Quantum Foundations of a Classical Universe Conference - Talks
Title: Quantum Mechanics With Horizons
Abstract: One of the major outstanding puzzles in modern physics is how to make sense of horizons in quantum mechanics. A horizon in classical physics means that there are observers in different spacetime regions who never get to talk to each other, even in principle, or who can only communicate for a finite amount of time before going their separate ways. The most naive attempts to introduce quantum mechanics to these scenarios lead to some unpalatable results, e.g., the black hole information paradox and associated topics. I want to give a general overview of the subject, with special focus on black hole horizons and de Sitter horizons and problems they each present to us. I suspect that progress can be made by properly understanding the emergence of classicality in spacetimes with horizons. It's difficult to give a good reference for these ideas, since they are speculative and each person has their own opinion on how it will all turn out when the dust is settled. Some interesting and recent places to start [are below].
Title: De Sitter Space Without Quantum Fluctuations
Abstract: We argue that, under certain plausible assumptions, de Sitter space settles into a quiescent vacuum in which there are no quantum fluctuations. Quantum fluctuations require time-dependent histories of out-of-equilibrium recording devices, which are absent in stationary states. For a massive scalar field in a fixed de Sitter background, the cosmic no-hair theorem implies that the state of the patch approaches the vacuum, where there are no fluctuations. We argue that an analogous conclusion holds whenever a patch of de Sitter is embedded in a larger theory with an infinite-dimensional Hilbert space, including semiclassical quantum gravity with false vacua or complementarity in theories with at least one Minkowski vacuum. This reasoning provides an escape from the Boltzmann brain problem in such theories. It also implies that vacuum states do not uptunnel to higher-energy vacua and that perturbations do not decohere while slow-roll inflation occurs, suggesting that eternal inflation is much less common than often supposed. On the other hand, if a de Sitter patch is a closed system with a finite-dimensional Hilbert space, there will be Poincare recurrences and Boltzmann fluctuations into lower-entropy states. Our analysis does not alter the conventional understanding of the origin of density fluctuations from primordial inflation, since reheating naturally generates a high-entropy environment and leads to decoherence.
K. Boddy, S. Carroll & J.P., De Sitter Space Without Quantum Fluctuations (arXiv:1405.0298.)
Title: We need anthropics, but it's not coming through for us
Abstract: Inflation generically leads to an infinitely large universe, where everything possible actually happens. To make sense of probabilities in such a universe, we need anthropic ideas that tell us to expect to be typical observers. But even to define "typical" requires solving the measure problem. Many measures have been suggested, but all give paradoxical results (arXiv:1202.3376). And even in a finite universe, to define what qualifies as an observer is very difficult, with all ideas fraught with serious problems (arXiv:1008.0808, arXiv:1304.2625). Thus our work is cut out for us.
Title: Observational Probabilities in Quantum Cosmology
Abstract: In quantum cosmology, we need not only the dynamical laws of physics (e.g., the algebra of quantum operators) and the quantum state of the universe (giving expectation values to the operators) but also rules for extracting observational probabilities from the quantum state. I have shown that these probabilities cannot be given by Born's rule interpreted mathematically as the rule that the observational probabilities are given by the expectation values of projection operators. However, the next simplest option seems to be that the relative probabilities are given by normalizable expectation values of other positive operators, one for each observation. Finding these operators is one way to state the measure problem of cosmology. Some preliminary ideas for part of the structure of these operators will be discussed, as well as how these ideas fit within a Bayesian analysis for ultimate theories.
D.N.P., Insufficiency of the Quantum State for Deducing Observational Probabilities (arXiv:0808.0722).
D.N.P., The Born Rule Fails in Cosmology (arXiv:0903.4888).
D.N.P., Born Again (arXiv:0907.4152).
D.N.P., Born's Rule Is Insufficient in a Large Universe (arXiv:1003.2419).
Title: Locating Yourself in a Large Universe
Abstract: The universe is obviously a big place, but modern physics frequently envisions scenarios in which it is very large indeed: large enough that any allowed local macrostate (such as the one describing you and the room you are sitting in) is likely to exist more than once, perhaps an infinite number of times. This situation induces "self-locating uncertainty," in which we can know the state of the universe exactly and still not know where we are in it. I will argue that a unique prescription for dealing with such uncertainties is provided by the "Epistemic Separability Principle," which holds that credences assigned to local circumstances should be independent of what is happening in distant parts of the universe. The ESP leads to Laplace's Principle of Indifference in cases of classical uncertainty, to the Born Rule in Everettian quantum mechanics, and a simple solution to problems of mixed classical/quantum uncertainty (such as quantum Sleeping Beauty puzzles).
