Tails of gravitational waves and mechanics of compact binaries

by Luc Blanchet and Alexandre Le Tiec

The first law of binary black hole mechanics can be extended to include non local tail effects.

Ever since Kepler’s discovery of the laws of planetary motion, the “two-body problem” has always played a central role in gravitational physics. In Einstein’s general theory of relativity, the simplest and most “universal,” purely gravitational, two-body problem is that of a binary system of black holes. The inspiral and merger of two compact objects (i.e. bodies whose radius is comparable to their mass, in “geometric” units where G = c = 1) produces copious amounts of gravitational radiation, as was recently discovered by LIGO’s multiple detections of gravitational waves from black hole binary systems.


Alexandre Le Tiec (left) celebrates the detection of gravitational waves and Luc Blanchet (right) thinks about gravitational waves in Quy Nhon, Vietnam

In general relativity, the inspiral and onset of the merger of two compact objects is indeed universal, as it does not depend on the nature of the bodies, be they black holes or neutron stars, or possibly more exotic objects like boson stars or even naked singularities. However, the gravitational waves generated during the post-merger phase depend on the internal structure of the compact objects, and in the case of neutron stars should reveal many details about the scenario for the formation of the final black hole after merger, and the equation of state of nuclear matter deep inside the neutron stars

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Why we built the Holometer

by The Holometer Team: Aaron Chou, Henry Glass, H Richard Gustafson, Craig Hogan, Brittany L Kamai, Ohkyung Kwon, Robert Lanza, Lee McCuller, Stephan S Meyer, Jonathan Richardson, Chris Stoughton, Ray Tomlin and Rainer Weiss.

In a patch of prairie west of Chicago, amidst the rusting relics of 20th century particle beam experiments, we’ve built a new kind of device, designed to monitor positions of isolated, stationary massive bodies—or more precisely, to measure their spacelike correlations in time—with unprecedented fidelity and precision.  Why?


The Holometer Team
Fermi National Accelerator Laboratory: Aaron Chou (Co-PI, project manager), Henry Glass, Craig Hogan (Project Scientist), Chris Stoughton  and Ray Tomlin.          Massachusetts Institute of Technology: Rainer Weiss               University of Chicago: Brittany L.Kamai,Ohkyung Kwon, Robert Lanza, Lee McCuller   Stephan S Meyer (Co-PI) and Jonathan Richardson
University of Michigan: H. Richard Gustafson

The motivation for our experiment starts with a foundational conflict of the two great pillars of physics, relativity and quantum mechanics.  In relativity, space-time is built out of a continuum of events with definite locations in space and time, and it is based on a principle of invariance, that no measurable physical effect can depend on an arbitrary choice of coordinates.  Somehow, that classical world shares dynamical energy and information with quantum mechanical systems built out of a set of states that may be discrete, that are in general indeterminate superpositions of different possibilities not localized in space or time, and that only have physical meaning when correlated, in the context of a specific measurement, with the apparatus of an observer.  Physicists have tried to reconcile these incompatible ideas for a century, starting with famous dialogs between the founding fathers, Einstein and Bohr.

In practice, the conflict has remained theoretical, since it has not led to any problem predicting the results of actual experiments.  But that success is itself a problem: there are no experiments that could give us clues to general principles that may govern a deeper level of reality where a space-time grows out of a quantum system.

Indeed, experiments today solidly confirm both relativity and quantum physics.  Energy transformations of dynamical space-time were spectacularly displayed by the recent detection of gravitational waves from black hole binary inspiral and coalescence.  Delocalized quantum states of particles appear in modern experiments in the form of real-life spooky spacelike correlations that directly challenge Einstein’s notions of reality and locality.


The Fermilab Holometer under construction

Still, no experiment has measured a quantum behavior of space-time itself.  The reason often cited is that the scale where quantum dynamics overwhelms classical space-time, the Planck time, about 10-43 seconds,  lies far beyond the reach of direct metrology.  However, if quantum states are truly delocalized, it may be possible to reach Planck-scale precision in measurements of correlations in space-time position over a macroscopic volume.  The Fermilab Holometer, as we’ve called our machine, is designed to test for such exotic correlations, providing an experimental window into the principles and symmetries of the quantum system that gives rise to space and time.

Theory has provided some important clues that quantum geometry may produce significant exotic correlations in space-time position even on macroscopic scales.  Hints from several directions suggest that the amount of quantum information in a volume of space-time of any size—the number of degrees of freedom—is finite and holographic, given by the area of a two-dimensional bounding surface in Planck units.  The theory of black hole evaporation also suggests that quantum states of geometry are not themselves localized in space and time, but are distributed over a volume as large as the event horizon or curvature radius.

