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We discuss recent applications of Euclidean path integrals to the black hole information problem. In calculations with replica wormholes as the next-to-leading order correction to the Gibbons-Hawking saddlepoint, the radiation density matrix approaches a pure state at late times, following the Page curve. We compare unitary evaporation of black holes (in real time), mediated by calculable quantum hair effects, with the replica wormhole results. Both replica wormhole and quantum hair approaches imply that radiation states are macroscopic superpositions of spacetime backgrounds, invalidating firewall and monogamy of entanglement constructions. Importantly, identification of modes inside the horizon with radiation modes (i.e., large scale nonlocality across the horizon) is not required to provide a physical picture of unitary evaporation. Radiation modes can encode the interior information while still remaining independent degrees of freedom., Comment: 11 pages, 1 figure

We consider quantum gravitational corrections to the Oppenheimer-Snyder metric describing time-dependent dust ball collapse. The interior metric also describes Friedmann-Lemaitre-Robertson-Walker cosmology and our results are interpreted in that context. The exterior corrections are an example of quantum hair, and are shown to persist throughout the collapse. Our results show the quantum hair survives throughout the horizon formation and that the internal state of the resulting black hole is accessible to outside observers., Comment: 13 pages

We calculate quantum gravitational corrections to the amplitude for the emission of a Hawking particle by a black hole. We show explicitly how the amplitudes depend on quantum corrections to the exterior metric (quantum hair). This reveals the mechanism by which information escapes the black hole. The quantum state of the black hole is reflected in the quantum state of the exterior metric, which in turn influences the emission of Hawking quanta.

We give an elementary account of quantum measurement and related topics from the modern perspective of decoherence. The discussion should be comprehensible to students who have completed a basic course in quantum mechanics with exposure to concepts such as Hilbert space, density matrices, and von Neumann projection (``wavefunction collapse'')., Comment: 8 pages, 2 figures

We demonstrate the existence of quantum hair in electrodynamics and gravity using effective action techniques. In the case of electrodynamics we use the Euler-Heisenberg effective action while in the case of quantum gravity we use the unique effective action. We give a general formulation of these effects which applies to both theories and discuss analogies and differences between them. Furthermore, we present a QED analog to black hole evaporation. Spontaneous pair production in the external field of a ball of charge is analogous to Hawking radiation from black holes. Assuming spherical symmetry, the Gauss law prevents the external field from depending on the density profile of the ball. Quantum corrections violate these expectations, showing that quantum radiation can encode classically forbidden information about the source., Comment: 10 pages

In this invited review, we describe Hawking's information paradox and a recently proposed resolution of it. Explicit calculations demonstrate the existence of quantum hair on black holes, meaning that the quantum state of the external graviton field depends on the internal state of the black hole. Simple quantum mechanics then implies that Hawking radiation amplitudes depend on the internal state, resulting in a pure final radiation state that preserves unitarity and, importantly, violates a factorization assumption which is central to the original paradox. Black hole information is encoded in entangled macroscopic superposition states of the radiation., Comment: 7 pages

It has been shown that the quantum state of the graviton field outside a black hole horizon carries information about the internal state of the hole. We explain how this allows unitary evaporation: the final radiation state is a complex superposition which depends linearly on the initial black hole state. Under time reversal, the radiation state evolves back to the original black hole quantum state. Formulations of the information paradox on a fixed semiclassical geometry describe only a small subset of the evaporation Hilbert space, and do not exclude overall unitarity., Comment: 10 pages. Published version (typos corrected): Physics Letters B Volume 827, 10 April 2022, 136995

We explore the relationship between the quantum state of a compact matter source and of its asymptotic graviton field. For a matter source in an energy eigenstate, the graviton state is determined at leading order by the energy eigenvalue. Insofar as there are no accidental energy degeneracies there is a one to one map between graviton states on the boundary of spacetime and the matter source states. A typical semiclassical matter source results in an entangled asymptotic graviton state. We exhibit a purely quantum gravitational effect which causes the subleading asymptotic behavior of the graviton state to depend on the internal structure of the source. These observations establish the existence of ubiquitous quantum hair due to gravitational effects., Comment: 12 pages

