School of Natural Sciences

Entanglement and the Geometry of Spacetime

By Juan Maldacena 

Two papers written by Albert Einstein and Members at the Institute in 1935 on quantum mechanics and black holes initially seemed to be completely disconnected but recent research by Juan Maldacena suggests that they are closely connected.

Can the weird quantum mechanical property of entanglement give rise to wormholes connecting far away regions in space?

In 1935, Albert Einstein and collaborators wrote two papers at the Institute for Advanced Study. One was on quantum mechanics [1] and the other was on black holes [2]. The paper on quantum mechanics is very famous and influential. It pointed out a feature of quantum mechanics that deeply troubled Einstein. The paper on black holes pointed out an interesting aspect of a black hole solution with no matter, where the solution looks like a wormhole connecting regions of spacetime that are far away. Though these papers seemed to be on two completely disconnected subjects, recent research has suggested that they are closely connected.

Einstein’s theory of general relativity tells us that spacetime is dynamical. Spacetime is similar to a rubber sheet that can be deformed by the presence of matter. A very drastic deformation of spacetime is the formation of a black hole. When there is a large amount of matter concentrated in a small enough region of space, this can collapse in an irreversible fashion. For example, if we filled a sphere the size of the solar system with air, it would collapse into a black hole. When a black hole forms, we can define an imaginary surface called “the horizon”; it separates the region of spacetime that can send signals to the exterior from the region that cannot. If an astronaut crosses the horizon, she can never come back out. She does not feel anything special as she crosses the horizon. However, once she crosses, she will be inevitably crushed by the force of gravity into a region called “the singularity” (Figure 1a).

Infinite in All Directions

This original painting was created by Robbert Dijkgraaf, Director of the Institute and Leon Levy Professor, to commemorate the celebration in Freeman Dyson’s honor, “Dreams of Earth and Sky.” The title is taken from a book written in 1895 by Konstantin Tsiolkovsky, a Russian schoolteacher who worked out the mathematics of interplanetary rocketry in the nineteenth century. “The Earth is the cradle of the mind,” Tsiolkovsky wrote, “but we cannot live forever in a cradle.”

In 2013, Freeman Dyson celebrated his ninetieth birthday and also marked his sixtieth year as a Professor at the Institute for Advanced Study, the longest tenure of any Faculty member in the Institute’s history. When Dyson first arrived as a Member in 1948, the Institute was less than twenty years old. “Dreams of Earth and Sky,” a conference and celebration conceived by Dyson’s colleagues in the School of Natural Sciences and held September 27–28, provided a perspective on his work and impact across the sciences and humanities. The program featured a range of talks on mathematics, physics, astronomy, and public affairs that reflect both the diversity of Dyson’s interests and his ability to open new dialogues.

The son of composer Sir George Dyson and Mildred Atkey, Dyson was born in Crowthorne, England, on December 15, 1923. He worked as a civilian scientist for the Royal Air Force in World War II, and graduated from Cambridge University in 1945 with a B.A. degree in mathematics. He went on to Cornell University as a graduate student in 1947 and worked with Hans Bethe and Richard Feynman. One of Dyson’s most notable contributions to science was the unification of the three versions of quantum electrodynamics invented by Feynman, Julian Schwinger, and Sin-Itiro Tomonaga. Dyson then worked on nuclear reactors, solid state physics, ferromagnetism, astrophysics, and biology, looking for problems where mathematics could be usefully applied. Author of numerous articles and books about science for the general public, he has also been heavily invested in human issues, from arms control and space travel to climate studies. Dyson once remarked that he was “obsessed with the future.” His keen observations and sense of wonder, which have inspired generations here at the Institute and beyond, are powerful testaments to the freedom provided by the Institute to follow one’s future, wherever it may lead.

