of Sydney. He works primarily on the physics of spacetime, but is also engaged in projects relating to public health and financial economics. He has written/edited several books on the philosophy of physics: The Structural Foundations of Quantum Gravity (OUP, 2006 - coedited with S. French and J. Saatsi), Symmetry, Structure and Spacetime (Elsevier, 2007), and The Ashgate Companion to Contemporary Philosophy of Physics (Ashgate, 2008).

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The 'frozen' character of general relativity (and background independent theories) is usually considered to be a problem for the theory. However, the most obvious resolution of this problem, involving correlations between dynamical variables, can be shown to provide a natural explanation of the appearance of time in timeless mathematical structures. I argue that this response can resolve a problem with Tegmark's extreme structuralist position, namely how to account for the appearance of time and change given that the structures in question are taken to be mathematical and, therefore, timeless.

Author Bio

Dean Rickles is a lecturer in History and Philosophy of Science at the University of Sydney. He works primarily on the physics of spacetime, but is also engaged in projects relating to public health and financial economics. He has written/edited several books on the philosophy of physics: The Structural Foundations of Quantum Gravity (OUP, 2006 - coedited with S. French and J. Saatsi), Symmetry, Structure and Spacetime (Elsevier, 2007), and The Ashgate Companion to Contemporary Philosophy of Physics (Ashgate, 2008).

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Many Times

By Steven Weinstein

By Steven Weinstein

Essay Abstract

The possibility of physics in multiple time dimensions is investigated. Drawing on recent work by Walter Craig and myself, I show that, contrary to conventional wisdom, there is a well-posed initial value problem---deterministic, stable evolution---for theories in multiple time dimensions. Though similar in many ways to ordinary, single-time theories, the multi-time theories have some rather intriguing properties which suggest new directions for the understanding of fundamental physics.

Author Bio

I'm an assistant professor in the Dept. of Philosophy at the University of Waterloo, and an affiliate of the Perimeter Institute for Theoretical Physics. I've previously taught at Princeton University and Dartmouth College. In addition to time, I'm interested in the foundations of quantum theory, quantum gravity, and thermodynamics, as well as other, more generally philosophical issues such as the problem of induction and the nature of the mind. When I have time, I play a highly-modified '52-reissue Telecaster through an original '56 Fender Deluxe. As loud as possible.

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The possibility of physics in multiple time dimensions is investigated. Drawing on recent work by Walter Craig and myself, I show that, contrary to conventional wisdom, there is a well-posed initial value problem---deterministic, stable evolution---for theories in multiple time dimensions. Though similar in many ways to ordinary, single-time theories, the multi-time theories have some rather intriguing properties which suggest new directions for the understanding of fundamental physics.

Author Bio

I'm an assistant professor in the Dept. of Philosophy at the University of Waterloo, and an affiliate of the Perimeter Institute for Theoretical Physics. I've previously taught at Princeton University and Dartmouth College. In addition to time, I'm interested in the foundations of quantum theory, quantum gravity, and thermodynamics, as well as other, more generally philosophical issues such as the problem of induction and the nature of the mind. When I have time, I play a highly-modified '52-reissue Telecaster through an original '56 Fender Deluxe. As loud as possible.

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Fourth Juried Prizes

Whither Time's Arrow?

By Gavin Crooks

By Gavin Crooks

Essay Abstract

In our everyday lives we have the sense that time flows inexorably from the past into the future; that time has a definite direction; and that the arrow of time points towards a future of greater entropy and disorder. But in the microscopic world of atoms and molecules the direction of time is indeterminate and ambiguous.

Author Bio

Gavin Crooks is divisional fellow in Physical Biosciences at Lawrence Berkeley National Laboratory. He obtained his Ph.D. from the University of California, Berkeley. His current research interests include the thermodynamics of molecular machines and solar energy capture. http://threeplusone.com

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In our everyday lives we have the sense that time flows inexorably from the past into the future; that time has a definite direction; and that the arrow of time points towards a future of greater entropy and disorder. But in the microscopic world of atoms and molecules the direction of time is indeterminate and ambiguous.

