Scientific Series

Non-normalizable quantum states are usually discarded as mathematical artefacts in quantum mechanics. However, such states naturally occur in quantum gravity as solutions to physical constraints. This suggests reconsidering the interpretation of such states. Some of the existing approaches to this question seek to redefine the inner product, but this arguably leads to further challenges. 

In this talk, I will propose an alternative interpretation of non-normalizable states using pilot-wave theory. First, I will argue that the basic conceptual structure of the theory contains a straightforward interpretation of these states. Second, to better understand such states, I will discuss non-normalizable states of the quantum harmonic oscillator from a pilot-wave perspective. I will show that, contrary to intuitions from orthodox quantum mechanics, the non-normalizable eigenstates and their superpositions are bound states in the sense that the pilot-wave velocity field vy→0 at large ±y. Third, I will introduce a new notion of equilibrium, named pilot-wave equilibrium, and use it to define physically-meaningful equilibrium densities for such states. I will show, via an H-theorem, that an arbitrary initial density with compact support relaxes to pilot-wave equilibrium at a coarse-grained level, under assumptions similar to those for relaxation to quantum equilibrium. I will conclude by discussing the implications for pilot-wave theory, quantum gravity and quantum foundations in general. 

Based on:

I. Sen. "Physical interpretation of non-normalizable harmonic oscillator states and relaxation to pilot-wave equilibrium" arXiv:2208.08945 (2022)

Zoom link:  https://pitp.zoom.us/j/93736627504?pwd=VGtxZE5rTFdnT1dqZlFRWTFvWlFQUT09

Quantum correlations in general and quantum entanglement in particular embody both our continued struggle towards a foundational understanding of quantum theory as well as the latter’s advantage over classical physics in various information processing tasks. Consequently, the problems of classifying (i) quantum states from more general (non-signalling) correlations, and (ii) entangled states within the set of all quantum states, are at the heart of the subject of quantum information theory.

In this talk I will present two recent results (from https://journals.aps.org/pra/abstract/10.1103/PhysRevA.106.062420 and https://arxiv.org/abs/2207.00024) that shed new light on these problems, by exploiting a surprising connection with time in quantum theory:

First, I will sketch a solution to problem (i) for the bipartite case, which identifies a key physical principle obeyed by quantum theory: quantum states preserve local time orientations—roughly, the unitary evolution in local subsystems.

Second, I will show that time orientations are intimately connected with quantum entanglement: a bipartite quantum state is separable if and only if it preserves arbitrary local time orientations. As a variant of Peres's well-known entanglement criterion, this provides a solution to problem (ii).

Zoom link:  https://pitp.zoom.us/j/97607837999?pwd=cXBYUmFVaDRpeFJSZ0JzVmhSajdwQT09

Scientific programs involving joint analyses of different tracers of large-scale structure and CMB are increasingly gaining attention as they often increase the prospects to detect and characterise new signals by reducing systematics, cancelling cosmic variance and breaking degeneracies. In this talk, I will demonstrate how these programs will provide the most precise tests of fundamental physics by measuring galaxy peculiar velocity throughout cosmic time, opening new and unique windows into unexplored epochs of structure formation such as the epoch helium reionization, making pioneering first detections of multiple CMB signals and reducing the confusion effects from scattering and lensing on the CMB, while not requiring new experiments other than those being built or proposed.

Zoom link:  https://pitp.zoom.us/j/98508740176?pwd=a3BUc1lpZi82c0R0SkJyd1FPRFRUZz09

The observation of the Cosmic Microwave Background (CMB) is a powerful probe to unravel many mysteries of the late-time Universe. During the first half of the talk, I will discuss how future low-noise and high-resolution CMB experiments can be used to probe the detailed physics of reionization, constraining the morphology, shape, and temperature of ionized bubbles. Furthermore, I will talk about the prospects of LSS x CMB to understand the thermodynamic properties of gas in the halos. In the second part of my talk, I will also talk about "line intensity mapping", a novel technique that will provide us with new information from the star formation in galaxies to the expansion of our Universe. Mentioning the viable challenges, I will discuss the estimators to extract the signal in the presence of interlopers and instrumental noise. I will also describe how the MLIM could help us to perform cross-correlations with complementary probes such as CMB lensing and galaxy field. In the end, I will present the constraints on astrophysical and cosmological parameters that we hope to achieve from future intensity mapping observations.