Such results raise the possibility that a laboratory-scale experiment, with enough sensitivity and the right configuration, could measure new spacelike correlations from Planck-scale quantum geometry.  When studying correlations in space-time position, it may not be necessary to resolve a Planck time directly in the time domain.  Instead, extrapolations of standard quantum theory suggest that Planck-scale effects should appear in the “strain noise power spectral density”: a mean square dimensionless strain, or fractional length distortion, per frequency interval.

 The Holometer resembles a scaled-down version of LIGO (see our instrumentation paper in CQG, http://iopscience.iop.org/article/10.1088/1361-6382/aa5e5c).  It consists of two Michelson interferometers with 40-meter arms, located right next to each other, whose signals are correlated in real time.  The data acquisition system operates fast enough to keep track of positions across the 40-meter device in both space and time.  We’ve shown that we can measure spacelike correlations to a precision of attometers, with a bandwidth of more than 10 MHz—several times faster than the time it takes the laser light to traverse the apparatus.  That sensitivity allows us to measure exotic correlations with strain noise power spectral densities substantially less than a Planck time.

The Holometer Layout

An aerial view showing the layout of both the First and Second-Generation Holometers

Over the course of hundreds of hours, light traverses the apparatus about a trillion times, and the instrument measures self-interference from about 1028 photons, allowing a measurement of strain noise density, limited mainly by quantum statistical noise, about 28 orders of magnitude smaller than the period of the laser light.  So far, measurements are consistent with zero exotic noise from the space-time itself to much better than Planck precision.  This clean null result, reported in https://doi.org/10.110/PhysRevLett.117.111102, verifies the power of the technique. Along the way, it also places unique constraints on gravitational waves at megahertz frequencies not reachable by LIGO; see http://journals.aps.org/prd/abstract/10.1103/PhysRevD.95.063002.

The physical significance of the null result for quantum geometry can be interpreted in terms of models based on symmetries at the Planck scale. Like the famous Michelson-Morley experiment that demonstrated a frame-independent speed of light long before relativity was discovered, it verifies an exact symmetry.  Some day, that symmetry may be understood as a consequence of more fundamental principles of the quantum system that underlies space-time.

The null result has already inspired our next experiment, which will measure a different symmetry at similar sensitivity. During the last year, we have changed the physical layout of the interferometer light paths to include a bend and a transverse segment, so that it can now detect correlated rotational fluctuations.  The reconfigured apparatus will allow us to measure fluctuations in rotation of the local inertial frame that correspond to mean square variations in angular direction per frequency interval less than a Planck time.  Rotational fluctuations of this magnitude, with a specific frequency spectrum (see the calculations in arXiv:1607.03048, arXiv:1509.07997), would be expected if the local inertial frame emerges from a quantum system at the Planck scale.

[1] Chou, A.S., Gustafson, R., Hogan, C., Kamai, B., Kwon, O., Lanza, R., McCuller, L., Meyer, S.S., Richardson, J., Stoughton, C. and Tomlin, R., 2016. First measurements of high frequency cross-spectra from a pair of large Michelson interferometers. Physical Review Letters, 117, p.111102. https://doi.org/10.110/PhysRevLett.117.111102

[2] Chou, A.S., Gustafson, R., Hogan, C., Kamai, B., Lanza, R., Larson, S.L., McCuller, L., Meyer, S.S., Richardson, J., Stoughton, C. and Tomlin, R., 2016. MHz Gravitational Wave Constraints with Decameter Michelson Interferometers. Physical Review D, 95, 063002. http://journals.aps.org/prd/abstract/10.1103/PhysRevD.95.063002

[3] Hogan, C., Kwon, O. and Richardson, J., 2016. Statistical Model of Exotic Rotational Correlations in Emergent Space-Time. arXiv preprint arXiv:1607.03048. arXiv: 1607.03048

[4] Hogan, C., 2015. Exotic Rotational Correlations in Quantum Geometry. arXiv preprint arXiv:1509.07997. arXiv: 1509.07997

Read the full article in Classical and Quantum Gravity:
The Holometer: an instrument to probe Planckian quantum geometry
Aaron Chou et al. 2017 Class. Quantum Grav. 34 065005

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Can one hear the shape of an ultra compact object?

by Sebastian Völkel and Kostas Kokkotas

A journey from ultra compact objects to quasi-normal modes and back

Never before has gravitational wave research been more promising and attractive than nowadays. With the repeated detection of gravitational waves from binary black hole mergers by LIGO [1–3], not only the long-standing pursue for one of Einstein’s most challenging predictions was confirmed, but also a milestone for many future applications reaching from fundamental physics to astronomy was set. One of the many applications that could follow is addressed in our new CQG paper [4] and shall be broadly presented within a more general introduction to some recent developments in the following lines.

