Current explorations​​​​​​

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​Ongoing projects:

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From statistical rules to living structures

Currently I am exploring polymer physics and statistical mechanics, with a particular focus on biophysical systems. Through Monte Carlo simulations and lattice-based polymer models, I am studying how constraints and heterogeneity in update rules could model polymer dynamics in active environments. Through a research internship at Montpellier’s Charles Coulomb Laboratory, I am particularly involved in the biophysical modeling of bacterial DNA segregation and the ParABS system. A work in progress, but the physics feels wonderfully alive!

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From heartbeats to heartbreaks

I am also independently exploring synchronization - be it in oscillators or societies! On one side, I am studying synchronization in coupled oscillator networks (Kuramoto dynamics + nonlinear feedback) across different topologies; this has relevance in understanding phenomena like cardiac contraction and arrhythmias. On the other, I am exploring possible pathways to extend my dyadic emotional dynamics framework toward social dynamics: asking how emotional alignment, feedback and randomness scale from two minds to many. These projects are actively evolving (within the bounds of my current commitments), and you’ll find some of my early groundwork below.​

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​Questions that keep me up at night:

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Quantum uncertainty and entropy

Can microscopic quantum indeterminacy meaningfully inform why macroscopic entropy increases in our universe, and how does this relate to the true origin of the arrow of time? Also, how does information fit into the picture? To what extent can spacetime curvature (gravity) be reinterpreted as statistical or information-theoretic effects? (See this)

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Is mathematics just a language, or part of reality itself?

Do deep algebraic and symmetry structures simply describe physics, or do they precede it - hinting that reality may emerge from fundamentally mathematical or non-physical frameworks?​ (Emergence of spacetime, division algebra/extra dimension approaches to unification etc., see this)

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Quantum foundations - interpretation or inevitability?

Are “interpretations” of quantum mechanics genuinely meaningful windows into reality, or are they just stories we tell on top of a perfectly predictive formalism? And is it even possible, in principle, to know which (if any) reflects what the universe is actually doing? (Of course, quantum mechanics is not the complete story, so it’s too early to draw conclusions about what’s “really going on.”)

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Weak versus strong emergence

Can complex systems, in principle, be fully explained by underlying microscopic laws (weak emergence), or do genuinely new, irreducible principles arise at higher levels of organization that no amount of reduction can recover (strong emergence)? If both weak and strong emergence can apply to different systems, is there a deeper pattern that governs when each type of emergence appears? Further, could the fundamental laws of physics have been different? Are our deepest laws inevitable outcomes of consistency and symmetry, or simply emergent from contingent intellectual constructions shaped by historical choices and minimal-modification principles?​

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Consciousness - emergent mechanism or something fundamentally different?

Is consciousness ultimately explainable through known physics and the structure-interaction dynamics of the brain, or does its subjective, first-person nature point to genuinely new principles beyond conventional science, forever limiting a purely third-person explanation? 

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Are we living in a simulation? (I know, not academia-friendly, but definitely insomnia-friendly!)

We experience reality entirely through our senses and cognitive machinery - meaning everything we “know” is already filtered, interpreted and reconstructed internally. If consciousness can only access processed data rather than any objective external truth, how certain can we really be that this world is fundamentally “real” rather than instantiated? If we treated civilization as a many-body evolutionary system - billions of humans initialized with simple shared traits and some randomness, and let the whole thing run - would different “universes” meaningfully diverge, or would they statistically drift toward similar outcomes? If complex societies tend, over time, toward (for instance) hierarchy, collapse etc., does that increase the plausibility that we are part of a simulated or transient construct? And if we are in a simulation, what would count as serious evidence: computational limits, subtle anomalies in physical law or what? (Interestingly, recent work suggests, using Gödel-style limits on computation, that a fully algorithmic simulation of our universe is mathematically impossible - either killing the classic simulation fantasy, or forcing us to imagine a simulator that isn’t really computational in any ordinary sense, see this)

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​And since you are here...