We show that the precision of an angular measurement or rotation (e.g., on the orientation of a qubit or spin state) is limited by fundamental constraints arising from quantum mechanics and general relativity (gravitational collapse). The limiting precision is $r^{-1}$ in Planck units, where $r$ is the physical extent of the (possibly macroscopic) device used to manipulate the spin state. This fundamental limitation means that spin states $S_1$ and $S_2$ cannot be experimentally distinguished from each other if they differ by a sufficiently small rotation. Experiments cannot exclude the possibility that the space of quantum state vectors (i.e., Hilbert space) is fundamentally discrete, rather than continuous. We discuss the implications for finitism: does physics require infinity or a continuum?, Comment: 10 pages. Version to appear in Physics Letters B

Decoding the genome confers the capability to predict characteristics of the organism(phenotype) from DNA (genotype). We describe the present status and future prospects of genomic prediction of complex traits in humans. Some highly heritable complex phenotypes such as height and other quantitative traits can already be predicted with reasonable accuracy from DNA alone. For many diseases, including important common conditions such as coronary artery disease, breast cancer, type I and II diabetes, individuals with outlier polygenic scores (e.g., top few percent) have been shown to have 5 or even 10 times higher risk than average. Several psychiatric conditions such as schizophrenia and autism also fall into this category. We discuss related topics such as the genetic architecture of complex traits, sibling validation of polygenic scores, and applications to adult health, in vitro fertilization (embryo selection), and genetic engineering., Comment: 33 pages, 7 figures, 1 table, A version of this article was prepared for "Genomic Prediction of Complex Traits", Springer Nature book series "Methods in Molecular Biology"

For any choice of initial state and weak assumptions about the Hamiltonian, large isolated quantum systems undergoing Schrodinger evolution spend most of their time in macroscopic superposition states. The result follows from von Neumann's 1929 Quantum Ergodic Theorem. As a specific example, we consider a box containing a solid ball and some gas molecules. Regardless of the initial state, the system will evolve into a quantum superposition of states with the ball in macroscopically different positions. Thus, despite their seeming fragility, macroscopic superposition states are ubiquitous consequences of quantum evolution. We discuss the connection to many worlds quantum mechanics., Comment: version to appear in Foundations of Physics

Quantum gravitational effects suggest a minimal length, or spacetime interval, of order the Planck length. This in turn suggests that Hilbert space itself may be discrete rather than continuous. One implication is that quantum states with norm below some very small threshold do not exist. The exclusion of what Everett referred to as maverick branches is necessary for the emergence of the Born Rule in no collapse quantum mechanics. We discuss this in the context of quantum gravity, showing that discrete models (such as simplicial or lattice quantum gravity) indeed suggest a discrete Hilbert space with minimum norm. These considerations are related to the ultimate level of fine-graining found in decoherent histories (of spacetime geometry plus matter fields) produced by quantum gravity., Comment: 10 pages, 1 figure

We construct genomic predictors for heritable and extremely complex human quantitative traits (height, heel bone density, and educational attainment) using modern methods in high dimensional statistics (i.e., machine learning). Replication tests show that these predictors capture, respectively, $\sim$40, 20, and 9 percent of total variance for the three traits. For example, predicted heights correlate $\sim$0.65 with actual height; actual heights of most individuals in validation samples are within a few cm of the prediction. The variance captured for height is comparable to the estimated SNP heritability from GCTA (GREML) analysis, and seems to be close to its asymptotic value (i.e., as sample size goes to infinity), suggesting that we have captured most of the heritability for the SNPs used. Thus, our results resolve the common SNP portion of the "missing heritability" problem -- i.e., the gap between prediction R-squared and SNP heritability. The $\sim$20k activated SNPs in our height predictor reveal the genetic architecture of human height, at least for common SNPs. Our primary dataset is the UK Biobank cohort, comprised of almost 500k individual genotypes with multiple phenotypes. We also use other datasets and SNPs found in earlier GWAS for out-of-sample validation of our results., Comment: 17 pages, 10 figures

