arXiv subjects
Publications and source records attributed to T. Banks.
We argue that the correlation between the modular Hamiltonians of two causal diamonds related by a finite time translation is equal to the uncertainty in the modular Hamiltonian of the diamond in their overlap. In a separate section we investigate the relation between entropy fluctuations in a diamond, and length fluctuations calculated from the 't Hooft commutation relations.
A detailed analysis of ground-based CCD UBV photometry and space-based Gaia Data Release 3 (DR3) data for the open clusters King 6 and NGC 1605 was performed. Using the pyUPMASK algorithm on Gaia astrometric data to estimate cluster membership probabilities, we have identified 112 stars in King 6 and 160 stars in NGC 1605 as the statistically most likely members of each cluster. We calculated reddening and metallicity separately using UBV two-color diagrams to estimate parameter values via independent methods. The color excess $E(B-V)$ and photometric metallicity [Fe/H] for King 6 are $0.515 \pm 0.030$ mag and $0.02 \pm 0.20$ dex, respectively. For NGC 1605, they are $0.840 \pm 0.054$ mag and $0.01 \pm 0.20$ dex. With reddening and metallicity kept constant, we have estimated the distances and cluster ages by fitting PARSEC isochrones to color-magnitude diagrams based on the Gaia and UBV data. Photometric distances are 723 $\pm$ 34 pc for King 6 and 3054 $\pm$ 243 pc for NGC 1605. The cluster ages are $200 \pm 20$ Myr and $400 \pm 50$ Myr for King 6 and NGC 1605, respectively. Mass function slopes were found to be 1.29 $\pm$ 0.18 and 1.63 $\pm$ 0.36 for King 6 and NGC 1605, respectively. These values are in good agreement with the value of Salpeter (1955). The relaxation times were estimated as 5.8 Myr for King 6 and 60 Myr for NGC 1605. This indicates that both clusters are dynamically relaxed since these times are less than the estimated cluster ages. Galactic orbit analysis shows that both clusters formed outside the solar circle and are members of the young thin-disc population.
We argue that no theoretical model of quantum gravity in a causal diamond whose boundary has finite maximal area, can be verified with arbitrary precision by experiments done in that diamond. This shows in particular that if our own universe remains in an asymptotically future de Sitter state for a time long enough for our local group of galaxies to collapse into a black hole, then no information processing system with which we can communicate could ever distinguish between many competing models of the AsdS universe. This article is written in an attempt to be accessible to a wide audience, so certain elementary facts about quantum mechanics are reviewed, briefly.
We review ideas relating the breaking of Supersymmetry in de Sitter (dS) space-time to amplitudes in which gravitinos are reflected from the dS horizon. A self consistent evaluation of such amplitudes leads to the estimate $m_{3/2} = K Λ^{1/4}$, with a constant $K$ that is not easily calculable. LHC bounds on superpartner masses, plus the structure of low energy effective field theory then imply that there must be new superfields with standard model quantum numbers in the region below $100$ TeV. Only one class of models, the Pyramid Schemes, has been found, which is compatible with one loop coupling unification. They have a new strongly coupled gauge sector with a confinement scale in the multi TeV region. We outline the general predictions of these models, which include Dirac gauginos and a novel solution of the strong CP problem. The models all appear to have a "little hierarchy problem": the expectation value of the standard model Higgs field, and its mass, must be a factor of $10$ or more smaller than the masses of the second Higgs doublet or standard model superpartners. Since all of these models contain uncertainties from the strong coupling physics, as well as the physics of the dS horizon, it is difficult to determine how serious this fine tuning problem is.
