The Quantum Universe

The following sections are included:

• Contents
• Preface

The familiar theories of physics share the feature that the application of the theory to make predictions in specific circumstances can be done by means of an algorithm. We propose a more precise formulation of this feature — one based on the issue of whether or not the physically measurable numbers predicted by the theory are computable in the mathematical sense. Applying this formulation to an approach to quantum theory of gravity, indications imply that there may exist no such algorithms in this case. Finally, we discuss the issue of whether the existence of an algorithm to implement a theory should be adopted as a criterion for acceptable physical theories.

Many advances in physics have in common that some idea which was previously accepted as fundamental, general and inescapable was subsequently seen to be consequent, special and dispensable. The idea was not truly a general feature of the world, but only perceived to be general because of our special place in the universe and the limited range of our experience. It was excess baggage which had to be jettisoned to reach a more general perspective. This article discusses excess baggage from the perspective of quantum cosmology which aims for a theory of the universe’s quantum initial state. We seek to answer the question: “Which features of our current theoretical framework are fundamental and which reflect our special position in the universe or its special initial condition?” Past instances of cosmological excess baggage are reviewed, such as the idea that the Earth was at the center of the universe or that the second law of thermodynamics was fundamental. Examples of excess baggage in our current understanding are the notion that measurement is central to formulating quantum mechanics, a fundamental quantum mechanical arrow of time, and the idea that a preferred time is needed to formulate quantum theory. We speculate on candidates for future excess baggage.

Sources of predictability in the basic laws of physics are described in the most general theoretical context — the quantum theory of the universe as a whole.

The following sections are included:

• Introduction
• Different Things Fall with the Same Acceleration in a Gravitational Field
• The Fundamental Laws of Physics
• Quantum Mechanics
• A Theory of Everything is Not a Theory of Everything
• Reduction
• The Main Points Again
• Acknowledgment
• References

Existing physical theories do not predict every feature of our experience, but only certain regularities of that experience. That difference between what could be observed and what can be predicted is one kind of limit on scientific knowledge. Such limits are inevitable if the world is complex and the laws governing the regularities of that world are simple. Another kind of limit on scientific knowledge arises because even simple theories may require intractable or impossible computations to yield specific predictions. A third kind of limit concerns our ability to know theories through the process of induction and test. Quantum cosmology — that part of science concerned with the quantum origin of the universe and its subsequent evolution — displays all three kinds of limits. This paper briefly describes quantum cosmology and discusses these limits. The place of the other sciences in this most comprehensive of physical frameworks is described.

The world is four-dimensional according to fundamental physics, governed by basic laws that operate in 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. What is the origin of this division? What is its four-dimensional description? Is this the only way experience can be organized consistently with the basic laws of physics? This paper reviews such questions through simple models of information gathering and utilizing systems (IGUSes), such as ourselves…

A pedagogical introduction is given to the quantum mechanics of closed systems, most generally the universe as a whole. Quantum mechanics aims at predicting the probabilities of alternative coarse-grained time histories of a closed system. Not every set of alternative coarse-grained histories that can be described may be consistently assigned probabilities because of quantum mechanical interference between individual histories of the set. In “Copenhagen” quantum mechanics, probabilities can be assigned to histories of a subsystem that have been “measured”. In the quantum mechanics of closed systems, containing both observer and observed, probabilities are assigned to those sets of alternative histories for which there is negligible interference between individual histories as a consequence of the system’s initial condition and dynamics. Such sets of histories are said to decohere. We define decoherence for closed systems in the simplified case when quantum gravity can be neglected and the initial state is pure. Typical mechanisms of decoherence that are widespread in our universe are illustrated…

Feynman’s sum-over-histories formulation of quantum mechanics is reviewed as an independent statement of quantum theory in spacetime form. It is different from the usual Schrödinger–Heisenberg formulation that utilizes states on spacelike surfaces because it assigns probabilities to different sets of alternatives. In a sum-over-histories formulation, alternatives at definite moments of time are more restricted than in usual quantum mechanics because they refer only to the coordinates in terms of which the histories are defined. However, in the context of the quantum mechanics of closed systems, sum-over-histories quantum mechanics can be generalized to deal with spacetime alternatives that are not “at definite moments of time”. An example in field theory is the set of alternative ranges of values of a field averaged over a spacetime region. An example in particle mechanics is the set of the alternatives defined by whether a particle never crosses a fixed spacetime region or crosses it at least once. The general notion of a set of spacetime alternatives is a partition (coarse-graining) of the histories into an exhaustive set of exclusive classes. With this generalization, the sum-over-histories formulation can be said to be in fully spacetime form with dynamics represented by path integrals over spacetime histories and alternatives defined as spacetime partitions of these histories. When restricted to alternatives at definite moments of times, this generalization is equivalent to Schrödinger–Heisenberg quantum mechanics. However, the quantum mechanics of more general spacetime alternatives does not have an equivalent Schrödinger–Heisenberg formulation. We suggest that, in the quantum theory of gravity, the general notion of “observable” is supplied by diffeomorphism invariant partitions of spacetime metrics and matter field configurations. By generalizing the usual alternatives so as to put quantum theory in fully spacetime form, we may be led to a covariant generalized quantum mechanics of spacetime free from the problem of time.

