Things Change – Even in Hamiltonian General Relativity!

by J. Brian Pitts.


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

Black holes without special relativity

By Jishnu Bhattacharyya, Mattia Colombo and Thomas Sotiriou.

Black holes are perhaps the most fascinating predictions of General Relativity (GR). Yet, their very existence (conventionally) hinges on Special Relativity (SR), or more precisely on local Lorentz symmetry. This symmetry is the local manifestation of the causal structure of GR and it dictates that the speed of light is finite and the maximal speed attainable. Accepting also that light gravitates, one can then intuitively arrive at the conclusion that black holes should exist — as John Michell already did in 1783!

One can reverse the argument: does accepting that black holes exist, as astronomical observations and the recent gravitational wave direct detections strongly suggest, imply that Lorentz symmetry is an exact symmetry of nature? In other words, is this ground breaking prediction of GR the ultimate vindication of SR?

Jishnu Bhattacharyya, Mattia Colombo and Thomas Sotiriou from the School of Mathematical Sciences, University of Nottingham.

Jishnu Bhattacharyya, Mattia Colombo and Thomas Sotiriou from the School of Mathematical Sciences, University of Nottingham.

These questions might seem ill-posed if one sees GR simply as a generalisation of SR to non-inertial observers. On the same footing, one might consider questioning Lorentz symmetry as a step backwards altogether. Yet, there is an alternative perspective. GR taught us that our theories should be expressible in a covariant language and that there is a dynamical metric that is responsible for the gravitational interaction. Universality of free fall implies that 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

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

CQG+ Insight: Chiral Gravity

by Kirill Krasnov

Kirill Krasnov

Kirill Krasnov, Professor of Mathematical Physics, University of Nottingham. Pictured here visiting Newstead Abbey, Nottinghamshire

We seem to live in four space-time dimensions, and so should take the structures available in this number of dimensions seriously. One of these is chirality, see below for clarifications on my usage of this term. Related to chirality, there is a remarkable phenomenon occurring in General Relativity (GR) in four space-time dimensions. This phenomenon is so stunning that I would like to refer to it as the chiral miracle. It is well-known to experts. Still, even after almost 40 years after it had appeared in the literature, it has not become part of the background of all GR practitioners. I would like to use this CQG+ insight format to try to rectify this.

I start by reviewing the notion of chirality in four space-time dimensions. I then describe the “chiral miracle” that allows for chiral description(s) of gravity in Continue reading

Book Review: The Springer Handbook of Spacetime

David Garfinkle

David Garfinkle is Professor of Physics at Oakland University. His research is in numerical relativity: the use of computer simulations to study the properties of strong gravitational fields.

Review of “The Springer Handbook of Spacetime” edited by Abhay Ashtekar and Vesselin Petkov

The word “Handbook” in the title is something of a misnomer: it is perhaps better to think of this book as a collection of mini review articles on various topics in relativity.  The best way to use the book is to think of a topic in relativity about which you would say “I wish I knew and understood more about X, but I don’t have the time to read a review article about X, nor the expertise to understand a typical review article on the subject.”  Then look in the book to see if there is a chapter on X, and if so, read it.  (Then repeat the process for each X).  Each mini review article comprises a chapter and the chapters are organized in sections that reflect a particular aspect of relativity.

The first two sections, Introduction to Spacetime Structure and Foundational Issues concentrate mostly on the basic properties of spacetime and on philosophical issues connected with special and general relativity.  I found these sections Continue reading

Taking Newton into space

The test mass retroreflector

Schematic of M R Feldman et al‘s  proposed experiment. The test mass retroreflector, exhibiting harmonic motion within the tunnel of the larger layered sphere, is represented by the filled black circle on the left. Determinations of the round trip light-time from the host spacecraft (on the right) using an onboard ranging system provide measurements of the period of the oscillator.

Newton’s gravitational constant, G, is crucial for fundamental physics: it governs how much spacetime curves for a given mass, is essential for metrology, and might give clues to a deeper understanding of quantum gravity. However, G continues to present unexpected issues in need of resolution. Determinations over the last thirty years have yielded inconsistencies between experiments significantly greater than their reported individual uncertainties, oddly with possible periodic behavior. To push forward, the National Science Foundation (NSF) has recently called for new “high-risk/high-impact” proposals to produce a step-change improvement in measurements (NSF 16-520).

