Analog models of General Relativity: Talks

Conference Poster

Aim of the workshop:


This workshop was an interdisciplinary endeavor which brought together a number of people from the condensed matter community, optics community, and from the theoretical relativity community.

In many ways the main issue was whether condensed matter and/or optical systems could be used to mimic aspects of general relativity; and what the prospects are for medium-term/short-term experimental implementation of these analog systems.

Secondary themes were:

Below we provide abstracts for all the presentations, and copies of the transparencies whenever they are available. Eventually (soon) we will link in more detailed write-ups of each presentation as they become available.

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Index to the presentations:

Invited Presentations:

Analog models for General Relativity: Introduction and Survey

Matt Visser (Washington University in Saint Louis, USA).


In this introductory talk I will survey the various "analog models" for general relativity currently being investigated. These analog models include acoustics in flowing fluids, quasi-particles in superfluids, flowing Bose-Einstein condensates, slow light, nonlinear electrodynamics, the Scharnhorst effect, and more.
The common theme in all these analog models is the presence of a second "effective" Lorentzian metric that governs the propagation of perturbative fluctuations and/or quasi-particles. This effective metric forces the fluctuations to exhibit many of the kinematic features of general relativity, though dynamic features [those specifically based on the Einstein-Hilbert action] typically do not carry over.
It seems plausible that we might be able to construct analog horizons in the laboratory in the not too distant future. Such analog horizons are expected to exhibit Hawking radiation, but possibly without any analog of Bekenstein entropy. Analog models of general relativity are useful probes of Hawking radiation: Because the short-distance physics is explicitly known (atomic physics), the cutoff is physically understood---this helps clarify the role of trans-Planckian frequencies in general relativity black holes, which in these condensed-matter analogs are replaced by "trans-Bohrian" physics.
The long-range prospects for laboratory investigation of these phenomena is extremely encouraging.

Transparencies:
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Effective gravity and quantum field theory in superfluids

Grigori Volovik (Helsinki University of Technology, Finland, and Landau Institute for Theoretical Physics, Russia).

I discuss the origin of the effective gravitational and gauge fields in Fermi superfluids. I will show that these fields necessarily arise together with chiral fermions as the collective bosonic and fermionic modes of the Fermi system, if the Fermi system belongs to a special topological class. It is important that the fermionic vacuum of the Standard Model belongs to the same class, which probably indicates the common origin of the gravitational and gauge fields in a quantum vacuum of high-energy physics and in that of superfluid 3He-A. This similarity allows us to simulate many properties of quantum vacuum. In particular experiments on the axial anomaly in the effective field theory have been conducted in 3He-A, which verified the Adler-Bell-Jackiw anomaly equation. I will discuss also the cut-off problem in the effective theories in condensed matter, where the trans-Planckian physics is well determined. This allows us in particular to consider the cosmological constant problem from the condensed matter point of view. The analogy with superfluids shows that the fermionic vacuum is not gravitating in equilibrium, i.e. the cosmological constant is exactly zero in equilibrium vacuum due to the vacuum stability condition. On the other hand, for the non-equilibrium state, such as in expanding universe, one must expect that the vacuum contribution to the Einstein equations would be of order of matter contribution. This is in agreement with the latest evidence of the accelerating universe. I will also consider different effective spacetime metrics, which can be simulated in superfluids, including event horizon, ergoregion, rotating vacuum, antigravitating string, spinning string, inflation, etc.

Transparencies:
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Black Holes, Dumb Holes and Entropy

Bill Unruh (University of British Columbia, Canada).

This is an overview type talk where I talk about the problems of black hole evaporation, about what Dumb holes can contribute to the discussion, (and can't), and about the entropy of black holes.

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Dissipation effects in vacuum. Towards a collective description of gravitational interactions in quantum black hole physics

Renaud Parentani (Tours University, France).

