Boltzmann Brains Research Articles

Bayes Keeps Boltzmann Brains at Bay

Bayes Keeps Boltzmann Brains at Bay

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.

A Bayesian analysis of self-undermining arguments in physics

Some theories in physics seem to be ‘self-undermining’: that is, if they are correct, we are probably mistaken about the evidence that apparently supports them. For instance, certain cosmological theories have the apparent consequence that most observers are so-called ‘Boltzmann brains’, which exist only momentarily and whose apparent experiences and memories are not veridical. I provide a Bayesian analysis to demonstrate why theories of this kind are not after all supported by the apparent evidence in their favour, taking advantage of the split between ‘primary evidence’, which directly supports a theory, and ‘proximal evidence’, which is our evidence (largely records and testimony) for the primary evidence. Certain contexts in physics generate what David Albert (2000) has called cognitive instability, or an argument that a theory is what we might call self-undermining. The abstract form of such an argument is: the evidence supports theory T, but conditional on theory T, it is extremely likely that I am mistaken about the evidence.

The Bohmian Approach to the Problems of Cosmological Quantum Fluctuations

There are two kinds of quantum fluctuations relevant to cosmology that we focus on in this article: those that form the seeds for structure formation in the early universe and those giving rise to Boltzmann brains in the late universe. First, structure formation requires slight inhomogeneities in the density of matter in the early universe, which then get amplified by the effect of gravity, leading to clumping of matter into stars and galaxies. According to inflation theory, quantum fluctuations form the seeds of these inhomogeneities. However, these quantum fluctuations are described by a quantum state which is homogeneous and isotropic, and this raises a problem, connected to the foundations of quantum theory, as the unitary evolution alone cannot break the symmetry of the quantum state. Second, Boltzmann brains are random agglomerates of particles that, by extreme coincidence, form functioning brains. Unlikely as these coincidences are, they seem to be predicted to occur in a quantum universe as vacuum fluctuations if the universe continues to exist for an infinite (or just very long) time, in fact to occur over and over, even forming the majority of all brains in the history of the universe. We provide a brief introduction to the Bohmian version of quantum theory and explain why in this version, Boltzmann brains, an undesirable kind of fluctuation, do not occur (or at least not often), while inhomogeneous seeds for structure formation, a desirable kind of fluctuation, do.

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.

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.

Computational complexity of the landscape II—Cosmological considerations

We propose a new approach for multiverse analysis based on computational complexity, which leads to a new family of “computational” measure factors. By defining a cosmology as a space–time containing a vacuum with specified properties (for example small cosmological constant) together with rules for how time evolution will produce the vacuum, we can associate global time in a multiverse with clock time on a supercomputer which simulates it. We argue for a principle of “limited computational complexity” governing early universe dynamics as simulated by this supercomputer, which translates to a global measure for regulating the infinities of eternal inflation. The rules for time evolution can be thought of as a search algorithm, whose details should be constrained by a stronger principle of “minimal computational complexity”. Unlike previously studied global measures, ours avoids standard equilibrium considerations and the well-known problems of Boltzmann Brains and the youngness paradox. We also give various definitions of the computational complexity of a cosmology, and argue that there are only a few natural complexity classes.

A-symmetric confirmation and anthropic skepticism

In recent years, anthropic reasoning has been used to justify a number of controversial skeptical hypotheses (both scientific and philosophical). In this paper, we consider two prominent examples, viz. Bostrom’s ‘Simulation Argument’ and the problem of ‘Boltzmann Brains’ in big bang cosmology. We argue that these cases call into question the assumption, central to Bayesian confirmation theory, that the relation of evidential confirmation is universally symmetric. We go on to argue that the fact that these arguments appear to contradict this fundamental assumption should not be taken as an immediate refutation, but should rather be seen as indicative of the peculiar role that the relevant hypotheses play in their respective epistemic frameworks.

A scientific model of pantheism

Given the scientific possibility of Boltzmann Brains, and the theory from philosophy of mind known as Functionalism, it is quite possible to construct a model of pantheism which is not as implausible as restricted theism or traditional models of pantheism. The aim of this article is to explain how this might work, but also to say why, in the end, it will not do the same job as restricted theism, even if it turned out to be true. The article does not aim to defend its premises, such as pantheism or functionalism, in more than a cursory way; the conclusions of the article are tentative and conditional: if functionalism is true, then physicalist pantheism may be true.

The possible resolution of Boltzmann brains problem in phantom cosmology

We consider the well-known Boltzmann brains problem in the framework of simple phantom energy models with little rip and big rip singularities. It is shown that these models (i) satisfy the observational data and (ii) may be free from the Boltzmann brains problem. Human observers in phantom models can exist only during a certain period t < tf (tf is the lifetime of the universe) via the Bekenstein bound. If the fraction of unordered observers in this part of the universe history is negligible as comparison with ordered observers, than the Boltzmann brains problem does not appear. The bounds on model parameters derived from such a requirement do not contradict to the allowable range according to the observational data.

Long-time asymptotics of a Bohmian scalar quantum field in de Sitter space-time

We consider a model quantum field theory with a scalar quantum field in de Sitter space-time in a Bohmian version with a field ontology, i.e., an actual field configuration $\varphi({\bf x},t)$ guided by a wave function on the space of field configurations. We analyze the asymptotics at late times ($t\to\infty$) and provide reason to believe that for more or less any wave function and initial field configuration, every Fourier coefficient $\varphi_{\bf k}(t)$ of the field is asymptotically of the form $c_{\bf k}\sqrt{1+{\bf k}^2 \exp(-2Ht)/H^2}$, where the limiting coefficients $c_{\bf k}=\varphi_{\bf k}(\infty)$ are independent of $t$ and $H$ is the Hubble constant quantifying the expansion rate of de Sitter space-time. In particular, every field mode $\varphi_{\bf k}$ possesses a limit as $t\to\infty$ and thus "freezes." This result is relevant to the question whether Boltzmann brains form in the late universe according to this theory, and supports that they do not.

