General relativity: Cosmologist discusses Einstein’s theory
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Travelling backwards in time is thought to be a physical impossibility. However, according to astrophysicist Dr Paul Sutter of the Ohio State University, scientists have conceived of universes where such may be not only possible, but “easy” — and all it takes is a rotating cosmos. This idea is found in the work undertaken by Austria–Hungary born researcher Professor Kurt Gödel back in 1949.
Prof Gödel — who is commonly considered to be one of the most significant logicians of all time — was a neighbour of the noted physicist Albert Einstein when both worked at the Institute for Advanced Study in Princeton, New Jersey.
The pair were known to take walks together between the institute, although the nature of their conversations is said to have been a mystery to the other members of the centre.
However, late in his life — according to the German economist Oskar Morgenstern — Prof Einstein said that his “own work no longer meant much, that he came to the Institute merely […] to have the privilege of walking home with Gödel.”
Regardless of what the pair actually talked about, what is known is that Prof Gödel developed an interest in physics during his time at the Institute, and in particular in his friend Einstein’s work on general relativity.
The theory of general relativity explains how objects with mass distort the fabric of space and time, an effect that we experience as gravity.
Dr Sutter told Universe Today: “Gödel was curious as to whether relativity could allow time travel into the past.
“Einstein’s theory purported to be an ultimate framework for the nature of space and time, and as far as we know, time travel into the past is forbidden.
“So, Gödel reckoned that general relativity should automatically disallow it.”
What the logician determined, however, is that general relativity can be compatible with time travel into the past — just as long as the universe has been set in motion.
This very particular solution to Einstein’s field equations — which is known at the Gödel metric, or the “Gödel universe” — involves a rotating universe and a special value for the cosmological constant.
In Prof Einstein’s work, the constant was introduced to counterbalance the effect of gravity and achieve a static universe, as per the contemporary understanding of the cosmos.
While Einstein set the cosmological constant to zero, the rotation of Gödel’s solution requires a negative value to resist the resulting centrifugal force and keep the universe static
The Gödel universe has some very unusual properties — in particular, how particles in spacetime can follow what is known as a “closed timelike curve”.
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Dr Sutter explained: “Gödel found that if you follow a particular path in this rotating universe, you can end up in your own past.
“You would have to travel incredibly far — billions of light years — to do it, but it can be done.
“As you travel, you would get caught up in the rotation of the universe. That isn’t just a rotation of the stuff in the cosmos, but of both space and time themselves.
“In essence, the rotation of the universe would so strongly alter your potential paths forward that those paths loop back around to where you started.
“You would set off on your journey and never travel faster than the speed of light, and you would find yourself back where you started — but in your own past.”
There is, however, no need to start worrying about slipping down a closed timelike curve and setting off mind-boggling temporal paradoxes and breaking the web of time.
This is because all cosmological observations by researchers to date suggest that our universe is not rotating.
Dr Sutter concluded: “We are protected from Gödel’s problem of backwards time travel — but it remains to this day a mystery why general relativity is okay with this seemingly impossible phenomenon.
“Gödel used the example of the rotating universe to argue that general relativity is incomplete — and he may yet be right.”
The Gödel metric was first described in the journal Reviews of Modern Physics.
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