Articles from the Institute Letter

Additional articles from new and past issues of the Institute Letter will continue to be posted over time and as they become available.

By Juan Maldacena

Albert Einstein, pictured at left with J. Robert Oppenheimer at the Institute, tried to disprove the notion of black holes that his theory of general relativity and gravity seemed to predict. Oppenheimer used Einstein's theory to show how black holes could form.

The ancients thought that space and time were preexisting entities on which motion happens. Of course, this is also our naive intuition. According to Einstein’s theory of general relativity, we know that this is not true. Space and time are dynamical objects whose shape is modified by the bodies that move in it. The ordinary force of gravity is due to this deformation of spacetime. Spacetime is a physical entity that affects the motion of particles and, in turn, is affected by the motion of the same particles. For example, the Earth deforms spacetime in such a way that clocks at different altitudes run at different rates. For the Earth, this is a very small (but measurable) effect. For a very massive and very compact object the deformation (or warping) of spacetime can have a big effect. For example, on the surface of a neutron star a clock runs slower, at 70 percent of the speed of a clock far away.

In fact, you can have an object that is so massive that time comes to a complete standstill. These are black holes. General relativity predicts that an object that is very massive and sufficiently compact will collapse into a black hole. A black hole is such a surprising prediction of general relativity that it took many years to be properly recognized as a prediction. Einstein himself thought it was not a true prediction, but a mathematical oversimplification. We now know that they are clear predictions of the theory. Furthermore, there are some objects in the sky that are probably black holes.  

  

Black holes are big holes in spacetime. They have a surface that is called a “horizon.” It is a surface that marks a point of no return. A person who crosses it will never be able to come back out. However, he will not feel anything special when he crosses the horizon. Only a while later will he feel very uncomfortable when he is crushed into a “singularity,” a region with very high gravitational fields. The horizon is what makes black holes “black”; nothing can escape from the horizon, not even light. Fortunately, if you stay outside the horizon, nothing bad happens to you. The singularity remains hidden behind the horizon.

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By Scott Tremaine

Scott Tremaine explores the stability of our solar system, one of the oldest problems in theoretical physics, dating back to Isaac Newton.

The stability of the solar system is one of the oldest problems in theoretical physics, dating back to Isaac Newton. After Newton discovered his famous laws of motion and gravity, he used these to determine the motion of a single planet around the Sun and showed that the planet followed an ellipse with the Sun at one focus. However, the actual solar system contains eight planets, six of which were known to Newton, and each planet exerts small, periodically varying, gravitational forces on all the others.

The puzzle posed by Newton is whether the net effect of these periodic forces on the planetary orbits averages to zero over long times, so that the planets continue to follow orbits similar to the ones they have today, or whether these small mutual interactions gradually degrade the regular arrangement of the orbits in the solar system, leading eventually to a collision between two planets, the ejection of a planet to interstellar space, or perhaps the incineration of a planet by the Sun. The interplanetary gravitational interactions are very small—the force on Earth from Jupiter, the largest planet, is only about ten parts per million of the force from the Sun—but the time available for their effects to accumulate is even longer: over four billion years since the solar system was formed, and almost eight billion years until the death of the Sun.

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By Matthew Kahle

Matthew Kahle, Member (2010-11) in the School of Mathematics, writes about his interest in thinking about what it might be like inside a black hole. This illustration (Figure 1.), from Kip Thorne's Black Holes and Time Warps: Einstein's Outrageous Legacy (W. W. Norton & Company, Inc., 1994), suggests a few probabilities.

I sometimes like to think about what it might be like inside a black hole. What does that even mean? Is it really “like” anything inside a black hole? Nature keeps us from ever knowing. (Well, what we know for sure is that nature keeps us from knowing and coming back to tell anyone about it.) But mathematics and physics make some predictions.

John Wheeler suggested in the 1960s that inside a black hole the fabric of spacetime might be reduced to a kind of quantum foam. Kip Thorne described the idea in his book Black Holes & Time Warps as follows (see Figure 1).