Author Bio

Gavin Crooks is divisional fellow in Physical Biosciences at Lawrence Berkeley National Laboratory. He obtained his Ph.D. from the University of California, Berkeley. His current research interests include the thermodynamics of molecular machines and solar energy capture. http://threeplusone.com

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The rediscovery of time through its disappearance

By Alexis de Saint-Ours**

By Alexis de Saint-Ours**

Essay Abstract

There is many misunderstandings within the relationship between time and becoming. It is common to say that things become in time but also that time flows. Is time the unchanging scene of what changes or the essence of becoming? With the concept of background independence, General Relativity has changed our understanding of space and time. Space and time can not anymore be considered as the passive containers of localisation and becoming. What are the foundational significance and epistemological impact of background independence? We uphold that it has changed and clarified the long-standing debate between time and becoming, but also that it gives an a posteriori answer to Bergson's criticism of time in physics. Time has often appeared as something less concrete and more immaterial than becoming. In this perspective, time has been understood as the structure of becoming or the concept whose content is change. The disappearance of the time coordinate and the relational understanding of evolution in General Relativity and a fortiori in Quantum Gravity, modify and reconfigure this traditional relation between time and becoming.

Author Bio

I am teaching assistant and associate researcher at the University of Paris 8. My work concerns philosophy of modern and contemporary physics, philosophy of time and the philosophical status of diagrams in mathematics and physics. My doctorate, which I will defend early next year, is about "Time and Relation in Relativity and Quantum Gravity".

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There is many misunderstandings within the relationship between time and becoming. It is common to say that things become in time but also that time flows. Is time the unchanging scene of what changes or the essence of becoming? With the concept of background independence, General Relativity has changed our understanding of space and time. Space and time can not anymore be considered as the passive containers of localisation and becoming. What are the foundational significance and epistemological impact of background independence? We uphold that it has changed and clarified the long-standing debate between time and becoming, but also that it gives an a posteriori answer to Bergson's criticism of time in physics. Time has often appeared as something less concrete and more immaterial than becoming. In this perspective, time has been understood as the structure of becoming or the concept whose content is change. The disappearance of the time coordinate and the relational understanding of evolution in General Relativity and a fortiori in Quantum Gravity, modify and reconfigure this traditional relation between time and becoming.

Author Bio

I am teaching assistant and associate researcher at the University of Paris 8. My work concerns philosophy of modern and contemporary physics, philosophy of time and the philosophical status of diagrams in mathematics and physics. My doctorate, which I will defend early next year, is about "Time and Relation in Relativity and Quantum Gravity".

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Time is not the problem

By Olaf Dreyer

By Olaf Dreyer

Essay Abstract

Attempts to quantize general relativity encounter an odd problem. The Hamiltonian that normally generates time evolution vanishes in the case of general relativity as a result of diffeomorphism invariance. The theory seems to be saying that time does not exist. The most obvious feature of our world, namely that time seems to progress and that the world changes accordingly becomes a problem in this presumably fundamental theory. This is called the problem of time. In this essay we argue that this problem is the result of an unphysical idealization. We are caught in this "problem of time" trap because we took a wrong turn in the early days of relativity by permanently including a split of geometry and matter into our physical theories. We show that another possibility exists that circumvents the problem of time and also sheds new light on other problems like the cosmological constant problem and the horizon problem in early universe cosmology.

Author Bio

Olaf Dreyer's research focuses on novel approaches to quantum gravity and the foundations of quantum theory. He obtained a Ph.D. in quantum gravity from Pennsylvania State University and he held a postdoctoral position at the Perimeter Institute for Theoretical Physics and a Marie Curie fellowship at Imperial College of Science, Technology, and Medicine. He is currently a postdoctoral fellow at MIT.

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Attempts to quantize general relativity encounter an odd problem. The Hamiltonian that normally generates time evolution vanishes in the case of general relativity as a result of diffeomorphism invariance. The theory seems to be saying that time does not exist. The most obvious feature of our world, namely that time seems to progress and that the world changes accordingly becomes a problem in this presumably fundamental theory. This is called the problem of time. In this essay we argue that this problem is the result of an unphysical idealization. We are caught in this "problem of time" trap because we took a wrong turn in the early days of relativity by permanently including a split of geometry and matter into our physical theories. We show that another possibility exists that circumvents the problem of time and also sheds new light on other problems like the cosmological constant problem and the horizon problem in early universe cosmology.