We reformulate Holographic Space-time (HST) Models as Hilbert bundles over the space of time-like geodesics on a background manifold. The background, following Jacobson, is viewed as a hydrodynamic flow, which the quantum model must reproduce. Work of many authors, but particularly the Verlindes, Carlip and Solodukhin, suggest that the relevant quantum model is a sequence of 1+1 dimensional conformal field theories (CFT) on the boundaries of nested causal diamonds. Finiteness of the entropy suggests the CFTs be built from cutoff fermion fields, and the spin/statistics connection, combined with Connes' demonstration that Riemannian geometry is encoded in the Dirac equation, suggests that these fields are labelled by the cutoff eigenspectrum of the Dirac operator on the holoscreen of each diamond. This leads to a natural conjecture for the density matrix of arbitrary diamonds and,in a subclass of space-times, for the time evolution operator between them. We conjecture that the 't Hooft commutation relations on diamond boundaries are related to Schwinger terms in U(1) currents constructed from the fermion fields. We review the notion of "locality as constraints on holographic variables" discovered by Fiol, Fischler and the present author and, in an appendix, explain how it differs from the notion of locality arising from tensor network constructions in AdS/CFT.
This paper presents photometric, astrometric, and kinematic analyses of the open clusters NGC 189, NGC 1758 and NGC 7762 based on CCD UBV photometric and Gaia Data Release 3 (DR3) data. According to membership analyses, we identified 32, 57 and 106 most probable member stars with membership probabilities $P\geq 0.5$ in NGC 189, NGC 1758 and NGC 7762, respectively. The color excesses and photometric metallicities of each cluster were determined separately using UBV two-color diagrams. The color excess $E(B-V)$ is $0.590 \pm 0.023$ mag for NGC 189, $0.310 \pm 0.022$ mag for NGC 1758 and $0.640 \pm 0.017$ mag for NGC 7762. The photometric metallicity [Fe/H] is $-0.08 \pm 0.03$ dex for both NGC 189 and NGC 1758, and $-0.12 \pm 0.02$ dex for NGC 7762. Distance moduli and ages of the clusters were obtained by comparing PARSEC isochrones with the color-magnitude diagrams constructed from UBV and Gaia photometric data. During this process, we kept as constant color excess and metallicity for each cluster. The estimated isochrone distance is $1201 \pm 53$ pc for NGC 189, $902 \pm 33$ pc for NGC 1758 and $911 \pm 31$ pc for NGC 7762. These are compatible with the values obtained from trigonometric parallax. Ages of the clusters are $500\pm 50$ Myr, $650\pm 50$ Myr and $2000\pm 200$ Myr for NGC 189, NGC 1758 and NGC 7762, respectively. Galactic orbit integration of the clusters showed that NGC 1758 completely orbits outside the solar circle, while NGC 189 and NGC 7762 enter the solar circle during their orbits.
The Holographic Space-time (HST) model of inflation has a potential explanation for dark matter as tiny primordial black holes. Motivated by a recent paper of Barrau\cite{barrau} we propose a version of this model where some of the Inflationary Black Holes (IBHs), whose decay gives rise to the Hot Big Bang, carry the smallest value of a discrete symmetry charge. The fraction $f$ of IBHs carrying this charge is difficult to estimate from first principles, but we fix it by requiring that the crossover between radiation and matter domination occurs at the correct temperature $T_{eq} \sim 1 eV = 10^{-28} M_P$. The fraction is small, $f \sim 2\times 10^{-9}$ so we believe this gives an extremely plausible model of dark matter.
We review and clarify ideas proposed many years ago for understanding cosmology in a holographic framework. The basic strategy is to use Jacobson's\cite{ted95} identification of Einstein's equations with the hydrodynamic equations of the "Area = 4 Entropy" law for causal diamonds, to identify a quantum system whose hydrodynamics match those of a given space-time. This can be done exactly for a system with any positive cosmological constant, which saturates the entropy bound for all times. The quantum system is a sequence of (cut-off) $1+1$ dimensional CFTs, with central charge proportional to the entropy in causal diamonds along an FRW geodesic. This matches with a recent\cite{BZ} proposal that the modular Hamiltonian of any causal diamond for non-negative c.c. is the $L_0$ generator of such a CFT. When an early de Sitter era is followed by slow roll expansion of the horizon, disjoint horizon volumes (which are gauge copies in an eternal dS space, but become physical due to slow roll expansion of the horizon area) manifest as a dilute gas of black holes in a post-inflationary era. Entropy fluctuations of individual black holes manifest as CMB fluctuations, and the tensor/scalar ratio is suppressed by an extra factor of the slow roll parameter $ε$. Black hole evaporation provides the Hot Big Bang and baryogenesis. Black hole mergers can easily provide a source of primordial BH dark matter that dominates radiation at a temperature of $1$ eV, but numerical simulations are required to determine whether the model can explain the actual dark matter in our universe.