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Let me share two principles I try to live by in research, and in life

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• ​Ask questions: Start with any question - however stupid it may sound - and keep asking why. This will lead you down a beautiful path, until you reach a “why” that very few have dared to ask, and the answer to which is not known.

• Remember the scope of the lens you’re using: If you only count integers, you miss the infinite structure between them. That’s fine when integers are all you need - but in research, never forget what your framework includes, and what it leaves out.​​

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Selected scientific articles​​​​​​

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Monte Carlo Simulations of Polymer Dynamics on a 2D Lattice: Rouse Constraints, Heterogeneous Update Rules and Emergent Global Behavior, 2025 

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Bibliographic project (Supervisor: Dr Jean-Charles Walter, Laboratoire Charles Coulomb, Montpellier Université)

DOI: 10.5281/zenodo.17772077

Full-text: Click here​​

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In this report, we study polymer dynamics using a discrete, lattice-based analogue of the Rouse model, where monomers move subject to a nearest-neighbor distance constraint (we analyze the polymers both with and without self-avoidance). Through Monte Carlo simulations, we quantify chain evolution via the end-to-end distance, radius of gyration and mean-squared displacement, observing a subdiffusive-to-diffusive crossover consistent with Rouse scaling (when self-avoidance is neglected). Building on this, we construct several alternating-rule toy models (alternating copolymers) and a block-copolymer toy model that impose spatially heterogeneous geometric constraints. By changing only which moves different monomers may attempt - without adding forces, potentials or energetic biases - we make the polymers break detailed balance and generate a spectrum of nonequilibrium responses. Some remain close to Rouse-like behavior due to geometric suppression of rule heterogeneity, while others exhibit strong nonequilibrium expansion driven by bond-length fluctuations. We study the block-copolymer model in particular detail. In this model, two halves of the chain evolve under distinct dynamical rules with temporal heterogeneity in addition to geometric heterogeneity. We systematically analyze the diffusion of both halves separately, as well as the diffusion of the center of mass, for different degrees of heterogeneity in the biased update frequency and different chain lengths. In the appendices, we look at a minimal model of polymer collapse where only the end monomers experience an energetic attraction, and finally also reconstruct the mean-field phase diagram of the magnetic polymer model of Garel et al. (1999).​​​

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Dyadic Emotional Modeling: A Nonlinear Dynamics Approach, 2025 

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DOI: 10.5281/zenodo.16622702​

Full-text: Click here

Slides: Click here

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In this work, we present a mathematical model for studying the emotional and relationship dynamics between two individuals. Our framework is based on a system of four coupled nonlinear differential equations, two of which represent the time evolution of the emotional states of the two individuals, and the other two equations represent how their feelings for each other evolve over time. The differential equations were designed to reflect key features of emotional and relationship dynamics, drawing on insights from empirical psychological studies. Our model incorporates features such as internal emotional regulation, asymmetrical relationship influence, reciprocity and noise (external and internal). We further define a parameter that quantifies the overall emotional alignment between the two individuals, and study its evolution over time for different initial conditions. Numerical simulations reveal realistic behavior such as emotional damping, fluctuating interpersonal influence and stabilization over time. It should be noted that our model is based on certain assumptions and limitations. For instance, in its current form, our model only applies to two individuals who are familiar with each other. Nevertheless, within these limitations and under these assumptions, our model is a unified and general framework for dyadic emotional and relationship dynamics across all possible interpersonal scenarios, including friendship, hostility, asymmetry and emotional misalignment.​​​

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Path Integral Formulation of Quantum Mechanics, 2025 

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Undergraduate dissertation (Supervisor: Dr Tanaya Bhattacharyya, St Xavier’s College, Kolkata)​

