The Clock and the Quantum: Time and Quantum Foundations - 2008

In 1898, Poincaré identified two fundamental issues in the theory of time: 1)What is the basis for saying that a second today is the same as a second tomorrow? 2) How can one define simultaneity at spatially separated points? Poincaré outlined the solution to the first problem { which amounts to a theory of duration { in his 1898 paper, and in 1905 he and Einstein simultaneously solved the second problem. Einstein\'s daring and elegant approach so gripped the imagination of theoreticians, especially after Minkowski\'s introduction of spacetime,that the definition of duration, and with it the theory of clocks, has received virtually no attention for over a century. This is a remarkable state of affairs and is a major cause of the conceptual confusion surrounding the problem of time in the canonical approach to the creation of a quantum theory of gravity. In my talk I shall develop Poincaré\'s outline into a potentially definitive theory of duration and clocks.

I will examine a number of time-related issues arising in quantum theory, and in particular attempt to address the following basic questions from a quantum perspective: 1. What is a clock? 2. Why do uniformly moving clocks dilate? 3. What is the behaviour of accelerating clocks?

Are time and space independently existing entities? Or is their existence secondary in that they are merely properties of other, more fundamental physical systems? The parameters of this enduring debate have shifted according to the physical theory in which it are set. In the 17th century, Newton\'s notions of Absolute Time and Space strongly favored the idea of independently existing times and spaces. Yet Leibniz famously plagued Newton by pointing to changes that Newton must suppose real even though they issued in no observable differences. Most recently, with the advent of general relativity and quantum theories of gravity that seek to incorporate it, the balance has shifted once again. Is the independence of space and time now finally revealed by the metric field of space and time absorbing the matter of the gravitational fields? Or has time and space has lost its independence from matter in so far as space and time have been absorbed into the matter of the gravitational field? The focus of my talk will be an intermediate episode of this debate that plays out in the context of special relativity. Lorentz noted that moving electrodynamical systems slow in time and shrink in space. The realist tradition explains this slowing and shrinking through the adaptation of matter fields to a real, independently existing Minkowski spacetime. A dissident constructive tradition has long felt that the reverse is the case. These spatio-temporal effects are best explained by the properties of matter theories, most notably, their Lorentz covariance. Harvey Brown has advocated a form of this latter constructivism in his Physical Relativity: Space- time Structure from a Dynamical Perspective. This debate between these two views has proven hard to resolve. That is largely because the notion of explanation is not sufficiently understood for us to adjudicate cleanly between competing claims of what explains what better. In my talk, I will review a new approach to the debate. Constructivists have tacitly assumed a technical result, that it is indeed possible to construct a Minkowski spacetime from Lorentz covariant matter theories. I will show that this is incorrect. This construction project can succeed only in so far as constructivists presume antecedently the basic tenets of the realist view of spacetime. Hence constructivism fails as an alternative to realism about spacetime.

A brief review of the Two State Vector Formalism (TSVF) will be presented. It will be argued that we need to consider also backwards evolving quantum state because information given by forwards evolving quantum states is not complete. Both past and future measurements are required for providing complete information about quantum systems. Peculiar properties of pre- and post-selected quantum systems which can be efficiently analyzed in the framework of the TSVF and which can be observed using weak measurements will be described. An example is a particle reaching a certain location without being on the path that leads to and from this location. An extension of the TSVF to multiple space-time points will be discussed.

My favorite version of quantum mechanics is Bohmian mechanics, a theory about particle trajectories. What is so great about it is that it removes all the mystery from quantum mechanics. I will provide a Bohmian perspective on some issues about time, including time measurements (Why is there no time operator?), tunnelling times (How long did the particle stay inside the barrier?), and the problem of time in quantum gravity (How can it be that the wave function of the Wheeler-de Witt equation is time-independent?). I will particularly address the arrow of time, including the question whether quantum measurements are examples of fundamental time asymmetry (like PCT violations, as Roger Penrose has suggested) or merely of irreversibility (like thermodynamics), and the problem how to transfer Boltzmann\'s explanation of the arrow of time from classical to quantum mechanics.

The presumed irreversibility of quantum measurements (whatever they are) leads, in conventional approaches to quantum theory, to an asymmetry between state preparation and post-selection. Is it possible that a trajectory can be predicted from the former, yet not inferred from the latter? Especially in light of the exciting applications of non-unitary operations (i.e., postselection) in quantum information, it becomes timely to reconsider how much one can say about a post-selected subensemble. I will review the weak-measurement formalism of Aharonov, Vaidman et al., and discuss some applications and extensions. These will include a proposed experiment to study the duration of the tunneling process (a question controversial since the 1930s) and a recently completed experiment aiming to \'resolve\' Hardy\'s retrodiction paradox.