Zoom link:  https://pitp.zoom.us/j/93308659447?pwd=VVM2czBWc0NTeTA5eTRWdzVFRUtndz09

Superdeterminism has received a recent surge of attention in the foundations community. A particular superdeterministic proposal, named Invariant-set theory, appears to bring ideas from several diverse fields (eg. number theory, chaos theory etc.) to quantum foundations and provides a novel justification for the choice of initial conditions in terms of state-space geometry. However, the lack of a concrete hidden-variable model makes it difficult to evaluate the proposal from a foundational perspective. 

In this talk, I will critically analyse this superdeterministic proposal in three steps. First, I will show how to build a hidden-variable model based on the proposal's ideas. Second, I will analyse the properties of the model and show that several arguments that appear to work in the proposal (on counter-factual measurements, non-commutativity etc.) fail when considered in the model. Further, the model is not only superdeterministic but also nonlocal, $\psi$-ontic and contains redundant information in its bit-string. Third, I will discuss the accuracy of the model in representing the proposal. I will consider the arguments put forward to claim inaccuracy and show that they are incorrect. My results lend further support to the view that superdeterminism is unlikely to solve the puzzle posed by the Bell correlations.

Based on the papers: 

1. I. Sen. "Analysis of the superdeterministic Invariant-set theory in a hidden-variable setting." Proc. R. Soc. A 478.2259 (2022): 20210667.

2. I. Sen. "Reply to superdeterminists on the hidden-variable formulation of Invariant-set theory." arXiv:2109.11109 (2021).

Zoom link:  https://pitp.zoom.us/j/99415427245?pwd=T3NOWUxKTENnMThRVEd3ZTRzU3ZKZz09

In the first part of my talk, I present the effective-field theory (EFT)-based cosmological full-shape analysis of the anisotropic power spectrum of eBOSS quasars. We perform extensive tests of our pipeline on simulations, paying particular attention to the modeling of observational systematics. Assuming the minimal ΛCDM model, we find the Hubble constant H0 = (66.7 ± 3.2) km/s/Mpc, the matter density fraction Ωm = 0.32 ± 0.03, and the late-time mass fluctuation amplitude σ8 = 0.95 ± 0.08. These measurements are fully consistent with the Planck cosmic microwave background results. Our work paves the way for systematic full-shape analyses of quasar samples from future surveys like DESI. I also present the cosmological constraints from the full-shape BOSS+eBOSS data in various extensions of the ΛCDM model, such as massive neutrinos, dynamical dark energy and spatial curvature.

In the second part, I study the one-point probability distribution function (PDF) for matter density averaged over spherical cells. The leading part to the PDF is defined by the dynamics of the spherical collapse whereas the next-to-leading part comes from the integration over fluctuations around the saddle-point solution. The latter calculation receives sizable contributions from unphysical short modes and must be renormalized. We propose a new approach to renormalization by modeling the effective stress-energy tensor for short perturbations. The model contains three free parameters which can be related to the counterterms in the one-loop matter power spectrum and bispectrum. We demonstrate that this relation can be used to impose priors in fitting the model to the PDF data. We confront the model with the results of high-resolution N-body simulations and find excellent agreement for cell radii r≥10 Mpc/h at all redshifts up to z=0.

Zoom link:  https://pitp.zoom.us/j/92219627192?pwd=eGg4MDUrbGlrR2JqY0xyWHdwQ2lZZz09

Factorization algebras are local-to-global objects, much like sheaves, and it is natural to ask what kind of topology, geometry, and physics they are sensitive to. We will examine this question with a focus on less-perturbative phenomena, touching on topics like moduli of vacua for 4-dimensional gauge theories and Dijkgraaf-Witten-type TFTs. Apologies hereby issued in advance to the (hopefully) friendly audience (and to my collaborators!) for speaking before achieving complete clarity.

Zoom link:  https://pitp.zoom.us/j/94417858154?pwd=ak54UFpPb3hFbnBwcUlnMnhCdG1odz09

Phase transitions in everyday systems are often catalysed by the presence of impurities, but in cosmology we typically assume the initial state is a homogeneous vacuum. In this talk I will discuss how topological defects can seed first order phase transitions in the early universe, causing them to proceed much more rapidly than in the usual case. The field profiles describing the decay do not have the typically assumed O(3)/O(4) symmetry, requiring an extension of the usual decay rate calculation. To numerically determine the saddle point solutions which describe the decay we use a new algorithm based on the mountain pass theorem. I will present results showing the significance of this effect for catalysis by magnetic monopoles in a simplified model, then discuss the same effect for domain walls catalysing the electroweak phase transition. The presence of domain walls can significantly modify the predictions for gravitational wave signal which may be observed with LISA.