Author Bio

Olaf Dreyer's research focuses on novel approaches to quantum gravity and the foundations of quantum theory. He obtained a Ph.D. in quantum gravity from Pennsylvania State University and he held a postdoctoral position at the Perimeter Institute for Theoretical Physics and a Marie Curie fellowship at Imperial College of Science, Technology, and Medicine. He is currently a postdoctoral fellow at MIT.

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Weakening Gravity's Grip on the Arrow of Time

By Maulik Parikh

By Maulik Parikh

Essay Abstract

The future differs from the past: it has more entropy. No theoretical framework including inflation has yet provided a dynamical origin for this elementary fact, the thermodynamic arrow of time. I argue that by weakening the strength or range of gravity at early times, one can find a natural way to obtain the smooth conditions present in the early universe.

Author Bio

Maulik Parikh is a theoretical high-energy physicist. He did his bachelor's at the University of California at Berkeley followed by a PhD in physics from Princeton University. After post-doctoral stints at the University of Utrecht in the Netherlands and at Columbia University, he is now faculty at the Inter-University Centre for Astronomy and Astrophysics (IUCAA) in India. In 2004 he won the Gravity Research Foundation essay competition for a paper he wrote on black holes.

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The future differs from the past: it has more entropy. No theoretical framework including inflation has yet provided a dynamical origin for this elementary fact, the thermodynamic arrow of time. I argue that by weakening the strength or range of gravity at early times, one can find a natural way to obtain the smooth conditions present in the early universe.

Author Bio

Maulik Parikh is a theoretical high-energy physicist. He did his bachelor's at the University of California at Berkeley followed by a PhD in physics from Princeton University. After post-doctoral stints at the University of Utrecht in the Netherlands and at Columbia University, he is now faculty at the Inter-University Centre for Astronomy and Astrophysics (IUCAA) in India. In 2004 he won the Gravity Research Foundation essay competition for a paper he wrote on black holes.

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Quantum Measurement as an Arrow of Time

By C. Vinson**

By C. Vinson**

Essay Abstract

The orthodox perspective on the arrow of time originating from entropy suggests it comes about from an initial condition on the universe. I explore the possibility of a different arrow of time originating from the behavior of measurements in quantum mechanics and its connection with the thermodynamic arrow, as well as building an analogy between the decoherence perspective on quantum measurement and the arguments that place the thermodynamic arrow as an initial condition. Together, these ideas suggest two alternative possibilities for physics: one where quantum measurement introduces a time-reversal asymmetry in the dynamics of physical law, and another where the universe started in a particular state that creates both the quantum measurement and thermodynamic arrows. Finally, I argue there's no a priori reason to prefer one of these perspectives over the other given the current state of experiment and theory, so the neglect of the former in favor of the latter is not justified.

Author Bio

C. Vinson developed an interest in physics, particularly the physics of time, at an early age and followed it as far as graduate school at the University of Maryland; but decided not to pursue theoretical physics as a career and now matriculates at the University of North Carolina, Greensboro, studying library and information science.

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The orthodox perspective on the arrow of time originating from entropy suggests it comes about from an initial condition on the universe. I explore the possibility of a different arrow of time originating from the behavior of measurements in quantum mechanics and its connection with the thermodynamic arrow, as well as building an analogy between the decoherence perspective on quantum measurement and the arguments that place the thermodynamic arrow as an initial condition. Together, these ideas suggest two alternative possibilities for physics: one where quantum measurement introduces a time-reversal asymmetry in the dynamics of physical law, and another where the universe started in a particular state that creates both the quantum measurement and thermodynamic arrows. Finally, I argue there's no a priori reason to prefer one of these perspectives over the other given the current state of experiment and theory, so the neglect of the former in favor of the latter is not justified.

Author Bio

C. Vinson developed an interest in physics, particularly the physics of time, at an early age and followed it as far as graduate school at the University of Maryland; but decided not to pursue theoretical physics as a career and now matriculates at the University of North Carolina, Greensboro, studying library and information science.