We present photometric, astrometric, and kinematic studies of the old open star clusters NGC 1193 and NGC 1798. Both of the clusters are investigated by combining data sets from Gaia EDR3 and CCD UBV observational data. Analysis of the radial distribution of stars through the cluster regions indicates that the cluster limit radii are $r_{\rm lim}=8'$ for both of the clusters. We determine the membership probabilities of stars considering Gaia EDR3 proper motion and trigonometric parallax data, resulting in 361 stars in NGC 1193 and 428 in NGC 1798 being identified as most likely cluster members, having membership probabilities greater than P>0.5. Mean proper motion components are estimated as ($μ_α\cos δ$, $μ_δ) = (-0.207(0.009), -0.431(0.008)$) for NGC 1193 and ($μ_α\cos δ$, $μ_δ)=(0.793(0.006), -0.373(0.005)$) mas/yr for NGC 1798. E(B-V) color excesses were derived for NGC 1193 as $0.150(0.037)$ and for NGC 1798 as 0.505(0.100) mag through the use of two-color diagrams. Photometric metallicities are also determined from two-color diagrams with the results of [Fe/H] = -0.30(0.06) dex for NGC 1193 and [Fe/H]=-0.20(0.07) dex for NGC 1798. The isochrone fitting distance and age of NGC 1193 are 5562(381) pc and 4.6(1) Gyr, respectively. For NGC 1798, these parameters are 4451(728) pc and 1.3(0.2) Gyr. These ages indicate that NGC 1193 and NGC 1798 are old open clusters. The overall present-day mass function slopes for main-sequence stars are found as 1.38(2.16) for NGC 1193 and 1.30(0.21) for NGC 1798, which are in fair agreement with the value of Salpeter (1955). Kinematic and dynamic orbital calculations indicate that NGC 1193 and NGC 1798 belong to the thick-disk and thin-disk populations, respectively. In addition, both of the clusters were born outside the solar circle, and both orbit in the metal-poor region of the Galactic disk.
We show that a recent reformulation of hydrodynamic equations for a large class of models consisting of q-dits on a graph with short range interactions is sufficient for understanding chaotic behavior. Any such system consists of large subsystems coupled together by interactions whose relative strength goes to zero with the subsystem size. In the absence of conservation laws other than energy, the Hamiltonians of the subsystems form a complete set of commuting operators. The hydrodynamic variables are the block diagonal matrix elements $ρ(e(X))$ of the density matrix in the joint eigenbasis of the subsystem Hamiltonians, averaged over energy bins. To leading order in the inverse subsystem size, $ρ(e(X); t)$ satisfies a classical stochastic equation, which for certain systems takes the form of a functional Fokker-Planck equation. In such systems the time averaged spectral form factors can be written as a two dimensional Euclidean functional integral, on a space with multiple disconnected boundaries. The failure of factorization in this representation is attributable to the time averaging necessary to apply the hydrodynamic approximation. The bulk Euclidean action is purely topological. We make tentative explorations of the special properties of the system that are required in order to have a representation as a functional integral over metrics.
This study calculated astrophysical parameters, as well as kinematic and galactic orbital parameters, of the open clusters NGC 1664 and NGC 6939. The work is based on CCD UBV and Gaia photometric and astrometric data from ground and space-based observations. Considering Gaia Early Data Release 3 (EDR3) astrometric data, we determined membership probabilities of stars located in both of the clusters. We used two-color diagrams to determine $E(B-V)$ color excesses for NGC 1664 and NGC 6939 as $0.190 \pm 0.018$ and $0.380 \pm 0.025$ mag, respectively. Photometric metallicities for the two clusters were estimated as [Fe/H] = $-0.10 \pm 0.02$ dex for NGC 1664 and as [Fe/H] = $-0.06 \pm 0.01$ dex for NGC 6939. Using the reddening and metallicity calculated in the study, we obtained distance moduli and ages of the clusters by fitting PARSEC isochrones to the color-magnitude diagrams based on the most likely member stars. Isochrone fitting distances are $1289 \pm 47$ pc and $1716 \pm 87$ pc, which coincide with ages of $675 \pm 50$ Myr and $1.5 \pm 0.2$ Gyr for NGC 1664 and NGC 6939, respectively. We also derived the distances to the clusters using Gaia trigonometric parallaxes and compared these estimates with the literature. We concluded that the results are in good agreement with those given by the current study. Present day mass function slopes were calculated as $Γ=-1.22\pm0.33$ and $Γ=-1.18\pm0.21$ for NGC 1664 and NGC 6939, respectively, which are compatible with the Salpeter (1955) slope. Analyses showed that both of clusters are dynamically relaxed. The kinematic and dynamic orbital parameters of the clusters were calculated, indicating that the birthplaces of the clusters are outside the solar circle.
