Gödel Universe & Van Stockum's Time Machine

Gödel Universe & Van Stockum's Time Machine

by : Aria Ratmandanu 

Gödel Universe

       In 1949, Kurt Gödel, the great mathematical logician, found an even stranger solution to Einstein’s equations. He assumed that the entire universe was rotating. Like the Van Stockum cylinder, one is swept up by the molasses-like nature of space-time. By taking a rocket ship around the Gödel universe, you return to your starting point but shift back in time.

        In Gödel’s universe, a person can, in principle, travel between any two points in space and time in the universe. Every event, in any time period, can be visited, no matter how distant in the past. Because of gravity, there is a tendency for Gödel’s universe to collapse on itself. Hence, the centrifugal force of rotation must balance this gravitational force. In other words, the universe must spin above a certain speed. The larger the universe, the greater the ten- dency to collapse, and the faster the universe would have to spin to prevent collapse.

Solution of Einstein's Equation found by Kurt Gödel.

        For a universe our size, for example, Gödel calculated that it would have to rotate once every 70 billion years, and the minimum radius for time travel would be 16 billion light-years. To travel back in time, however, you would have to travel just below the speed of light.

     Gödel was well aware of the paradoxes that could arise from his solution—the possibility of meeting yourself in the past and altering the course of history. “By making a round trip on a rocket ship in a sufficiently wide course, it is possible in these worlds to travel into any region of the past, present, and future, and back again, exactly as it is possible in other worlds to travel to distant parts of space,” he wrote. “This state of affairs seems to imply an absurdity.

      For it enables one to travel into the near past of those places where he has himself lived. There he would find a person who would be himself at some earlier period of life. Now he could do something to this person which, by his memory, he knows has not happened to him.”

     Einstein was deeply disturbed by the solution found by his friend and neighbor at the Institute for Advanced Study at Princeton. His response is quite revealing:

"Kurt Gödel’s essay constitutes, in my opinion, an important contribution to the general theory of relativity, especially to the analysis of the concept of time. The problem here involved disturbed me already at the time of the building up of the general theory of relativity, without my having succeeded in clarifying it . . . The distinction “earlier- later” is abandoned for world-points which lie far apart in a cosmo- logical sense, and those paradoxes, regarding the direction of the causal connection, arise, of which Mr. Gödel has spoken . . . It will be interesting to weigh whether these are not to be excluded on physical grounds."

      Einstein’s response is interesting for two reasons. First, he admitted that the possibility of time travel bothered him when he first formulated general relativity. Since time and space are treated like a piece of rubber that can bend and warp, Einstein worried that the fabric of space-time would warp so much that time travel might be possible. Second, he ruled out Gödel’s solution on the basis of “phys- ical grounds”—that is, the universe does not spin, it expands.

      When Einstein died, it was widely known that his equations allowed for strange phenomena (time travel, wormholes). But no one gave them much thought because scientists felt they could not be re- alized in nature. The consensus was that these solutions had no basis in the real world; you would die if you tried to reach a parallel universe via a black hole; the universe did not spin; and you cannot make infinite cylinders, making time travel an academic question. 

Van Stockum's Time Machine

      Einstein’s theory links space and time into an inseparable unity. As a result, any wormhole that connects two distant points in space might also connect two distant points in time. In other words, Einstein’s theory allows for the possibility of time travel.

       The concept of time itself has evolved over the centuries. To Newton, time was like an arrow; once fired, it never changed course and traveled unerringly and uniformly to its target. Einstein then introduced the concept of warped space, so time was more like a river that gently speeded up or slowed down as it meandered through the universe. But Einstein worried about the possibility that perhaps the river of time can bend back on itself. Perhaps there could be whirlpools or forks in the river of time.

       In 1937, this possibility was realized when W. J. Van Stockum found a solution to Einstein’s equations which permitted time travel. He began with an infinite, spinning cylinder. Although it’s not physically possible to build an infinite object, he calculated that if such a cylinder spun around at or near the speed of light, it would drag the fabric of space-time along with it, much like molasses is dragged along with the blades of a blender. (This is called frame-dragging, and it has now been experimentally seen in detailed pho- tographs of rotating black holes.)

      Anyone brave enough to travel around the cylinder would be swept along, attaining fantastic speeds. In fact, to a distant observer, it would appear that the individual was exceeding the speed of light. Although Van Stockum himself did not realize it at the time, by making a complete trip around the cylinder, you could actually go back in time, returning before you left. If you left at noon, then by the time you returned to your starting point, say, it might be 6 p.m. the previous night. The faster the cylinder spun, the further back in time you would go (the only limitation being that you could not go further back in time than the creation of the cylinder itself).

       Since the cylinder is like a maypole, every time you danced around the pole, you would wind up further and further back in time. Of course, one could dismiss such a solution because cylinders cannot be infinitely long. Also, if such a cylinder could be built, the centrifugal forces on the cylinder, because it spins near the speed of light, would be enormous, causing the material that made up the cylinder to fly apart.