# Collaborative Research Elucidates Artificial and Quantum Gravity

#### Studies by recent graduates and Physics Professor John Lindner yield insight into the topic

WOOSTER, Ohio — Artificial gravity fields, like the ones in Star Trek and Star Wars, enable fictional crews to walk normally inside a spacecraft and not float around like astronauts onboard the International Space Station. But is it possible to create such fields?

Brian Maddock, a sophomore physics and mathematics double major, posed that question to John Lindner, professor of physics at Wooster, during a conversation at one of the weekly Physics Table gatherings last year. Lindner responded by saying he wasn’t sure, but he knew someone who could figure it out.

That someone turned out to be Larry Markley, a 2012 Wooster graduate who was working with Einstein's theory of general relativity. “General Relativity (GR) is our best theory of gravity,” says Lindner. “It includes Newton's theory of gravity as a limiting case, but describes new phenomena like black holes. In GR, time is the fourth dimension, and large masses like stars and planets curve spacetime, while small masses like spacecraft move along the corresponding straightest possible paths. Curved spacetime means space is warped (so that the sum of the angles of a triangle is no longer 180 degrees) and time is slowed by different amounts in different places.”

Markley had been investigating perturbed spacetimes that were curved, not just by mass, but also by energy and stress (like pressures, tensions, and shears). However, Markley and Lindner, who was his adviser, altered the course of the research in response to Maddock’s intriguing question. “By mathematically specifying the spacetime curvature we wanted, namely flat outside our cylindrical spacecraft and curved inside, we were able to run Einstein's equations backward and find the energy and stress necessary to produce an artificial gravity field,” explains Lindner. “As we expected, the matter required to produce the artificial gravity field is ‘exotic’, which means it may be difficult or impossible to build in practice. Nevertheless, this theoretical spacetime engineering illuminates Einstein's theory and the connection between matter and gravity.”

The research was the focus of Markley’s Senior Independent Study (I.S.) project (Wooster’s nationally acclaimed undergraduate research program) and was later summarized in an article by Markley and Lindner, titled “Artificial Gravity Field,” and published last month in Results in Physics, a new scholarly journal.

A similar conversation also resulted in a collaborative project on a related topic by another recent graduate. Norman Israel, who graduated with Markley, asked Lindner about time travel and quantum gravity during his first-year physics lab. Thus began a conversation that would last for four years.

“Theories of quantum gravity attempt to unite Einstein's theory of General Relativity, where gravity results from the curvature of space and time, and quantum mechanics, where atoms have both wave and particle aspects and often behave probabilistically rather than deterministically,” explains Lindner. “Quantum gravity is necessary to fully understand things like black holes and the ‘Big Bang,’ but it has been terribly difficult to consistently formulate such a theory.

“Norman and I considered several approaches to quantum gravity, including superstring theory and loop quantum gravity, but decided to explore a relatively new approach called Causal Dynamical Triangulation (CDT),” adds Lindner. “CDT constructs a model of spacetime from triangular-like building blocks by gluing their time-like edges in the same direction. CDT calculates the expected size and shape of the universe by taking a weighted average over all possible spacetimes, or equivalently, over all possible spatial histories.”

Beginning with his Junior I.S. and continuing through his Senior I.S., Israel and Lindner created a computer simulation of a CDT universe of one time and one space dimension. “We demonstrated that it exhibited the predicted large fluctuations in size,” says Lindner. “This result supports other work suggesting that classical spacetime can emerge from the vacuum fluctuations of a CDT universe whose building blocks have three space and one time dimensions. A cool feature of Norman's quantum gravity simulation is that it does not require a supercomputer. In fact, it runs on a laptop.”

This collaboration led to another article, "Quantum Gravity on a Laptop: 1+1 Dimensional Causal Dynamical Triangulation Simulation,” published in Results in Physics late last year.

“It is unusual for undergraduates to contribute to the subject areas of General Relativity and Quantum Gravity,” says Lindner. “Wooster’s curriculum prepared them for these remarkable senior projects, and I had an opportunity to do cutting-edge gravity research as a result to their questions, interests, and enthusiasm. Both projects were wonderful collaborations.”