Boltzmann Brain Research Articles

Lessons from the void: What Boltzmann brains teach

AbstractSome physical theories predict that almost all brains in the universe are Boltzmann brains, that is, short‐lived disembodied brains that are accidentally assembled as a result of thermodynamic or quantum fluctuations. Physicists and philosophers of physics widely regard this proliferation as unacceptable, and so take its prediction as a basis for rejecting these theories. But the putatively unacceptable consequences of this prediction follow only given certain philosophical assumptions. This paper develops a strategy for shielding physical theorizing from the threat of Boltzmann brains. The strategy appeals to a form of phenomenal externalism about the physical basis of consciousness. Given that form of phenomenal externalism, the proliferation of Boltzmann brains turns out to be benign. While the strategy faces a psychophysical fine‐tuning problem, it both alleviates cosmological fine‐tuning concerns that attend physics‐based solutions to Boltzmann brain problems and pays explanatory dividends in connection with time's arrow.

Fluctuations of subsystem entropies at late times

We study the fluctuations of subsystem entropies in closed quantum many-body systems after thermalization. Using a combination of analytics and numerics for both random quantum circuits and Hamiltonian dynamics, we find that the statistics of such entropy fluctuations is drastically different than in the classical setting. For instance, shortly after a system thermalizes, the probability of entropy fluctuations for a subregion is suppressed in the dimension of the Hilbert space of the complementary subregion. This suppression becomes increasingly stringent as a function of time, ultimately depending on the exponential of the Hilbert space dimension, until extremely late times when the amount of suppression saturates. We also use our results to estimate the total number of rare fluctuations at large timescales. We find that the "Boltzmann brain" paradox is largely ameliorated in quantum many-body systems, in contrast with the classical setting.

Black holes and uptunneling suppress Boltzmann brains

Eternally inflating universes lead to an infinite number of Boltzmann brains but also an infinite number of ordinary observers. If we use the scale factor measure to regularize these infinities, the ordinary observers dominate the Boltzmann brains if the vacuum decay rate of each vacuum is larger than its Boltzmann brain nucleation rate. Here, we point out that nucleation of small black holes should be counted in the vacuum decay rate, and this rate is always larger than the Boltzmann brain rate, if the minimum Boltzmann brain mass is more than the Planck mass. We also discuss nucleation of small, rapidly inflating regions, which may also have a higher rate than Boltzmann brains. This process also affects the distribution of the different vacua in eternal inflation.

Law without law: from observer states to physics via algorithmic information theory

According to our current conception of physics, any valid physical theory is supposed to describe the objective evolution of a unique external world. However, this condition is challenged by quantum theory, which suggests that physical systems should not always be understood as having objective properties which are simply revealed by measurement. Furthermore, as argued below, several other conceptual puzzles in the foundations of physics and related fields point to limitations of our current perspective and motivate the exploration of an alternative: to start with the first-person (the observer) rather than the third-person perspective (the world).In this work, I propose a rigorous approach of this kind on the basis of algorithmic information theory. It is based on a single postulate: that universal induction determines the chances of what any observer sees next. That is, instead of a world or physical laws, it is the local state of the observer alone that determines those probabilities. Surprisingly, despite its solipsistic foundation, I show that the resulting theory recovers many features of our established physical worldview: it predicts that it appears to observers as if there was an external world that evolves according to simple, computable, probabilistic laws. In contrast to the standard view, objective reality is not assumed on this approach but rather provably emerges as an asymptotic statistical phenomenon. The resulting theory dissolves puzzles like cosmology's Boltzmann brain problem, makes concrete predictions for thought experiments like the computer simulation of agents, and suggests novel phenomena such as ``probabilistic zombies'' governed by observer-dependent probabilistic chances. It also suggests that some basic phenomena of quantum theory (Bell inequality violation and no-signalling) might be understood as consequences of this framework.