Quantum exclusion of positive cosmological constant?

We show that a positive cosmological constant is incompatible with the quantum‐corpuscular resolution of de Sitter metric in form of a coherent state. The reason is very general and is due to the quantum self‐destruction of the coherent state as a result of the scattering of constituent graviton quanta. This process creates an irreversible quantum clock, which precludes eternal de Sitter. It also eliminates the possibility of Boltzmann brains and Poincare recurrences. This effect is expected to be part of any microscopic theory that takes into account the quantum corpuscular structure of the cosmological background. This observation puts the cosmological constant problem in a very different light, promoting it, from a naturalness problem, into a question of quantum consistency. We are learning that quantum gravity cannot tolerate exceedingly‐classical sources.

Avoiding Boltzmann Brain domination in holographic dark energy models

In a spatially infinite and eternal universe approaching ultimately a de Sitter (or quasi-de Sitter) regime, structure can form by thermal fluctuations as such a space is thermal. The models of Dark Energy invoking holographic principle fit naturally into such a category, and spontaneous formation of isolated brains in otherwise empty space seems the most perplexing, creating the paradox of Boltzmann Brains (BB). It is thus appropriate to ask if such models can be made free from domination by Boltzmann Brains. Here we consider only the simplest model, but adopt both the local and the global viewpoint in the description of the Universe. In the former case, we find that if a dimensionless model parameter c, which modulates the Dark Energy density, lies outside the exponentially narrow strip around the most natural c=1 line, the theory is rendered BB-safe. In the latter case, the bound on c is exponentially stronger, and seemingly at odds with those bounds on c obtained from various observational tests.

A note on Boltzmann brains

Understanding the observed arrow of time is equivalent, under general assumptions, to explaining why Boltzmann brains do not overwhelm ordinary observers. It is usually thought that this provides a condition on the decay rate of every cosmologically accessible de Sitter vacuum, and that this condition is determined by the production rate of Boltzmann brains calculated using semiclassical theory built on each such vacuum. We argue, based on a recently developed picture of microscopic quantum gravitational degrees of freedom, that this thinking needs to be modified. In particular, depending on the structure of the fundamental theory, the decay rate of a de Sitter vacuum may not have to satisfy any condition except for the one imposed by the Poincaré recurrence. The framework discussed here also addresses the question of whether a Minkowski vacuum may produce Boltzmann brains.

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.

Multivacuum initial conditions and the arrow of time

Depending on the type and arrangement of metastable vacua in the theory, initial conditions in a de Sitter vacuum with arbitrarily large entropy can be compatible with the observed arrow of time, if the causal patch or related measures are used to regulate divergences. An important condition, however, is that the initial vacuum cannot produce observers from rare fluctuations (Boltzmann brains). Here we consider more general initial conditions where multiple vacua have nonzero initial probability. We examine whether the prediction of an arrow of time is destroyed by a small initial admixture of vacua that can produce Boltzmann brains. We identify general criteria and apply them to two nontrivial examples of such initial probability distributions. The Hartle-Hawking state is superexponentially dominated by the vacuum with smallest positive cosmological constant, so one might expect that other initial vacua can be neglected; but in fact, their inclusion drastically narrows the range of theory parameters for which an arrow of time is predicted. The dominant eigenvector of the global rate equation of eternal inflation is dominated by the longest-lived metastable vacuum. If an arrow of time emerges in the single-initial-vacuum approximation, then we find that this conclusion survives the admixture of other initial vacua. By global-local measure duality, this result amounts to a successful consistency test of certain global cutoffs, including light-cone time and scale-factor time.

Probability distributions for quantum stress tensors in four dimensions

We treat the probability distributions for quadratic quantum fields, averaged with a Lorentzian test function, in four-dimensional Minkowski vacuum. These distributions share some properties with previous results in two-dimensional spacetime. Specifically, there is a lower bound at a finite negative value, but no upper bound. Thus arbitrarily large positive energy density fluctuations are possible. We are not able to give closed form expressions for the probability distribution, but rather use calculations of a finite number of moments to estimate the lower bounds, the asymptotic forms for large positive argument, and possible fits to the intermediate region. The first 65 moments are used for these purposes. All of our results are subject to the caveat that these distributions are not uniquely determined by the moments. However, we also give bounds on the cumulative distribution function that are valid for any distribution fitting these moments.We apply the asymptotic form of the electromagnetic energy density distribution to estimate the nucleation rates of black holes and of Boltzmann brains.

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.

Cosmic Transmutation Conjecture

This paper analyzes the big trip phenomenon, restricting it to happen only in the context of the multiverse when the involved wormhole is asymptotically flat and recent criticisms are pointless. A new kind of Lorentzian asymptotically anti-de Sitter wormholes is considered in some detail and it is seen that such wormholes cannot contribute the big trip phenomenon. The ideas of big trip, multiverse and Boltzmann brains are then used to advance the conjecture of cosmic transmutation according to which the host universe where one of the mouths of a grown up wormhole is inserted may be converted into a universe similar to the traveling one if the latter contains a civilization which is typical also in the host universe. The origin of life in the context of the multiverse is then briefly discussed.

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.