Research Interests

Research Interests

In my journey as a theoretical physicist, the interconnectivity of seemingly unrelated aspects of Nature's working, and how simple, yet powerful ideas thread it together has always fascinated me. I am interested in studying foundational questions in quantum mechanics and its broader impact in cosmology, gravity, and their signatures in experiment.

Quantum mechanics, gravity, and cosmology have emerged as three key pillars of our fundamental understanding of the universe, and have been tremendously successful in making quantitative predictions for experiments in their respective domains. We anticipate an elegant unification of the microscopic quantum laws with those of gravity and cosmology that govern physics at the largest scales in our universe. However, quantum mechanics and gravity find themselves at strong odds in their current formulation, both conceptually and mathematically, and how they connect with underlying reality. Part of the disconnect can be attributed to the fact that we tend to think in terms of classical ideas such as "space," "particles" and "fields". Such constructions may not have a place in the fundamental ontology of quantum mechanics, which at its heart, simply describes the evolution of a state vector in an abstract Hilbert space. We typically start with some classical theory and then "quantize" it. Presumably Nature works the other way around: it is quantum-mechanical from the start, and a classical limit emerges in the right circumstances.

That should answer your question why this website is called what is it called.

My work falls into three broad categories all hinged on quantum mechanics and quantum information, with an eye towards understanding their role in fundamental questions in gravity and cosmology: (i.) the role of quantum mechanics in the cosmological evolution of the universe, particularly early universe physics, (ii.) emergence of structure in quantum theory with an eye towards quantum gravity, and (iii.) tests of fundamental physics based on ideas at the intersection of quantum information and gravity.

On a slightly tangential note, I am also interested in looking at connections between physics, statistics, and engineering. One such direction I have worked on is the application of Information Field Theory, in particular perturbative field theory techniques (basically Feynman diagrams) to Civil Engineering.

Let me walk you through each of these directions in brief. Do expand on each sub-topic to know more:

Quantum Effects in Cosmology

A Quantum Big Bang

Cosmology, in particular the physics of the early universe, offers us the ultimate quantum lab, uniquely suited to study imprints of first-principle quantum mechanics on the evolution of the cosmos. To explain the remarkable uniformity and large scale homogeneity in the universe, among other things, it is posited that the universe in its early stages underwent a brief period of exponential expansion of space, called "inflation." Quantum fluctuations seeded in this inflationary epoch are then stretched with the expansion of space, and eventually leads to all structure we observe today. In one stroke, this idea unveils a beautiful connection between the largest structures in the cosmos and the fundamental laws of physics at the smallest scales. While compelling, the exact mechanism behind inflation and the ensuing quantum dynamics are not well understood. The role of quantum physics in cosmology, albeit not yet fully understood, is expected to be even more profound, going beyond its role in seeding structure-forming perturbations. Recent advances in high energy physics and quantum information point toward a deeper connection, whereby space itself is a consequence of entanglement of underlying quantum degrees of freedom.

Most physical mechanisms proposed for inflation are typically classical in nature (such as the "slow roll model"), and attempts to source it quantum mechanically often fall short since quantum field theoretic modes have an equation of state not compatible with inflation. In a recent paper (linked to the right), Olivier Doré and I showed that inflation can indeed be sourced by quantum degrees of freedom by taking this "entanglement-geometry" connection seriously which interprets cosmic expansion as growing entanglement between the "qubits" which make up space. My current work involves making this model more robust, which we expect will eventually provide a unified framework to explain all major epochs in standard big bang cosmology from quantum dynamics. We are developing techniques to numerically simulate the quantum states of various field theoretic modes with time-dependent, cosmologically-relevant Hamiltonians, and using them to feedback into Einstein's equations in an iterative way.

