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A Duality out of String Theory

In the story called Einstein's Lenses, we will be exploring physics at the frontier through the eyes of Rigby Zinq as she attempts to solve a murder. Early on in the story she finds a number of references to something called "Einstein's Lenses" in a dead woman's journal. In this post, we will explain some of the concepts and applications of holography that are introduced in The Crime Scene.

A case for fundamental physics

Each year, there are an incredible number of new technologies created, many of which have their roots in fundamental physics discoveries. They are often intended to help us lead healthier, safer, and happier lives through developments in medicine, industry, and entertainment. Attempting to understand the most basic building blocks of nature is often initiated for the sake of exploration and the hope that, someday, it will be useful. Without trying to gain a deeper understanding of the world around us in this way, we would not have a great many existing inventions. I'd like to highlight two modern technologies that rely on advancements in fundamental physics that you may have found useful to you. Later in this post, I'll discuss a relatively new discovery in fundamental physics that is helping us to understand materials with great potential for use in a range of industrial applications.

The two pieces of technology I’m going to discuss are MRI machines and GPS. You may have been inside an MRI machine. It is a non-invasive medical imaging device and the acronym MRI stands for magnetic resonance imaging. There's an article on the American Physical Society website that details the history of MRI machines. They describe how physicists, in particular Isidor Isaac Rabi, were searching for ways to examine certain characteristics of atoms and molecules, an endeavor in fundamental physics. Dr. Rabi was awarded the Nobel Prize in 1944, and I quote “for his resonance method for recording the magnetic properties of atomic nuclei”. This work eventually led to the MRI, which was first used on a living person in 1977.

GPS (or global positioning system) technologies are another good example of when fundamental physics has allowed us to create tech that revolutionized the way we live. GPS makes use of special and general relativity. This theory of gravity explains the very fabric of our world, spacetime. General relativity has crucially altered our understanding of fundamental physics. There's an older way to describe gravity, developed by Newton, but if you stopped there, without the discovery of general relativity, GPS could not work as we know it today. There's an excellent article on NASA's website called 100 Years of General Relativity and at the end of the article they remark, that without correcting for effects due to special and general relativity, there would be errors that offset the true location of businesses, roads, and homes in the system by around 6 miles per day. You might have expected these corrections to be small, but clearly they are rather significant!

Recently, there has been a lot of attention paid to a discovery that comes out of a motivation to understand a theory of quantum gravity. This discovery, commonly referred to as holography, has been helping us to understand properties of various materials, such as superconductors, that could foster new technologies. A quick Wiki search on the technological applications of superconductivity will show you that superconductors are useful in a multitude of ways. From reducing the cost of providing electricity to consumers to developing new medical technologies and quantum computers, superconductors are full of possibility. Yet, the best understood superconductors have to be placed in ultra cold environments, that may make them challenging and cost-prohibitive to use.

A key feature of superconductivity is that the material has zero resistance, and one of the goals for superconducting research is to develop materials with zero resistance at room temperature. Materials that have zero resistance above -200 degrees Celsius are considered high temperature superconductors. Although, the high temperature superconductor record temperatures for observing zero resistance are much higher than -200 degrees Celsius, we are still far away from room temperature superconductivity. One of the first questions you might want to ask to make progress on raising that temperature, is how do high temperature superconductors work? How do the electrons in these materials come together to produce the properties we see in the lab? However, high temperature superconductivity remains a bit of a mystery. Traditional methods to approach similar types of materials have failed to describe high temperature superconductors. And that is where holography steps in. This discovery that comes out of string theory, is helping us to unravel the mysteries of high temperature superconductivity.

A Duality out of String Theory - Holography

Holography tells us that, in certain cases, gravity can be thought of as an emergent phenomena. In these cases, we can think of quantum systems, like a collection of electrons, as viewed from another perspective. Holography can translate systems of electrons and atoms, described by a purely quantum mechanical theory, into a black hole. This method of analysis may seem surprising, but perhaps more surprising is how well the method is proving to work.

The figure below represents two ways to describe the same system. The orange ring is the shadow of a black hole and the black cube is a superconducting piece of material called bismuth strontium calcium copper oxide.

Looking at materials we commonly view as purely quantum mechanical, like the cube above, in terms of a dual gravitational description came out of string theory about 20 years ago. It is called holography because the gravitational description has one extra dimension as compared to the quantum mechanical description. Much like an optical hologram or 3D movies, the emergent gravitational description can be seen as encoded on a lower dimensional surface.

What do we mean by an emergent gravitational description?

Emergent phenomena come about due to a collection of smaller things. We call the emergent behavior macroscopic and the smaller things microscopic. There are many examples of emergent behavior in physics. One example is thermodynamics. You do not need to know the details of the atomic structure to understand how pistons move in an engine or how efficient your refrigerator is. Heat emerges out of a collection of particles. It is a macroscopic quantity. Another example is fluid dynamics. Consider water flowing out of the pipe in your sink at home. You can feel the water pressure and temperature. These things you can feel are due to a collection of individual particles. The pressure and temperature emerges out of that collection of particles.

Holography, like the water example above, tells us that the force that holds the Earth bound to the Sun, can be thought of, in certain cases, as emerging from subatomic particle behavior. Gravity is like the pressure or the temperature of the water and is something that can be seen as due to collective behavior of its microscopic constituents. This discovery is absolutely groundbreaking. It offers us a completely new way to look at gravity.

Einstein's Lenses

Have you ever been to a 3D movie? You walk into the theater and they hand you a pair of glasses. You feel a bit funny putting them on, but when you get to the jump scene, all the fuss seemed worth it. Have you ever worn rose tinted lenses? At some point in time in your life someone may have told you that you were wearing rose tinted lenses. Perhaps you spun a bad situation into a good one. Einstein's lenses can be thought of as a cross between 3D glasses at the movies and the more abstract rose tinted lenses. They are meant to embody the string theory's holography. Through them, systems of electrons would begin to look like a black hole. And sometimes seemingly impossible to solve physics problems would become solvable. These special lenses are introduced in the first part of the first chapter of Einstein's Lenses called, The Crime Scene. Stayed tuned to the murder mystery series to see how they are used in the story later on down the line.

Now, of course, Einsteins lenses aren't exactly for sale at your nearest supermarket, but if you would like to know more about holography, I have a couple of options for you. The founder of holography is Juan Maldacena. The original paper from 1998 is called, "The Large N Limit of Superconformal Field Theories and Supergravity". A layman's version of holography was also written by Juan Maldacena and can be found in Scientific American, "The Illusion of Gravity".

Make sure to check out the holographic murder mystery that is paired with this blog post, Einstein's Lenses: The Crime Scene. Stay tuned for a future post by Erin Blauvelt's that will give an overview of a specific application of holography to high temperature cuprate superconductors.

Author: Erin Blauvelt

PhD Candidate

Lehigh University

Image credit for EHT image (obtained from wiki)- first ever image of a black hole captured by the Event Horizon Telescope

This image has been altered to have a larger black background. It has been altered as well to be in the lens of the sunglasses. Creative Commons License -

Image credit for superconducting material - James Slezak, Cornell Laboratory of Atomic and Solid State Physics. This image has been altered to be placed in a black background of a larger image. Creative Commons License -


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