Zoom link:  https://pitp.zoom.us/j/96182819088?pwd=cXhnVjFlT0tkc1VsRld0Yk43bFROUT09

Inspired by the emergence of bulk diffeomorphism invariance in holography, I will give an explicit description how entanglement between quantum subsystems can lead to emergent gauge symmetry in a classical limit. Along the way, I will provide a precise characterisation of when it is consistent to treat a quantum subsystem classically in such a limit, and show that this gives strong constraints on the entanglement structure of classical states. I will explain how this generically leads to emergent fundamentally non-local classical degrees of freedom, which may nevertheless be accounted for in a kinematically local way if one employs an appropriately redundant description. The mechanism I describe is general and elementary, but for concreteness I will exhibit a toy example involving three entangled spins at high angular momentum, and I will also describe a significant generalisation of this toy example based on coadjoint orbits. If there is time, I will discuss evidence for the role this phenomenon plays in gravity. This talk is based on arXiv:2209.03979.

Zoom link:  https://pitp.zoom.us/j/92066956880?pwd=OTRySTlOVGgvM3RCRmkzWHFVSUF3Zz09

Gravitational waves emitted by compact binaries enable unprecedented tests of gravity at highly non-linear regimes, as well as the underlying cosmological model. Going beyond the current null tests of gravity requires accurate theoretical modelling of the waveforms in viable extensions of General Relativity. In the first part of this talk, I will present the recent results and physical insights from analytical modelling of the gravitational waves in the so-called Einstein-scalar-Gauss-Bonnet gravity. Being a sub-class of both Horndeski and quadratic gravity, this theory introduces non-linear curvature corrections to strong-field regime of gravity, allows for hairy-black hole solutions, and scalar-induced tidal deformations. I will present the gravitational-wave signatures of theory’s curvature corrections and the prospects of testing the features of this theory through gravitational wave observations. In the second part of the talk, I will discuss the prospects of using compact mergers for cosmological tests by solely relying on their gravitational wave signals. Using recent constraints on the equation-of-state of neutron stars from multi-messenger observations of NICER and LIGO/Virgo, I show possible bounds on the Hubble constant (H0) found from (single and multiple) neutron star-black hole standard sirens in the next-generation gravitational wave detector era. I show that such systems could enable unbiased 13% - 4% precision measurement of H0 (68% credible interval) within an observation time-frame of hours to a day.

Zoom link:  https://pitp.zoom.us/j/93964588227?pwd=cGsxcEZHRlNjd3R5eHg5dzdtT2lndz09

Central to many of the paradoxes arising in quantum theory is that the act of measurement cannot be understood as merely revealing the pre-existing values of some hidden variables, a phenomenon known as contextuality. In the past few years quantum contextuality has been formalized in a variety of ways; operation-theoretic, sheaf-theoretic, (hyper)graph-theoretic, and cohomological. In this seminar we will discuss the simplicial approach to contextuality introduced in arXiv:2204.06648, which builds off the earlier sheaf-theoretic approach of Abramsky-Brandenberger (arXiv:1102.0264) and the cohomological approach of Okay, et al. (arXiv:1701.01888). In the simplicial approach measurement scenarios and their statistics can be modeled topologically as simplicies using the theory of simplicial sets. The connection to topology provides an additional analytical handle, allowing for a rigorous study of both state-dependent and state-independent contextuality. Using this formalism we present a novel topological proof of Fine's theorem for characterizing noncontextuality in Bell scenarios.

Zoom link:  https://pitp.zoom.us/j/93748699892?pwd=SVhVaTdoRmlwaGdCZVdIWVlKTktjQT09

In this talk I will describe a topological response theory that predicts the physical manifestation of a class of topological invariants in systems with crystalline symmetry. I focus on two such invariants, the 'discrete shift' and a quantized charge polarization. Guided by theory, I discuss how these invariants can be extracted from lattice models by measuring the fractional charge at lattice disclinations and dislocations, as well as from the angular and linear momentum of magnetic flux. These methods are illustrated using the Hofstadter model of spinless fermions in a background magnetic field; they give new topological invariants in this model for the first time since the quantized Hall conductance was computed by TKNN in 1982.

Zoom link:  https://pitp.zoom.us/j/93633131128?pwd=d2h4U1l0ZVU5aE1ORURkdFNSanB4dz09