Gravitation in terms of observables: breathing new life into a bold proposal of Mandelstam

By Rodolfo Gambini and Jorge Pullin

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Rodolfo Gambini and Jorge Pullin have been collaborating for 27 years

In the 1960’s Stanley Mandelstam set out to reformulate gravity and gauge theories in terms of observable quantities. The quantities he chose are curves, but specified intrinsically. The simplest way of understanding what does “specified intrinsically” means is to think how the trajectory of a car is specified by a GPS unit. The unit will give commands “turn right”, “advance a certain amount”, “turn left”. In this context “right” and “left” are not with respect to an external coordinate system, but with respect to your car. The list of commands would remain the same whatever external coordinate system one chooses (in the case of a car it could be a road marked in kilometres or miles, for instance). The resulting theories are therefore automatically invariant under coordinate transformations (invariant under diffeomorphisms). They can therefore constitute a point of departure for the quantization of gravity radically different from other ones. For instance, they would share in common with loop quantum gravity that both are loop-based approaches. However, in loop quantum gravity one has to implement the symmetry of the theory under diffeomorphisms. Intrinsically defined loops, on the other hand, are space-time diffeomorphism invariant, therefore such a symmetry is already implemented. It is well known that in loop quantum gravity diffeomorphism invariance is key in selecting in almost unique way the inner product of the theory and therefore on determining the theory’s Hilbert space. Intrinsically defined loops are likely to be endowed with a very different inner product and Hilbert space structure. In fact, since the loops in the Mandelstam approach are space-time ones it lends itself naturally to an algebraic space-time covariant form of quantization.

Some features of the Cosmos in Loop Quantum Gravity

By Parampreet Singh, Louisiana State University, USA

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CQG Editorial Board member, Param Singh, Guest Edited the Applications of loop quantum gravity to cosmology focus issue in 2016 and 2017

A successful union of Einstein’s general relativity and quantum theory is one of the most fundamental problems of theoretical physics. Though a final theory of quantum gravity is not yet available, its lessons and techniques can already be used to understand  quantization of various spacetimes. Of these, cosmological spacetimes are of special interest. They provide a simpler yet a non-trivial and a highly rich setting to explore detailed implications of quantum gravitational theories. Various conceptual and technical difficulties encountered in understanding quantum dynamics of spacetime in  quantum gravity can be bypassed in such a setting. Further, valuable lessons can be learned for the quantization of more general spacetimes.

In the last decade, progress in loop quantum gravity has provided avenues which allow us to reliably answer various interesting questions about the quantum dynamics of spacetime in the cosmological setting. Quantum gravitational dynamics of cosmological spacetimes obtained using techniques of  loop quantum gravity leads to a novel picture where singularities of Einstein’s theory of general relativity are overcome and a new window opens to test loop quantum gravity effects through astronomical observations.

The scope of the Focus Issue: Applications of loop quantum gravity to cosmology, published last year in CQG, is to provide a snapshot of some of the rigorous and novel results on this research frontier in the cosmological setting.

Black and White Hole Twins Connected by Quantum Gravity

By Javier Olmedo, Sahil Saini and Parampreet Singh

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Black holes are perhaps the most exotic objects in our Universe with very intriguing properties. The event horizon does not allow light and matter to escape, and hides the central singularity. As in the case of the big bang singularity, the central singularity is a strong curvature singularity where all in-falling objects are annihilated irrespective of their strength. Since singularities point out pathologies of general relativity, a more fundamental description obtained from quantum gravity must resolve the problem of singularities. Singularity resolution is also important for resolving many of the paradoxes and conundrums that plague the classical theory such as the cosmic censorship conjecture, black hole evaporation, black hole information loss paradox, etc.