Four-volume cutoff measure of the multiverse

Predictions in an eternally inflating multiverse are meaningless unless we specify the probability measure. The scale-factor cutoff is perhaps the simplest and most successful measure which avoid catastrophic problems such as the youngness paradox, runaway problem, and Boltzmann brain problem, but it is not well defined in contracting regions with a negative cosmological constant. In this paper, we propose a new measure with properties similar to the scale-factor cutoff which is well defined everywhere. The measure is defined by a cutoff in the 4-volume spanned by infinitesimal comoving neighborhoods in a congruence of timelike geodesics. The probability distributions for the cosmological constant and for the curvature parameter in this measure are similar to those for the scale factor cutoff and are in a good agreement with observations.

Does my total evidence support that I’m a Boltzmann Brain?

A Boltzmann Brain, haphazardly formed through the unlikely but still possible random assembly of physical particles, is a conscious brain having experiences just like an ordinary person. The skeptical possibility of being a Boltzmann Brain is an especially gripping one: scientific evidence suggests our actual universe’s full history may ultimately contain countless short-lived Boltzmann Brains with experiences just like yours or mine. I propose a solution to the skeptical challenge posed by these countless actual Boltzmann Brains. My key idea is roughly this: the skeptical argument that you’re one of the Boltzmann Brains requires you to make a statistical inference (most Fs are Gs, this is an F, so it’s probably a G), but the Principle of Total Evidence blocks us from making the inference (because I also know this F is an FH, and most FHs are not Gs). I discuss how my solution contrasts with a recent suggestion, made by Sean Carroll and David Chalmers, for how to address the skeptical challenge posed by Boltzmann Brains. And I discuss how my solution handles certain relevant concerns about what to do when we have higher-order evidence indicating that our first-order evidence is misleading.

Expansionism, Extremism, and Exceptionalism in Life

AbstractThis article explores how taking physical cosmology and the entities that populate its fringes on their own terms might prompt anthropology to rethink what and how it thinks of life. Physical cosmologists work with inanimate matter that lies at the frontier of existential possibility, positing scales and concepts that seem to negate commonsense notions of life and nonlife. Although a common reaction in anthropology when faced with such infinite, nonhuman, and abstract landscapes is to try to crowbar “everyday life” back in, we argue that conceptual space needs to be made for another style of engagement between anthropology and physical cosmology. Taking the Boltzmann Brain as an example of life not only beyond the human but also beyond life as we know it, we start to flesh out a different sort of speculative, transdisciplinary endeavor.

De Sitter Space Without Dynamical Quantum Fluctuations

We argue that, under certain plausible assumptions, de Sitter space settles into a quiescent vacuum in which there are no dynamical quantum fluctuations. Such fluctuations require either an evolving microstate, or time-dependent histories of out-of-equilibrium recording devices, which we argue 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 dynamical 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, nor does it affect the existence of non-dynamical vacuum fluctuations such as those that give rise to the Casimir effect.

Tuning, ergodicity, equilibrium, and cosmology

I explore the possibility that the cosmos is fundamentally an equilibrium system, and review the attractive features of such theories. Equilibrium cosmologies are commonly thought to fail due to the ``Boltzmann Brain'' problem. I show that it is possible to evade the Boltzmann Brain problem if there is a suitable coarse grained relationship between the fundamental degrees of freedom and the cosmological observables. I make my main points with simple toy models, and then review the de Sitter equilibrium model as an illustration.

Spacetime Average Density (SAD) cosmological measures

The measure problem of cosmology is how to obtain normalized probabilities of observations from the quantum state of the universe. This is particularly a problem when eternal inflation leads to a universe of unbounded size so that there are apparently infinitely many realizations or occurrences of observations of each of many different kinds or types, making the ratios ambiguous. There is also the danger of domination by Boltzmann Brains. Here two new Spacetime Average Density (SAD) measures are proposed, Maximal Average Density (MAD) and Biased Average Density (BAD), for getting a finite number of observation occurrences by using properties of the Spacetime Average Density (SAD) of observation occurrences to restrict to finite regions of spacetimes that have a preferred beginning or bounce hypersurface. These measures avoid Boltzmann brain domination and appear to give results consistent with other observations that are problematic for other widely used measures, such as the observation of a positive cosmological constant.