C. Sebans & S.C., Self-Locating Uncertainty and the Origin of Probability in Everettian Quantum Mechanics (arXiv:1405.7577).
C. Sebans & S.C., Many Worlds, the Born Rule, and Self-Locating Uncertainty (arXiv:1405.7907).
Title: Subjective Bayesianism and Quantum Mechanics
Abstract: Subjective Bayesians allow arbitrary priors over all objects not known with certainty, including theories, imperfect evidence, the (generally mixed) quantum state of a subsystem, the full quantum state of the multiverse, and the xerographic distribution over copies of the observer. All apparent paradoxes can be avoided by carefully stating what is known with certainty ("at least one copy of me has awoken in a blue room"), or carefully specifying relevant priors. "Principles" purporting to make objective choices for certain priors (e.g., choosing a uniform xerographic distribution with probability one) are inconsistent with the notion that all science should be provisional. Quantum probabilities via the Born Rule can be treated as objective chances that must be taken into account in assigning priors, or (following the ideas of Vaidman and Carroll & Sebens) taken to arise from branch-location uncertainty (which should then be quantified with its own xerographic distribution).
M.S., Subjective and Objective Probabilities in Quantum Mechanics (arXiv:quant-ph/0501009).
M.S. & J. Hartle, Science in a Very Large Universe (arXiv:0906.0042, arXiv:1004.3816; latter is a 3-page summary of the main point).
General article on subjective Bayesianism: Bayesian Epistemology.
Title: Could a Quantum Computer Have Subjective Experience?
Abstract: Following Deutsch and others in the 1980s, I'll argue that we can throw many debates about the quantum/classical boundary into much sharper relief by examining the possibility of conscious quantum computers: entities designed to violate the heuristic that "anything too much like ourselves" can be well-approximated using classical probability theory. After explaining some of the paradoxes to which conscious quantum computers give rise, I'll then discuss a speculative viewpoint that regards irreversible decoherence as a fundamental aspect of subjective experience: a viewpoint that (among other things) would rule out conscious quantum computers. I'll then explore the implications of that viewpoint for some other issues in science and philosophy, including Boltzmann brains, Newcomb's problem, and free will.
S.A., The Ghost in the Quantum Turing Machine (http://www.scottaaronson.com/papers/giqtm3.pdf).
Title: Quantum Theory of the Classical
Abstract: I will describe three insights into the transition from quantum to classical. I will start with (i) a minimalist (decoherence-free) derivation of preferred states. Such pointer states define events (e.g., measurement outcomes) without appealing to Born's rule . Probabilities and (ii) Born's rule can be then derived from the symmetries of entangled quantum states. Derivation of Born's rule will be the focus of my presentation. With probabilities at hand one can analyze information flows from the system to the environment in course of decoherence. They explain how (iii) robust "classical reality" arises from the quantum substrate by accounting for objective existence of pointer states of quantum systems through redundancy of their records in the environment. Taken together, and in the right order, these three advances elucidate quantum origins of the classical.
W.H.Z., Quantum Darwinism (arXiv:0903.5082).
Title: Mass density quantum mechanics and the Lorentzian quantum reality problem
Abstract: The quantum reality problem is that of finding a mathematically precise definition of a sample space of configurations of beables, events, histories, paths, or other mathematical objects, and a corresponding probability distribution, for any given closed quantum system. Given a solution, we can postulate that physical reality is described by one randomly chosen configuration drawn from the sample space. For a physically sensible solution, this postulate should imply quasiclassical physics in realistic models. In particular, it should imply the validity of Copenhagen quantum theory and classical dynamics in their respective domains. A Lorentzian solution applies to relativistic quantum theory or quantum field theory in Minkowski space and is defined in a way that respects Lorentz symmetry. We outline a new solution to the non-relativistic and Lorentzian quantum reality problems, and associated new generalizations of quantum theory.
A.K., A Solution to the Lorentzian Quantum Reality Problem (arXiv:1311.0249).
