Professor Steve Carlip


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My Research

"Quantum gravity is notoriously a subject
where problems vastly outnumber results."
-Sidney Coleman
One of the deepest problems of modern physics is that of reconciling our well-established theories of fundamental processes at very small scales, as described by quantum field theory, with those at very large scales, as described by general relativity. Efforts to formulate a consistent quantum theory of gravity date back to at least 1930 -- here is a nice history -- but despite seventy-five years of work, we still seem far from an answer. While such a unification is probably unimportant at laboratory scales, it is vital for understanding the physics of strong gravitational fields: in the cosmology of the very early Universe, for example, and in the formation and evaporation of black holes.

But the study of quantum gravity is difficult, and the main thing we have learned in these years of research is that the obvious approaches don't work. The difficulties are partly technical -- general relativity is a complicated, nonlinear theory -- but we face deep conceptual problems as well. According to general relativity, gravity is a consequence of the geometry of spacetime. That means that when we talk about quantizing gravity, we really mean "quantizing space and time themselves." We don't know what a completed quantum theory of gravity will look like, but we will surely end up with a picture of the Universe quite unlike anything we now imagine.

In the past few years, two promising new approaches to these problems have emerged. The first is string theory, a model in which elementary particles are not treated as pointlike objects, but instead as extended one-dimensional "strings." (Here is a nice nontechnical introduction.) The second is a reformulation of general relativity in terms of new variables -- "self-dual connections" or "Ashtekar variables" -- that behave more like those of conventional quantum field theories. This approach is now often called "quantum geometry." More recently, a new method, "causal dynamical triangulations," has also shown promise. Gary Au has written a nice nontechnical paper based on interviews with physicists working on string theory and quantum geometry, and I have written a more technical review of a variety of approaches to the problem.

An alternative general strategy for research is to explore simpler models that share the underlying conceptual features of quantum gravity while avoiding the technical difficulties. For example, general relativity in 2+1 dimensions -- two spatial dimensions plus time -- has the same basic structure as the full (3+1)-dimensional theory, but it is technically much simpler, and the implications of quantum gravity can be examined in detail.

For the past few years, I have concentrated on three areas of research:

I have also run a seminar on career prospects and options for physics graduates.

(2+1)-Dimensional Quantum Gravity

General relativity in 2+1 dimensions -- that is, two spatial dimensions plus time -- has proven to be a very useful model for exploring the conceptual foundations of quantum gravity. In three spacetime dimensions, general relativity has finitely many physical degrees of freedom, and there are no freely propagating gravitational waves. As a result, quantum gravity reduces to a special instance of ordinary quantum mechanics, and problems such as nonrenormalizability that are associated with quantum field theory disappear. But the model is still a coordinate-invariant theory of spacetime geometry, and most of the conceptual issues of the full theory remain.

In all, roughly 15 different approaches to quantizing (2+1)-dimensional gravity have been developed. Most of these are discussed in a book I wrote in 1998 for Cambridge University Press. The model has offered insight into such issues as the nature of time in quantum gravity, the source of black hole entropy, and the question of whether the topology of space can change. Here is a paper I wrote with Jeanette Nelson comparing two interesting approaches.

A recent review article I wrote on general relativity in 2+1 dimensions for the on-line journal Living Reviews in Relativity can be found here. Another review is here, this one discussing what we know about the microscopic "statistical mechanics" that presumably underlies (2+1)-dimensional black hole entropy. An older and more general review I wrote on (2+1)-dimensional black holes is here. For some research papers on the statistical mechanics of the (2+1)-dimensional black hole, look here and here.

Black Hole Thermodynamics

Thanks to the work of Hawking and Bekenstein, we have known for 25 years that black holes are thermal objects, with characteristic temperatures, entropies, and radiation spectra. But we still do not really understand why black holes behave this way -- we don't know what microscopic quantum states are responsible for the "statistical mechanics" that leads to these thermodynamic properties. This problem serves as a key test for any attempt to quantize gravity: a model that cannot reproduce the Bekenstein-Hawking entropy for a black hole in terms of microscopic quantum gravitational states is unlikely to be right.