Watchers of the multiverse

An unresolved question in inflationary cosmology is the assignment of probabilities to different types of events that can occur in the eternally inflating multiverse.We explore the possibility that the resolution of this ``measure problem" may rely on non-standard dynamics in regions of high curvature. In particular, ``big crunch" singularities at the future boundary of bubbles with negative vacuum energy density may lead to bounces, where contraction is replaced by inflationary expansion driven by different vacua in the landscape. Similarly, singularities inside of black holes might be gateways to other inflating vacua.This would drastically affect the global structure of the inflating multiverse. We consider a measure based on a probe geodesic which undergoes an infinite numberof passages through crunches. This can be thought of as the world-line of an eternal ``watcher", collecting data in an orderly fashion. We compare this to previous approaches to the measure problem. The watcher's measure is independent of initial conditions and does not suffer from ambiguities associated with the choice of a cut-off surface. Another potential benefit from passing through crunches is that theobservations collected by the watcher may easily depart fromergodicity, in very generic landscapes. This may significantlyalleviate the problem of Boltzmann Brain dominance.

Cycles in the multiverse

Eternal inflation is a seemingly generic consequence of theories that give rise to accelerated expansion of the universe and possess multiple vacuum states. Making predictions in an eternally inflating universe is notoriously difficult because one must compare infinite quantities, and a wide variety of regulating procedures yield radically different results. This is the measure problem of eternal inflation. In this paper, we analyze models of eternal inflation which allow for the possibility of cyclic bubble universes: in each bubble, standard cosmological evolution is re-played over and over again. Eternal inflation can generically arise in cyclic models that include a dark energy dominated phase. In such models, several problematic consequences of standard regulating procedures, such as the youngness and Boltzmann Brain problems, are substantially alleviated. We discuss the implications for making predictions in cyclic models, as well as some general implications for understanding the measure problem in eternal inflation.

Physical theories, eternal inflation, and the quantum universe

We present a framework in which well-defined predictions are obtained in an eternally inflating multiverse, based on the principles of quantum mechanics. We show that the entire multiverse is described purely from the viewpoint of a single "observer," who describes the world as a quantum state defined on his/her past light cones bounded by the (stretched) apparent horizons. We find that quantum mechanics plays an essential role in regulating infinities. The framework is "gauge invariant," i.e. predictions do not depend on how spacetime is parametrized, as it should be in a theory of quantum gravity. Our framework provides a fully unified treatment of quantum measurement processes and the multiverse. We conclude that the eternally inflating multiverse and many worlds in quantum mechanics are the same. Other important implications include: global spacetime can be viewed as a derived concept; the multiverse is a transient phenomenon during the world relaxing into a supersymmetric Minkowski state. We also present a theory of "initial conditions" for the multiverse. By extrapolating our framework to the extreme, we arrive at a picture that the entire multiverse is a fluctuation in the stationary, fractal "mega-multiverse," in which an infinite sequence of multiverse productions occurs. The framework discussed here does not suffer from problems/paradoxes plaguing other measures proposed earlier, such as the youngness paradox, the Boltzmann brain problem, and a peculiar "end" of time.

Agnesi weighting for the measure problem of cosmology

The measure problem of cosmology is how to assign normalizedprobabilities to observations in a universe so large that it may havemany observations occurring at many different spacetime locations. Ihave previously shown how the Boltzmann brain problem (that observationsarising from thermal or quantum fluctuations may dominate over ordinaryobservations if the universe expands sufficiently and/or lasts longenough) may be ameliorated by volume averaging, but that still leavesproblems if the universe lasts too long. Here a solution is proposedfor that residual problem by a simple weighting factor 1/(1+t2) tomake the time integral convergent. The resulting Agnesi measure appearsto avoid problems other measures may have with vacua of zero or negativecosmological constant.

