How Gödel broke the taboo of time travel

When you are talking about Kurt Gödel with me, you'd better be careful as you are probably speaking with the one of the biggest admirers of him in the universe. It's unarguable that he is one of the greatest minds in the science history however for me he is rather an inspiration to follow an academic career. Once the famous mathematician Fermat wrote for his mysterious claim, later known as "Fermat's Last Theorem" in Arithmetica as follows : "I have discovered a truly marvelous proof of this, which this margin is too narrow to contain". I can confıdently repeat this statement for Gödel. This margin is too narrow to contain him.

Until several decades, time travel has only been a topic of sci-fi movies, books and articles and merely an imagination of human mind, along with other supposed superstitions. Probably , people were having a "thoughtless" fun while reading Memoirs of the Twentieth Century, in 1733, in which a guardian angel was traveling to 1997-98 from the present. But I do not think people were just "enjoying" themselves on the discussions about the TV series Lost, while brainstorming on conspiracy theories based on time travel and Einstein's relativity theory. (Get over it, the series did not have a scientific point at all :) )

But , if time travel suddenly started being taken seriously by physicists and scientists in general, who broke this long-lasting taboo?

Gödel's Universe

In 1949, Gödel published a paper called "An example of a new type of cosmological solutions of Einstein's field equations of gravitation" to honor his best friend and Princeton neighbor Einstein. In his paper, he constructed a hypothetical universe, derived from the equations of the general theory of relativity, that admits time travel into the past; it is infinite, static (not expanding), rotating, with non-zero cosmological constant. It was an exact solution to Einstein's field equations and it had many, literally many strange properties.

I am not sure if Einstein felt quite honored though. Gödel must have been quite an annoying person for the scientists of his time.First, with his "Incompleteness theorem", he probably ruined everyone’s day in math, which basically pointed out that every system of math capable of computing addition and multiplication produces some true conclusions that the system itself can’t even prove it is true.

His new universe was also annoying for physicists, especially for Einstein. He tried without success to find an error in Gödel's physics or a missing element in relativity itself that would rule out the applicability of Gödel's results-but he failed.

The results were shocking. In Gödel's hypothetical universe, you could not only travel "anywhere" but "anywhen" also.


How is time travel possible in Gödel's universe?

Schematic view of Gödel's universe

 Above, the two vertical lines are a world line of a matter particle (which may be regarded as a galaxy). These particles are always at the same distant. However, the center vertical line is a center of rotational symmetry.  The rotation of the universe  (which Gödel introduced into his model) produces a peculiar effect on the light-cones, as is shown in the figure above. The center light-cone is up-right, but as we go farther from the center, the light-cone tilts and widens. For the universe is rotating around this center , according to special relativity, the velocity of a particle changes the hypersurface of simultaneity and also the direction of the time axis. 

In the Gödel's universe, there is a critical distance from the center; at which the light-cone becomes tangent to the plane (hypersurface) of simultaneity of the central light-cone. And beyond this critical circle,( see the circles in the first figure of this topic) the light-cone straddle the plane. This means that a light ray can go below the plane , as shown above.

The shocking implication of the mentioned phenomena is that, this makes time travel possible! Imagine that , in the above figure, your galaxy was once at point p. But now you are at q. In order to visit p again in the timeline , you first accelerate and aim at the outside of the critical circle for the light rays to be able to go below the plane. Then when you passed the critical circle, you go downward for a while, enough below the original hypersurface at p. Next, you aim at the critical circle (below p, of course), and if you passed it, you aim at p, from the past region of p. Thus you came back to your past by also travelling through your future! This makes defining the cosmological time  impossible! (This section is a summary of Hawking and Ellis,1973) 

 Time travel is possible.....theoretically

This seems all fine, but if this is a hypothetical universe, how did that help breaking the taboo of time travel in science communities? Well, because Gödel showed that you can "theoretically" make time travel possible, without having to deal with practical issues. Since then there have been lots of hypesthesia for time travel, which requires another article to explain.(along with the paradoxes they brought. See: Grandfather paradox)

Who knows? Maybe one day the humanity will be able to travel through the time. One thing that is certain to me is that, we will need more geniuses to chit chat with each other as below.

Gödel and Einstein