DOI: 10.5281/zenodo.15564781

Full-text: Click here​

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In this report, we present a rigorous introduction to Feynman’s path integral formulation of quantum mechanics. We start by outlining the motivation behind the path integral formulation of quantum mechanics. Then we build the mathematics required for defining the sum-over-paths and derive the free particle propagator, as well as the propagator for a particle with a non-zero potential energy, with particular focus on linear and quadratic potential energies. We use these results to arrive at some standard results in quantum physics using path integrals: namely Planck-Einstein equation, de-Broglie equation and Schrödinger equation. This helps us appreciate the equivalence between the path integral and the canonical formulation, as well as understand the difference in the approaches employed by the two formulations to arrive at the results. We also use Python to generate plots of the free particle wave function and propagator as functions of position and time, and explore the conceptual difference between the wave function in canonical quantum mechanics and the propagator used in the path integral formulation. Finally, we also introduce the basic idea behind perturbation theory, by using the free particle propagator to study a particle that moves between two potential-free points in spacetime, but via intermediate points with non-zero potentials, in one of the appendices.  ​​​

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Magnetization in the 1D Ising Model and the Metropolis Algorithm: A Glimpse into Statistical Physics and Monte Carlo Simulations, 2025 

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DOI: 10.5281/zenodo.17992558​

Full-text: Click here​

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In this report, we explore the one-dimensional Ising model using exact analytical methods and Monte Carlo simulations. Although it is the simplest nontrivial, exactly solvable lattice model, the 1D Ising system still captures cooperative low-temperature behavior, making it an ideal platform for understanding numerical sampling techniques. Analytically, the 1D model shows no true thermodynamic phase transition at finite temperature; finite-size effects lead to nonzero low-temperature magnetization. By comparing transfer-matrix results, mean-field approximations and Metropolis Monte Carlo data, we demonstrate how fluctuations and correlations - ignored in mean-field theory - remain crucial even in this minimal spin system. We also visualize space-time spin evolution across temperatures, revealing the crossover from stable ordered domains to rapidly fluctuating disordered states as thermal agitation competes with coupling. Though brief and unoriginal in results, the report emphasizes a pedagogical viewpoint, using the 1D Ising model as a laboratory to understand ergodicity, equilibration and emergent order, while highlighting its role as a testing ground for numerical methods despite the absence of true phase transitions. We also briefly discuss the 2D Ising model in the end.    ​​​

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Investigations on the Fundamental Domain of the Modular Group, 2024 

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Summer research project (Supervisor: Dr Ketan Patel, Physical Research Laboratory, Ahmedabad)​

DOI: 10.5281/zenodo.15737745​

Full-text: Click here​

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The aim of this study is to understand the fundamental domain of the modular group, and investigate the nature of transformations that map points outside the fundamental domain to points inside the fundamental domain of the modular group. This has also been verified computationally: the upper half complex plane has been divided into appropriate regions and a Python simulation has been run to verify the transformations that maps the points inside the fundamental domain for each region. This enriches our understanding of modular groups, which is crucial to understand modular forms, which have wide-ranging applications in the fields of mathematics, physics and even beyond.     ​​​

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Selected presentations​​​​​​

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Exploring Synchronized Oscillations in Kuramoto-type Oscillators with Nonlinear Feedback, 2025 

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Summer research project (Supervisor: Prof Sitabhra Sinha, Institute of Mathematical Sciences, Chennai)

DOI: 10.5281/zenodo.18028157

Slides: Click here​​

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Synchronization is a hallmark of complex systems, emerging from the interplay of randomness, coupling and nonlinear dynamics. In this presentation, I explore synchronization in a system of coupled oscillators using the Kuramoto model, with an additional nonlinear feedback term. I examine how frequency distributions, coupling strength and network topology influence synchronization. I study the time series of the phases of the oscillators for fully-connected and loosely-connected networks, and also for different lattices (toroidal, square and hexagonal). I also investigate cluster synchronization arising from multimodal frequency distributions. Together, these results show how randomness (in the initial phases and frequencies of the oscillators), combined with coupling and nonlinear feedback, gives rise to rich collective behavior.​​​

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Path Integrals, Uncertainty, Entropy and Information (100 Years of Quantum Mechanics), 2025 