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Condensed matter lessons about the origin of time

By Gil Jannes**

By Gil Jannes**

Essay Abstract

It is widely hoped that quantum gravity will shed a profound light on the origin of time in physics. The currently dominant approaches to a candidate quantum theory of gravity have quite naturally evolved from general relativity, on the one hand, and from particle physics, on the other hand. In this essay, I will argue that a third important branch of 20th century "fundamental" physics, namely condensed-matter physics, also offers an interesting perspective on quantum gravity, and thereby on the problem of time. The bottomline might sound disappointing to those who have become used to claims that quantum gravity or a "Theory of Everything" will solve most of the conceptual problems of fundamental physics: To understand the origin of time, experimental input is needed at much higher energies than what is available today. Moreover, it is far from obvious that we will ever discover the true origin of physical time, even if we become able to directly probe physics at the Planck scale. But we might learn plenty of interesting lessons about time and the structure of our universe in the process.

Author Bio

The author has studied electronical engineering, philosophy and fundamental physics at the universities of Leuven (Belgium) and Madrid (Spain). He is currently pursuing a PhD in quantum gravity from a condensed-matter perspective.

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It is widely hoped that quantum gravity will shed a profound light on the origin of time in physics. The currently dominant approaches to a candidate quantum theory of gravity have quite naturally evolved from general relativity, on the one hand, and from particle physics, on the other hand. In this essay, I will argue that a third important branch of 20th century "fundamental" physics, namely condensed-matter physics, also offers an interesting perspective on quantum gravity, and thereby on the problem of time. The bottomline might sound disappointing to those who have become used to claims that quantum gravity or a "Theory of Everything" will solve most of the conceptual problems of fundamental physics: To understand the origin of time, experimental input is needed at much higher energies than what is available today. Moreover, it is far from obvious that we will ever discover the true origin of physical time, even if we become able to directly probe physics at the Planck scale. But we might learn plenty of interesting lessons about time and the structure of our universe in the process.

Author Bio

The author has studied electronical engineering, philosophy and fundamental physics at the universities of Leuven (Belgium) and Madrid (Spain). He is currently pursuing a PhD in quantum gravity from a condensed-matter perspective.

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The Garden of Forking Paths: Time as an Expanding Labyrinth

By Paul Halpern

By Paul Halpern

Essay Abstract

We speculate that the arrow of time stems from the growth of an information space housing the full gamut of quantum states in the universe. As this information space dynamically expands, in conjunction with the growth of the physical universe, the network of alternatives would become increasingly complex, explaining why wave-function collapse is future-directed and why causality due to conscious decision-making is in the forward direction. In other words, an arrow of information entropy increase would set the order of cause and effect. Because the labyrinth of possibilities could grow in a deterministic fashion, yet the choices themselves could be arbitrary, our model could offer a means of reconciling mechanistic, probabilistic, and freely-chosen aspects of how natural interactions transpire. We examine how this model bears on the question of time travel, and contrast its implications with those of earlier descriptions of time as a cycle or as a steady stream.

Author Bio

Paul Halpern is Professor of Physics at the University of the Sciences in Philadelphia. After receiving a PhD from Stony Brook University, he has published a number of articles in the fields of general relativity, complexity theory, cultural aspects of science, and the history of physics. The author of 11 popular science books, he has been the recipient of a Guggenheim Fellowship, a Fulbright Award, and an Athenaeum Literary Award.

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We speculate that the arrow of time stems from the growth of an information space housing the full gamut of quantum states in the universe. As this information space dynamically expands, in conjunction with the growth of the physical universe, the network of alternatives would become increasingly complex, explaining why wave-function collapse is future-directed and why causality due to conscious decision-making is in the forward direction. In other words, an arrow of information entropy increase would set the order of cause and effect. Because the labyrinth of possibilities could grow in a deterministic fashion, yet the choices themselves could be arbitrary, our model could offer a means of reconciling mechanistic, probabilistic, and freely-chosen aspects of how natural interactions transpire. We examine how this model bears on the question of time travel, and contrast its implications with those of earlier descriptions of time as a cycle or as a steady stream.

Author Bio

Paul Halpern is Professor of Physics at the University of the Sciences in Philadelphia. After receiving a PhD from Stony Brook University, he has published a number of articles in the fields of general relativity, complexity theory, cultural aspects of science, and the history of physics. The author of 11 popular science books, he has been the recipient of a Guggenheim Fellowship, a Fulbright Award, and an Athenaeum Literary Award.