We explain the measure problem (cf. origin of the Born probability rule) in no-collapse quantum mechanics. Everett defined maverick branches of the state vector as those on which the usual Born probability rule fails to hold -- these branches exhibit highly improbable behaviors, including possibly the breakdown of decoherence or even the absence of an emergent semi-classical reality. Derivations of the Born rule which originate in decision theory or subjective probability (i.e., the reasoning of individual observers) do not resolve this problem, because they are circular: they assume, a priori, that the observer occupies a non-maverick branch. An ab initio probability measure is sometimes assumed to explain why we do not occupy a maverick branch. This measure is constrained by, e.g., Gleason's Theorem or envariance to be the usual Hilbert measure. However, this ab initio measure ultimately governs the allocation of a self or a consciousness to a particular branch of the wavefunction, and hence invokes primitives which lie beyond the Everett wavefunction and beyond what we usually think of as physics. The significance of this leap has been largely overlooked, but requires serious scrutiny., Comment: 13 pages, 1 figure. To appear in International Journal of Modern Physics D. arXiv admin note: substantial text overlap with arXiv:1110.0549

Let $A$ be subsystem of a larger system $A \cup B$, and $\psi$ be a typical state from the subspace of the Hilbert space ${\cal H}_{AB}$ satisfying an energy constraint. Then $\rho_A(\psi)= {\rm Tr}_B | \psi \rangle \langle \psi |$ is nearly thermal. We discuss how this observation is related to fast thermalization of the central region ($\approx A$) in heavy ion collisions, where $B$ represents other degrees of freedom (soft modes, hard jets, collinear particles) outside of $A$. Entanglement between the modes in $A$ and $B$ plays a central role: the entanglement entropy $S_A$ increases rapidly in the collision. In gauge-gravity duality, $S_A$ is related to the area of extremal surfaces in the bulk, which can be studied using gravitational duals., Comment: 4 pages, 2 figures, v3: version to appear in MPLA. arXiv admin note: text overlap with arXiv:1205.1584

Dark energy (i.e., a cosmological constant) leads, in the Newtonian approximation, to a repulsive force which grows linearly with distance and which can have astrophysical consequences. For example, the dark energy force overcomes the gravitational attraction from an isolated object (e.g., dwarf galaxy) of mass $10^7 M_\odot$ at a distance of $~ 23$ kpc. Observable velocities of bound satellites (rotation curves) could be significantly affected, and therefore used to measure or constrain the dark energy density. Here, {\it isolated} means that the gravitational effect of large nearby galaxies (specifically, of their dark matter halos) is negligible; examples of isolated dwarf galaxies include Antlia or DDO 1903, Comment: 5 pages, v3: version to appear in Astroparticle Physics

Quantized fields (e.g., the graviton itself) in de Sitter (dS) spacetime lead to particle production: specifically, we consider a thermal spectrum resulting from the dS (horizon) temperature. The energy required to excite these particles reduces slightly the rate of expansion and eventually modifies the semiclassical spacetime geometry. The resulting manifold no longer has constant curvature nor time reversal invariance, and back-reaction renders the classical dS background unstable to perturbations. In the case of AdS, there exists a global static vacuum state; in this state there is no particle production and the analogous instability does not arise., Comment: 3 pages, v2: version to appear in JHEP

We introduce a statistical method that can reconstruct nonlinear genetic models (i.e., including epistasis, or gene-gene interactions) from phenotype-genotype (GWAS) data. The computational and data resource requirements are similar to those necessary for reconstruction of linear genetic models (or identification of gene-trait associations), assuming a condition of generalized sparsity, which limits the total number of gene-gene interactions. An example of a sparse nonlinear model is one in which a typical locus interacts with several or even many others, but only a small subset of all possible interactions exist. It seems plausible that most genetic architectures fall in this category. Our method uses a generalization of compressed sensing (L1-penalized regression) applied to nonlinear functions of the sensing matrix. We give theoretical arguments suggesting that the method is nearly optimal in performance, and demonstrate its effectiveness on broad classes of nonlinear genetic models using both real and simulated human genomes., Comment: 20 pages, 8 figures. arXiv admin note: text overlap with arXiv:1408.3421

