The Quantum Universe

• Guide to Use
• Introductory
• Essays on Physical Theory
• Decoherent Histories QM
  • Overview
  • Fundamentals
  • Generalizations-NoQG
  • Generalizations-withQG
  • Extended Probabilities
• No Boundary Quantum State
  • Simplicial Approx
  • Formulation
  • Predictions
• Probability in Quantum Mechanics
• Quasiclassical Realms
• Arrows of Time
• Anthropic Reasoning in QC
• Alternative Formulations of QM
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Arrows of Time

As far as we know, the fundamental dynamical laws are time neutral --- preferring no direction of time over another. Yet our universe exhibits a number of `arrows of time' --- general phenomena that distinguish directions in time. There is the thermodynamic arrow of time --- the fact that presently isolated systems are mostly evolving towards equilibrium in the same direction of time. There is the electromagnetic arrow of time --- electromagnetic radiation is retarded. There is the psychological arrow of time --- we remember the past, experience the present, and predict the future. There are the arrows of time supplied by the expansion of the universe and the growth of inhomogeneity. And then, there is the quantum mechanical arrow of time defined in Copenhagen quantum mechanics by the direction in time the wave function of a subsystem is reduced on measurement. The papers below in various ways show how arrows of time arise in quantum cosmology from asymmetries in quantum conditions that specify our universe even though the dynamical laws are time neutral.

Time Symmetry and Asymmetry in Quantum Mechanics and Quantum Cosmology (96).

(with M. Gell-Mann) Decoherent histories quantum mechanics is formulated time neutrally as a generalized quantum theory with both initial and final conditions without a quantum mechanical arrow of time. All arrows of time, including the quantum mechanical one, arise from differences between these initial and final conditions. Data in our universe are consistent with a special low entropy initial state, and a final condition of indifference represented by a density matrix proportional to the unit matrix. That arrangement explains the thermodynamic and apparent quantum mechanical arrow of time. But it is an experimental question of how close the final condition of the universe is to indifference.

Quantum Pasts and the Utility of History (117)

This article describes the process of retrodicting the past in quantum cosmology with quantum probabilities conditioned on present data. There is not just one past but many different possible ones. Retrodicting a past is useful because it can help with predicting the future.

Entropy of Classical Histories (120)

(with T. Brun) We consider a number of proposals for the entropy of sets of classical coarse-grained histories based on the procedures of Jaynes, and prove a series of inequalities relating these measures. We then examine these as a function of the coarse-graining for various classical systems, and show explicitly that the entropy is minimized by the finest-grained description of a set of histories. We propose an extension of the second law of thermodynamics to the entropy of histories. We briefly discuss the implications for decoherent or consistent history formulations of quantum mechanics.

The Physics of Now (132)

The world is four-dimensional according to fundamental physics --- governed by laws operatingin a spacetime that has no unique division into space and time. Yet our subjective experience of this world is divided into present, past, and future. This paper addresses the questions of how this organization can be consistent with physics through simple models of information gathering and utilizing systems (IGUSes) such as ourselves. Past, present, and future are not properties of four-dimensional spacetime but notions describing how individual IGUSes process information.The past, present, and future of an IGUS can be described in four-dimensional terms. The present, for instance, is not a moment of time in the sense of a spacelike surface in spacetime. Rather there is a notion of present at each point along an IGUS’ world line. The common present of many localized IGUSes is an approximate notion appropriate when they are sufficiently close to each other and have relative velocities much less than that of light. Some features of the present, past, and future organization are closely related to basic physical laws such as the thermodynamic and electromagnetic arrows of time. But modes of organization that are different from present, past and future can be imagined that are also consistent with the basic laws of physics. We speculate why the present, past, and future organization might be adaptive.

Quasiclassical Coarse Grainings and Thermodynamic Entropy (138)

(with M. Gell-Mann) The thermodynamic arrow of time is associated with the increase of a globally defined entropy. An entropy is defined by a coarse graining. Coarse-graining is also necessary to define decoherent sets of alternative histories of the universe. This paper is mostly concerned with characterizing the coarse grainings that define the histories of the quasiclassical realms. We show that this coarse graining is the same at th e one that defines the usual entropy of chemistry and physics. That entropy was low for the initial state of our universe and has been increasing every since.

Arrows of Time in the Bouncing Universes of the No-Boundary Quantum State (147)

(with T. Hertog) We derive the arrows of time of our universe that follow from the no-boundary theory of its quantum state (NBWF) in a minisuperspace model. Arrows of time are viewed four-dimensionally as properties of the four-dimensional Lorentzian histories of the universe arising from the conditions that specify it. For histories with a regular ‘bounce’ at a minimum radius we find that the NBWF predicts fluctuations that are small at the bounce and grow in the direction of expansion on either side. For recollapsing classical histories with big bang and big crunch singularities we find that the fluctuations are small near one singularity and grow through the expansion and recontraction to the other singularity. The arrow of time defined by the growth in fluctuations thus points in one direction over the whole of a recollapsing spacetime but is bidirectional in a bouncing spacetime. We argue that the electromagnetic, thermodynamic, and psychological arrows of time are aligned with the fluctuation arrow.

The Quantum Mechanical Arrows of Time (150)

The quantum mechanical arrow of time is usually assumed to coincide with the direction of the thermodynamic arrow. But in quantum cosmology we seek an explanation of all observed arrows, and the relations between them, in terms of the conditions that specify our particular universe. This paper investigates the directions quantum mechanical and thermodynamic arrows in the time-neutral formulation of quantum mechanics for a number of model cosmologies in fixed background spacetimes. We find that a general universe may not have well defined arrows of either kind. When arrows are emergent they need not point in the same direction over the whole of spacetime. Rather they may be local, pointing in different directions in different spacetime regions. Local arrows can therefore be consistent with global time symmetry.