Wormholes and time travel

Dr Peter Taylor,  a lecturer at the DCU School of Mathematical Sciences and former recipient of the Irish Research Council’s ELEVATE research fellowship, talks to us about the scientific credibility of time travel. His research focuses mainly on classical and quantum aspects of black holes.

Time travel has fascinated humankind long before Marty McFly and his DeLorean graced our movie screens. The ability to influence our own past is, for obvious reasons, very appealing, not least to Science Fiction writers. It also leads to an infinite cascade of troubling contradictions. But is there any scientific credibility to the idea?

It seems that this begs a more fundamental question, one which Albert Einstein also pondered while working as a clerk in a Swiss patent office in the early 20th century, that is, what is time? Taking the pragmatic point-of-view, we might say that time is simply one of four numbers used to describe the location of any event, the other three being the position in space of the event. What Einstein realized is that there is no unique way to identify the time and position of an event, that what one perceives as the time and position is dependent on the motion of that observer. Space and time are in fact conflated in a single 4-dimensional spacetime and consequently, time itself is relative. This is famously captured in the Twin Paradox: Imagine newborn identical twins, one of which makes a return journey to the next nearest star system at a speed of about 80% of the speed of light and the other remains on earth. When the twin who made the long journey returns, she is 6 years old, while the twin who remained on earth is 10 years old! So it seems Einstein discovered the secret to youth: chuck your anti-wrinkle cream and invest in a highspeed rocket! An even more extreme version of this paradox features in Christopher Nolan’s recent blockbuster Interstellar. But slowing down time is one thing, this is not what we usually mean by time travel. Let’s imagine that the twin who remained on earth became embittered later in life that her sibling born on the same day is now several years younger. Could she travel on a high-speed rocket ship and go back to an event before her twin left the earth and change her history? What is needed is a rocket-ship that travels faster than the speed of light, that’s quite a bit faster than the 88mph threshold of the DeLorean! However, Einstein showed that an infinite amount of power is needed to accelerate the rocket beyond the speed of light; a physical impossibility.

Depending on your perspective, you may be relieved or disappointed that our familiar notions of causality are preserved, at least in the context of Einstein’s Special Theory of Relativity. But this is not the end of the story. Ten years after publishing his Special Theory, Einstein figured out how to incorporate gravity into this picture, which is known as Einstein’s General Theory of Relativity. In this picture, the spacetime that represents the 4-dimensional interconnection of space and time is curved. When gravity is very weak, the geometry of the spacetime is essentially flat (so for example the sum of angles in a triangle add up to 180 degrees, parallel lines don’t intersect etc.). However, when objects are very massive, and gravitational effects are very strong, the geometry of spacetime becomes curved or distorted, so for example, the angles in a triangle no longer add up to 180 degrees. Can an object distort the spacetime in such a way as to allow time travel? One way to view this is to recall from the Twin Paradox that time travel is closely related to traveling faster than the speed of light. Or put another way, if we start from a point A, can we arrive at point B before a light signal can? Imagine a flat A4 page with two points A and B marked at opposite ends of the page. If we now bend the page over into a C-shape and connect A and B by a short bridge, there is two different ways to get between the points: the shortcut through the bridge or the long way around the bend. If we imagine a light signal starting from A and going the long way around, we could arrive at B before the light ray by going through the bridge. This type of shortcut in spacetime is known as a wormhole and if the ends of the wormhole are moving relative to each other in a certain way, it is possible to arrive back at point A before you left! That is to say it is possible to time travel through a wormhole.

But do the equations of Einstein’s theory allow spacetimes with wormholes? Interestingly, they do. There are many perfectly legitimate wormhole solutions. So why haven’t we been inundated with time traveling tourists from the future? Kip Thorne, the scientific consultant and executive producer for Interstellar and one of the world’s leading relativists, showed that the kind of matter needed to sustain a wormhole curves geometry in the opposite way to ordinary matter. Such exotic matter possesses negative mass and negative energy density and there is no known classical matter with such properties. Again it seems the universe has shut the door to time travel in our face. But yet again, things are not that simple. So far, we have completely ignored the other great Intellectual Revolution of the 20th century: Quantum Mechanics. And in Quantum Theory, one is allowed to have negative energy densities locally in spacetime so long as, on average, the energy density remains positive. In fact, it is possible to observe such negative energy densities in the lab, an example being the Casimir effect. The experiment consists of two parallel conductive plates a very short distance apart, what one measures is a small force pushing the plates together. The force is due to lower energy density of the quantum vacuum fluctuations between the plates than the region outside. Since far from the plates we just have empty space and therefore the energy density is zero, the region between the plates must be negative.

So where does that leave time travel? We know that spacetime is curved and we know that we can use quantum fields to curve it in the way needed to produce a wormhole. The essential ingredients appear to be there for time travel to be possible. However, since quantum effects are typically only important on very small scales, it is unlikely that we would be able to produce a wormhole large enough for a rocket-ship to traverse. But since we don’t yet fully understand how gravity and quantum theory interact, we cannot rule out the possibility just yet. Moreover, if one takes higher-dimensional theories such as string theory and alternative theories of gravity seriously, then all bets are off and we ought to take wormholes and time travel seriously too. On the other hand, perhaps Stephen Hawking’s pragmatic perspective will satisfy most readers: “There is also strong experimental evidence in favor of the conjecture (that the laws of physics prevent time travel) from the fact that we have not been invaded by hordes of tourists from the future.”

In conclusion, time travel remains theoretically plausible but improbable. The upside is that we most likely will never have to confront the contradictions and paradoxes that time travel invokes. The downside is you will never get back the 10 minutes you spent reading this blog!