How do genes affect cognitive ability or other human quantitative traits such as height or disease risk? Progress on this challenging question is likely to be significant in the near future. I begin with a brief review of psychometric measurements of intelligence, introducing the idea of a "general factor" or g score. The main results concern the stability, validity (predictive power), and heritability of adult g. The largest component of genetic variance for both height and intelligence is additive (linear), leading to important simplifications in predictive modeling and statistical estimation. Due mainly to the rapidly decreasing cost of genotyping, it is possible that within the coming decade researchers will identify loci which account for a significant fraction of total g variation. In the case of height analogous efforts are well under way. I describe some unpublished results concerning the genetic architecture of height and cognitive ability, which suggest that roughly 10k moderately rare causal variants of mostly negative effect are responsible for normal population variation. Using results from Compressed Sensing (L1-penalized regression), I estimate the statistical power required to characterize both linear and nonlinear models for quantitative traits. The main unknown parameter s (sparsity) is the number of loci which account for the bulk of the genetic variation. The required sample size is of order 100s, or roughly a million in the case of cognitive ability., Comment: 30 pages, 13 figures; v2 minor edits

BICEP2 observations, interpreted most simply, suggest an era of inflation with energy densities of order ($10^{16}\, {\rm GeV})^4$, not far below the Planck density. However, models of TeV gravity with large extra dimensions might allow a very different interpretation involving much more modest energy scales. We discuss the viability of inflation in such models, and conclude that existing scenarios do not provide attractive alternatives to single field inflation in four dimensions. Because the detection of tensor modes strengthens our confidence that inflation occurred, it disfavors models of large extra dimensions, at least for the moment., Comment: 4 pages, v3: version to appear in JHEP

Nonlinear modifications of quantum mechanics generically lead to nonlocal effects which violate relativistic causality. We study these effects using the functional Schrodinger equation for quantum fields and identify a type of nonlocality which causes nearly instantaneous entanglement of spacelike separated systems. We describe a simple example involving widely separated wave-packet (coherent) states, showing that nonlinearity in the Schrodinger evolution causes spacelike entanglement, even in free field theory., Comment: 12 pages, 1 figure, v2: version to appear in IJMPA

We show that the signal-processing paradigm known as compressed sensing (CS) is applicable to genome-wide association studies (GWAS) and genomic selection (GS). The aim of GWAS is to isolate trait-associated loci, whereas GS attempts to predict the phenotypic values of new individuals on the basis of training data. CS addresses a problem common to both endeavors, namely that the number of genotyped markers often greatly exceeds the sample size. We show using CS methods and theory that all loci of nonzero effect can be identified (selected) using an efficient algorithm, provided that they are sufficiently few in number (sparse) relative to sample size. For heritability h2 = 1, there is a sharp phase transition to complete selection as the sample size is increased. For heritability values less than one, complete selection can still occur although the transition is smoothed. The transition boundary is only weakly dependent on the total number of genotyped markers. The crossing of a transition boundary provides an objective means to determine when true effects are being recovered; we discuss practical methods for detecting the boundary. For h2 = 0.5, we find that a sample size that is thirty times the number of nonzero loci is sufficient for good recovery., Comment: 30 pages, 11 figures. Version to appear in journal GigaScience

Unitary black hole evaporation necessarily involves a late-time superposition of decoherent states, including states describing distinct spacetimes (e.g., different center of mass trajectories of the black hole). Typical analyses of the black hole information problem, including the argument for the existence of firewalls, assume approximate unitarity ("factorization of unitarity") on each of the decoherent spacetimes. This factorization assumption is non-trivial, and indeed may be incorrect. We describe an ansatz for the radiation state that violates factorization and which allows unitarity and the equivalence principle to coexist (no firewall). Unitarity without factorization provides a natural realization of the idea of black hole complementarity., Comment: 4 pages revtex; v2 added discussion of dimensionality of BH internal Hilbert space