The Absolute Elsewhere

By Pia de Jong 

Punch cartoon inspired by seven-year-old Freeman Dyson
Immersed in Freeman Dyson’s World
 
In 1930, the British satirical magazine Punch published a cartoon of a boy, lying on his side on the lawn, reading a book on relativity. When asked where his sister is, he replies, “Somewhere in the absolute elsewhere.”

That boy was the seven-year-old Freeman Dyson. He did not understand why his father had sent his remark to Punch. It was after all technically correct. What was so funny about it?

Dyson grew up to be a world-famous mathematician, physicist, astronomer, and an elegant writer. For sixty years, he has worked at the Institute for Advanced Study. On December 15, he will be ninety. An elfin man with pointed ears and mischievous blue eyes, he still walks faithfully to his office every morning, invariably dressed as the British boarding school boy he once was—with a tweed jacket and tie.

To celebrate Dyson’s ninetieth birthday, a conference was held in his honor at the Institute. He himself gave it the title “Dreams of Earth and Sky.” The speakers, also all chosen by him, were just as exciting as the Jules Verne books he devoured as a child—until he realized that they lived only in science fiction.

Thus, I find myself immersed in his fascinating world. I hear the English Astronomer Royal, Martin Rees, talk about alternative universes. I see a map of the nearest stars where extraterrestrial life might really exist. Magic formulas, the interior of the Earth, climate change, nuclear disarmament, life on Mars—ideas that are often as controversial as those of Dyson himself. But also with an equally infectious enthusiasm about everything there is to discover. If I were a child, Dyson would be my hero, and I would want to be an astronomer. Happily, there are many children in the audience.

Curiosities: Pursuing the Monster

By Siobhan Roberts 

What lies beneath a structure with an unimaginable 196,883 dimensions?

In 1981, Freeman Dyson addressed a typically distinguished group of scholars gathered at the Institute for a colloquium, but speaking on a decidedly atypical subject: “Unfashionable Pursuits.”

The problems which we face as guardians of scientific progress are how to recognize the fruitful unfashionable idea, and how to support it.
   To begin with, we may look around at the world of mathematics and see whether we can identify unfashionable ideas which might later emerge as essential building blocks for the physics of the twenty-first century.*

He surveyed the history of science, alighting eventually upon the monster group—an exquisitely symmetrical entity within the realm of group theory, the mathematical study of symmetry. For much of the twentieth century, mathematicians worked to classify “finite simple groups”—the equivalent of elementary particles, the building blocks of all groups. The classification project ultimately collected all of the finite simple groups into eighteen families and twenty-six exceptional outliers. The monster was the last and largest of these exceptional or “sporadic” groups.

How Open-Source Ideas Can Help Us Study Exoplanets

By Hanno Rein 

The customizable Comprehensive Exoplanetary Radial Chart illustrates the radii of planets according to colors that represent equilibrium temperatures, eccentricity, and other data relevant to assessing their potential habitability.

Pluto, the ninth planet in our solar system1 was discovered in 1930, the same year the Institute was founded. While the Institute hosted more than five thousand members in the following sixty-five years, not a single new planet was discovered during the same time.

Finally, in 1995, astronomers spotted an object they called 51 Pegasi b. It was the first discovery of a planet in over half a century. Not only that, it was also the first planet around a Sun-like star outside our own solar system. We now call these planets extrasolar planets, or in short, exoplanets.

As it turns out, 51 Pegasi b is a pretty weird object. It is almost as massive as Jupiter, but it orbits its host star in only four days. Jupiter, as a comparison, needs twelve years to go around the Sun once. Because 51 Pegasi b is very close to the star, its equilibrium temperature is very high. These types of planets are often referred to as “hot Jupiters.”

Since the first exoplanet was discovered, the technology has improved dramatically, and worldwide efforts by astronomers to detect exoplanets now yield a large number of planet detections each year. In 2011, 189 planets were discovered, approximately the number of visiting Members at the Institute every year. In 2012, 130 new planets were found. As of May 20 of this year, the total number of confirmed exoplanets was 892 in 691 different planetary systems.

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