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The Production of Time

By Adam Daniel Helfer

By Adam Daniel Helfer

Essay Abstract

I suggest that measurement in quantum theory should be regarded as a sense of time (of things *happening*), which is as important as the conventional relativistic notion of time. A key question -- of basic physical interest whether one accepts the arguments here or not -- is, What physical criteria determine when a measurement takes place? I suggest a way in which the answer to this may be bound up with the resolution of some pathologies associated with the stress-energy operator, and may at the same time determine the cosmic flow of time. The problem of reconciling the quantum sense of time (measurement) and the conventional relativistic one gives some indication that the the correct "quantization" of gravity is essentially different from that of other fields.

Author Bio

Adam Helfer works on general relativity and quantum field theory.

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I suggest that measurement in quantum theory should be regarded as a sense of time (of things *happening*), which is as important as the conventional relativistic notion of time. A key question -- of basic physical interest whether one accepts the arguments here or not -- is, What physical criteria determine when a measurement takes place? I suggest a way in which the answer to this may be bound up with the resolution of some pathologies associated with the stress-energy operator, and may at the same time determine the cosmic flow of time. The problem of reconciling the quantum sense of time (measurement) and the conventional relativistic one gives some indication that the the correct "quantization" of gravity is essentially different from that of other fields.

Author Bio

Adam Helfer works on general relativity and quantum field theory.

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The Nature of Time: from a Timeless Hamiltonian Framework to Clock Time of Metrology

By Enrico Prati

By Enrico Prati

Essay Abstract

The problem of the Nature of Time is twofold: whether or not time is a fundamental quantity of Nature, and how does clock time of metrology emerge in the experimental description of dynamics. This work strongly supports the fundamental timelessness of Nature. However, the correct view that physics is described by relations between variables does not addresses the second problem of how time does emerge at the macroscopic scale on the ground of a timeless framework. In this work ordinary Hamiltonian dynamics is first recast in a timeless formalism capable to provide a definition of parameter time on the basis of the only generalized coordinates, together with the Hamiltonian invariance on trajectories, and a variational principle. Next, clock time emerges as a discrete macroscopic quantity by considering subsystems cyclic in the phase space, to which other subsystems refer. Suitable cyclic phenomena, under sufficiently restrictive assumptions on their stability (like atomic clocks) are indeed a good approximation of the canonical parameter time and describe time evolution of physical quantities by means of the same simple dynamical laws.

Author Bio

Enrico Prati is research scientist of Italian CNR at the Laboratorio Nazionale MDM. His main research interests are quantum transport, spin dynamics and decoherence in nanoscaled quantum devices, and the transition from quantum to classical physics. He is also involved in the broad field of emerging properties of metamaterials. He is particularly interested in the foundations of the physics of time. He has received the 2004 URSI-B Commission Young Scientist Award for his research in metamaterials.

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The problem of the Nature of Time is twofold: whether or not time is a fundamental quantity of Nature, and how does clock time of metrology emerge in the experimental description of dynamics. This work strongly supports the fundamental timelessness of Nature. However, the correct view that physics is described by relations between variables does not addresses the second problem of how time does emerge at the macroscopic scale on the ground of a timeless framework. In this work ordinary Hamiltonian dynamics is first recast in a timeless formalism capable to provide a definition of parameter time on the basis of the only generalized coordinates, together with the Hamiltonian invariance on trajectories, and a variational principle. Next, clock time emerges as a discrete macroscopic quantity by considering subsystems cyclic in the phase space, to which other subsystems refer. Suitable cyclic phenomena, under sufficiently restrictive assumptions on their stability (like atomic clocks) are indeed a good approximation of the canonical parameter time and describe time evolution of physical quantities by means of the same simple dynamical laws.

Author Bio

Enrico Prati is research scientist of Italian CNR at the Laboratorio Nazionale MDM. His main research interests are quantum transport, spin dynamics and decoherence in nanoscaled quantum devices, and the transition from quantum to classical physics. He is also involved in the broad field of emerging properties of metamaterials. He is particularly interested in the foundations of the physics of time. He has received the 2004 URSI-B Commission Young Scientist Award for his research in metamaterials.

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Is the notion of time really fundamental?

