# An Exciting Mysterious World — Spacetime

by Jackie Swift

Albert Einstein’s theory of relativity introduced the notion that space and time are actually one four-dimensional continuum — known as spacetime — which can bend, warp, and curve. A hundred years later, scientists are still seeking to understand spacetime’s makeup and the rules that govern how it functions.

“Comprehending the fundamental theory of spacetime is linked to the problem of understanding the constituents of matter and how they interact, especially gravity and how it fits in with everything else,” explains Thomas Hartman, Physics at Cornell University. Hartman studies high-energy theoretical physics. His goal is to bring to light the fundamental properties of nature, which derive from the subatomic world of quantum physics.

# Quantum Gravity and It Effects on Spacetime

Much of Hartman’s research is based on the idea of emergent spacetime, which postulates that spacetime is not a fundamental property of the universe. “It’s emergent, which means it has to come out of the theory,” he says. “You have to have some microscopic constituents of spacetime that interact with each other in some very complicated way, and then spacetime comes out of that.”

The idea of emergent spacetime originated in the 1970s when scientists began doing thought experiments with black holes. Nowadays, researchers studying quantum field theory, which incorporates quantum mechanics and the theory of relativity principles, use emergent spacetime to develop a set of ideas about how to understand quantum gravity.

“Usually in physics we think of space as simply existing, and then something happens in a given space,” Hartman says. “But in quantum gravity, you can’t look at it that way. When you have gravity around, spacetime wants to do something. It needs to respond. It has to be dynamical; it has to change with time. There can be all sorts of crazy things happening at microscopic scales in spacetime itself.”

# A Quantum Soup

Understanding how quantum gravity works is one of the big unsolved problems of quantum field theory, Hartman explains. The other is the problem of strong coupling, or strongly interacting matter. “We understand the problem of weakly interacting constituents of matter,” he says. “That’s when particles only occasionally collide with each other and interact. But with strongly interacting matter, the particles interact so much, you end up with a soup of quantum stuff. You can’t even talk about individual particles any more. In that case, it’s very hard to apply the usual methods of quantum field theory.”

“You have to have some microscopic constituents of spacetime that interact with each other in some very complicated way, and then spacetime comes out of that.”

Enter emergent spacetime, which links the problems of quantum gravity and strong coupling together. “In some cases, emergent spacetime shows that these two problems are exactly equivalent to each other,” Hartman says. “You can use strongly coupled matter to study quantum gravity and vice versa. This is called a duality, and it’s a tool to work on both of these hard problems together and try to use one to learn about the other.”

# Experimenting with Black Holes

Through duality, there is a mathematical equivalence between the properties of black holes and the properties of strongly coupled quantum matter. Taking advantage of that, Hartman and his colleagues have been working on thought experiments wherein they imagine various particles entering or passing close to a black hole.

“We throw stuff at black holes and calculate what comes out,” Hartman says. “We use that to learn something about how quantum matter behaves. Then we take what we learn about quantum matter, and we apply it to more ordinary stuff like the phase transition of boiling water, which can be described as a strongly coupled field theory.”

By studying correlation functions, the basic observables of a strongly interacting system, the researchers capture the physics of the quantum material. “What we found by using black holes is a new set of constraints on quantum matter and new equations that are satisfied by the correlation functions,” Hartman says. “Some of these have been tested by numerical simulations of these systems and confirmed.”

# The Black Hole Information Paradox

Taking a further look at black holes, Hartman is working on another project seeking to make progress on the black hole information paradox first identified by theoretical physicist Stephen Hawking. By discovering that black holes evaporate, Hawking showed the physics of black holes are incompatible with quantum mechanics, the body of laws governing subatomic particles. The problem is that black holes lose information. “Schrödinger’s equation, the basic formulation of how quantum mechanics works, has a precise mathematical way in which it preserves information,” Hartman says. “This process of black hole evaporation violates that fundamental tenet.”

This means there’s either something wrong with scientists’ understanding of black holes or with their comprehension of how spacetime works, or the fundamental rule of information preservation is flawed. Scientists have come at the problem from all three possible angles. “For a long time there have been different ideas about how this information paradox might be solved,” Hartman says. “There’s no answer yet.”

Hartman has been working on one of these ideas of emergent spacetime, exploring a way in which information from a black hole can escape. Normally this is thought to be impossible because the gravitational force of a black hole is so immense even light cannot escape it, and nothing can go faster than the speed of light. Through duality, Hartman and his colleagues have focused on subtle effects in quantum gravity called non-perturbative effects. “Lots of times duality can give you ideas about what the answer should be even when the equation is too hard to solve,” he says. “It gives you a different way of thinking about the problem.”

# Toy Models for Studying How Information Escapes from Black Holes

Using what’s called a toy model — a simplified mathematical model with many details removed — the researchers have studied the problem in two dimensions (one dimension of space and one of time) instead of the normal four dimensions (three of space and one of time).

“We have a toy model where we understand some of the effects that link the inside of a black hole with the outside,” Hartman says. “The answer appears to be a wormhole — a tunnel with each end in separate points of spacetime.”

# The Fun, and Weirdness, of Quantum Mechanics

Hartman knew he wanted to be a scientist from an early age and was pulled toward the abstract area of theoretical physics by the weirdness of quantum mechanics.

“Quantum mechanics is such a counterintuitive set of ideas,” he says. “I was intrigued by how bizarre it was. The same goes for general relativity, which I love teaching. It’s so completely different from other physics classes students have taken. There’s a lot of fun math and surprising ideas. We talk about black holes and wormholes. I’ve even given a lecture about time machines.”

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