Related Papers:

From Quantum to Galaxies

  • Current observations suggests that the inhomogeneities we observe in the Universe such as stars, planets, galaxies or clusters of galaxies are the results of very early quantum fluctuations when the Universe was only a fraction of second old, which then get amplified by gravity throughout cosmic times. Cosmological observations and in particular ambitious galaxy surveys offer the possibility to test and possibly quantitatively understand this process. I have recently started thinking about the quantum-to-classical transition of primordial fluctuations by studying decoherence and the interactions by which quantum information is mediated between fluctuations and gravity. Our proposed research aims at revisiting and enriching the relation between the observed distribution of galaxies and early quantum phenomena. Inspired by recent development in quantum mechanics, we will investigate new observational signatures of the quantum origins of our Universe and in the process will investigate how to use galaxy surveys to test quantum mechanics, one of the pillars of modern physics.

Quantum Vacuum Energy

Another interesting direction is to understand the Hilbert space structure of the quantum theory relevant to cosmology. Motivated by the Holographic principle and its applicability to horizons like the de Sitter patch of the universe we live in, we wrote a paper where we argued, in a model independent way, that the Hilbert space of quantum gravity is locally finite-dimensional. This is in stark contrast to quantum field theory, where the Hilbert space is infinite-dimensional. Formulating a quantum theory hinged on finite-dimensional algebraic constructions can have physical consequences for long standing questions in cosmology, such as the "cosmological constant problem," which deals with the blaring inconsistency between the predicted and observed value of vacuum energy in the universe. In 2018, I studied the role of the generalized Clifford algebra (also known as Generalized Pauli Operators) which offers a natural paradigm for studying finite-dimensional conjugate variables and the role they can play in modifying a theory's spectrum from the usual infinite-dimensional case. Based on this, in 2019 I led a research project where we took into account gravitational effects at zeroth order to show how finite-dimensionality leads to a natural suppression of vacuum energy. I am currently working on extending this approach, and with Oliver Friedrich, we are applying this formulation to the expanding universe and study how dynamical dark energy might be a consequence of finite-dimensional effects.Related Papers:

Emergence of Structure in Hilbert Space

Mad-Dog Everettianism

During my PhD at Caltech, Sean Carroll and I laid out a broad outline for a program that takes quantum mechanics in its minimal form to be the fundamental ontology of the universe. Everything else, including features like space-time, matter and gravity associated with classical reality, are emergent from these minimal quantum elements. Hence, in the context of a quantum theory of gravity, one should therefore try "gravitatizing" quantum mechanics instead of quantizing classical gravity, an approach we called "Mad-dog Everettianism: Quantum Mechanics at its Most Minimal.

The basic idea hinges on that quantum theories are defined simply by the spectrum of their Hamiltonians. (This is natural in separable Hilbert spaces, although defining theories on non-separable Hilbert spaces also requires a preferred algebra of observables.) Such a program creates the problem of going from such a meager amount of data (a list of energy eigenvalues, maybe some starting quantum state) and creating out of it the whole world. One step has been taken by
Cotler et al., who show that a notion of "locality" can be fixed purely from the spectrum. Sean Carroll and I have been pushing further on this problem, developing new tools for defining structure in otherwise bare Hilbert spaces.

Related Papers:

Emergence of Classicality

I am also interested in understanding what governs the non-trivial subsystem structure associate classical reality with. What determines how degrees of freedom are partitioned between spacetime and matter fields? What dictates the split between system and environment in the decoherence paradigm? (This latter question is sometimes referred to as the "Set Selection" or the "generalized preferred basis" problem in the quantum foundations literature). In the presence of gravity, locality and subsystem 
structure are more subtle than in traditional laboratory settings, and so it is an interesting direction to investigate them as emergent phenomena from first-principles. In work that will appear soon, we establish an algorithm harnessing tools in quantum information, based on entanglement and entropic structures, that distinguishes quasi-classical tensor factorizations of Hilbert space from arbitrary ones and explicitly connects these characteristics of classical factorizations with features of the Hamiltonian. We also generalized this discussion to direct sum decompositions of Hilbert space where, with an eye towards understanding how lattice structures (and thus, superpositions of many background geometries) can emerge in Hilbert space, we studied toy models where geometric states evolve locally within each such direct sum factor. In addition to emergent classicality, extension of our work on preferred decompositions of Hilbert space can segue into understanding important questions in theories with duals such as AdS/CFT (which represent different factorizations of the same underlying Hilbert space); horizon complementarity and the information paradox; and the emergence of spacetime and matter from basic quantum elements.

