The Science of Interstellar

^{Fig. 13.6. Slowing down by slingshots in a target black-hole binary.}

As exciting as these three far-future propulsion systems may seem, they truly are far future. Using twenty-first-century technology, we are stuck with thousands of years to reach other solar systems. The only hope (an exceedingly faint hope) for faster interstellar travel, in the event of an earthly disaster, is a wormhole like that in Interstellar, or some other extreme form of spacetime warp.

IV THE WORMHOLE

14 Wormholes

How Wormholes Got Their Name

My mentor, John Wheeler, gave astrophysical wormholes their name. He based it on wormholes in apples (Figure 14.1). For an ant walking on an apple, the apple’s surface is the entire universe. If the apple is threaded by a wormhole, the ant has two ways to get from the top to the bottom: around the outside (through the ant’s universe) or down the wormhole. The wormhole route is shorter; it’s a shortcut from one side of the ant’s universe to the other.

^{Fig. 14.1. An ant explores a wormhole-endowed apple.}

The apple’s delicious interior, through which the wormhole passes, is not part of the ant’s universe. It is a three-dimensional bulk or hyperspace (Chapter 4). The wormhole’s wall can be thought of as part of the ant’s universe. It has the same dimensionality as the universe (two dimensions) and it joins onto the universe (the apple’s surface) at the wormhole’s entrance. From another viewpoint, the wormhole’s wall is not part of the ant’s universe; it is just a shortcut by which the ant can travel across the bulk, from one point in its universe to another.

Flamm’s Wormhole

In 1916, just one year after Einstein formulated his general relativistic laws of physics, Ludwig Flamm in Vienna discovered a solution of Einstein’s equations that describes a wormhole (though he did not call it that). We now know that Einstein’s equations allow many kinds of wormholes (wormholes with many different shapes and behaviors), but Flamm’s is the only one that is precisely spherical and contains no gravitating matter. When we take an equatorial slice through Flamm’s wormhole, so it and our universe (our brane) have just two dimensions rather than three, and when we then view our universe and the wormhole from the bulk, they look like the left part of Figure 14.2.

With one of our universe’s dimensions lost from the picture, you must think of yourself as a two-dimensional creature confined to move on the bent sheet or on the wormhole’s two-dimensional wall. There are two routes for travel from location A in our universe to location B: the short route (dashed blue curve) down the wormhole’s wall, or the long route (dashed red curve) along the bent sheet, our universe.

Of course, our universe is really three dimensional. The concentric circles in the left part of Figure 14.2 are really the nested green spheres shown to the right. As you enter the wormhole along the blue path from location A, you pass through spheres that get smaller and smaller. Then the spheres, though nested inside each other, cease changing circumference. And then, as you exit the wormhole toward location B, the spheres get larger and larger.

For nineteen years, physicists paid little attention to Flamm’s outrageous solution of Einstein’s equations, his wormhole. Then in 1935 Einstein himself and fellow physicist Nathan Rosen, unaware of Flamm’s work, rediscovered Flamm’s solution, explored its properties, and speculated about its significance in the real world. Other physicists, also unaware of Flamm’s work, began to call his wormhole the “Einstein-Rosen bridge.”

^{Fig. 14.2. Flamm’s wormhole.}

Wormhole Collapse

It is often difficult to extract, from the mathematics of Einstein’s equations, a full understanding of their predictions. Flamm’s wormhole is a remarkable example. From 1916 until 1962, nearly a half century, physicists thought that the wormhole is static, forever unchanging. Then John Wheeler and his student Robert Fuller discovered otherwise. Looking much more closely at the mathematics, they discovered that the wormhole is born, expands, contracts, and dies, as shown in Figure 14.3.

Initially, in picture (a), our universe has two singularities. As time passes, the singularities reach out to each other through the bulk and meet to create the wormhole (b). The wormhole expands in circumference, (c) and (d), then shrinks and pinches off (e), leaving behind the two singularities (f). The birth, expansion, shrinkage, and pinch-off happen so quickly that nothing, not even light, has time to travel through the wormhole from one side to the other. Anything or anyone that attempts the trip will get destroyed in the pinch-off!