In Hawking's derivation of black hole radiation, the radiation field obeys a linear d'Alembertian equation. Instead, when taking gravitational interactions into account, one obtains non-linear effects between infalling and outgoing field configurations which are governed by their stress tensor. When the infalling configurations are in their vacuum state (that is, when no infalling quanta cross the horizon) the dominant interactions come from the fluctuations of the stress tensor and not from its mean value. Moreover, these interactions grow arbitrarily when outgoing quanta are traced backward in time near the black hole horizon. This means that the near horizon description of the state of the radiation field can no longer be approximated by a tensor product of an outgoing sector and an infalling one. This entanglement prevents the occurrence of trans-Planckian frequencies in matrix elements. To actually compute these non-linear effects we worked in an eikonal approximation, to lowest order in the gravitational coupling. In this approximation, the infalling vacuum fluctuations act as a stochastic environment for the outgoing quanta. Then, the near horizon propagation of outgoing quanta resembles that of phonons in a moving random medium.


Related articles:
Related lecture notes (an introduction to sound propagation in a random medium):
Write up:

Effective geometry in nonlinear electrodynamics

Mario Novello (Centro Brasileiro de Pesquisas Fisicas, Brazil).

Photons in the non-linear regime of Electrodynamics propagate along null geodesics in an effective geometry that depends on the background field. We analyse such phenomena both in the general case of non-linear Lagrangians and in a non-linear dielectric medium. This property is not restricted to photons but can be generalized to non-Abelian theories (gluons) and to higher spins. We discuss the case of non-linear spin-2 massless field. A series of examples (confinement of gluons, electromagnetic wormhole, closed space-time paths for the photon, etc) will be presented in this workshop (see contributions by Bergliaffa and Salim).
The result stated above allows a geometrization of the force that a photon experiences due to non-linear electromagnetic phenomena. It will be shown that it is possible to go one step further and extend such geometrization to the dynamics of the field itself in the case of Born-Infeld electrodynamics.

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Light in moving media

Ulf Leonhardt (University of St. Andrews, Scotland).

Light in a moving medium turns out to behave like light in a gravitational field (in a curved space-time). Effects that resemble the marvels of general relativity are usually extremely small. However, one could employ electromagnetically induced transparency to see some spectacular phenomena. In particular, one could create the analog of a black hole.

Transparencies:
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Quasi-gravity versus pseudo-gravity

Brandon Carter (Observatoire de Paris-Meudon, France).

The distinction between ``q-gravity'' and ``p-gravity'' theories is discussed in terms of illustrative examples. The term ``q-gravity'' (short for quasi-gravity) is to be understood here as referring to theories involving mathematical entities, and in particular a spacetime metric, analogous to but qualitatively different from the corresponding genuinely gravitation structures. The prototype example for such a q-gravity structure is the Unruh (sonic) metric in simple fluid and particularly superfluid mechanics. On the other hand the term ``p-gravity'' (short for pseudo-gravity) is to be understood here as referring to theories involving physical phenomena that effectively simulate (and may be experimentally difficult to distinguish from) effects of genuinely gravitational origin. The prototype example of a p-gravitational phenomenon is that of a centrifugal force --- such as the contribution from the earth's rotation, which adds to the dominant genuinely gravitational contribution to give the total effective Galilean gravitational field that is measured by an accelerometer at the earth's surface. A different kind of example arising in the currently fashionable context of brane world cosmology is the artificial gravity-like attraction between massive particles that may come into effect (in addition to their genuinely gravitational interaction) if our 4-dimensional brane world is subject to acceleration relative to the 5 or higher dimensional bulk.

Write up:

Black holes, Hawking radiation, entropy, and information loss in a thin film of 3He-A

Ted Jacobson (University of Maryland, USA).

The causal structure of the effective black hole spacetimes corresponding to certain 3He-A textures will be discussed. A model of black hole formation and subsequent evaporation will be presented which exhibits the transfer of information to a disconnected "baby universe".

Transparencies: Related articles:
Write up:


Noninertial quantum mechanical fluctuations in the laboratory

Haret Rosu (Guanajuato University, Mexico).

