Classical Mechanics

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.