CQG+ format pictures

About the Authors (Left to right): Sebastian Völkel is a first-year PhD student in the Theoretical Astrophysics group of Professor Kostas Kokkotas at the University of Tübingen, located in the south of Germany. Among his research interests is the study of compact objects along with their gravitational wave properties.  Professor Kostas Kokkotas is leading the group of Theoretical Astrophysics at the University of Tübingen. The focus of his research is on the dynamics of compact objects (neutron stars & black-holes), gravitational waves and alternative theories of gravity. More information about the group can be found here.

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The silence deep within the universe

by Astrid Eichhorn, Sebastian Mizera and Sumati Surya

Silence is a rare commodity in our everyday, technology-driven lives; from the outright blare of car horns in India, to the quieter, but persistent sounds of mobile phones in Germany, constantly alerting us to the incoming messages, to the 24 hour news cycle on Canadian TV. Finding a few quiet moments, unhindered by the constant onslaught of information requires a considerable effort. Indeed, it often feels that noise, not silence is the generic state of our world.

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

by Ivan Agullo, Abhay Ashtekar and Brajesh Gupt

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 10^{65} 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: Gupt, Ashketar and Agullo

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

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Can boundaries and Hamiltonians get along?

by J. Fernando Barbero G., Benito A. Juárez-Aubry, Juan Margalef-Bentabol and
Eduardo J. S. Villaseñor.

Boundaries are ubiquitous in physics, if anything because most material objects tend to have one… In the context of gravity they play a number of interesting roles: from the definition of conserved quantities in asymptotically flat spacetimes to holography (no lasers here, sorry) or the modeling of black holes. A natural question in the context of the canonical quantization of gravitational theories is how to obtain their Hamiltonian description – in particular the constraints – in the presence of boundaries.


Eduardo and Fernando trying to get inspiration for the new group logo

“Juan, can you hear us?”

“Yes, the connection seems to be working better these days.”

“Hi Benito. Good to see you! Can you also see us?”

“Sorry for the delay, it is early in the morning here. Yeah, I can see you perfectly. Hi, Eduardo and Fernando! Hi, Juan!”

“Hi, there!”

“So, as I told you in my last email, we have to write this CQG+ Insight piece about our traces paper. You know, it should be informative, informal and infused with deep physical insights, so, any suggestions? — Yes, Fernando.”

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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.

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Interview with Daniela Saadeh: winner of the IOP Gravitational Physics Group (GPG) thesis prize

Daniela Saadeh

Daniela Saadeh – UCL Astrophysics Group

CQG is proud to sponsor the IOP Gravitational Physics Group (GPG) thesis prize. This year the prize was awarded to Daniela Saadeh, who we have interviewed below. Congratulations Daniela!

Can you tell us a little bit about the work in your thesis?

A fundamental assumption of the standard model of cosmology is that the large-scale Universe is isotropic – i.e. that its properties are independent of direction. Historically, this concept stemmed from the Copernican Principle, the philosophical statement that we do not occupy a ‘special’ place in the Universe. In physical terms, this idea is converted into the assumption that all positions and directions in the Universe are equivalent, so that no observer is ‘privileged’.

However, assumptions must be tested, especially foundational ones. General relativity – our standard theory of gravity – allows for many ways in which spacetime could be anisotropic: directional symmetry is not fundamentally required. If the Universe were indeed to be anisotropic, we would actually need to carefully revise our understanding (for instance, calculations about its history or content). Making this health check is very important! Continue reading

Is the Cosmic Microwave Background Gaussian?

by Thomas Buchert, Martin J. France & Frank Steiner.

Thomas Buchert is Professor of Cosmology at the University of Lyon 1, working at the ‘Centre de Recherche Astrophysique de Lyon’ (CRAL)

This challenging question touches on the initial conditions of the primordial Universe, on modeling  assumptions, and statistical ensembles generating the Cosmic Microwave Background.

Our CQG paper explores model-independent approaches to these challenges.

We observe only a single Universe, the one we live in. We cannot rerun cosmic history to see how actual observations might have varied. Nor can we communicate with distant aliens to build an ensemble of observations of the Universe from different vantages in space and time. The only possibility that remains is to make a model of the Universe. Running this model a large number of times, we can generate an ensemble of realizations of the Cosmic Microwave Background (CMB) sky maps. In principle, it is then possible to answer the question, whether there is a single realization of the chosen model that agrees with what is observed. Moreover, we should determine the probability of finding this single realization within the ensemble of patterns that our model allows. To do this we have to Continue reading

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