In response, we propose taking advantage of the classic gravity train mechanism by Continue reading

Some memories from meeting Einstein in 1951 – 1952

Yvonne Choquet-Bruhat

Yvonne Choquet-Bruhat is a French mathematician and physicist, renowned for her pioneering work on the initial value problem of General Relativity. Her work was one of the “Milestones of General Relativity” featured in a recent CQG focus issue. She has been on the faculty of the University of Marseille, the University of Reims and the University Pierre-et-Marie-Curie in Paris. She was the first woman to be elected to the French Academy of Sciences and is a Grand Croix of the Legion of Honour of France. She is also an elected member of the American Academy of Arts and Sciences. This reminiscence of Einstein was presented at the conference “A Century of General Relativity” held in Berlin, 30 November to 5 December, 2015. This image of Yvonne Choquet-Bruhat has been obtained from Wikipedia where it was made available by Momotaro under a CC-BY-SA 2.0 license. It is included within this article on that basis and attributed to Oberwolfach Photo Collection. 

I met Einstein in 1951 at the Institute for Advanced Study in Princeton. I was making there a postdoctoral stay, as assistant to the great mathematician Jean Leray, a part-time permanent professor at the IAS. I had defended a thesis on General Relativity under the official direction of André Lichnerowicz, but it was Jean Leray who had encouraged me to attack the problem of the existence of solutions of the Einstein equations taking given initial values, without assuming their analyticity. When I told Lichnerowicz about Leray’s suggestion, he said “it is too difficult for a beginner”. In fact it was not so difficult. In harmonic coordinates, called then “isotherm”, introduced by Lanczos, DeDonder and Georges Darmois, the Einstein equations in vacuum look like a system of quasidiagonal, quasilinear system of second order partial differential equations hyperbolic for a Lorentzian metric. I found by chance an article written in French by Continue reading

General Relativity turns 100!

Clifford M Will

Clifford Will is the Editor-in-Chief of Classical and Quantum Gravity, Distinguished Professor of Physics at the University of Florida, Chercheur Associé at the Institut d’Astrophysique de Paris, and James McDonnell Professor of Space Sciences Emeritus at Washington University in St. Louis.

November 4, 1915 was a Thursday. It was the day that Albert Einstein gave the first of a series of four weekly lectures to the Prussian Academy of Sciences in Berlin. His life was a mess. He was separated from his wife Mileva, who had moved to Zurich taking his sons with her. He was having an affair with his second cousin Elsa. He was working night and day, was barely eating, and was suffering from stomach pains. He had agreed to give these lectures to present his theory of gravity but he still didn’t have it. To make matters worse, David Hilbert was racing to find the field equations first, and Einstein feared he would be beaten. Yet by the third lecture, Continue reading

Spontaneous Scalarization: Dead or Alive?

Read the full article for free* in Classical and Quantum Gravity:
Slowly rotating anisotropic neutron stars in general relativity and scalar-tensor theory
Hector O Silva, Caio F B Macedo, Emanuele Berti and Luís C B Crispino 2015 Class. Quantum Grav. 32 145008

*until 21/10/15

Emanuele Berti and Hector Okada da Silva

Hector O. Silva (right) is a graduate student of Professor Emanuele Berti (left) in the gravity group at the University of Mississippi (USA).

This is a time for celebration for anyone with even a passing interest in gravity. Einstein’s general theory of relativity is turning 100, Advanced LIGO started the first observing run on September 18, and LISA Pathfinder is scheduled to launch in the Fall. While we celebrate the centenary of general relativity, we should also remember that there are many good reasons why the theory may well require modifications. Cosmological observations indicate that most of the Continue reading

Local and gauge invariant observables in gravity

Read the full article for free* in Classical and Quantum Gravity:
Local and gauge invariant observables in gravity
Igor Khavkine 2015 Class. Quantum Grav. 32 185019

*until 14/10/15

Generalized locality leads to lots of observables in gravity

Igor Khavkine

Igor Khavkine is finishing up his term as a postdoctoral researcher at the University of Trento, Italy. His main interests are mathematical aspects of classical and quantum field theory, with an emphasis on gravity.

The problem of observables in general relativity is essentially as old as the theory itself. Einstein’s guiding principle of “general covariance”, that is, explicit tensorial transformation of basic physical fields and their equations under general coordinate transformations, leads to a formulation of the theory with “gauge” degrees of freedom. Those are degrees of freedom that, simply speaking, don’t contain any physical information and can be arbitrarily altered by the application of a coordinate transformation or, more abstractly, a diffeomorphism. Such a formulation is simple and Continue reading