Dr. Javier Olmedo is a postdoctoral researcher at Pennsylvania State University

Sahil Saini is a graduate student at Louisiana State University

Dr. Parampreet Singh is an associate professor at Louisiana Stare University

Black holes have mirror versions too. Known as white holes, these are solutions of general relativity with the same spacetime metric.  If the black holes do not allow even the light to escape once it enters the horizon, thus nothing can enter the white hole horizon. Light and matter can only escape from the white hole. It has sometimes been speculated that black hole and white hole solutions can be connected, providing gateways between different universes or travelling within the same universe, but details have been sparse. The reason is due to the presence of the central singularity which does not allow a bridge between the black and white holes.

Can observations determine the quantum state of the very early Universe?

by Ivan Agullo, Abhay Ashtekar and Brajesh Gupt

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Can observations determine the quantum state of the very early Universe?

Can we hope to know even in principle what the universe was like in the beginning? This ancient metaphysical question has acquired new dimensions through recent advances in cosmology on both observational and theoretical fronts. To the past of the surface of last scattering, the universe is optically opaque. Yet, theoretical advances inform us that dynamics of the universe during earlier epochs leaves specific imprints on the cosmic microwave background (CMB). Therefore, we can hope to deduce what the state of the universe was during those epochs. In particular, success of the inflationary scenario suggests that the universe is well described by a spatially flat Friedmann, Lemaître, Robertson, Walker (FLRW) space-time, all the way back to the onset of the slow roll phase. This is an astonishingly early time when space-time curvature was some times that on the horizon of a solar mass black hole and matter density was only 11 orders of magnitude smaller than the Planck scale.

Clockwise from top left: Brajesh Gupt (Pennsylvania State University), Abhay Ashtekar (Pennsylvania State University) and Ivan Agullo (Louisiana State University)

Are you going to Loops’ 17?

At the beginning of next week Jennifer Sanders and I will be representing the CQG editorial team at the Loops’ 17 conference at the University of Warsaw in Poland.

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

by Parampreet Singh.

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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

Propagation in the absence of classical spacetime

Written by Madhavan Varadarajan

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The author’s research group busy at work. Madhavan Varadarajan is a Professor at the Raman Research Institute in Bangalore, India.

At the Planck scale of 10⁻³³cm, where the very notion of classical spacetime ceases to exist due to large quantum fluctuations of spacetime geometry, can meaning be given to the notion of “causality”? We are interested in this question in the context of Loop Quantum Gravity (LQG).

The basic quantum states of LQG are labelled by graphs. Each such state describes discrete one dimensional excitations of spatial geometry along the edges of its graph label. These ‘graphical’ states provide the

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.

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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?

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.

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

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

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

Book Review: The Singular Universe and the Reality of Time

Julian Barbour is an independent theoretical physicist and Visiting Professor in Physics at the University of Oxford. He has specalized in the relational aspects of dynamics.

Review of “The Singular Universe and the Reality of Time” by Roberto Mangabeira Unger and Lee Smolin

The Singular Universe is effectively two separate books held together by some common ideas. Roberto Mangabeira Unger is a philosopher, social and legal theorist and politician who helped to bring about democracy in Brazil and has twice been appointed as its Minister of Strategic Affairs (in 2007 and 2015). According to Wikipedia (current entry), “his work begins from the premise that no natural social, political or economic arrangements underlie individual or social activity.” A similar spirit informs his approach to cosmology. Lee Smolin is of course well known as one of the creators of loop quantum gravity and as the author of several popular-science books. For brevity, I shall refer to the authors as RMU and LS. The book is over 500 pages in length. The first part, by RMU, is more than twice the length of LS’s and could have been shortened without loss of essential content. There is a final 20-page section detailing differences of view, which are substantial in some cases because RMU advocates a much greater break with the conventional approach to science than LS.

The two authors are agreed that a new ‘historical’ approach to cosmology is needed. For RMU, the mere fact that the universe has been shown to have a history is enough to indicate that the methods hitherto used to study the universe must be radically modified. LS argues for a new approach because of our failures to understand the history and properties of the universe as so far discovered. He points out that,