Below the Surface
If waves and particles are like the turbulence on the surface of a pond, the connection between that turbulence and events in the interior of the pond was first described by a mathematical principle discovered in 1997. In a landmark paper, Juan Maldacena, an Argentinian-American physicist then at Harvard University and now at the Institute for Advanced Study in Princeton, N.J., showed that events taking place in a 3-D region of space mathematically correspond to very different events taking place on that region’s 2-D boundary. (Events in 4-D also correspond to events in 3-D, and 5-D to 4-D and so on.)
To simplify: A Physicist introduced a theory explaining 2-D
particle space was influenced by the 3-D
hidden force. And that 4-D would in turn influence that 3-D space.
Consider the 3-D interior and 2-D surface of the metaphoric pond. For the correspondence to work, the interior must be mathematically described by string theory, in which electrons, photons, gravitons and the rest of nature’s building blocks are invisibly small, one-dimensional lines, or “strings.” Mass and other macroscopic properties correspond to the strings’ vibrations, and interactions between different kinds of matter and forces come from the way strings split and connect. These strings live inside the pond.
Explaining the model: a pond of invisible strings attaching to a flat surface of particles.
Now, imagine that the 2-D surface of the pond is described by quantum mechanics. Particles are the splashes on the surface, and waves are the cascade of ripples from those splashes. On the surface of this imaginary pond, there is no force of gravity.
Explaining the model: Gravity effects the inside of the pond and pulls upon it's surface- the particles and waves we can see.
Maldacena’s discovery, known as the holographic duality, showed that events in the interior region, which involve gravity and are described by string theory, are mathematically translatable to events on the surface, which are gravity-free and described by quantum particle theories.
Holographic duality illustrated here as "the pond", now has mathematically proof.
“To understand this relationship, the crucial aspect is when the gravity theory is easy to analyze, then the particles on the boundary” — or, in the pond analogy, the surface — “are interacting very strongly with each other,” Maldacena said. The converse is also true: When the particles are calm on the surface, as they are in most forms of matter, then the situation in the pond’s interior is extremely complicated.
That contrast is what makes the duality useful.
SImplified as: Scientists find it easy to analyze when the observable surface of the " holographic pond" is very chaotic or very calm. The duality being that when the surface is chaotic, the inside of the "holographic pond" is calm.
The strange class of materials that includes cuprates belongs in the first category; experiments suggest that particles in these materials interact so strongly with one another that they lose their individuality. Physicists say the particles are “strongly correlated.” The wavy ripples corresponding to each overlap so much that a kind of swarm effect is believed to occur. Strongly correlated matter can behave in diverse and unexpected ways that are difficult or in some cases impossible to describe with known quantum mechanical methods, said Sean Hartnoll, a physics professor at Stanford University. “You need a different way of looking at them than starting from single particle descriptions,” he said. “You don’t try to explain the ocean in terms of individual water molecules.”
The activity of Cuprates interacting so much that they lose their individuality, creates a “swarm effect”, and it allows a window into the hidden world.
If strongly correlated matter is thought of as “living” on the 2-D surface of a pond, the holographic duality suggests that the extreme turbulence on that surface is mathematically equivalent to still waters in the interior. Physicists can get at the surface-level behavior by studying the parallel, but much simpler, situation below. “You can compute things in that tranquil world,” Zaanen said.
The findings support there's an inverse relationship between a chaotic 2-D surface and a calm 3-D interior of strings.
Scientists used a chaotic surface to analyze the hidden world beneath.
In the mathematical parlance of the holographic duality, certain strongly correlated matter in 2-D corresponds, in 3-D, to a black hole — an infinitely dense object with an inescapable gravitational pull, which is mathematically simple. “These very complicated quantum mechanical collective effects are beautifully captured by black hole physics,” said Hong Liu, an associate professor of physics at the Massachusetts Institute of Technology. “For strongly correlated systems, if you put an electron into the system, it will immediately ‘disappear’ — you can no longer track it.” It’s like an object falling into a black hole.
The findings support black hole physics.
Increasingly over the past decade, studying the black hole equivalents of strongly correlated forms of matter has yielded groundbreaking results, such as a new equation for the viscosity of strongly interacting fluids and a better grasp of interactions between quarks and gluons, which are particles found in the nuclei of atoms.
Matter described as having a chaotic surface of the "pond", have provided evidence to the interaction of quarks and gluons.
(Continued)