Cosmological observations show that on the largest scales accessible to our telescopes, the universe is very uniform, and the same laws of physics operate in all the parts of it that we can see. As Andrei Linde, 2014 Kavli Prize Laureate in Astrophysics, explains, rather paradoxically, the theory that explains this uniformity also predicts that on extremely large scales, the situation may look totally different. Instead of being a single spherically symmetric balloon, our universe may look like a multiverse—a collection of many different exponentially large balloons with different laws of physics operating in each. In the beginning, this picture looked more like a piece of science fiction than a scientific theory. However, recent developments in inflationary cosmology, particle physics, and string theory provide strong evidence supporting this new cosmological paradigm.
To most physicists, almost everything about evolution is puzzling. What determines how much complexity can — and has — evolved? Why is there so much biological diversity on all scales of differences? How could evolution select for future “evolvability”? Why doesn’t evolution get slower and slower? One of the roles of theory is to frame questions — or at least limited versions of them — more precisely. And another is to reduce — or redirect — puzzlement by developing and analyzing simple caricature models to see what should be expected rather than be surprising. This talk by Daniel Fisher will outline some recent progress in these directions, particularly by statistical physics ways of thinking.
Abstract: It is often said that general relativity and quantum mechanics are separate subjects that don’t fit together comfortably. There is a tension, even a contradiction between them—or so one often hears. I take exception to this view. I think that exactly the opposite is true. It may be too strong to say that gravity and quantum mechanics are exactly the same thing, but those of us who are paying attention, may already sense that the two are inseparable, and that neither makes sense without the other. Two things make me think so. The first is ER=EPR, the equivalence between quantum entanglement and spatial connectivity. In its strongest form ER=EPR holds not only for black holes but for any entangled systems—even empty space. One may say that the most basic property of space—its connectivity—is due to the most quantum property of quantum mechanics: entanglement.
The second has to do with the dynamics of space, in particular its tendency to expand. One sees this in cosmology, but also behind the horizons of black holes. The expansion is thought to be connected with the tendency of quantum states to become increasingly computationally complex: a “second law of quantum complexity.” If one pushes these ideas to their logical limits, quantum entanglement of any kind implies the existence of hidden Einstein-Rosen bridges which have a strong tendency to grow, even in situations which one naively would think have nothing to do with gravity. To summarize this viewpoint in a short slogan: Wherever there is quantum mechanics, there is also gravity.
String theory has enjoyed tremendously fruitful interactions with modern mathematics. Some of the simplest and most interesting questions in number theory and geometry involve counting (for instance, determining numbers of integer solutions to certain equations).
In this talk, Shamit Kachru will discuss how in the process of answering natural physical questions — such as about strong coupling dynamics in quantum field theories, black hole physics and solutions of Einstein’s equations — string theory uses (and sometimes solves) those counting problems. The talk will begin with a general discussion of string compactifications with supersymmetry, and the special role played by Calabi-Yau manifolds. Mirror symmetry will appear as a first example where striking applications to geometry occur. The use of string techniques to solve strongly coupled supersymmetric non-Abelian gauge theories will be a natural sequel, and Kachru will close with recent work relating this circle of ideas to the long-standing problem of determining a Ricci-flat metric on a compact Calabi-Yau manifold.
When Shannon formulated his groundbreaking theory of information in 1948, he did not know what to call its central quantity, a measure of uncertainty. It was von Neumann who recognized Shannon’s formula from statistical physics and suggested the name entropy. This was but the first in a series of remarkable connections between physics and information theory. Later, tantalizing hints from the study of quantum fields and gravity, such as the Bekenstein-Hawking formula for the entropy of a black hole, inspired Wheeler’s famous 1990 exhortation to derive “it from bit.” That three-syllable manifesto asserted that to properly unify the geometry of general relativity with the indeterminacy of quantum mechanics, it would be necessary to inject fundamentally new ideas from information theory. Wheeler’s vision was sound, but it came twenty-five years early. Only now is it coming to fruition, with the twist that classical bits have given way to the qubits of quantum information theory.
This talk by Patrick Hayden will provide a tour of some of the recent developments at the intersection of quantum information and fundamental physics that are the source of this renewed excitement.
None of us were consulted when the universe was created. And yet it is tempting to ask not only how the universe evolves, but also why, and could it be different? Our universe weighs more than 1050 tons. Could it be created “on the cheap”? Would it require a comprehensive project plan, and if so, where was this plan written before the universe was born? Can we study the evolution of the universe by cosmological observations, and then “play the movie back” to the origin of time, or will something unavoidably prevent us from doing it? Why do we live in a 4-dimensional space-time? Why is the universe comprehensible? We will try to approach these and other similar questions in the context of the theory of the inflationary multiverse.
Many mathematical concepts trace their origins to everyday experience, from astronomy to mechanics. Remarkably, ideas from quantum theory turn out to carry tremendous mathematical power too, even though we have little intuition dealing with elementary particles. The bizarre quantum world not only represents a more fundamental description of nature, it also inspires a new realm of mathematics that might be called “quantum mathematics” that turns out to be a powerful tool to solve deep outstanding mathematical problems. Similarly, new mathematical ideas address some of the most fundamental questions in physics, such as the Big Bang, black holes, and the ultimate fate of space, time, and matter.
Robbert Dijkgraaf, Director of the Institute for Advanced Study and Leon Levy Professor since 2012, is a mathematical physicist who has made significant contributions to string theory and the advancement of science education. He is President of the InterAcademy Partnership, a past President of the Royal Netherlands Academy of Arts and Sciences, and a distinguished public policy adviser and advocate for science and the arts. For his contributions to science, he has received the Spinoza Prize, the highest scientifc award in the Netherlands, and has been named a Knight of the Order of the Netherlands Lion. He is a member of the American Academy of Arts and Sciences and the American Philosophical Society. He is also a trained artist, writer, and popular lecturer.
Black hole and cosmological horizons -- from which nothing can escape according to classical gravity -- play a crucial role in physics. They are central to our understanding of the origin of structure in the universe, but also lead to fascinating and persistent theoretical puzzles. They have become accessible observationally to a remarkable degree, albeit indirectly. These lectures will start by introducing horizons and how they arise in classical gravity (Einstein's general relativity). In the early universe, the uncertainty principle of quantum mechanics in the presence of a horizon introduced by accelerated expansion (inflation) leads to a beautifully simple, and empirically tested, theory of the origin of structure. Its effects reach us in tiny fluctuations in the background radiation we observe from the time when atoms first formed.
This theory, and the observations, are sensitive to very high energy physics, including effects expected from a quantum theory of gravity such as string theory. Modeling the early universe within that framework helps us better understand the inflationary process and its observational signatures. Analyzing the `big data' from the early universe -- which continues to pour in -- is a major effort. This provides concrete tests of theoretical models of degrees of freedom and interactions happening almost 14 billion years ago.
Our understanding breaks down if we push further back in time, or into black hole horizons. This challenges us to determine more precisely how and why our existing theories fail. I will explain these basic puzzles, and conclude with some of the latest results on this question in string theory, which exhibits interesting new effects near black hole horizons.