We analysed the open clusters Czernik 2 and NGC 7654 using CCD UBV photometric and Gaia Early Data Release 3 (EDR3) photometric and astrometric data. Structural parameters of the two clusters were derived, including the physical sizes of Czernik 2 being r=5 and NGC 7654 as 8 min. We calculated membership probabilities of stars based on their proper motion components as released in the Gaia EDR3. To identify member stars of the clusters, we used these membership probabilities taking into account location and the impact of binarity on main-sequence stars. We used membership probabilities higher than $P=0.5$ to identify 28 member stars for Czernik 2 and 369 for NGC 7654. We estimated colour-excesses and metallicities separately using two-colour diagrams to derive homogeneously determined parameters. The derived $E(B-V)$ colour excess is 0.46(0.02) mag for Czernik 2 and 0.57(0.04) mag for NGC 7654. Metallicities were obtained for the first time for both clusters, -0.08(0.02) dex for Czernik 2 and -0.05(0.01) dex for NGC 7654. Keeping the reddening and metallicity as constant quantities, we fitted PARSEC models using colour-magnitude diagrams, resulting in estimated distance moduli and ages of the two clusters. We obtained the distance modulus for Czernik 2 as 12.80(0.07) mag and for NGC 7654 as 13.20(0.16) mag, which coincide with ages of 1.2(0.2) Gyr and 120(20) Myr, respectively. The distances to the clusters were calculated using the Gaia EDR3 trigonometric parallaxes and compared with the literature. We found good agreement between the distances obtained in this study and the literature. Present day mass function slopes for both clusters are comparable with the value of Salpeter (1955), being X=-1.37(0.24) for Czernik 2 and X=-1.39(0.19) for NGC 7654.
We present reddening, photometric metallicity, age and distance estimates for the Frolov 1 and NGC 7510 open clusters based on CCD UBV photometric and Gaia data. Photometric observations were collected using the 1-m telescope of the TÜBİTAK National Observatory. Gaia DR2 proper motion data in the direction of two groupings were used to identify cluster membership. We determined mean proper motion values ($ μ_α\cosδ, μ_δ$) = ($-3.02\pm 0.10$, $-1.75 \pm 0.08$) and ($-3.66 \pm 0.07$, $-2.17 \pm 0.06$) mas yr$^{-1}$ for Frolov 1 and NGC 7510, respectively. We used two-colour diagrams to obtain $E(B-V)$ colour excesses for Frolov 1 and NGC 7510 as $0.65\pm0.06$ and $1.05\pm0.05$ mag, respectively. We derived the photometric metallicity of Frolov 1 as [Fe/H] = 0.03$\pm$0.03 dex and adopted a solar metallicity for NGC 7510. Based on these reddening and metallicities we determined the distance moduli and ages of the clusters via fitting PARSEC isochrones to the cluster colour-magnitude diagrams. Isochrone fitting distances for Frolov 1 and NGC 7510 are $2864 \pm 254$ and $2818 \pm 247$ pc, respectively, which correspond to the ages $35\pm 10$ Myr and $18\pm 6$ Myr. We also calculated mean Gaia distances and compared them with those given in the literature and in this study, concluding that our results are in good agreement with previous work. Finally, we calculated the mass function slopes as being $X=-1.21\pm0.18$ for Frolov 1 and $X=-1.42\pm0.27$ for NGC 7510.
