In this blog, we will be talking about the latest Google Summer of Code project named “How Machine Learning is Helping us Solve the Quantum Black Hole Problem”.
The project is being carried out under the mentorship of Gaurav Khanna, a professor at the University of Massachusetts. His research involves
How Machine Learning is Helping us Solve the Quantum Black Hole Problem.
By: Tanya Agarwal, May 21, 2021.
An important open question in theoretical physics is: can we fully describe a black hole using quantum mechanics? In other words, can we explain all the properties of black holes using the same laws that govern small objects-i.e., quantum mechanics? The answer to this question has been a long-standing mystery since black holes were first discovered back in 1916.
In order to answer this question, we need to solve the equation that describes how a black hole behaves with respect to its size and mass (which we call Schwarzschild radius). Unfortunately, there is no exact solution known for this equation and so it must be solved numerally.
In my work as part of Google Summer of Code program (GSoC), I am trying out different machine learning algorithms on simulated data which will help me find an approximate solution for our problem while reducing computational cost required by traditional numerical methods at higher precision levels.
The purpose of this blog is to introduce you to the latest GSoC 2021 project and how it is helping us solve the Quantum Black Hole Problem.
The project titled “Adventures in Hyperspace: An Implementation of Tensor Network Theory” will be mentored by Prof. Kallol Sen and implemented by Pratyush Sahu, a PhD student at IIT Kanpur. The project aims at implementing a novel algorithm called tensor network theory. This algorithm can be used for quantum simulation i.e., simulating quantum systems on classical computers as well as carrying out quantum machine learning tasks like training neural networks using tensor networks.
The project was selected from among hundreds of other proposals submitted to Google Summer of Code 2021 program. The selection process was rigorous and involved evaluation by several experts in the field and finally Google representatives.
The Quantum Black Hole Problem is one of the major open problems in theoretical physics today. It is at the heart of our understanding of the nature of spacetime and gravity, which we believe are described by General Relativity (GR). However, GR is incomplete because it cannot describe gravitational effects at very small scales (of the order of Planck length or 10-35 meters). To explain such short distances we need to use quantum
The latest GSoC 2021 project is all about how machine learning can help us solve the problem of quantum black holes.
What are Quantum Black Holes?
A quantum black hole is a black hole that forms when a star collapses under its own gravity. In this case, the star’s mass becomes so dense that it cannot support itself and begins to collapse into itself, creating what is known as a singularity.
How do they work?
Quantum black holes work by using Einstein’s theory of general relativity to describe what happens when matter and energy are extremely close together. The theory of relativity describes gravity as the curvature of space around massive bodies, such as stars and planets.
This curvature causes light rays traveling near massive objects like black holes to bend and curve in a way that is not predicted by Newtonian laws of physics or other theories based on classical mechanics. As such, these objects are often referred to as “curved space-time singularities” because they represent regions where space-time becomes infinitely curved or infinitely small, making them invisible to our eyes but detectable through their gravitational effects on nearby objects such as stars and galaxies.
In other words, when there is massive amounts of energy present in an area such
Every year in the summer, students from all over the world participate in Google Summer of Code. This is a global program focused on bringing more student developers into open source software development. Students work with an open source organization on a 3 month programming project during their break from school.
This year I am working with Prof. Suvrat Raju and Dr. Suresh Govindarajan from the International Centre for Theoretical Sciences (ICTS), Bangalore, India. IIT Madras is one of the academic partner institutes of ICTS, so you can say that my mentor Prof. Suvrat Raju is also my PhD guide!
I will be working on a Machine Learning (Neural Network) approach to solve the Quantum Black Hole Problem which is based on Quantum Information Theory and Statistical Mechanics.
Since we have already started our project, here are some details about my project:
The quantum black hole information problem has been one of the central issues in physics over the past few decades, with many important advances achieved by both theorists and experimentalists. We propose a radically new approach to addressing this problem using ideas from quantum information theory and statistical mechanics. The proposed approach uses a combination of classical Monte Carlo methods and machine learning techniques to
This blog was written by Emma Chapman, one of our Machine Learning GSoC students.
This year I am excited to be taking part in the Google Summer of Code program, working with the Quansight team on a project for astropy. My project is focused on using machine learning techniques to help solve problems in astrophysics; specifically, we are looking at how these techniques can be used to develop an improved model for black hole spin.
Black holes are regions of space where gravity is so strong that not even light can escape. A rotating black hole has spin, which has a dramatic effect on how it interacts with matter and light; yet it is notoriously difficult to determine because the observations we have of black holes are ambiguous and incomplete (we will talk more about this later). As a consequence, there is currently a lot of research being done to develop new techniques for estimating spin from observations. These techniques usually involve complicated computer simulations and analysis; my project aims to improve this process by using machine learning (ML) algorithms instead.
My work will build on top of a dataset of simulated observations produced by Adrian Hamers, an Astrophysicist at Leiden University in the Netherlands who collaborated with astropy last year as part of another GSoC project: “
Our research group is working on understanding the inner workings of black holes, especially as applied to the quantum mechanical regime. Note that in the following we will use Planck units, where
G = c = hbar = kB = 1. This choice is arbitrary and can be changed to SI units at any time by going through dimensional analysis.
The Einstein field equations have a repulsive gravitational solution, which is known as an anti-de Sitter (AdS) spacetime:
Where rho0 is the cosmological constant. In fact, AdS spacetime represents a sort of idealized cosmology, where the universe has no spatial curvature and is expanding at a constant rate. The only gravitational force present in AdS spacetime is due to its negative cosmological constant. A solution to the Einstein field equations describing a black hole with mass M and angular momentum J in AdS spacetime is known as a Kerr-AdS black hole:
This exact solution was first discovered by Carter in 1968 [1] and was later rediscovered by Hawking [2]. The geometry of the Kerr-AdS black hole is given by its ergoregion:
A full derivation of this geometry is given in [3].