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Quantum foundations summer school, 2025 (Bhaktivedanta Institute, Kolkata and Centre for Development of Advanced Computing, Patna)

Slides: Click here

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In this presentation, I discuss key ideas beyond standard quantum mechanics, focusing on the path integral formulation, uncertainty, entropy and information. I cover how Feynman’s path integrals provide a global picture of quantum evolution, contrast propagators with wave functions and clarify the physical meaning of uncertainty. I finally also attempt to draw out a potential connection between quantum uncertainty, entropy and the arrow of time.​​​​

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The Fundamental Domain of the Modular Group, 2025 

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Paper presentation competition, Spectrum 2024 (Annual fest, Department of Physics, St Xavier’s College, Kolkata)

Slides: Click here

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This presentation is about the modular group and how its generators act on the complex upper half-plane, leading to the definition of the fundamental domain. I discuss how modular transformations map any point in the upper half-plane uniquely into this domain and illustrate this visually with simulations.​​​​

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Assessing Large Language Model Reasoning on Ordinary Differential Equations, 2025 

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Non-core unit on AI, 2025 (Inter-Disciplinary In-Lab (IDIL) Graduate Program, Montpellier Université)

Slides: Click here

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This short-term project was carried out in the first semester of my Masters course as part of a non-core unit on the impact of Large Language Models across various disciplines, under the guidance of Prof Ovidiu Radulescu and Dr Gabriele Orlando. In the presentation, I systematically evaluate how a general-purpose Large Language Model (ChatGPT-5.1) reasons about Ordinary Differential Equations (ODEs). Through carefully controlled prompts, the same ODEs were presented as text as well as visual plots, in order to assess the model’s mathematical reasoning, visual interpretation and consistency. The study demonstrates that while the model performs confidently on familiar and well-documented systems (such as harmonic oscillators), it struggles with backward inference from graphs, subtle distinctions (like additive phase difference versus multiplicative phase factors) and complex or less conventional ODE systems. The analysis also highlights issues such as susceptibility to prompt phrasing, getting stuck in a particular line of reasoning and unreliable reproducibility. The results show that LLMs can provide useful intuition when properly guided – but should never be trusted blindly for mathematical correctness.​​​​​​​​

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Assembly Theory and the Evolution of Complex Systems, 2024 

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Paper presentation competition, Spectrum 2024 (Annual fest, Department of Physics, St Xavier’s College, Kolkata)

Slides: Click here

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In this presentation, I introduce complexity science as a key emerging theme in modern physics, explaining why many natural systems cannot be understood by analyzing their parts alone. I discuss measures of complexity, assembly theory and the crucial role of history, selection and copy number in shaping complex structures. The presentation also highlights emergence, downward causation, competing effects and why complexity thrives “at the edge of chaos.” I conclude by discussing how ordered complexity can arise from randomness.

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Emergence and Consciousness, 2023

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Summer Opportunity of Academic Research, 2023 (Laney Graduate School, Emory University, Atlanta) 

Slides: Click here

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In this presentation, I talk about the concept of emergence, explaining how complex properties arise from interactions among simpler components, with consciousness used as a possible example. I examine whether consciousness is best understood as an emergent property of matter or a fundamental feature of the universe, drawing on perspectives from physics and neuroscience. I also explore weak versus strong emergence, emphasizing open questions about whether existing physical laws are sufficient to explain consciousness or whether new principles are required.

