Time travel is really out of reach

July 1949: When Kurt Gödel proved that time travel is possible

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Be it to see the deceased in the past or to take a trip into the future - the question of whether time travel is possible has preoccupied people for millennia. Tinkering with the transience of the world is not just the stuff that science fiction films are made of. Science has also been dealing with it for several decades. A fascinating example is a work by the mathematician, logician and philosopher Kurt Gödel, which is celebrating its 70th birthday these days and in whose honor a conference took place at the University of Vienna last week.

A 70th birthday was also the reason why Gödel's essay with the somewhat cumbersome title "An Example of a New Type of Cosmological Solutions of Einstein's Field Equations of Gravitation" was written at all. Shortly after Gödel emigrated from Vienna to the USA in 1940, he met Albert Einstein, 27 years his senior. Every day they walked together to the Institute for Advanced Study at Princeton, where they both worked, and then back home. The friendship between the two was so close that Einstein is even said to have said once that he would only come to the institute "to have the privilege of being able to walk home with Godel". In turn, the physicist Freeman Dyson reported about Godel that he was "the only one at the institute who was on an equal footing with Einstein".

A new universe

Albert Einstein celebrated his 70th birthday in 1949. A whole series of scientific papers was dedicated to him on this occasion. Gödel also insisted on writing an essay on the subject. The four-page paper appeared in the journal "Reviews of Modern Physics" in July 1949 and contained nothing less than a new universe.

A new universe? In 1915 Einstein presented the field equations of his general theory of relativity. These equations allow multiple mathematical solutions - in theory, each of them is a different universe.

"Before Gödel, everyone only found solutions that describe slowly expanding universes," says John D. Barrow, theoretical physicist at Cambridge University, one of the speakers at the Gödel conference last week in Vienna. "But Godel's solution was completely different: it doesn't expand, but it rotates." The most unusual thing about the Godel universe, however, was that it included the possibility of time travel.

No spaceship needed

A journey through time in the Gödelian sense should not be imagined as a rapid journey with a sleek spaceship. There is also no need to jump into a black hole or the like. Mathematically speaking, time travel in the Godel universe is a closed line of movement: if you draw the movement of a body on a space-time diagram, you get a closed line. Thus, in a sense, the future merges into the past, and strictly speaking, the future can no longer be clearly distinguished from the past.

Barrow compares the conventional conception of time to a march of soldiers, with one person walking behind the next. Everyone can say who is in front of him and who is behind him. In the Godel universe, however, people move in a closed circle. Then it is no longer possible to say who is going ahead and who is afterwards.

So how can you imagine a journey through time in the Godel universe? "It's not like science fiction that you can go back in time, change it and create a contradiction, for example by murdering yourself as a child," says Barrow. Gödel's time travel is less about a movement than about a story that is inherently free of contradictions. "There is only one past and you cannot change it, you can only be part of it."

The grip on the rifle

How this could work is made clear by Barrow with the following example: Imagine being able to go back to your own past. You see your own mother holding you as a baby. You pick up a rifle with the intention of shooting yourself as a baby. As you try to pull the trigger, you feel a pain in your shoulder that comes from an injury sustained as a very small child. The trigger is pulled uncontrollably, a shot is fired but does not hit. The mother is frightened. She drops the baby and it hurts its shoulder.

Einstein did not think that such time travel through closed lines of motion would be possible according to his general theory of relativity, but to everyone's surprise Gödel was able to show that this is at least theoretically possible. Today we know that there is a high probability that we do not live in a Godel universe. From observations of distant objects we can conclude that our universe is expanding at an accelerated rate - the Godel universe, however, is not expanding.

Bizarre properties

Furthermore, Gödel's solution provides that the universe rotates. But even this prediction contradicts astronomical observations. Are Godel's theories long out of date and completely void for us? Not at all. "Godel made something visible that was not expected," says Barrow. "There can be properties of the universe that are not locally evident, but extremely bizarre globally." In other words: If you just look at how the universe behaves in our immediate vicinity, that does not mean that it cannot have completely exotic properties globally.

"Godel showed that there is no such thing as cosmic time," says Palle Yourgrau, professor of philosophy at Brandeis University in Massachusetts, who has written several books on Godel's work. "You should never underestimate Godel. Everything he did was incredibly profound." Although Godel had only studied physics for three years before turning to mathematics, he was well informed. "People thought that Einstein taught Gödel physics. But that was not the case, they discussed physical questions on an equal footing."

Fatal contradictions

How extensively Gödel dealt with all conceivable topics was also shown in 1947 during his preparations for the naturalization procedure in the USA. For months he meticulously studied the history of the country and the US Constitution. The logician was horrified to see inconsistencies in the central legal document of the USA. According to Gödel, it is legally possible to establish a dictatorship in the USA.

His friends Albert Einstein and Oskar Morgenstern urgently advised Gödel not to mention this in order not to endanger his naturalization. The two accompanied him to the hearing. As Morgenstern later recalled, everything was going very well until the judge remarked that a regime like the one in Nazi Germany would be impossible in the USA - whereupon Gödel exclaimed: "Yes, I can prove it!" The judge, who is familiar with Einstein, is said to have replied to Morgenstern's relief: "Oh God, let's leave that." The procedure was decided positively. (Tanja Traxler, David Rennert, July 31, 2019)

Knowledge: The universe according to Kurt Gödel

In 1949 the mathematician and logician Kurt Gödel found a solution to the general theory of relativity, which describes a universe in which time travel is possible. Because the so-called Godel universe provides closed lines of movement.

The conference "Does Future lie in the Past?" for the 70th anniversary of Gödel's groundbreaking work took place last week at the University of Vienna. It was organized by the Kurt Gödel Society, supported by the University of Vienna, the Institute for Discrete Mathematics and Geometry of the TU Vienna, the Austrian Academy of Sciences, the research platform "Testing quantum and gravity interface with single photons" of the university Vienna, the Vienna Center for Logic and Algorithms of the TU Wien, the Department Vienna Circle of the University of Vienna and the Vienna Circle Society.

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