Title: Amplification, Redundancy, and the Quantum Chernoff Information
Abstract: Amplification was regarded, since the early days of quantum theory, as a mysterious ingredient that endows quantum microstates with macroscopic consequences, key to the "collapse of the wavepacket", and a way to avoid embarrassing problems exemplified by Schrodinger's cat. Such a bridge between the quantum microworld and the classical world of our experience was postulated ad hoc in the Copenhagen Interpretation. Quantum Darwinism views amplification as replication, in many copies, of the information about quantum states. We show that such amplification is a natural consequence of a broad class of models of decoherence, including the photon environment we use to obtain most of our information. This leads to objective reality via the presence of robust and widely accessible records of selected quantum states. The resulting redundancy (the number of copies deposited in the environment) follows from the Quantum Chernoff Information that quantifies the information transmitted by a typical elementary subsystem of the environment.
M.Z., C.J. Riedel, & W. Zurek, Amplification, Redundancy, and the Quantum Chernoff Information (arXiv:1312.5373). <xsscleaned_tag>
Title: Depth and Complexity of Classical States
Abstract: Though dynamical considerations, such as the form of the Hamiltonian, are needed get definitions of classicality off the ground by identifying subsystems, we attempt to proceed statically thereafter, defining classicality, complexity, and observership as properties of (some) quantum states. We regard classicality as a prerequisite for complexity, and complexity as a prerequisite for observers. We use the quantum Darwinism approach to define classicality via redundant correlations, and the logical depth approach to define complexity as the presence of internal classical evidence of a nontrivial causal history. In this talk we propose to continue in that direction and define observership as a static property, representing not consciousness, but internal classical evidence of scientific activity, i.e. of a more or less successful effort by the system to understand or explain its own plausible causal history.
References: C.H.B., Logical depth and physical complexity in The Universal Turing Machine - a Half-Century Survey, ed. Rolf Herken, Oxford University Press, 227-257, (1988).
C.H.B., What increases when a self-organizing system organizes itself?
Title: Classical Behavior of Quantum Systems
Abstract: A quantum system behaves classically when the probability is high for histories of its motion exhibiting correlations in time governed by deterministic, classical laws. These probabilities depend on both the quantum state and the coarse graining that defines the histories. There are thus no `classical states' by themselves, but only relative to a coarse graining that defines the histories.
We assume the standard decoherent (or consistent) histories formulation of quantum mechanics for closed systems. Notions of environment and records emerge automatically from a specification of the coarse graining, not as separate postulates of quantum mechanics. Anthropic reasoning is also automatic for probabilties for observations.
A striking feature of our quantum universe is the wide range of time, place, and scale on which the laws of classical physics hold to an excellent approximation. Such a realm of classical predictability does not emerge generally in any quantum universe but is a consequence of the specific quantum state of ours. We sketch the origin of the quasiclassical realm stressing the importance of classical spacetime. In particular we show how the variables of classical physics are singled out.
We describe a program of finding a complexity based measure of classicality on sets of decoherent histories in variables other than the usual classical ones. That could help answer the question of whether the classical realm is unique in its high level of predictability, simplicity, and interest.
J.H., The Quasiclassical Realms of this Quantum Universe (arXiv:0806.3776).
Title: Redundant Records of Consistent Histories
Abstract: Motivated by the important role played by redundancy in identifying the small subset of quantum states with objective classical structure, we formalize redundant records in the consistent histories approach to quantum mechanics. Using the orthogonality of records on subsystems, and Finkelstein's concept of partial-trace consistency, we identify certain histories that are not just consistent but redundantly consistent. The requirement of redundant records is proposed to reduce the size of the so-called set-selection problem. In fact, we introduce a unique multi-partite extension of the Schmidt decomposition (greatly generalizing the tri-orthogonal decomposition theorem) suggesting that redundant records may provide an essenitally complete solution to the problem, thereby objectively identifying branch structure in the wavefunction. However, there is still significant mathematical work to be done understanding robustness to perturbations and imperfect records.
C.J.R., W. Zurek, & M. Zwolak, The Objective Past of a Quantum Universe - Part 1: Redundant Records of Consistent Histories (arXiv:1312.0331).
C.J.R., Local Records and Global Entanglement: A Unique Multi-Partite Generalization of the Schmidt Decomposition (arXiv:1310.4473).