This award supports research to understand the properties of "negative energy." One focus is on methods of indirectly detecting this unusual form of energy using, in part, techniques developed in the field of quantum optics. The PI and a collaborator will work with an experimentalist to determine if such detection is feasible. A second major focus will be to study the distribution of energy fluctuations in the vacuum. Contrary to our experience in everyday life, the laws of quantum physics tell us that "empty" space is not really empty but consists of ever-present fluctuations of energy. The average value of the energy in empty space is zero, as one would expect, but quantum mechanics says that there must be fluctuations around this mean value. In order to average out to zero, there must be both negative as well as positive fluctuations. What is the likelihood then of getting a negative value in a single measurement? Previous work yields a surprisingly high probability for one spatial dimension. Current efforts are geared toward trying to determine the form of this "probability distribution" in the three-spatial-dimensional world in which we live.
The laws of quantum mechanics allow the existence of states of energy that are lower than that of the vacuum. If there are no restrictions on negative energy, then bizarre macroscopic effects might become possible. These would include wormholes and warp drives for faster-than light travel, violations of the second law of thermodynamics (e.g., refrigerators with no power sources), and the destruction of black holes. However, the same laws of quantum mechanics which allow this form of energy to exist severely limit its behavior. Typically, the longer the negative energy lasts, the smaller its magnitude. This work lies at the juncture of the fields of quantum theory, Einstein's general relativity, and thermodynamics. The only direct probe of negative energy is gravity, but the amounts of negative energy obtainable in the laboratory are minute. Therefore, one has to resort to indirect detection, such as measuring the effect of negative energy on atomic decay rates. The issue of the form of the probability distribution for energy fluctuations is key to understanding the structure of the vacuum, and has implications for other fields such as cosmology. Undergraduates are being prepared to engage in this research through Mathematica-based courses developed by the PI.
In classical physics, the energy density (energy per unit volume) is always a positive quantity. However, the laws of quantum mechanics allow the energy density to become temporarily negative, even in the vacuum! The energy density of the vacuum is constantly fluctuating, positive here and negative there, ever changing, with the average value always turning out to be zero. Now suppose you wanted to make a single measurement of the energy density of the vacuum at a single point in space. What would your chances be of getting a negative result? Work done by Larry Ford at Tufts University, Chris Fewster at the University of York and me, showed that the surprising result is that your chances of measuring the energy density to be negative would be about 84%! What keeps the average energy density of the vacuum zero is that, although the chances are greater that you will measure a negative energy density, the magnitude of the negative energy fluctuations are small compared to the less frequent but larger positive energy density fluctuations you would measure. One of the implications of these results is that, in a gas at high energy, the vacuum fluctuations would be larger than the normal thermal fluctuations in the gas. This is exciting and might be experimentally measurable. The same laws of quantum mechanics that predict the existence of negative energy also severely limit what you can do with it. It turns out that the more negative energy you want, the shorter the time interval over which it can last. These restrictions have come to be known as "Quantum Inequalities", a topic first initiated by Ford. They severely limit the production of macroscopic effects using negative energy, such as time machines, refrigerators without power sources, warp drives, and the possible structure of traversable wormholes. The quantum inequalities were initially derived for inertial (non-accelerated) observers in flat (no gravity) spacetime. However, it turns out that the quantum inequalities for inertial observers in flat spacetime, when properly applied, can still be used to severely limit the characteristics of traversable wormholes, and make the possibility of warp drives extremely unlikely. A popular description of these topics is given in a book that I coauthored with Allen Everett entitled, "Time Travel, and Warp Drives: A Scientific Guide to Shortcuts through Time and Space", which was published by the University of Chicago Press in 2011. The book is scheduled to be translated into Japanese and Chinese, and Allen and I have given several interviews on these topics. Although the existence of negative energy is fleeting, it may still be possible to detect it experimentally. Atoms in states of higher energy can decay into lower energy states when their electrons "jump" from a higher to a lower state. The laws of quantum mechanics say that the time over which this happens cannot be predicted with certainty for a single atom. However, one can get a prediction for large number of atoms. This is called the "lifetime" of the atom. Ford and I considered a possible experiment where one sends a large stream of excited atoms through a very thin cavity. The cavity contains what is known as a "squeezed state", where the energy density can oscillate very rapidly between positive and negative. (Squeezed states are routinely produced in quantum optics labs around the world.) The box has to be thin enough so that an atom goes through just during a period of negative energy before the subsequent positive energy occurs. Ford and I were able to show that in such an experiment, there would be an increase in the lifetime of the atoms (i.e., the atoms would take longer to decay). Although difficult to achieve, such an effect may be observable in future experiments, using large numbers of atoms. In another part of the project, Ford and I examined the negative energy experienced by a particle undergoing sinusoidal motion in a squeezed state, and was thus subject to a changing velocity, and hence an acceleration. There we found that the particle could experience a decreasing energy (i.e., increasing negative energy). Surprisingly, this effect persisted for arbitrarily small velocities. However, we were able to show that these results in no way invalidate nor undermine either the validity or utility of the quantum inequalities for inertial observers. In particular, they do not change previous constraints on the production of macroscopic effects with negative energy, e.g., the maintenance of traversable wormholes. Such effects as those discussed above might be observable for excited atoms undergoing circular motion, or for the alignment of electron spins for electrons circulating in a uniform magnetic field. All of the research done in this project will further our knowledge of this fascinating type of energy and also yield new insights as to the remarkable quantum-mechanical nature of the vacuum.