We discuss the black hole information problem, including the recent claim that unitarity requires a horizon firewall, emphasizing the role of decoherence and macroscopic superpositions. We consider the formation and evaporation of a large black hole as a quantum amplitude, and note that during intermediate stages (e.g., after the Page time), the amplitude is a superposition of macroscopically distinct (and decohered) spacetimes, with the black hole itself in different positions on different branches. Small but semiclassical observers (who are themselves part of the quantum amplitude) that fall into the hole on one branch will miss it entirely on other branches and instead reach future infinity. This observation can reconcile the subjective experience of an infalling observer with unitarity. We also discuss implications for the nice slice formulation of the information problem, and to complementarity., Comment: 3 pages, 1 figure, revtex

We show that big bang cosmology implies a high degree of entanglement of particles in the universe. In fact, a typical particle is entangled with many particles far outside our horizon. However, the entanglement is spread nearly uniformly so that two randomly chosen particles are unlikely to be directly entangled with each other -- the reduced density matrix describing any pair is likely to be separable., Comment: 5 pages, 3 figures, revtex. arXiv admin note: text overlap with arXiv:0908.1265

I give a brief introduction to many worlds or "no wavefunction collapse" quantum mechanics, suitable for non-specialists. I then discuss the origin of probability in such formulations, distinguishing between objective and subjective notions of probability., Comment: 7 pages, 2 figures. This version to appear as a Brief Review in Modern Physics Letters

We study the gravitational effects of a planar domain wall on quantum fluctuations of a massless scalar field during inflation. By obtaining an exact solution of the scalar field equation in de Sitter space, we show that the gravitational effects of the domain wall break the rotational invariance of the primordial power spectrum without affecting the translational invariance. The strength of rotational violation is determined by one dimensionless parameter $\beta$, which is a function of two physical parameters, the domain wall surface tension $\sigma$ and cosmological constant $\Lambda$. In the limit of small $\beta$, the leading effect of rotational violation of the primordial power spectrum is scale-invariant., Comment: 5 pages, no figure; Section 2 is added; Introduction and Section 4 are modified; In v3, primordial curvature perturbation is discussed in Sec. 4; Introduction, Sec 2, and Sec 4 are modified

We describe paths in the configuration space of (3+1) dimensional QED whose relative quantum phase (or relative phase in the functional integral) depends on the value of the theta angle. The final configurations on the two paths are related by a gauge transformation but differ in magnetic helicity or Chern-Simons number. Such configurations must exhibit gauge potentials that fall off no faster than 1/r in some region of finite solid angle, although they need not have net magnetic charge (i.e., are not magnetic monopoles). The relative phase is proportional to theta times the difference in Chern-Simons number. We briefly discuss some possible implications for QCD and the strong CP problem., Comment: v2 contains Note Added after Conclusions

We describe a simple gedanken experiment which illustrates the physical effects of the QED theta angle, a fundamental parameter of Nature that has yet to be measured. The effects are manifest in quantum phases analogous to those in the Aharonov-Bohm effect, although they are not intrinsically topological. We also derive the quantum phases using a functional Schrodinger approach, and generalize the results to non-Abelian gauge theories., Comment: 4 pages, latex, 1 figure

We analyze 5 years of student records at the University of Oregon to estimate the probability of success (as defined by superior undergraduate record; sufficient for admission to graduate school) in Physics and Mathematics as a function of SAT-M score. We find evidence of a nonlinear threshold: below SAT-M score of roughly 600, the probability of success is very low. Interestingly, no similar threshold exists in other majors, such as Sociology, History, English or Biology, whether on SAT combined, SAT-R or SAT-M. Our findings have significant implications for the demographic makeup of graduate populations in mathematically intensive subjects, given the current distribution of SAT-M scores., Comment: 9 pages, 4 figures

