1 22 June 2010 M.E. Hogan University of Massachusetts Dartmouth Foundational Questions Institute Cosmic Recall, Decoherence, and the Arrow of Time In the following, I will summarize some of the research I have worked on over the past semester. This research broadly falls under the topic of quantum cosmology, the application of quantum mechanics and, more recently, theories of quantum (and post-quantum) gravity to questions relating to the origin, structure, and evolution of the universe as a whole. The questions raised are some of the most important in science, as they deal with the fundamental nature of reality of the largest, and smallest, of scales. Some of the ideas contained herein may be considered speculative, but science cannot progress without a healthy bit of speculation, and it is possible that some, or even many, of these ideas will become testable, either soon, or at some time further in the future. This work was supported by the Fundamental Questions Institute (FQXi) under the gracious guidance of Professor Gaurav Khanna at the University of Massachusetts Dartmouth. I ǁas diƌeĐted to ǁoƌk iŶ thƌee ŵaiŶ diƌeĐtioŶs. The fiƌst, the issue of ĐosŵiĐ ƌeĐall, ĐoŶĐeƌŶs ǁhetheƌ a ĐLJĐliĐ universe, experiencing a quantum bounce at the point of the classical initial singularity due to the effects of discrete spacetime in loop quantum cosmology (LQC), will remember its previous state before the bounce. This issue is important because the classical entropy of the previous universe is assumed, and has been calculated for certain models, to be arbitrarily large, and this is generally seen to be incompatible with the current observations that our present universe began in an exceptionally low-entropy state. The concept of cosmic recall refers to this preservation of entropy and other similar fundamental constants present in the preceding spacetime manifold's configuration through the quantum bounce, and it is a matter of (often heated) contention as to whether this represents a valid phenomenon in our universe. Second, there is the issue of quantum decoherence. According to the orthodox Copenhagen interpretation of quantum mechanics, when a system is measured, its wavefunction collapses to a particular eigenfunction belonging to its configuration space, and this process is fundamentally irreversible. This, however, is incompatible with the assumption that all physical processes are (in principle) reversible and symmetric with respect to time, and is often seen to be intimately related to the Arrow of Time, as discussed below. This issue is also often seen to be quite a controversial one, and our coverage of this topic, for now, shall be rather brief. Finally, as eluded to above, there is the problem of entropy and the Arrow of Time. The laws of physics seem to be symmetric with respect to the three classical macroscopic dimensions of space, but are fundamentally asymmetric in time. It is possible for an object to move arbitrarily (subject to physical laws) in any direction of space, but only forward in time. This is most commonly seen to be a consequence of the similarly-monotonic arrow of entropy, which must also always increase (or at least stay constant). These fundamental issues are discussed at great length in Sean Carroll's recently- published tome, From Eternity to Here (2010), as well as in several of his more recent papers; these were the primary source for the related content discussed herein, though, as always, other sources have been referenced when it was appropriate. In addition, I have investigated other related areas of quantum gravity and quantum cosmology that maybe of relevance to the present arguments. These will be expanded upon below as they are relevant. Cosmic Recall The fiƌst issue ǁe ǁill ĐoŶsideƌ is that of ĐosŵiĐ ƌeĐall ǁithin loop quantum cosmology. Loop quantum cosmology (LQC) is a symmetry-reduced application of loop quantum gravity (LQG, also known as quantum geometry) with