What we don't know about time

String theory has transformed our understanding of geometry, topology and spacetime. Thus, for this special issue of Foundations of Physics commemorating "Forty Years of String Theory", it seems appropriate to step back and ask what we do not understand. As I will discuss, time remains the least understood concept in physical theory. While we have made significant progress in understanding space, our understanding of time has not progressed much beyond the level of a century ago when Einstein introduced the idea of space-time as a combined entity. Thus, I will raise a series of open questions about time, and will review some of the progress that has been made as a roadmap for the future.Comment: 15 pages; Essay for a special issue of Foundations of Physics commemorating "Forty years of string theory

Quantum geometry and gravitational entropy

Most quantum states have wavefunctions that are widely spread over the accessible Hilbert space and hence do not have a good description in terms of a single classical geometry. In order to understand when geometric descriptions are possible, we exploit the AdS/CFT correspondence in the half-BPS sector of asymptotically AdS_5 x S^5 universes. In this sector we devise a "coarse-grained metric operator" whose eigenstates are well described by a single spacetime topology and geometry. We show that such half-BPS universes have a non-vanishing entropy if and only if the metric is singular, and that the entropy arises from coarse-graining the geometry. Finally, we use our entropy formula to find the most entropic spacetimes with fixed asymptotic moments beyond the global charges.Comment: 29 pages, 2 figures; references adde

Nodulation and nitrogen fixation in chickpea (Cicer arietinum L.) under salt stress

The effects of salt stress on the growth, nodulation and N accumulation during the vegetative phase was studied in chickpea (Cicer arietinum). Growth and N accumulation were adversely affected by salinity. The larger control plants produced new nodules but the existing nodules on stressed plants grew larger than those of control plants. All plants had similar %N contents but the total plant N was less in stressed plants due to the reduced growth of these plants. Reduced plant vigour was the primary effect of salt stress and was mediated through processes other than symbiotic N fixation

Tuning phase-stability and short-range order through Al-doping in (CoCrFeMn)100-xAlx high entropy alloys

For (CoCrFeMn)$_{100-x}$Al$_{x}$ high-entropy alloys, we investigate the phase evolution with increasing Al-content (0 $\le$ x $\le$ 20 at.%). From first-principles theory, the Al-doping drives the alloy structurally from FCC to BCC separated by a narrow two-phase region (FCC+BCC), which is well supported by our experiments. We highlight the effect of Al-doping on the formation enthalpy and electronic structure of (CoCrFeMn)$_{100-x}$Al$_{x}$ alloys. As chemical short-range order (SRO) in multicomponent alloys indicates the nascent local order (and entropy changes), as well as expected low-temperature ordering behavior, we use thermodynamic linear-response within density-functional theory to predict SRO and ordering transformation and temperatures inherent in (CoCrFeMn)$_{100-x}$Al$_{x}$. The predictions agree with our present experimental findings, and other reported ones.Comment: 27 pages, 9 figures, 1 tabl

Typicality versus thermality: An analytic distinction

In systems with a large degeneracy of states such as black holes, one expects that the average value of probe correlation functions will be well approximated by the thermal ensemble. To understand how correlation functions in individual microstates differ from the canonical ensemble average and from each other, we study the variances in correlators. Using general statistical considerations, we show that the variance between microstates will be exponentially suppressed in the entropy. However, by exploiting the analytic properties of correlation functions we argue that these variances are amplified in imaginary time, thereby distinguishing pure states from the thermal density matrix. We demonstrate our general results in specific examples and argue that our results apply to the microstates of black holes.Comment: 22 pages + appendices, 3 eps figure

Deconstruction and Holography

It was recently pointed out that the physics of a single discrete gravitational extra dimension exhibits a peculiar UV/IR connection relating the UV scale to the radius of the effective extra dimension. Here we note that this non-locality is a manifestation of holography, encoding the correct scaling of the number of fundamental degrees of freedom of the UV theory. This in turn relates the Wilsonian RG flow in the UV theory to the effective gravitational dynamics in the extra dimension. The relevant holographic c-function is determined by the expression for the holographic bound. Holography in this context is a result of the requirements of unitarity and diffeomorphism invariance. We comment on the relevance of this observation for the cosmological constant problem.Comment: 11 pages, LaTe

An Effect of α′\alpha' Corrections on Racetrack Inflation

We study the effects of $\alpha '$ corrections to the K\"ahler potential on volume stabilisation and racetrack inflation. In a region where classical supergravity analysis is justified, stringy corrections can nevertheless be relevant for correctly analyzing moduli stabilisation and the onset of inflation.Comment: 13 pages, 4 figures. Typos corrected, references added, this version to appear in JHE

Developing a mental health index using a machine learning approach: Assessing the impact of mobility and lockdown during the COVID-19 pandemic

Governments worldwide have implemented stringent restrictions to curtail the spread of the COVID-19 pandemic. Although beneficial to physical health, these preventive measures could have a profound detrimental effect on the mental health of the population. This study focuses on the impact of lockdowns and mobility restrictions on mental health during the COVID-19 pandemic. We first develop a novel mental health index based on the analysis of data from over three million global tweets using the Microsoft Azure machine learning approach. The computed mental health index scores are then regressed with the lockdown strictness index and Google mobility index using fixed-effects ordinary least squares (OLS) regression. The results reveal that the reduction in workplace mobility, reduction in retail and recreational mobility, and increase in residential mobility (confinement to the residence) have harmed mental health. However, restrictions on mobility to parks, grocery stores, and pharmacy outlets were found to have no significant impact. The proposed mental health index provides a path for theoretical and empirical mental health studies using social media. [Abstract copyright: © 2022 Elsevier Inc. All rights reserved.