An update is given on the exoplanet research collaboration between Nielsen (a marketing research company), Brigham Young University, and NZ universities with the National University of Singapore, which has been expanded to include a community college in the US. Key achievements from the past year are outlined, including density estimates for HD 209458 and Kepler 1 from radial velocity and transit fits. A comparison between the WinFitter optimizer and other techniques is outlined, showing that WinFitter estimated statistical errors are essentially in line (bar a scaling proportion) with those estimated via Markov Chain Monte Carlo techniques.
We reanalyze and expand upon models proposed in 2015 for linear dilaton black holes, and use them to test several speculative ideas about black hole physics. We examine ideas based on the definition of quantum extremal surfaces in quantum field theory in curved space-time. The low energy effective field theory of our model is the large N CGHS model, which includes the one loop effects that are taken into account in the "island" proposal for understanding the Page curve. Contrary to the results of the island analysis, that solution leads to a singular geometry for the evaporated black hole. If the singularity obeys Cosmic Censorship then Hawking evaporation leaves behind a remnant object with a finite fraction of the black hole entropy. If the singularity becomes naked at some point, boundary conditions on a time-like line emanating from that point can produce a sensible model where we expect a Page curve. We show that the fully UV complete model gives a correct Page curve, as it must since the model is manifestly unitary. Recent result on replicawormholes suggest that the island formula, which appears to involve only one loop computations, in fact encodes non-perturbative contributions to the gravitational path integral. The question of why Euclidean gravity computations can capture information about microscopic states of quantum gravity remains mysterious. In a speculative coda to the paper we suggest that the proper way of understanding the relation between Euclidean gravity path integrals and quantum spectra is via a statistical approach to Jacobson's interpretation of general relativistic field equations as the hydrodynamic equations of the area law for the maximal entropy of causal diamonds.
The formalism of Holographic Space-time (HST) is a translation of the principles of Lorentzian geometry into the language of quantum information. Intervals along time-like trajectories, and their associated causal diamonds, completely characterize a Lorentzian geometry. The Bekenstein-Hawking-Gibbons-'t Hooft-Jacobson-Fischler-Susskind-Bousso Covariant Entropy Principle, equates the logarithm of the dimension of the Hilbert space associated with a diamond to one quarter of the area of the diamond's holographic screen, measured in Planck units. The most convincing argument for this principle is Jacobson's derivation of Einstein's equations as the hydrodynamic expression of this entropy law. In that context, the null energy condition (NEC) is seen to be the analog of the local law of entropy increase. The quantum version of Einstein's relativity principle is a set of constraints on the mutual quantum information shared by causal diamonds along different time-like trajectories. The implementation of this constraint for trajectories in relative motion is the greatest unsolved problem in HST. The other key feature of HST is its claim that, for non-negative cosmological constant or causal diamonds much smaller than the asymptotic radius of curvature for negative c.c., the degrees of freedom localized in the bulk of a diamond are constrained states of variables defined on the holographic screen. This principle gives a simple explanation of otherwise puzzling features of BH entropy formulae, and resolves the firewall problem for black holes in Minkowski space. It motivates a covariant version of the CKN\cite{ckn} bound on the regime of validity of quantum field theory (QFT) and a detailed picture of the way in which QFT emerges as an approximation to the exact theory.
We investigate modifications of quantum mechanics (QM) that replace the unitary group in a finite dimensional Hilbert space with a finite group and determine the minimal sequence of subgroups necessary to approximate QM arbitrarily closely for general choices of Hamiltonian. This mathematical study reveals novel insights about 't Hooft's Ontological Quantum Mechanics, and the derivation of statistical mechanics from quantum mechanics. We show that Kornyak's proposal to understand QM as classical dynamics on a Hilbert space of one dimension higher than that describing the universe, supplemented by a choice of the value of a naturally conserved quantum operator in that classical evolution can probably be a model of the world we observe.
We recapitulate multiple arguments that Eternal Inflation, and the String Landscape are actually part of the Swampland: ideas in Effective Quantum Field Theory that do not have a counterpart in genuine models of Quantum Gravity.