John Wheeler

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 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.