Asymptotic safety (an ultraviolet fixed point with finite-dimensional critical surface) offers the possibility that a predictive theory of quantum gravity can be obtained from the quantization of classical general relativity. However, it is unclear what becomes of the singularities of classical general relativity, which, it is hoped, might be resolved by quantum effects. We study dust collapse with a running gravitational coupling and find that a future singularity can be avoided if the coupling becomes exactly zero at some finite energy scale. The singularity can also be avoided (pushed off to infinite proper time) if the coupling approaches zero sufficiently rapidly at high energies. However, the evolution deduced from perturbation theory still implies a singularity at finite proper time., Comment: 6 pages, latex. Version to appear in Physics Letters B

We investigate isolated white holes surrounded by vacuum, which correspond to the time reversal of eternal black holes that do not evaporate. We show that isolated white holes produce quasi- thermal Hawking radiation. The time reversal of this radiation, incident on a black hole precursor, constitutes a special preparation that will cause the black hole to become eternal., Comment: 5 pages, 2 figures, revtex; revised version to appear in Classical and Quantum Gravity

We propose a class of simple dark energy models which predict a late-time dark radiation component and a distinctive time-dependent equation of state $w(z)$ for redshift $z < 3$. The dark energy field can be coupled strongly enough to Standard Model particles to be detected in colliders, and the model requires only modest additional particle content and little or no fine-tuning other than a new energy scale of order milli-electron volts., Comment: 12 pages, 4 figures. Selected for Honorable Mention in the 2010 Gravity Research Foundation Essay awards

We analyze a data set comprised of academic records of undergraduates at the University of Oregon from 2000-2004. We find correlations of roughly 0.35 to 0.5 between SAT scores and upper division, in-major GPA (henceforth, GPA). Interestingly, low SAT scores do not preclude high performance in most majors. That is, the distribution of SAT scores after conditioning on high GPA (e.g., 3.5 or even 4.0) typically extends below 1000 (the average among test takers). We hypothesize that "overachievers" overcome cognitive deficits through hard work, and discuss to what extent they can be identified from high school records. Only a few majors seem to exhibit a "cognitive threshold" -- such that high GPA (mastery of the subject matter) is very unlikely below a certain SAT threshold (i.e., no matter how dedicated or hard working the student). Our results suggest that almost any student admitted to university can achieve academic success, if they work hard enough. In addition to our primary result, we find that the best predictor of GPA is a roughly equally weighted sum of SAT and high school GPA, measured in standard deviation units. Using a sub-population of honors college students, we can estimate how students at elite universities would fare at a typical state university, allowing us to comment on issues such as grade inflation. Finally, we observe that 1) SAT scores fluctuate little on retest (very high reliability), 2) SAT and GRE scores (where available) correlate at roughly 0.75 (consistent with the notion that both tests measure a stable general cognitive ability) and 3) the SAT distribution of students that obtained a degree does not differ substantially from that of the entering class., Comment: 27 pages, 13 figures

We investigate the experimental capabilities required to test whether black holes destroy information. We show that an experiment capable of illuminating the information puzzle must necessarily be able to detect or manipulate macroscopic superpositions (i.e., Everett branches). Hence, it could also address the fundamental question of decoherence versus wavefunction collapse., Comment: 10 pages, 4 figures, contribution to proceedings of the 1st Mediterranean Conference on Classical and Quantum Gravity.

We systematically study the unification of gauge couplings in the presence of (one or more) effective dimension-5 operators cHGG/4MPl, induced into the grand unified theory by gravitational interactions at the Planck scale MPl. These operators alter the usual condition for gauge coupling unification, which can, depending on the Higgs content H and vacuum expectation value, result in unification at scales MX significantly different than naively expected. We find non-supersymmetric models of SU(5) and SO(10) unification, with natural Wilson coefficients c, that easily satisfy the constraints from proton decay. Furthermore, gauge coupling unification at scales as high as the Planck scale seems feasible, possibly hinting at simultaneous unification of gauge and gravitational interactions. In the Appendix we work out the group theoretical aspects of this scenario for SU(5) and SO(10) unified groups in detail; this material is also relevant in the analysis of non-universal gaugino masses obtained from supergravity., Comment: 27 pages, 5 figures, 8 tables, 1 appendix, revtex; v2: introduction and conclusion expanded, references added, minor changes, version published in PRD