Related Papers:

Quantum State Reduction

I am also interested in better understanding quantum coarse-graining since it offers a natural paradigm for studying emergence of various phenomenon. I wrote a paper which describes a coarse-graining technique for a set of states in Hilbert space without relying on any preferred structure of locality or preferred set of observables. More recently, we studied more general ways of decomposing Hilbert space (than tensor products), in particular investigating reductions specified by a discrete set of observables not spanning the full algebra of observables. In such situations, the appropriate state-reduction map can be defined via a generalized bipartition, which is associated with the structure of irreducible representations of the algebra generated by the restricted set of observables, for which we developed a general, not inherently numeric, algorithm for finding irreducible representations of matrix algebras. Such generalized partitions of Hilbert space can have consequences for our understanding of questions such as the localization of quantum information in spatial regions in the presence of gravity. Partitions and coarse-graining could also be important in understanding how spacetime, just as the phases of a thermodynamic system emerges from the underlying quantum degrees of freedom.

Related Papers:

Quantum Structure of Spacetime

An important aspect of this emergence program is to understand the quantum mechanical footings of space and time itself. I worked on expanding the famous Page-Wootters construction of emergent time to relativistic quantum systems by treating space and time as bona fide quantum degrees of freedom on an equal footing in Hilbert space. I showed that, unlike the conventional textbook treatment, Klein-Gordon and Dirac equations in relativistic quantum mechanics can be unified in our paradigm by applying relativistic dispersion relations to eigenvalues rather than treating them as operator-valued equations. This also affords symmetry transformations a stronger quantum mechanical footing, for instance, global symmetries, such as Lorentz transformations, modify the decomposition of Hilbert space. This direction of research opens a wide variety of projects for students, both for beginning and advanced undergraduates. For example, undergraduates can explore extensions of the Page-Wootters formulation to basic quantum field theoretic setups, and how concepts of causality and locality can subsequently emerge. This also allows students to gain a better appreciation and understanding of advanced topics that are only briefly discussed in an undergraduate curriculum. Students, who have taken up upper-level coursework in quantum mechanics and relativity will work on more involved topics studying gravitational aspects, such as the emergence of curvature and gravitational back-reaction from quantum interactions between spacetime and matter. Such constructions also have the potential to naturally renormalize and regularize field theories.

Related Papers:

Experimental Tests of Fundamental Physics

Space-based Tests of Dark Energy & Quantum Gravity

Experiments of quantum gravity are conventionally believed to be prohibitive due to the high energy scales anticipated. However, recent advances in quantum information and quantum-first studies of gravity open new and exciting possibilities. I am part of a mission concept at the Jet Propulsion Laboratory to use space-based tests of gravity using atom interferometers called the Gravity Observation and Dark energy Detection Explorer in the Solar System (GODDESS) mission. Currently a NASA Innovative Advanced Concepts Phase II award, this concept consists of a constellation of 4 spacecraft, each equipped with 6 atom interferometers, that will place precise constraints on the gravitational force gradient. While the main science objective of this mission is to serve as a dark energy probe, we are actively working to expand the scope to detect and measure quantum gravitational effects. For instance, how a system processes and mediates quantum information in the presence of gravity can decidedly alter the statistics of the quantum state, which can then be measured by sensitive atom interferometers in space.

Related Papers:

Other Tests of First-Principle Quantum Gravity

  • Gravity can also, for instance, due to finite-dimensionality of its Hilbert space, induce modifications to the fundamental quantum structure, such as modifications to canonical commutation relations, uncertainty principle, and violations of fundamental symmetries like Lorentz invariance. My training in fundamental quantum mechanics will allow me to lead my group to work towards applying this quantum-first formalism to concrete experiments in quantum optics and opto-mechanics to probe gravitational physics imprinted in very basic structure of quantum mechanics. These can include modifications to canonical commutation relations due to gravity, corrections to Feynman diagrams due to finite-dimensional effects, and its impact on scattering processes in quantum field theory.

Synergy between Physics & Engineering

Information Field Theory & Societal Risk Mitigation