Boundaries, Corners and Creases

 by Joseph Samuel.


Cricketing nations have a very good idea what a boundary is, it’s good for a cool four runs, without the bother of running! Corners are tense moments in a football (soccer to some) match when a well struck ball can curve into the goal. The crease is what a batsman lunges for when the wicket keeper ….. wait! this is not a sports column, but CQG+! Let’s back up and explain what our paper really is about.

In a path integral approach to quantum gravity, one has to divide up spacetime into pieces and focus on the action within each piece. In the elementary case of particle mechanics, this “skeletonisation” converts the action expressed as a Riemann integral into a discrete sum. A desirable property of the action is that it should be additive when we glue the pieces back together. This is achieved only when one properly takes into account the boundaries of the pieces.  The boundaries can be spacelike, timelike or null. Much work has focused on the first two cases. The Einstein–Hilbert Action principle for spacetime regions with null boundaries has only recently attracted attention (look up the Arxiv for papers by E. Poisson et al and Parattu et al; references would not be consistent with the chatty, informal style of  CQG+). These papers deal with the appropriate boundary terms that appear in all boundary signatures.

Our paper (authors: Ian Jubb, Joseph Samuel, Rafael Sorkin and Sumati Surya) gives a unified approach to all boundary signatures using Cartan’s tetrad formalism. An unexpected feature of the boundary term required here is that it is not gauge invariant under local Lorentz transformations (although its variation is). As the tetrad formalism may not be familiar to some readers of CQG, we also give a treatment in terms of metrics. When the boundary has corners the action has to also contain corner terms. Cartan’s tetrad formalism gives a simple way to arrive at the corner terms, exploiting the gauge non invariance of the boundary terms.

Spacetime boundaries can be null. A classic example is the region exterior to a black hole, whose boundary is a frozen wavefront, the event horizon. Horizons can have creases where the null normal is discontinuous, as happens when new null generators enter (or leave) the horizon. Another example of a null boundary is that which appears in a Causal diamond. A causal diamond is the intersection of a past set with a future set and looks (when it is drawn on a blackboard) much like the diamond in a baseball game. Yet another example of a null boundary is Scri, asymptotic null infinity. Null boundaries deserve special attention since their normals are also their tangents. Our unified treatment paints all kinds of boundaries with the same brush.

A photograph taken on the terrace of the library building during the workshop around December 2015.

This work, involving a collaboration across continents had its genesis in a series of workshops organised at the Raman Research Institute in the last few years by Sumati Surya. Come December, when the skies are grey in the northern latitudes, some of our colleagues, like migrating birds, wing their way south, to the Raman Research Institue (RRI) in Bangalore, India. The photo above shows some of them with friends and families. Visible in the photograph are the four authors of our paper. The photograph is taken on the terrace of the library building, where the talks took place. The talks and discussions revolve around general relativity (mostly from the Causet point of view championed by Sorkin), Quantum Measure theory, entanglement entropy, the cosmological constant and topology change. Sometime in December 2014, the discussions around the meeting raised the question of null boundaries. This question was partly answered and then revived at the subsequent meetings and culminated in the paper. Do take a look at it.

A few words about the RRI campus may be in order here: it is wooded and distinctly cooler than the surrounding areas because of the foliage. The trees are home to a variety of bird, animal and insect life. Common birds are sunbirds, bulbuls, koels and barbets, whose calls you can listen to as a welcome distraction from work. There is a dwindling population of slender lorises and a thriving population of lazy cats. During November / December / January the skies are clear blue (though dotted with soaring kites) and the wooded campus attracts a seasonal feathered visitor, the paradise flycatcher. Each year these birds stop at the Institute campus for about two weeks before going further south to their destination in the Nilgiri hills. What attracts the birds here is probably the insect life, which is also pretty diverse (Arachnophobes are advised to desist from clicking on this link.).

The Raman Institute has groups doing research in four select areas of physics: Astrophysics, Theoretical Physics, Soft Condensed Matter and Light and Matter Physics. There is also research in chemistry and a substantial thrust in instrumentation related to Astronomical Observations at telescopes in India and around the world. For more information on this look at Facebook or Twitter. The theoretical physics group has interest mainly in General Relativity and Non equilibrium Statistical Physics. Apart from the permanent faculty at RRI, we have postdocs, PhD students and a vibrant Visiting Student program at the Bachelor’s and Master’s level. We also have an outreach programme to interface with schools and colleges. Check out our homepage for more details.


About the Author: I am a theoretical physicist at the Raman Research Institute. My interests include general relativity, optics, the geometric phase in quantum mechanics, DNA elasticity and science popularisation. I keep moderately fit by raising and lowering indices. I enjoy gardening and relax by cooking exquisitely textured lacy appams for my friends.