The talk extends and updates several sections of my review gr-qc/9406012, last updated in 1997. Spin flip synchrotron radiation is presented in some detail in the context of Bell and Leinaas proposal. Nonequilibrium effective temperatures from glass `thermodynamics' are discussed and considered as useful and quite general concepts for noninertial quantum mechanical fluctuations, though the analogy is not fully disentangled. Mane's proposal to identify the Hacyan-Sarmiento radiation with ordinary synchrotron radiation is also scrutinized. Finally, some other old and more recent `horizon' analogies are briefly surveyed.

Transparencies: Related article:

Write up:


Phonons and Forces: Momentum versus Pseudomomentum

Mike Stone (University of Illinois at Urbana-Champaign, USA).

1) Motivation: The Iordanskii Force
I briefly discuss Volovik's interpretation of the Iordanskii Force as an analogue of the gravitational Aharonov-Bohm effect. I then review the controversy as to whether the Iordanskii force really exists.

2) Forces and ``The Wave Momentum Myth''
The two-fluid model takes it for granted that phonons in a superfluid possess real (as opposed to pseudo-) momentum. The fluid mechanics literature, on the other hand, has long asserted that sound waves possess no real momentum. I review the history of acoustic radiation pressure and examine how these two opposing assertions are to be reconciled.

3) Energy and Momentum in Background Flows
I discuss the extent to which approximations behind the GR interpretation of the sound wave equation in a background flow are able to capture the true energy and momentum fluxes in the fluid.

References to related articles:
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Contributed Presentations:


Lorentzian geometries from Bose-Einstein condensates

Carlos Barceló (Washington University in Saint Louis, USA).

A wave that is propagating in spacetime can exhibit very different behaviour depending on the specific metric characteristics of the particular region being traversed. Many of these behaviours can be reproduced in laboratory settings with waves propagating through condensed matter materials that allow the manipulation of their local properties. In this respect some very promising systems are those given by Bose-Einstein condensates. We will show under what circumstances one can obtain an effective Lorentzian metric to describe the behaviour of linearized phase oscillations in a condensate.

Transparencies:
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A rotating vacuum, noise and the quantum Mach principle

Nami Fux Svaiter (Centro Brasileiro de Pesquisas Fisicas, Brazil).

In this work we consider a quantum version of Newton's bucket experiment in a flat spacetime: we take an Unruh-DeWitt detector in interaction with a real massless scalar field.
We calculate the detector's excitation rate when it is uniformly rotating around some fixed point and the field is prepared in the Minkowski vacuum and also when the detector is inertial and the field is in the Trocheries-Takeno vacuum state. These results are compared and the relations with a quantum version of the Mach's principle are discussed.

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Examples of gravitational-like systems in non-linear electrodynamics

Santiago Perez Bergliaffa (Centro Brasileiro de Pesquisas Fisicas, Brazil).

Some examples of effective metrics (generated by different non-linear electrodynamical theories) that mimic gravitational effects for photons will be presented.

Transparencies: Figures:
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Non-linear electrodynamics can generate closed spacelike paths for photons

Jose Salim (Centro Brasileiro de Pesquisas Fisicas, Brazil).

We show that non-linear electrodynamics may induce a photon to follow a closed curve in spacetime. We exhibit two specific cases in which such closed spacelike curves appear.

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Effective geometry in the Casimir vacuum

Matt Visser (Washington University in Saint Louis, USA).

In 1990 Scharnhorst noticed that photons exhibit anomalous propagation in the Casimir vacuum (the quantum vacuum between perfectly conducting parallel plates). This Scharnhorst effect can be phrased in the language of nonlinear electrodynamics provided one is careful to calculate the quantum expectation value of the "effective metric". Based on general symmetry arguments one can uniquely deduce the form of the quantum-averaged effective metric and demonstrate the complete absence of birefringence in the Casimir vacuum.

Transparencies:
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Last updated 24 October 2002
Mailbox Comments to: visser@mcs.vuw.ac.nz