One approach to the problem of time in canonical quantum gravity is to use correlations between a carefully chosen physical system and all other physical systems to provide a simulacrum of time. Time emerges as an ordering of correlated measurement results. In many ways this is an echo of an idea introduced by Poincare to give a geometric description of dynamical systems. Pullin and Gambini have addressed some objections to this approach using a consistent discretization, but in so doing introduce an intrinsic decoherence mechanism into physical theories. In this talk I will show how this approach leads to a simple form of intrinsic decoherence that has possible experimental consequences, among which are modifications to the dispersion relations of the electromagnetic field. This form of decoherence enables the emergence of semiclassical behavior of large systems.

In deBroglie-Bohm theory the quantum state plays the role of a guiding agent. In this seminar we will explore whether this is a universal feature shared by all hidden variable theories, or merely a peculiarity of the deBroglie-Bohm theory. We present the bare bones of a theory in which the quantum state represents a probability distribution and does not act as a guiding agent. The theory is also psi-epistemic according to Spekken\'s and Harrigan\'s definition. For simplicity we develop the model for a 1D discrete lattice but the generalization to higher dimensions is straightforward. The ontic state consists of a definite particle position and in addition possible non-local links between spatially separated lattice points. These non-local links comes in two types: directed links and non-directed links. Quantum superposition manifests itself through these links. Interestingly, this ontology seems to be the simplest possible and immediately suggested by the structure of quantum theory itself. For N lattice points there are N*3^(N(N-1)) ontic states growing exponentially with the Hilbert space dimension N as expected. We further require that the evolution of the probability distribution on the ontic state space is dictated by a master equation with non-negative transition rates. It is then easy to show that one can reproduce the Schroedinger equation if an only if there are positive solutions to a gigantic system of linear equations. This is a highly non-trivial problem and whether there exists such positive solutions or not is not clear at the moment. We end by speculating how one might incorporate gravity into this theory by requiring permutation invariance of the dynamical evolution law.

It is widely believed that the dynamical mechanism of decoherence plays a key role in understanding the emergence of classicality from quantum systems, via the environment-induced superselection of a preferred set of subsystem states, the density matrices for which are approximately diagonal in the pointer basis. In this talk, I prove that the vast majority of subsystems do *not* exhibit this behavior, regardless of the Hamiltonian. This shows that the emergence of classicality is highly state-dependent (as suggested by related work of Hartle and others).

A reference frame can be treated as a physical quantum object internal to the theory. Quantum reference frames whose size, and therefore accuracy, are bounded in some way necessarily limit one\'s ability to prepare states and to perform quantum operations and measurements on a system. The nature of these limitations is similar in many ways to that of decoherence. We investigate how a quantum reference frame of bounded size can be \'dequantized\', i.e., treated as external to the quantum formalism, in such a way as to induce an effective decoherence on any system described relative to it. In particular, we show that this decoherence has an interpretation as a lack of classical information about an ideal (infinite size) reference frame.

The unparalleled empirical success of quantum theory strongly suggests that it accurately captures fundamental aspects of the workings of the physical world. The clear articulation of these aspects is of inestimable value --- not only for the deeper understanding of quantum theory in itself, but for its further development, particularly for the development of a theory of quantum gravity. However, such articulation has traditionally been hampered by the fact that the quantum formalism consists of postulates expressed in an abstract mathematical language to whose elementary objects (complex vectors and operators) our physical intuition cannot directly relate. Recently, there has been growing interest in elucidating these aspects by expressing, in a less abstract mathematical language, what we think quantum theory might be telling us about how nature works, and trying to derive, or reconstruct, quantum theory from these postulates. In this talk, I describe a very simple reconstruction of the finite- dimensional quantum formalism. The derivation takes places with a classical probabilistic framework equipped with the information (or Fisher-Rao) metric, and rests upon a small number of elementary ideas (such as complementarity and global gauge invariance). The complex structure of quantum formalism arises very naturally. The derivation provides a number of non-trivial insights into the quantum formalism, such as the extensive nature of the role of information geometry in determining the quantum formalism, and the importance (or lack thereof) of assumptions concerning separated systems.