“This random, probabilistic froth is the thing of which the singularity is made, and the froth is governed by the laws of quantum gravity. In the froth, space does not have any definite shape (that is, any definite curvature, or even any definite topology). Instead, space has various probabilities for this, that, or another curvature and topology. For example, inside the singularity there might be a 0.1 percent probability for the curvature and topology of space to have the form shown in (a), and a 0.4 percent probability for the form in (b), and a 0.02 percent probability for the form in (c), and so on.”

In other words, perhaps we cannot say exactly what the properties of spacetime are in the immediate vicinity of a singularity, but perhaps we could characterize their distribution. By way of analogy, if we know that we are going to flip a fair coin a thousand times, we have no idea whether any particular flip will turn up heads or tails. But we can say that on average, we should expect about five hundred heads. Moreover, if we did the experiment many times we should expect a bell-curve shape (i.e., a normal distribution), so it is very unlikely, for example, that we would see more than six hundred heads.

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By Jeremy Adelman

Jeremy Adelman, Member (2001–02) in the School of Historical Studies, explores the complex nature of Albert O. Hirschman’s (above) optimism during his early years at the Institute.

Albert O. Hirschman became a permanent Faculty member of the Institute in 1974, moving from Harvard’s economics department to join Clifford Geertz in the creation of the School of Social Science. By then, Hirschman was not just famous for his writings about economic development and his analyses of Latin American political economies. His Exit, Voice, and Loyalty: Responses to Decline in Firms, Organizations, and States (Harvard University Press, 1970) had made him one of the country’s renowned social scientists.

Behind the scenes, however, his concerns were shifting; he was, he said, “retreating” into history and the study of the intellectual foundations of political economy. Retreat did not sever his interest in the present. If anything, it was the present that gnawed at him, especially in Latin America. In late summer 1973, Hirschman became the Chair of the Social Science Research Council Joint Committee for Latin American Studies. Ten days later, he learned of the violent overthrow of Chile’s socialist President, Salvador Allende, whom Hirschman had met and admired as an example of a “reform-monger,” a type he celebrated in Journeys Toward Progress (Twentieth Century Fund, 1963), his epic of Latin America’s hopeful 1960s. Allende’s death and the disappearance of friends and former students, indeed the wave of authoritarian regimes sweeping the region, shattered the optimism that had buoyed his thinking.

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By Stelios Michalopoulos

Stelios Michalopoulos, the Deutsche Bank Member (2010–11) in the School of Social Science, proposes that geography and trade opportunities forged the Islamic economic doctrine, which in turn influenced the economic performance of the Muslim world in the preindustrial era.

Karl Marx linked the structure of production to the formation of institutions. According to Marx, religion is like any other social institution in that it is dependent upon the economic realities of a given society, i.e., it is an outcome of its productive forces. In contrast, Max Weber highlighted the independent effect of religious affiliation on economic behavior. Weaving these insights together, my research with Alireza Naghavi and Giovanni Prarolo of the University of Bologna proposes that geography and trade opportunities forged the Islamic economic doctrine, which in turn influenced the economic performance of the Muslim world in the preindustrial era. Since Islam emerged in the Arabian peninsula when land dictated productive decisions, the arrangement of Islamic institutions had to be compatible with the conflicting interests of groups residing along regions characterized by a highly unequal distribution of agricultural potential.

In particular, we argue that the unequal distribution of land endowments conferred differential gains from trade across regions. In such an environment, it was mutually beneficial to establish an economic system that dictated both static and dynamic income redistribution. The latter was implemented by enforcing an equitable inheritance system, increasing the costs of physical capital accumulation, and rendering investments in public goods, through religious endowments, increasingly attractive. These Islamic economic principles allowed Muslim lands to flourish in the preindustrial world but limited the potential for growth in the eve of large-scale shipping trade and industrialization. In a stage of development when land attributes determine productive capabilities, regional agricultural suitability plays a fundamental role in shaping the potential of a region to produce a surplus and thus engage in and profit from trade. Based on this idea, we combined detailed data on the distribution of regional land quality and proximity to pre-Islamic trade routes with information on Muslim adherence across local populations.

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