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Selected essays

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Beyond Quantum Mechanics: Black Holes, Information, Unification, Extra Dimensions and the Future of Theoretical Physics, 2025 

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DOI: 10.5281/zenodo.16793345

Full-text: Click here​​

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Commemorating the first hundred years of quantum mechanics, in this essay we discuss some foundational (and often misunderstood) ideas in quantum mechanics and some novel approaches toward a theory of quantum gravity. ​ 

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On the Quantum Mechanical and Temporal Origins of Entropy: Exploring the Interplay between the Cosmological Arrow of Time, Thermodynamic Arrow of Time and Heisenberg’s Uncertainty Principle, 2025 

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DOI: 10.5281/zenodo.15669080

Full-text: Click here​​

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In this essay, we explore the possibility of understanding the increase in the entropy of our universe as a consequence of microscopic uncertainty, as dictated by the uncertainty principle in quantum mechanics. The question of the arrow of time is also addressed: whether the arrow of time is a result of the second law of thermodynamics or the other way round. The most widely accepted view, as of now, is that entropy is responsible for the unidirectional nature of time. However, we argue that the cosmological arrow of time – which is a result of the expansion of the universe – comes first, and the thermodynamic arrow of time and the second law of thermodynamics follow. And while quantum uncertainty might not be directly responsible for driving the increase in entropy, it certainly leaves room for entropy to increase in our universe. 

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Mathematics: The Future of Physics?, 2025 

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Pebbles 2025 (Annual magazine, Science Association, St Xavier’s College, Kolkata) 

PDF: Click here (page 140) ​​

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In this speculative essay, I argue that while recent decades have seen fewer fundamentally new breakthroughs in physics, further progress may instead come from mathematics, which often later reveals itself as the natural language of physical reality. The essay explores the idea that mathematics may underlie the universe at a deeper level, potentially explaining the emergence of physical spacetime and resolving conceptual tensions between major theories.  

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Energy versus Entropy: The Battle for the Control Wheel, 2025 

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Horizon 2025 (Annual magazine, Department of Physics, St Xavier’s College, Kolkata)

PDF: Click here (page 72) ​​

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This short essay briefly explores how the universe is driven by two fundamental players - energy, which tends to spread and stabilize systems, and entropy, which measures disorder and inevitably increases with time.   

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Boltzmann’s Past Hypothesis: Why Yesterday was Special?, 2025 

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The Journal of Young Physicists

Read: Click here ​​

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In this essay, I explain the arrow of time problem and discuss Boltzmann’s “past hypothesis,” which proposes that the universe began in an extraordinarily low-entropy state to account for why yesterday was “special” and why time appears to flow forward. I also explore its consequences, puzzles like Boltzmann brains, and why this idea may ultimately be a postulate we simply have to accept or reinterpret through broader cosmological ideas.      

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Complexity: The Next Big Thing in Physics, 2024 

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DOI: 10.5281/zenodo.13913639

Full-text: Click here​​

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This essay starts with a brief discussion on the various approaches to quantify complexity. Then assembly theory - a recent, novel and promising approach to study complex systems - is discussed in some detail. We also touch upon other new and relevant theories like constructor theory. Then some interesting properties of complex systems - like emergence, self-organization and unpredictability - are discussed. Then finally we demonstrate how ordered complexity can arise from randomness, and discuss consciousness from a complexity perspective. 

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A Discussion on the Theory of Everything, 2022

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Horizon 2022 (Annual magazine, Department of Physics, St Xavier’s College, Kolkata)

PDF: Click here (page 59)​​

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In this essay, I outline the quest for a “theory of everything,” explaining why unifying all four fundamental forces requires reconciling general relativity with quantum mechanics. I walk through major attempts toward this goal - like string theory and loop quantum gravity - highlighting both their promise and limitations. Finally, I reflect on whether a truly complete final theory is possible, suggesting that even the most elegant unifying framework may still rest on assumptions and leave some mysteries unresolved. ​      

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Did Einstein Believe in God?, 2020

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The Journal of Young Physicists

Read: Click here​​

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In this speculative piece, I explore the tension between science and religion, using Einstein’s view of God to emphasize my point. I trace how Einstein’s philosophical discomfort with quantum uncertainty and his deep faith in a precise, deterministic universe might have shaped his view of God. Ultimately, I argue that Einstein’s “God” was probably more a poetic symbol for the beauty and inevitability of fundamental physical laws than a figure of religion. ​​​​​​​​​​