Do Closed Timelike Curves Exist or Not?

From the lecture series: What Einstein Got Wrong

By Dan Hooper, Ph.D., The University of Chicago

The ‘closed timelike curve’ concept, introduced by Kurt Gödel, had highlighted logical inconsistencies with the concept of time, as we know it. These potential problems regarding time were further explored in the 1960s, when interest in general relativity was growing among scientists. Let’s first take a look at some of these potential problems, and then try to understand when a solution might be discovered.

Illustration of a wormhole or time vortex.
Artist impression of a closed spacetime. A closed timelike curve is essentially a world line of an object, which is closed in spacetime, allowing for the object to return to its starting point. (Image: Aliaksey Dobrolinski/Shutterstock)

Rotating Black Holes

In the 1960s, solutions to the field equations were found that describe not only stationary black holes, but also black holes that are rotating or spinning. To the surprise of many, these solutions appear to show that the space and time immediately surrounding a rotating black hole can also contain closed timelike curves.

Like in Gödel’s universe, the existence of rotating black holes seems to be logically problematic for general relativity, and for time itself.

Learn more about Einstein’s rejection of black holes.


Schwarzschild wormhole's embedding diagram.
Mathematical representation of a Schwarzschild wormhole, also known as a Einstein–Rosen bridge. Wormholes are a solution for the field equations of general relativity, allowing for the existence of closed timelike curves. (image: AllenMcC/CC BY-SA 3.0)

A wormhole is something like a portal—a portal that connects two points in space to each other. By travelling through a wormhole, one could—in principle—travel directly from one place to another.

It might not seem obvious, but it turns out that in order for something, like a wormhole, to be able to instantly transport something across space, it must also be able to function as a time machine. In fact, anything that is capable of moving from one place to another at a speed faster than the speed of light must also allow one to travel backward in time.

So, the existence of wormholes—or of anything else that enables one to travel faster than light—also implies the existence of closed timelike curves.

Learn more about the problems with time travel.

Uncertainty about Closed Timelike Curves

In recent decades, different physicists have expressed a wide range of views about the issues involved with closed timelike curves and time travel. Some work has been done during this time which seems to show that some of the logical paradoxes associated with time travel can be avoided, or circumvented. Other work has shown that some of the most problematic kinds of closed timelike curves seem unlikely to really exist.

This is a transcript from the video series What Einstein Got Wrong. Watch it now, on The Great Courses Plus.

The key point is that there’s still no clear or complete resolution to these issues. This is why Einstein’s rejection of Gödel’s objections seem that much more premature, because the same questions continue to linger till date.

Learn more about cosmology and the cosmological constant.

Stephen Hawking’s Chronology Protection Conjecture

In 1992, Stephen Hawking wrote a famous paper in which he took a different kind of approach to this issue. In his paper, Hawking didn’t try to argue how or why closed timelike curves don’t exist. Instead, Hawking simply declared that there must be something about our universe that makes it impossible for closed timelike curves to exist. Hawking called this his ‘chronology protection conjecture’.

What Hawking had in mind when he formulated his conjecture were the effects of what is known as quantum gravity. Hawking was basically suggesting that perhaps there is something about quantum gravity—something that we don’t know about yet—that makes it impossible for closed timelike curves to exist.

Stephen Hawking in 1974 during his induction in the Royal Society.
Stephen Hawking during his election as a member of the Royal Society in 1974. Hawking’s chronology protection conjecture hypothesis took a different approach to closed timelike curves. (Image: NASA/Public Domain)

Here we need to pause a moment and acknowledge that we don’t understand how quantum mechanics and the general theory of relativity work together or influence each other.

Maybe it comes down to string theory or something along those lines. Or maybe quantum gravity will be described by something else entirely. At this point in time, it’s wise to remain open-minded about how quantum mechanics and general relativity will ultimately be found to connect and unify with one another.

For most of the phenomena that we can test in our laboratories, or explore with our telescopes, the quantum effects of gravity aren’t very important, or even observable. This is one of the main reasons why it’s been so hard for us to learn more about quantum gravity and how it might work.

In his paper, Hawking didn’t claim to offer a well-defined solution to this problem. Instead, he essentially hypothesized that whatever the solution is, it will likely become apparent once we begin to understand the quantum nature of gravity. The fact is that we don’t know whether or not he is right.

Until we are able to understand the quantum nature of gravity, and how quantum mechanics and the general theory of relativity work together, the uncertainty about closed timelike curves will continue to persist. Having said that, it’s important that we continue to look for an explanation, and not dismiss it completely.

Einstein’s towering contribution to the scientific community is unquestionable, but even the great Einstein made some mistakes from time to time. Some of these mistakes were really just points of confusion that Einstein ultimately ended up correcting—either on his own or with input from others. Other mistakes that Einstein made were corrected when new evidence came to light.

When it comes to the issue of time, Einstein was only wrong in that he was so quick to dismiss the physical implications of Gödel’s result. It may turn out that one day we will understand why closed timelike curves don’t exist, and that could vindicate Einstein and the position that he took on this issue. As of now, no one knows how this question will play out.

Common Questions about Closed Timelike Curves

Q: Are closed timelike curves possible?

If a path through space and time can be created, which makes it possible for someone to be present for some event, and then to travel through space only to later encounter the same event again, then such a path would be called a closed timelike curve. A number of scientists have worked on this, but no clear answer has presented itself yet. We do not know for sure if closed timelike curves exist or not in our universe.

Q: What is the difference between rotating and non-rotating black holes?

A non-rotating, static or stationary black hole is theoretical in nature and the chances of such black holes actually existing in the cosmos are very slim. On the other hand, rotating black holes are expected to exist and cosmological solutions to field equations show that space and time immediately surrounding a rotating black hole can also contain closed timelike curves.

Q: Why is quantum gravity important?

A thorough understanding of the quantum nature of gravity can provide solutions for a number of scientific questions, including closed timelike curves. Stephen Hawking had hypothesized in his chronology protection conjecture that perhaps there is something about quantum gravity that makes it impossible for closed timelike curves to exist.

Q: Who discovered quantum gravity?

We do not yet know how quantum mechanics and the general theory of relativity work together. In 1935, Matvei Bronstein had tried to find an answer, which came to be known as the quantum theory of gravity. A deeper understanding of quantum gravity might also inform our knowledge of closed timelike curves.

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