Economics: Science, Craft, or Snake Oil? Institute for Advanced Study

I 1935, Albert Einstein and collaborators wrote two papers at the Institute for Advanced Study. One was on quantum mechanics [1] and the other was on black holes [2]. The paper on quantum mechanics is very famous and influential. It pointed out a feature of quantum mechanics that deeply troubled Einstein. The paper on black holes pointed out an interesting aspect of a black hole solution with no matter, where the solution looks like a wormhole connecting regions of spacetime that are far away. Though these papers seemed to be on two completely disconnected subjects, recent research has suggested that they are closely connected. Einstein’s theory of general relativity tells us that spacetime is dynamical. Spacetime is similar to a rubber sheet that can be deformed by the presence of matter. A very drastic deformation of spacetime is the formation of a black hole. When there is a large amount of matter concentrated in a small enough region of space, this can collapse in an irreversible fashion. For example, if we filled a sphere the size of the solar system with air, it would collapse into a black hole. When a black hole forms, we can define an imaginary surface called “the horizon”; it separates the region of spacetime that can send signals to the exterior from the region that cannot. If an astronaut crosses the horizon, she can never come back out. She does not feel anything special as she crosses the horizon. However, once she crosses, she will be inevitably crushed by the force of gravity into a region called “the singularity” (Figure 1a, page 12). Outside of the distribution of collapsing matter, black holes are described by a spacetime solution found by Karl Schwarzschild in 1916. This solution turned out to be very confusing, and a full understanding of its classical aspects had to wait until the 1960s. The original Schwarzschild solution contained no matter (Figure 1b, page 12). It is just vacuum everywhere, but it has both future and past singularities. In 1935, Einstein and Rosen found a curious aspect of this solution: it contains two regions that look like the outside of a black hole. Namely, one starts with a spacetime that is flat at a far distance. As we approach the central region, spacetime is deformed with the same deformation that is generated outside a massive object. At a fixed time, the geometry of space is such that as we move in toward the center, instead of finding a massive object, we find a second asymptotic region (Figure 1c, page 12). The geometry of space looks like a wormhole connecting two asymptotically flat regions. This is sometimes called the Einstein–Rosen bridge. They realized this before the full geometry was properly understood. Their motivation was to find a model for elementary particles where particles were represented by smooth geometries. We now think that their original motivation was misguided. This geometry can also be interpreted as a kind of wormhole that connects two distant regions in the same spacetime. John Wheeler and Robert Fuller showed that these Entanglement and the Geometry of Spacetime Can the weird quantum mechanical property of entanglement give rise to wormholes connecting far away regions in space? (Continued on page 14) (Continued on page 16) Fall