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with anything in our Universe, he discounted the “mirror universe”.
Kurt Gödel and the Rotating Universe
Kurt Gödel is unquestionably the greatest logician of the 20 th century, which has been the greatest
century for logic since Aristotle’s era. Despite this stature, his name is little known outside
professional circles of logic and mathematics. Part of the cause of his narrower fame probably lies in
the fact that Einstein’s theories were acclaimed as triumphs, while the initial judgment on Gödel’s
theorems was that they constituted a first-rate calamity for logic and mathematics. Namely, Gödel in
1931, at the age of only 25 proved the incompleteness of mathematics. Gödel’s First incompleteness
theorem showed that some perfectly well-formed arithmetical statements could never be proved true
or false. Worse, it showed that some arithmetical truths could never be proved true. Among physicists
Gödel is known as “the man who proved that time travel to the past was possible under Einstein’s
equations”, although this was just a trip outside his field. In 1949 Gödel, working with Einstein at
Princeton, published a paper called “An Example of a New Type of Cosmological Solutions of
Einstein’s Field Equations of Gravitation” (Reviews of Modern Physics, 1949:21;447).
In this paper Gödel described a rotating Universe. There are in fact solutions to Einstein’s field
equations that allow for “closed timelike curves” (CTCs), i.e., curves in space-time that are continuous,
can represent a causal process in time, and that loop back on themselves. Closed timelike curves
would obviously allow for a sort of backwards time travel. In his solution, if the Universe were infinite,
nonexpanding, and were rotating at a certain rate, the forward light cones would bend forward in the
direction of rotation until at a certain critical distance from the center of rotation, they would create a
closed timelike loop around the perimeter of rotation. In such a universe, “a traveler can move around
a circular path on a trip into his local future and end up in his own global past, without ever traveling
faster than light”.
In such a place, if a bullet is fired off from any point, its path will be swung around by the general spin.
In fact, Gödel’s space-time is so distorted by its spin that it contains paths which loop into the past. In
a universe like ours, such paths would be hundreds of millions of light years long, but the paths
shorten if the general density is higher. If a universe with a mass like ours were as Gödel describes, it
would have to rotate once every 70 billion (70 × 10 9 ) years, and the critical radius for the creation of
CTCs would be 16 billion (16 × 10 9 ) light-years from the center of rotation, which is about the edge of
our Universe. However, our Universe is nothing like this.
Einstein in his memoirs wrote that he devoted a lot of thinking to Gödel’s idea. He concluded that the
Universe has been expanding, and not rotating, ever since its creation in Big Bang.
Like in the case of Einstein-Rosen bridge, Einstein concluded that Gödel’s solution can be dismissed
for physical reasons.
Frank Tipler and the Rotating Cylinder
In 1949 Gödel rotated the entire Universe, while Frank Tipler in his approach for building the time
machine reduced the problem merely to the spinning an infinite cylinder.
In 1974 Tipler, a physics graduate student at the University of Maryland, has suggested a variant of
Gödel’s view that describes how one could create closed timelike curves using a rotating, infinitely
long cylinder (“Rotating Cylinders and the Possibility of Global Causality Violation”. Physical Review D
1974:9;2203-2206). One could spiral around the cylinder backwards in time, until one reached any
desired point in the past (except points in time before the creation of the cylinder).
The final sentence in Tipler’s paper says: In short, general relativity suggests that if we construct a
sufficiently large rotating cylinder, we create a time machine.
Nobody had ever before made such a statement in a respectable scientific journal. Fully aware of
difficulty to build such time machine, in his other paper, Tipler suggested the possibility of speeding up
the rotation of an existing star as an alternative approach.
The significance of Tipler’s result, and Gödel’s too (that bothered Einstein) is that they hold up a hope
for the physical possibility of time travel.
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