Human languages employ constructions that tacitly assume specific properties of the limited range of phenomena they have evolved to describe. These assumed properties are true features of that limited context, but may not be general or precise properties of all the physical situations allowed by fundamental physics. In brief, human languages contain “excess baggage” that must be qualified, discarded, or otherwise reformed to give a clear account, in the context of fundamental physics, of even the everyday phenomena that languages have evolved to describe. The surest route to clarity is to express the constructions of human languages in the language of fundamental physical theory, not the other way around. These ideas are illustrated by an analysis of the verb “to happen” and the word “reality” in special relativity and the modern quantum mechanics of closed systems.

From data in the present we can predict the future and retrodict the past. These predictions and retrodictions are for histories — most simply time sequences of events. Quantum mechanics gives probabilities for individual histories in a decoherent set of alternative histories. This paper discusses several issues connected with the distinction between prediction and retrodiction in quantum cosmology: the difference between classical and quantum retrodiction, the permanence of the past, why we predict the future but remember the past, the nature and utility of reconstructing the past(s), and information theoretic measures of the utility of history.

The most striking observable feature of our indeterministic quantum universe is the wide range of time, place and scale on which the deterministic laws of classical physics hold to an excellent approximation. This essay describes how this domain of classical predictability of everyday experience emerges from a quantum theory of the universe’s state and dynamics.

This essay considers a model quantum universe consisting of a very large box containing a screen with two slits and an observer (us) that can pass through the slits. We apply modern quantum mechanics of closed systems to calculate the probabilities for alternative histories of how we move through the universe and what we see. After passing through the screen with the slits, the quantum state of the universe is a superposition of classically distinguishable histories. We are then living in a superposition. Some frequently asked questions about such situations are answered using this model. The model’s relationship to more realistic quantum cosmologies is briefly discussed.

The familiar textbook quantum mechanics of laboratory measurements incorporates a quantum mechanical arrow of time — the direction in time in which state vector reduction operates. This arrow is usually assumed to coincide with the direction of the thermodynamic arrow of the quasiclassical realm of everyday experience. But in the more general context of 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 quantum mechanical and thermodynamic arrows in a 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.

Einstein wrote memorably that “The eternally incomprehensible thing about the world is its comprehensibility.” This paper argues that the universe must be comprehensible at some level for information gathering and utilizing subsystems such as human observers to evolve and function.

Two fundamental laws are needed for prediction in the universe: (1) a basic dynamical law and (2) a law for the cosmological initial condition. Quantum cosmology is the area of basic research concerned with the search for a theory of the initial cosmological state. The issues involved in this search are presented in the form of eight problems.

Prediction in quantum cosmology requires a specification of the universe’s quantum dynamics and its quantum state. We expect only a few general features of the universe to be predicted with probabilities near unity conditioned on the dynamics and quantum state alone. Most useful predictions are of conditional probabilities that assume additional information beyond the dynamics and quantum state. Anthropic reasoning utilizes probabilities conditioned on “us”. This paper discusses the utility, limitations and theoretical uncertainty involved in using such probabilities. The predictions resulting from various levels of ignorance of the quantum state are discussed.

Bayesian probability theory is used to analyze the oft-made assumption that humans are typical observers in the universe. Some theoretical calculations make the selection fallacy that we are randomly chosen from a class of objects by some physical process, despite the absence of any evidence for such a process or any observational evidence favoring our typicality. It is possible to favor theories in which we are typical by appropriately choosing their prior probabilities, but such assumptions should be made explicit to avoid confusion.

As observers of the universe, we are quantum physical systems within it. If the universe is very large in space and/or time, the probability becomes significant that the data on which we base predictions, is replicated at other locations in spacetime. The physical conditions at these locations that are not specified by the data may differ. Predictions of our future observations therefore require an assumed probability distribution (the xerographic distribution) for our location among the possible ones. It is the combination of basic theory plus the xerographic distribution that can be predictive and testable by further observations.

In the modern quantum mechanics of cosmology, observers are physical systems within the universe. They have no preferred role in the formulation of the theory nor in its predictions of third-person probabilities of what occurs. However, observers return to the importance for the prediction of first-person probabilities for what we observe of the universe: What is most probable to be observed is not necessarily what is most probable to occur. This essay reviews the basic framework for the computation of first-person probabilities in quantum cosmology starting with an analysis of very simple models. It is shown that anthropic selection is automatic in this framework, because there is no probability for us to observe what is where we cannot exist. First-person probabilities generally favor larger universes resulting from inflation, where there are more places for us to be. In very large universes, it is probable that our observational situation is duplicated elsewhere. The calculation of first-person probabilities then requires a specification of whether our particular situation is assumed to be typical of all the others. It is the combination of the model of the observational situation, including this typicality assumption, and the third-person theory, which is tested by observation. We conclude with a discussion of the first-person predictions of cosmological observables, such as the cosmological constant and features of the primordial density fluctuations, in the no-boundary quantum state of the universe, and a dynamical theory in which these are allowed to vary.