By Florian Girelli, Stefano Liberati & Lorenzo Sindoni

By Florian Girelli, Stefano Liberati & Lorenzo Sindoni

Essay Abstract

From the Physics point of view, time is now best described through General Relativity, as part of space-time which is a dynamical object encoding gravity. Time possesses also some intrinsic irreversibility due to thermodynamics, quantum mechanical effects... This irreversibility can look puzzling since time-like loops (and hence time machines) can appear in General Relativity (for example in the Godel universe, a solution of Einstein's equations). We take this apparent discrepancy as a warning bell pointing to us that time as we understand it, might not be fundamental and that whatever theory, lying beyond General Relativity, may not include time as we know it as a fundamental structure. We propose therefore, following the philosophy of analog models of gravity, that time and gravity might not be fundamental per se, but only emergent features. We illustrate our proposal using a toy-model where we show how the Lorentzian signature and Nordstrom gravity (a diffeomorphisms invariant scalar gravity theory) can emerge from a timeless non-dynamical space.

Author Bio

F. Girelli has done his PhD in Marseille (France). He went to the Perimeter Institute (Canada) and SISSA (Italy) for some postdocs. He is now postdoc at the University of Sydney. S. Liberati has done his PhD in SISSA. He did a postdoc at the University of Maryland (USA) before becoming assistant professor at SISSA. L. Sindoni is currently finishing his PhD at SISSA.

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From the Physics point of view, time is now best described through General Relativity, as part of space-time which is a dynamical object encoding gravity. Time possesses also some intrinsic irreversibility due to thermodynamics, quantum mechanical effects... This irreversibility can look puzzling since time-like loops (and hence time machines) can appear in General Relativity (for example in the Godel universe, a solution of Einstein's equations). We take this apparent discrepancy as a warning bell pointing to us that time as we understand it, might not be fundamental and that whatever theory, lying beyond General Relativity, may not include time as we know it as a fundamental structure. We propose therefore, following the philosophy of analog models of gravity, that time and gravity might not be fundamental per se, but only emergent features. We illustrate our proposal using a toy-model where we show how the Lorentzian signature and Nordstrom gravity (a diffeomorphisms invariant scalar gravity theory) can emerge from a timeless non-dynamical space.

Author Bio

F. Girelli has done his PhD in Marseille (France). He went to the Perimeter Institute (Canada) and SISSA (Italy) for some postdocs. He is now postdoc at the University of Sydney. S. Liberati has done his PhD in SISSA. He did a postdoc at the University of Maryland (USA) before becoming assistant professor at SISSA. L. Sindoni is currently finishing his PhD at SISSA.

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** FQXi would like to offer a special commendation to these winning essays written by either students or non-professionals. Nice work!!

Community Runners-up

Flowing with a Frozen River

By Cristinel Stoica

By Cristinel Stoica

Essay Abstract

For discussing foundational questions, like the nature of time, we need a framework. Ideally, this would be provided by a Theory of Everything. Until the discovery of TOE, I propose a mathematical structure that can be used to represent theories of Physics in a unitary framework, similarly to the way in which the group actions represent various geometries in the Erlangen program. This construction extracts essential aspects of various theories, concerning the space, time, physical law, and causality. I introduce a causal structure and apply it to models of time and time travel. I propose an argument, based on causality, for the initial singularity of the Universe, and for the physical reality of gauge potentials (all three related in an unexpected way). Then, I discuss a new version of Quantum Mechanics, that replaces the discontinuous wavefunction collapse with delayed initial conditions, and has significant implications on time and causality. After presenting the arrows of time as emergent phenomena, I discuss the mind and its perception of time as flowing, in the context of the block spacetime. Then, I apply the previous observations to analyze the possibility of free-will. I propose a hypothesis about the free-will, and a crucial experiment that can confirm or reject it.

Author Bio

Cristi Stoica has a master's degree in Differential Geometry with applications in Physics, and is enrolled in a doctoral program on the Fiber Bundle Geometry. He works as a computer programmer in the field of Computational Geometry. The present essay is based on the author's independent research.

