Albert Einstein

By John Wheeler 

The paper by Niels Bohr and John Wheeler on the mechanism of nuclear fission appeared in the Physical Review of September 1, 1939, the same day the war began.

The following excerpt is from remarks given by John Archibald Wheeler on March 27, 2000, in connection with the play Copenhagen by Michael Frayn. Wheeler was a Professor of Physics at Princeton University from 1938 until his retirement in 1976 and a Member of the Institute’s School of Mathematics (prior to the founding of the School of Natural Sciences) in the spring of 1937, when it was still temporarily housed in Fine Hall (now Jones Hall) at Princeton University. Niels Bohr, who had a twenty-year association with the Institute, first visited in the academic year 1938–39, when the Institute completed Fuld Hall. For more about Bohr and his relationship with Albert Einstein, one of the Institute’s first Professors, see the Spring 2009 Institute Letter.

If two such great thinkers as Bohr and Einstein, who had such a high regard for each other, could be brought together for a prolonged period, would not something emerge of great value to all of us? This thought and this hope animated the guiding spirits of the Princeton Institute for Advanced Study to invite Niels Bohr to come as a guest of the Institute for the entire spring semester of 1939. However, four days before Bohr boarded his America-bound ship, he learned from Otto Robert Frisch that Frisch and his aunt Lisa Meitner had solid evidence that a neutron splits the nucleus of uranium. As he crossed the Atlantic, Bohr’s vision turned more and more from the problem of quantum mechanics to the problems of nuclear physics. So January and February, March and April of 1939 saw him working, discussing, calculating, and writing, day after day, not with Einstein on quantum physics as intended, but with me on the nuclear physics of fission. Yes, of course, there were meetings Bohr had with Einstein but they were occasional and did not lead to the big push it takes to formulate a solid well-argued position. No. Fission, and what it meant and how it differed from one nucleus to another, and what those differences offered in the way of using the nucleus for a chain reaction stood at the center of our attention. . . .

In his conjectures, now collectively known as the Langlands program, Robert Langlands drew on the work of Hermann Weyl (above), André Weil, and Harish-Chandra, among others with extensive ties to the Institute.

It has been said that the goals of modern mathematics are recon­struction and development.¹ The unifying conjectures between number theory and representation theory that Robert Langlands, Professor Emeritus in the School of Mathematics, articulated in a letter to André Weil in 1967, continue a tradition at the Institute of advancing mathematical knowledge through the identification of problems central to the understanding of active areas or likely to become central in the future.

“Two striking qualities of mathematical concepts regarded as central are that they are simultaneously pregnant with possibilities for their own development and, so far as we can judge from a history of two and a half millennia, of permanent validity,” says Langlands. “In comparison with biology, above all with the theory of evolution, a fusion of biology and history, or with physics and its two enigmas, quantum theory and relativity theory, mathematics contributes only modestly to the intellectual architecture of mankind, but its central contributions have been lasting, one does not supersede another, it enlarges it.”²

In his conjectures, now collectively known as the Langlands program, Langlands drew on the work of Harish-Chandra, Atle Selberg, Goro Shimura, André Weil, and Hermann Weyl, among others with extensive ties to the Institute. 

Weyl, whose appointment to the Institute’s Faculty in 1933 followed those of Albert Einstein and Oswald Veblen, was a strong believer in the overall unity of mathematics, across disciplines and generations. Weyl had a major impact on the progress of the entire field of mathematics, as well as physics, where he was equally comfortable. His work spanned topology, differential geometry, Lie groups, representation theory, harmonic analysis, and analytic number theory, and extended into physics, including relativity, electromagnetism, and quantum mechanics. “For [Weyl] the best of the past was not forgotten,” notes Michael Atiyah, a former Institute Professor and Member, “but was subsumed and refined by the mathematics of the present.”³

By George Dyson 

In this 1953 diagnostic photograph from the maintenance logs of the IAS Electronic Computer Project (ECP), a 32-by-32 array of charged spots––serving as working memory, not display––is visible on the face of a Williams cathode-ray memory tube. Starting in late 1945, John von Neumann, Professor in the School of Mathematics, and a group of engineers worked at the Institute to design, build, and program an electronic digital computer.

I am thinking about something much more important than bombs. I am thinking about computers.––John von Neumann, 1946 

By Jeremy Bernstein 

Debates at the fifth Solvay Conference in Brussels in 1927 helped shape the modern interpretation of quantum mechanics. Participants included Niels Bohr (second row, far right) and Albert Einstein (first row, fifth from left).

In the two years I spent at the Institute, 1957–59, I had the opportunity of meeting two of the founders of the quantum theory—Niels Bohr and Paul Dirac. In the case of Bohr, perhaps “meeting” overstates the case. He was a Mem­ber in the spring of 1958 and Oppenheimer, who had known him since the 1920s and who had a feeling of adulation for him, decided that a fitting thing to do was to have a sort of seminar in which the physicists would trot out their wares with Bohr looking on and possibly commenting. As it happened, I had had a brief collaboration with T. D. Lee and C. N. Yang, who had won the Nobel Prize that fall. They had better things to tell Bohr than our modest work, so I was the designated spokesman. I was given ten minutes and took about three. After which Bohr commented, “Very interesting,” which meant he did not think so. If he had had any real interest, he would have engaged in a Socratic dialogue, which would have proceeded until he was satisfied. There is a famous story concerning Erwin Schrödinger—with whom I later spent an afternoon in Vienna—arriving in Copenhagen after having created his version of the quantum theory. Bohr disagreed with some of what Schrödinger was saying and pursued him into his bedroom where the now sick Schrödinger had taken refuge.

On a visit to the Institute ten years earlier, Bohr had written his wonderful account of his discussions with Einstein about the theory. Bohr found writing incredibly difficult and always had an amanuensis who acted as a sounding board. In this case, it was Abraham Pais who told the following story. Einstein had given Bohr his office for the visit and was in the adjoining smaller office of his assistant. Where the assistant had gone is not recorded. Bohr was facing away from the door and saying, “Einstein, Einstein” several times. As if summoned by a genie, Einstein stealthy came into the office. Before Bohr could turn around, Einstein helped himself to some of Bohr’s pipe tobacco. When Bohr did turn around, Einstein explained that his doctor had ordered him not to “buy” any more tobacco, but there was no injunction against his “stealing” some.

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.