A quantum theory of the universe consists of a theory of its quantum dynamics (H) and a theory of its quantum state (Ψ). The theory (H, Ψ) predicts quantum multiverses in the form of decoherent sets of alternative histories describing the evolution of the universe’s spacetime geometry and matter content. A small part of one of these histories is observed by us. These consequences follow: (a) The universe generally exhibits different quantum multiverses at different levels and kinds of coarse-graining. (b) Quantum multiverses are not a choice or an assumption, but are consequences of (H, Ψ) or not. (c) Quantum multiverses are generic for simple (H, Ψ). (d) Anthropic selection is automatic because observers are physical systems within the universe, not somehow outside it. (e) Quantum multiverses can provide different mechanisms for the variation of constants in effective theories (like the cosmological constant) enabling anthropic selection. (f) Different levels of coarse-grained multiverses provide different routes to calculation as a consequence of decoherence. We support these conclusions by analyzing the quantum multiverses of a variety of quantum cosmological models aimed at the prediction of observable properties of our universe. In particular, we show how the example of a multiverse consisting of a vast classical spacetime containing many pocket universes having different values of the fundamental constants, arises automatically as part of a quantum multiverse describing an eternally inflating false vacuum that decays by the quantum nucleation of true vacuum bubbles. In an FAQ section in Appendix A, we argue that the quantum multiverses of the universe are scientific, real, testable, falsifiable, and similar to those in other areas of science, even if they are not directly observable on arbitrarily large scales.

Usual quantum mechanics requires a fixed, background, spacetime geometry and its associated causal structure. A generalization of the usual theory may therefore be needed at the Planck scale for quantum theories of gravity in which spacetime geometry is a quantum variable. The elements of generalized quantum theory are briefly reviewed and illustrated by generalizations of usual quantum theory that incorporate spacetime alternatives, gauge degrees of freedom, and histories that move forward and backward in time. A generalized quantum framework for cosmological spacetime geometry is sketched. This theory is in fully four-dimensional form and free from the need for a fixed causal structure. Usual quantum mechanics is recovered as an approximation to this more general framework that is appropriate in those situations where spacetime geometry behaves classically.

What is the quantum state of the universe? That is the central question of quantum cosmology. This essay describes the place of that quantum state in a final theory governing the regularities exhibited universally by all physical systems in the universe. It is possible that this final theory consists of two parts: (1) a dynamical theory such as superstring theory, and (2) a state of the universe such as the no-boundary wave function. Both are necessary because prediction in quantum mechanics requires both a Hamiltonian and a state. The simplicity observed in the early universe gives hope that there is a simple, discoverable quantum state of the universe. It may be that the predictions of the quantum state for late time, low-energy observations can be summarized by an effective cosmological theory. That should not obscure the need to provide a fundamental basis for such an effective theory. It could be that there is one principle that determines both the dynamical theory and the quantum state. That would be a truly unified final theory.

When quantum mechanics was developed in the 1920s, another revolution in physics was just starting. It began with the discovery that the universe is expanding. For a long time, quantum mechanics and cosmology developed independently of one another. Yet the very discovery of the expansion would eventually draw the two subjects together because it implied the big bang where quantum mechanics was important for cosmology and for understanding and predicting our observations of the universe today. Textbook (Copenhagen) formulations of quantum mechanics are inadequate for cosmology for at least four reasons: (1) They predict the outcomes of measurements made by observers. But in the very early universe no measurements were being made and no observers were around to make them. (2) Observers were outside of the system being measured. But we are interested in a theory of the whole universe where everything, including observers, are inside. (3) Copenhagen quantum mechanics could not retrodict the past. But retrodicting the past to understand how the universe began is the main task of cosmology. (4) Copenhagen quantum mechanics required a fixed classical spacetime geometry, not least to give meaning to time in the Schrödinger equation. But in the very early universe spacetime is fluctuating quantum-mechanically (quantum gravity) and without definite value. A formulation of quantum mechanics general enough for cosmology was started by Everett and developed by many. That effort has given us a more general framework that is adequate for cosmology — decoherent (or consistent) histories quantum theory in the context of semiclassical quantum gravity. Copenhagen quantum theory is an approximation to this more general quantum framework that is appropriate for measurement situations. We discuss whether further generalization may still be required.

On September 25, 2014, Murray Gell-Mann was presented with the Helmholz Medal of the Berlin Brandenburg Academy of Sciences and Humanities in a ceremony at the Santa Fe Institute. The author, among others, was asked to speak for fifteen minutes on Murray and his accomplishments. The following is an edited transcription of the author’s speaking text.

The banquet for the July 2017 conference in Cambridge, UK celebrating Stephen Hawking’s 75th birthday was held in Trinity College on July 3rd. The organizers asked the author, among others, to give a ten-minute after-dinner talk on what it was like to work with Stephen. The following is an edited version of the author’s speaking text.

The following section is included:

• List of Essays with publication data and arXiv references