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For discussing foundational questions, like the nature of time, we need a framework. Ideally, this would be provided by a Theory of Everything. Until the discovery of TOE, I propose a mathematical structure that can be used to represent theories of Physics in a unitary framework, similarly to the way in which the group actions represent various geometries in the Erlangen program. This construction extracts essential aspects of various theories, concerning the space, time, physical law, and causality. I introduce a causal structure and apply it to models of time and time travel. I propose an argument, based on causality, for the initial singularity of the Universe, and for the physical reality of gauge potentials (all three related in an unexpected way). Then, I discuss a new version of Quantum Mechanics, that replaces the discontinuous wavefunction collapse with delayed initial conditions, and has significant implications on time and causality. After presenting the arrows of time as emergent phenomena, I discuss the mind and its perception of time as flowing, in the context of the block spacetime. Then, I apply the previous observations to analyze the possibility of free-will. I propose a hypothesis about the free-will, and a crucial experiment that can confirm or reject it.

Author Bio

Cristi Stoica has a master's degree in Differential Geometry with applications in Physics, and is enrolled in a doctoral program on the Fiber Bundle Geometry. He works as a computer programmer in the field of Computational Geometry. The present essay is based on the author's independent research.

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From time to timescape -- Einstein's unfinished revolution

By David L. Wiltshire

By David L. Wiltshire

Essay Abstract

I argue that Einstein overlooked an important aspect of the relativity of time in never quite realizing his quest to embody Mach's principle in his theory of gravity. As a step towards that goal, I broaden the Strong Equivalence Principle to a new principle of physics, the Cosmological Equivalence Principle, to account for the role of the evolving average regional density of the universe in the synchronisation of clocks and the relative calibration of inertial frames. In a universe dominated by voids of the size observed in large-scale structure surveys, the density contrasts of expanding regions are strong enough that a relative deceleration of the background between voids and the environment of galaxies, typically of order 10^{-10} m/s^2, must be accounted for. As a result one finds a universe whose present age varies by billions of years according to the position of the observer: a timescape. This model universe is observationally viable: it passes three critical independent tests, and makes additional predictions. Dark energy is revealed as a mis-identification of gravitational energy gradients and the resulting variance in clock rates. Understanding the biggest mystery in cosmology therefore involves a paradigm shift, but in an unexpected direction: the conceptual understanding of time and energy in Einstein's own theory is incomplete.

Author Bio

David Wiltshire did undergraduate studies in his native New Zealand, followed by a PhD in the Relativity and Gravitation Group at the University of Cambridge, UK, in the mid 1980s. After a variety of research and teaching positions in Italy, UK, and Australia he returned to NZ in 2001, where he is now Senior Lecturer at the University of Canterbury, Christchurch. He is known for his work in higher-dimensional gravity, brane worlds, black holes and quantum cosmology. His recent research has turned to the problem of dark energy, the averaging of the inhomogeneous universe and foundational implications for cosmology.

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I argue that Einstein overlooked an important aspect of the relativity of time in never quite realizing his quest to embody Mach's principle in his theory of gravity. As a step towards that goal, I broaden the Strong Equivalence Principle to a new principle of physics, the Cosmological Equivalence Principle, to account for the role of the evolving average regional density of the universe in the synchronisation of clocks and the relative calibration of inertial frames. In a universe dominated by voids of the size observed in large-scale structure surveys, the density contrasts of expanding regions are strong enough that a relative deceleration of the background between voids and the environment of galaxies, typically of order 10^{-10} m/s^2, must be accounted for. As a result one finds a universe whose present age varies by billions of years according to the position of the observer: a timescape. This model universe is observationally viable: it passes three critical independent tests, and makes additional predictions. Dark energy is revealed as a mis-identification of gravitational energy gradients and the resulting variance in clock rates. Understanding the biggest mystery in cosmology therefore involves a paradigm shift, but in an unexpected direction: the conceptual understanding of time and energy in Einstein's own theory is incomplete.

Author Bio

David Wiltshire did undergraduate studies in his native New Zealand, followed by a PhD in the Relativity and Gravitation Group at the University of Cambridge, UK, in the mid 1980s. After a variety of research and teaching positions in Italy, UK, and Australia he returned to NZ in 2001, where he is now Senior Lecturer at the University of Canterbury, Christchurch. He is known for his work in higher-dimensional gravity, brane worlds, black holes and quantum cosmology. His recent research has turned to the problem of dark energy, the averaging of the inhomogeneous universe and foundational implications for cosmology.

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And select the letter between 'S' and 'U':