Jonathan Oppenheim has moved to the University of Cambridge.

His new webpage is here at DAMTP. The old webpage is below for your viewing pleasure.

I am currently a Lady Davis Fellow at the Racah Institute of Physics, advised by Jacob Bekenstein.

Email: jono (at) phys.huji.ac.il
Phone: 972-2-658 5492
Fax: 972-2-561 1519
Address:Racah Institute of Physics, The Hebrew University, Givat Ram, Jerusalem 91904, Israel

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

Bohr weighing a clock

Research Interests

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

Quantum Gravity


Many researchers believe that understanding black hole thermodynamics is the key to understanding quantum gravity. It is perhaps interesting that one candidate for the entropy of black holes is the entanglement entropy of a quantum field on the black hole space-time. It has been shown that, generically, the entanglement entropy of a field is related to the area of boundaries, rather than the volume of space inside the boundary. In fact, the area scaling behavior of the entropy is not unique to black holes, but can also be seen as the result of long range interactions. I am currently studying various links between Einstein's field equations and thermodynamical equilibrium conditions. This has potentially interesting implications concerning the quantum theory of gravity. I am also looking at analogs of black holes which help to understand black-hole entropy.

Non-Extensive 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). I have also shown 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.

Quantum Information Theory

"You don't understand quantum mechanics, you just get used to it."
-- Richard Feynman (attributed).

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 including quantum data storage, quantum computation, quantum cryptography, and entanglement manipulation. I am particularly interested in the notion that the non-local behavior of quantum mechanics can be described in a manner analogous to thermodynamics. We have recently outlined the three laws of entanglement, and then shown that there are deviations from a reversible thermodynamical regime. I am also working on a new paradigm in which to understand quantum correlations and non-locality. This paradigm has led to the discovery of phase transitions. in entangled systems, and a new form of complementarity between classical and quantum information. Previous work is applicable to limitations on the speed of dynamical evolution, which gives some insight into operations performed on quantum computers.

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)

I am particularly 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. Generically, one finds that the only observables which are measurable, are those which don't evolve - which does not seem to lead to very interesting physics! Understanding the role of time is seen as key in attempts to quantize gravity.


Physics Resources