An important focus of my recent work here has been an attempt to understand how much of the statistical mechanics of black holes can be determined purely from general symmetries, independent of the details of quantum gravity. I have shown that a symmetry mechanism is at least plausible. (Here and here are some papers, and here is a review.) This idea would help explain one of the mysteries of this field, sometimes called the problem of universality: the fact that very different approaches to quantum gravity, with different starting points and different underlying degrees of freedom, all seem to give the same answer.

For slides and an audio presentation on this subject, go to my talk at the 1999 Institute for Theoretical Physics Program on the Classical and Quantum Physics of Strong Gravitational Fields. More interesting talks from this program can be found here.

Another interesting issue is whether "quasinormal modes" -- the damped oscillations of a disturbed black hole -- can tell us anything about black hole quantum mechanics. I've written two recent papers on this subject, one on (2+1)-dimensional black holes and another on the higher-dimensional black holes that are understood in string theory.

Other Research

I also work on a variety of other issues involving quantum gravity and "low dimensional physics," and on other areas in which geometry and topology are important to physics. Some of the questions I have studied include:

A few less technical areas I've worked in are the following:

My Students

I generally expect my graduate students to be fairly independent, and to complete at least one major project largely on their own (although with me as a resource, of course). Here are some papers written by my students while they were at Davis:

Michael Ashworth worked on coherent states in quantum gravity, and on conformal field theory from (2+1)-dimensional gravity.

Sayan Basu worked on covariant canonical quantization and, with a postdoc, on observational searches for violations of Lorentz invariance of a sort that might be produced by quantum gravity.

Yujun Chen made major progress in quantizing Liouville theory, particularly in the sector that is probably relevant to black hole entropy.

Russell Cosgrove studied the problem of time in quantum gravity. (See the discussion here of such conceptual problems.)

Eric Minassian worked on the question of singularities in (2+1)-dimensional quantum gravity

Careers for Physicists

Over the past decade, the career options available to graduates with Ph.D.s in physics have shifted dramatically. While the unemployment rate among new graduates is still low, the "traditional" academic path, graduate school to a postdoc to a faculty position, has become much more difficult. At the same time, industrial support for long term research and development in physics has declined, and government labs are, at best, hiring very slowly. Most current faculty members, on the other hand, followed a traditional path, and few are very familiar with the choices now available.

My "Careers in Physics" seminar for graduate students brings in a variety of speakers with physics degrees who have jobs outside academia, to describe their work and also to give some nuts-and-bolts advice about how to get a job. Past speakers have ranged from stock analysts to high school teachers to microwave engineers to radiation safety experts. We also invite occasional "skill" speakers, to address such issues as how to give a good talk and what to expect at a job interview.

For some interesting discussion of careers in science, see Science magazine's Next Wave. For statistics and more information about jobs in physics, look at the American Institute of Physics Career Services and Statistical Research pages, and at a very nice Physics and Astronomy Job Hunting Resources site. Job-hunting help is available at UC Davis from the Internship and Career Center.

Some General Relativity Links

If you're interested in learning more about general relativity and quantum gravity, here are some good starting places:

Some of My Honors and Awards


An Incomplete Glossary

Here are some slightly longer explanations of a few of the ideas I've mentioned elsewhere. Be warned -- the explanations here are, for the most part, drastic oversimplifications, and shouldn't be taken too literally. This section is still under construction (and will be for a long time...).


  • Black hole thermodynamics

  • Causal dynamical triangulations

  • Conceptual problems in quantum gravity

  • The cosmological constant

  • The Hartle-Hawking "no boundary" proposal

  • Hawking radiation

  • Loop quantum gravity: see Quantum geometry

  • Lower dimensional gravity

  • Quantum cosmology

  • Quantum geometry

  • Renormalization

  • String theory

  • Topological field theory

  • Topology and general relativity

  • How to Get Physics Papers on the Web

    Many of the links at this site are to the preprint arXiv, now located at Cornell, which contain huge numbers of electronically accessible preprints and papers in general relativity, high energy physics, and many other fields. To learn more about how to retrieve papers, go here. Papers in astronomy and astrophysics can also be found with the ADS Abstract Service.

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