Read the full article in Classical and Quantum Gravity:
Boundary and corner terms in the action for general relativity
Ian Jubb et al 2017 Class. Quantum Grav. 34 065006


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Things Change – Even in Hamiltonian General Relativity!

by J. Brian Pitts.


brianpittspic

J. Brian Pitts is a Senior Research Associate, Faculty of Philosophy, University of Cambridge.

Observables and the Problem of Time

Mixing gravity and quantum mechanics is hard. Many approaches start with a classical theory and apply the magic of quantization, so it is important to have the classical theory sorted out well first. But the “problem of time” in Hamiltonian General Relativity looms: change seems missing in the canonical formulation.

Are Hamiltonian and Lagrangian forms of a theory equivalent? It’s not so obvious for Maxwell’s electromagnetism or Einstein’s GR, for which the Legendre transformation from the Lagrangian to the Hamiltonian doesn’t exist. It was necessary to reinvent the Hamiltonian formalism: constrained Hamiltonian dynamics. Rosenfeld’s 1930 work was forgotten until after Dirac and (independently) Bergmann’s Syracuse group had reinvented the subject by 1950. Recently a commentary and translation were published by Salisbury and Sundermeyer.

As canonical quantum gravity grew in the 1950s, it seemed less crucial for Continue reading

Issue of the Beginning: Initial Conditions for Cosmological Perturbations

by Abhay Ashtekar and Brajesh Gupt.


ashtekar

Abhay Ashtekar holds the Eberly Chair in Physics and the Director of the Institute for Gravitation and the Cosmos at the Pennsylvania State University. Currently, he is a Visiting Professor at the CNRS Centre de Physique Théorique at Aix-Marseille Université.

Although our universe has an interesting and intricate large-scale structure now, observations show that it was extraordinarily simple at the surface of last scattering. From a theoretical perspective, this simplicity is surprising. Is there a principle to weed out the plethora of initial conditions which would have led to a much more complicated behavior also at early times?

In the late 1970s Penrose proposed such a principle through his Weyl curvature hypothesis (WCH) [1,2]: in spite of the strong curvature singularity, Big Bang is very special in that the Weyl curvature vanishes there. This hypothesis is attractive especially because it is purely geometric and completely general; it is not tied to a specific early universe scenario such as inflation.

However, the WCH is tied to general relativity and its Big Bang where classical physics comes to an abrupt halt. It is generally believed that quantum gravity effects would intervene and resolve the big bang singularity. The question then is Continue reading

Pants on fire!

One of the authors, Ian Jubb, discussing a pair of trousers with his colleagues at Imperial College London. Ian Jubb is currently the PhD student of Fay Dowker at Imperial College London.

One of the authors, Ian Jubb, discussing a pair of trousers with his colleagues at Imperial College London. Ian Jubb is currently the PhD student of Fay Dowker in the Theoretical Physics group at Imperial College London.

by Ian Jubb and Michel Buck.


Did you know that Quantum Gravity literally sets pants on fire?

Your pants are not just a nifty garment, they are also a perfect example of a space undergoing a process known as topology change. Take a space that initially consists of two separate circles. If they were to meet and merge into a single circle, the topology of the space would have changed. The trousers allow us to visualise each stage of this process, with cross sections higher up the trouser leg corresponding to later times in the process (if we hold the trousers upside-down, we get the reverse process, corresponding to a single circle splitting into two circles). Instead of viewing this process as the space changing in time, Einstein would tell us to view the trousers in their entirety, as one whole spacetime — the trousers spacetime.

But why should we care about spaces that can ‘split’ and ’attach’ like this? It turns out that there are good reasons to believe that Continue reading

Want to crush a singularity? First make it strong and then …

by Parampreet Singh.


Parampreet Singh

Parampreet Singh with a young student who often asks him the most difficult and so far unanswerable questions on the resolution of singularities. Dr Parampreet Singh is Associate Professor at Department of Physics and Astronomy at Louisiana State University.

Einstein’s theory of classical general relativity breaks down when spacetime curvature
becomes extremely large near the singularities. To answer the fundamental questions
about the origin of our Universe or what happens at the central singularity of the black holes thus lies beyond the validity of Einstein’s theory. Our research deals with discovering the framework which guarantees resolution of singularities.

It has been long expected that quantum gravitational effects tame the classical singularities leading to insights on the above questions. A final theory of quantum gravity is not yet there but the underlying techniques can be used to understand whether quantum gravitational effects resolve cosmological and black hole singularities. Our goal is Continue reading

Setting space on fire

by Yasaman K. Yazdi and Niayesh Afshordi.