COSMOLOGICAL MEASURES WITH VOLUME AVERAGING

It has been common for cosmologists to advocate volume weighting for the cosmological measure problem, weighting spatial hypersurfaces by their volume. However, this often leads to the Boltzmann brain problem, that almost all observations would be by momentary Boltzmann brains that arise very briefly as quantum fluctuations in the late universe when it has expanded to a huge size, so that our observations (too ordered for Boltzmann brains) would be highly atypical and unlikely. Here it is suggested that volume weighting may be a mistake. Volume averaging is advocated as an alternative. One consequence may be a loss of the argument that eternal inflation gives a nonzero probability that our universe now has infinite volume.

CRITICAL REVIEWS ON HOLOGRAPHIC MEASURE OVER THE MULTIVERSE

In this talk, the holographic measure based on black hole complementarity is critically reviewed. By noticing the similarities between the causal structure of an inflationary dS space and that of a black hole, we have considered the complementarity principle between the inside and the outside of the causal horizon as an attractive way to count the inflationary multiverse. Even though the holographic measure relieves the Boltzmann brain problem and stresses the physical reality based on observations, it could be challenged by the construction of counterexamples, both on regular black holes and charged black holes, to black hole complementarity.

Boltzmann brains and the scale-factor cutoff measure of the multiverse

To make predictions for an eternally inflating "multiverse", one must adopt a procedure for regulating its divergent spacetime volume. Recently, a new test of such spacetime measures has emerged: normal observers - who evolve in pocket universes cooling from hot big bang conditions - must not be vastly outnumbered by "Boltzmann brains" - freak observers that pop in and out of existence as a result of rare quantum fluctuations. If the Boltzmann brains prevail, then a randomly chosen observer would be overwhelmingly likely to be surrounded by an empty world, where all but vacuum energy has redshifted away, rather than the rich structure that we observe. Using the scale-factor cutoff measure, we calculate the ratio of Boltzmann brains to normal observers. We find the ratio to be finite, and give an expression for it in terms of Boltzmann brain nucleation rates and vacuum decay rates. We discuss the conditions that these rates must obey for the ratio to be acceptable, and we discuss estimates of the rates under a variety of assumptions.

De Sitter equilibrium as a fundamental framework for cosmology

Cosmology might turn out to be the study of fluctuations around a "de Sitter equilibrium" state. In this article I review the basic ideas and the attractive features of this framework, and respond to a number of common questions raised about the de Sitter equilibrium picture. I show that this framework does not suffer from the "Boltzmann Brain" problem, and relate this cosmological picture to recent work on the "clock ambiguity".

Stationary measure in the multiverse

We study the recently proposed ''stationary measure'' in the context of the string landscape scenario. We show that it suffers neither from the ''Boltzmann brain'' problem nor from the ''youngness'' paradox that makes some other measures predict a high CMB temperature at present. We also demonstrate a good performance of this measure in predicting the results of local experiments, such as proton decay.

Cosmological measures without volume weighting

Many cosmologists (myself included) have advocated volume weighting for the cosmologicalmeasure problem, weighting spatial hypersurfaces by their volume. However, this oftenleads to the Boltzmann brain problem, that almost all observations would be bymomentary Boltzmann brains that arise very briefly as quantum fluctuations inthe late universe when it has expanded to a huge size, so that our observations(too ordered for Boltzmann brains) would be highly atypical and unlikely. Hereit is suggested that volume weighting may be a mistake. Volume averaging isadvocated as an alternative. One consequence may be a loss of the argument thateternal inflation gives a nonzero probability that our universe now has infinitevolume.