Jonathan Oppenheim

Royal Society University Research Fellow at the Department of Applied Mathematics & Theoretical Physics (DAMTP), University of Cambridge

Email: J.Oppenheim (at) damtp.cam.ac.uk
Phone: +44 (0)1223 764 269 (although email is best)
Fax: +44 (0)1223 765 900
Address: Department of Applied Mathematics and Theoretical Physics, University of Cambridge,
Wilberforce Road,
Cambridge CB3 0WA, U.K.

You can find some of my archived publications here.

My Ph.D. thesis was on Quantum Time. It has many great cartoons drawn by the infamous French Situationist, Victoria Scott.

I study quantum information theory, quantum gravity, foundations of quantum mechanics. and thermodynamics in gravitational systems. My research interests are described below in more detail. There, you will also find links to some decent physics resources.

Bohr weighing a clock

News (updated sporadically)

Research Interests

I am currently engaged in research projects in several fields. I am particularly interested in quantum information theory, entanglement, black hole thermodynamics, and statistical mechanics in theories with long range interactions. Although these fields are often distinct, there are many conceptual overlaps, as can be seen below.

Quantum information theory

"You don't understand quantum mechanics, you just get used to it."
-- attributed to Feynman, borrowed from von Neumann.

Quantum information theory is currently a very exciting field, and we are constantly learning new and surprising things about quantum mechanics. I am presently studying various topics mostly in quantum information theory, quantum cryptography, and entanglement manipulation.

Much of my work is in understanding the basic blocks of quantum information theory -- what does it mean for one quantum system to have information about another system. This is often best understood through communication theory. If an individual has a lot of information about my system, then I don't need to send them many qubits for them to possess the rest of my state. It was this idea which led to state merging and negative information.

Quantum gravity and black hole thermodynamics


"The hardest thing of all is to find a black cat in a dark room,
especiall if there is no cat."
--Confucius

Many researchers believe that understanding black hole thermodynamics and the origin of black hole entropy is the key to understanding quantum gravity. At the moment, I'm interested in using tools from quantum information theory to understand problems such as black hole information loss, and information destruction. My latest project has been in showing that one can have information destruction, in a theory which is both local, and obeys conservation laws.

Statistical Mechanics and Thermodynamics


"In this house, young lady, we obey the laws of thermodynamics!"
--Homer Simpson

Ordinarily, when one looks at the thermodynamical properties of a system, one assumes that interactions are either short range, or are screened. However, when interactions are taken into account, one finds that quantities which are usually extensive (such as the energy and entropy which scale as the size of the system), or intensive (such as the temperature and pressure, which are independent of the system's size), no longer remain so. Examples of such cases are gravitational systems (and in particular, black holes), and systems with entanglement entropy. Understanding non-extensive statistical mechanics and thermodynamics may be highly important in understanding black holes and systems where the entropy of entanglement play a role.

I have been developing new methods for studying the thermodynamics of systems with long-range interaction. I have been looking at various scaling relations which become important in non-extensive systems (for example, the Gibbs-Duhem relation no longer holds). For example, entropy becomes area scaling, even before a black hole forms in a gravitational system. In other systems with long range interactions, I have found that for general classes of theories, the local temperatures of various parts of the system are not equal at equilibrium. Some of these relations may have important applications in cosmology.

Foundations of quantum mechanics

"It is very difficult to be more interesting than quantum mechanics."
--Gaspar, to the frustrated wife of a physicist (who shall remain anonymous)

As a general rule, I am interested in understanding how one might be able to generalize our current laws of evolution and the state space these laws act on. This is not only to understand what other laws might be possible, but also to understand what is so special about current physical laws and states.

Other areas of interest, include for example, probabilistic interpretations of unitaries. In quantum mechanics, outcomes of measurements on a state have a probabilistic interpretation while the evolution of the state is treated deterministically. However, it turns out that one can also treat the evolution as being probabilistic in nature and one can measure `which evolution' happened.

I am also interested in the role of time in quantum mechanics, which was the subject of my Ph.D thesis. There, it was proposed that there is a new fundamental limitation on the accuracy of measurements of the time of an event. It is also impossible to tell the past from the future

This subject becomes particularly important in closed systems, and it is then that one encounters various issues which bear strongly on attempts to quantize gravity.


Physics Resources

Other links for your pleasure