Niayesh Afshordi and Yasaman Yazdi discover that firewalls have consequences

Niayesh Afshordi and Yasaman Yazdi discover that firewalls have consequences. Yasaman K. Yazdi is a PhD candidate at the University of Waterloo and the Perimeter Institute for Theoretical Physics. Niayesh Afshordi is an associate professor at the University of Waterloo and the Perimeter Institute for Theoretical Physics.

Thought experiments highlight the edge of our understanding of our theories.  Sometimes, however, we can get so caught up in heated debates about the solution to a thought experiment, that we may forget that we are talking about physical objects, and that an actual experiment or observation may give the answer.  In this Insight we discuss a proposed solution to the black hole information puzzle, and a possible observational signal that might confirm it.

 

The black hole information puzzle and a potential solution

The black hole information loss problem is a decades old problem that highlights the tensions between some of the pillars of modern theoretical physics. It has evolved from being Continue reading

The possible emptiness of a final theory

Written by Jesper Møller Grimstrup, an independent danish theoretical physicist. He has collaborated with the mathematician Johannes Aastrup for more than a decade developing what they now call quantum holonomy theory. His present research is financed by an Indiegogo crowdfunding campaign (still open). Find more information on www.jespergrimstrup.org.


Could the laws of nature originate from a principle, that borders a triviality?

Does a final theory that cannot be explained by yet another, deeper theory, exist? What could such a theory possibly look like — and what might we learn from it?

J M Grimstrup

Jesper Møller Grimstrup

These are the million dollar questions. Will the ladder of scientific explanations that take us from biology to chemistry and down through atomic, nuclear and particle physics, end somewhere? Will we one day reach a point where it is clear that it is no longer possible to dig deeper into the fabric of reality? Will we reach the bottom?

Together with the mathematician Johannes Aastrup I have developed a new approach to this question. Our theory  we call it quantum holonomy theory is based on an elementary algebra, that essentially encodes how stuff is moved around in a three-dimensional space.

img_0192This algebra, which we call the quantum holonomy-diffeomorphism (QHD) algebra [1], is interesting for two reasons Continue reading

A Study of Time Delay from Different Time Zones

Netta Engelhardt (University of California, Santa Barbara) and Sebastian Fischetti (Imperial College) gave us an insight into their communication methods whilst collaborating for their research paper recently published in CQG.


Snetta

On a dark London evening and a sunny California day — January 19, 2016, to be precise — Netta sent Sebastian a Skype message:

Image_1

So began a new project for this dynamic duo, published recently in CQG. Unlike our previous project, this one presented a new challenge (with which researchers are all too familiar): we were separated by an eight-hour time difference. Thus began a three-way collaboration: Netta, Sebastian, and Skype (with the third member being the least cooperative).

The process began Continue reading

Why is our universe about to decay?

Dr Kin-ya Oda (left, Osaka university) and Dr Masatoshi Yamada (right, Kyoto university).

Dr Kin-ya Oda (left, Osaka university) and Dr Masatoshi Yamada (right, Kyoto university).

It has been revealed that we are living on the edge of vacuum instability by the discovery of Higgs particle at the Large Hadron Collider since 2012. The determination of Higgs mass finally provides the last-missed parameter, the Higgs self coupling, to be 0.12 in the Standard Model of particle physics after nearly half century of its foundation. This value completes the initial conditions for a set of differential equations, called renormalization group (RG) equations, which govern how particles interact at very high energy scales. It turns out that the self coupling can vanish or even become negative at the Planck scale, where the quantum gravity effects become significant. We note for later reference that the Yukawa coupling between the Higgs and top quark plays a crucial role to reduce the Higgs self coupling in its RG evolution. The Higgs potential is about to become Continue reading

Book review: Covariant Loop Quantum Gravity, an elementary introduction to quantum gravity and spinfoam theory

Rodolfo Gambini is Professor of Physics at Universidad de la República, Montevideo Uruguay

Rodolfo Gambini is Professor of Physics at Universidad de la República, Montevideo Uruguay

Review of “Covariant Loop Quantum Gravity, an elementary introduction to quantum gravity and spinfoam theory” by Carlo Rovelli and Francesca Vidotto

One of the central problems of contemporary physics is finding a theory that allows for describing the quantum behavior of the gravitational field. This book is a remarkable update on one of the most promising approaches for the treatment of this problem: loop quantum gravity. It places special emphasis on the covariant techniques, which provide with a definition of the path integral, an approach known as spin foams. It is a field that has undergone quite a bit of development in the last two decades. The book gives an overview of this area, discussing a series of results that are presented with great clarity. Both students and established researchers will benefit from the book, which provides a dependable introduction and reference material for further studies. Only a basic knowledge of general relativity, quantum mechanics and quantum field theory is assumed. The conceptual aspects and key ideas are discussed in the main body of the book and Continue reading