There and
Back Again

29 April 2013

Still from The Time Machine, MGM, 1960. MGM Studios
Still from The Time Machine, MGM, 1960.

When someone mentions time machines, you might think of fantastical machines such as Dr. Who’s TARDIS or the DeLorean in Back to the Future, but several physicists have made a serious study of time machines. Most of this work focuses on “what if” scenarios, which are really about testing the limits of a particular theoretical model, rather than actually engineering a device that can travel to the past.

The physics of time travel is based upon general relativity. If you’ve ever taken a physics course you might remember that the motion of objects is due to forces acting on them. That is, by pushing or pulling on them—either directly or by gravitational or electric fields—you can cause them to move. This is Newton’s physics, where objects fall because a gravitational force acts upon them.

But Einstein had a different way of looking at things. Through his theory of general relativity, Einstein demonstrated that gravity occurs because matter and energy distort space and time. For example, the mass of the Earth curves space around it. The motion of anything near the Earth, such as a satellite, is changed because of this spatial curvature, as if there were a force of gravity acting on it. Since space and time are connected, the mass of the earth also distorts time, which means a clock on the satellite ticks at a slightly different rate than a clock on the Earth. This effect on a satellite’s time is small (on the order of microseconds) but it is a measurable effect. In fact the satellites of the global positioning system have to take this time distortion into effect in order to work properly. If you’ve ever used a GPS receiver to find your way, you’ve counted on Einstein being right.

Although the mass of the Earth really does distort time, it doesn’t allow you to create a time machine. The clocks in satellites tick at different rates because of their motion around the Earth, but they always still tick forward. It is only the rate of their ticking that changes relative to other clocks on Earth. According to general relativity you can change the rate at which time flows but you can never quite stop time completely, and you can never cause your clocks to tick backwards. If that’s the case, it would seem that a true time machine—one that would let you travel into the past—is impossible.

But general relativity leaves the time-travel door open just a little. In Einstein’s theory time is connected to space, which means time can be bent in ways similar to the way space is bent by the Earth’s mass. So in principle time can be bent into a loop in such a way that it connects with its own past. If you found yourself in such a wibbly-wobbly space-time it would be possible to meet your younger self. Such a loop of time would be an actual time machine. As strange as this seems, there are examples of these time loops—what physicists call closed timelike curves (CTCs)—in general relativity.

One place where CTCs appear is in a solution to Einstein’s gravity equations known as the Godel Universe. This is a general relativistic description of a universe with an inherent rotation to it. If this were an accurate description of our universe then we would observe a rotational effect where distant galaxies are not only moving away from us, but also appearing to rotate about us. We don’t see any cosmic rotation among distant galaxies, so the Godel model doesn’t apply to our universe. While it is an interesting model, it is non-physical.

However CTCs also appear inside a rotating black hole. In general relativity, a rotating mass causes space and time to swirl around it a bit. This effect is known as frame dragging, and it has been observed experimentally by a satellite known as gravity probe b. Near a rotating black hole this effect is larger, but still not large enough to make a time machine. However, once you are within the event horizon of the black hole there are CTCs. This would imply that a time machine might be possible inside a black hole. The problem is that though they might exist inside a black hole, you would have to go into a black hole to travel in time, and once inside the black hole you would be trapped there forever. You couldn’t travel to this cosmic time machine, go into the past, and arrive back on Earth in the 1700s. The other problem is that just because general relativity works outside a black hole doesn’t mean it applies inside a black hole. The matter inside a black hole is so small and dense that quantum mechanics and particle physics comes into play, and we don’t have a solid understanding of quantum gravity. There might be something that prevents CTCs from forming inside a black hole.

Most physicists figure this must be the case, because CTCs create all sorts of problems with traditional physics. For example, CTCs can violate the principle of causality (basically cause and effect). This is popularized by the so-called grandfather paradox. Suppose you have a time machine, travel to the past, and accidentally kill your grandfather before he has a chance to woo your grandmother. By preventing their offspring you have prevented your own existence. But that means you couldn’t have travelled back in time, so you couldn’t have killed your grandfather. But that means you didn’t kill your grandfather, which means you were born, which means you did kill your grandfather, which means…

So what would really happen in this case? The answer is unclear, because such a time loop violates causality. The cause and effect contradict each other. In many science fiction stories this is solved by simply declaring that history rewrites itself, or that there are parallel timelines and such. We’ll look at parallel universes later, but this doesn’t solve the problem. The CTCs that general relativity allows exist in a single universe. Following the physics, we can’t simply invoke parallel universes to solve a tricky problem.

One possible solution is to impose what is called the “self-consistency” principle. This requires that any “time machine” example must be self consistent. So the grandfather paradox mentioned above is forbidden because it is not self-consistent. What would be allowed is for you to go back in time and wound your grandfather. While in the hospital he meets a kindly doctor who turns out to be your future grandmother. So your trip back in time caused your grandparents to meet, which allowed you to be born. Perfectly self consistent.

But this solution doesn’t prevent every problem. Suppose when you were 16 a stranger gives you a book. As you read through the book you find it is a set of instructions for building a time machine. It even includes all the background physics necessary to make it work. You go to college, study physics, and your doctoral dissertation is on the physics of time travel (which you got from the book). This groundbreaking work wins you the Nobel prize, and with the prize money you build a time machine, travel back in time and present your younger self with the book on time travel you once received… from yourself.

This is self consistent, but we seem led to ask where the book came from. Yes, you got it from yourself, but that doesn’t seem to be a satisfying answer. Where did the knowledge of time travel originate? The only answer is that the book is itself a closed timelike curve. It doesn’t have an origin. It just is.

Various theories have been proposed to provide a more satisfying answer to examples such as this. They invoke aspects of quantum mechanics, thermodynamics, entropy, information theory, and on and on down the rabbit hole. None of these models provide a completely satisfying description of time travel that makes sense. This is why most physicists figure time travel is impossible. There isn’t a clear way for it to make physical sense. Stephen Hawking went so far as to propose a chronology protection conjecture, which proposes that all macroscopic CTCs are physically impossible.

Still, there are a few physicists who think time machines are possible. For example, Ron Mallett at the University of Connecticut has found a solution to general relativity that allows for CTCs without an event horizon.1 What Mallett has shown is that light can curve space and time in the same way as mass. By creating a rotating ring of laser light it is possible to distort space and time in a way similar to the way it is distorted by the rotating mass of a black hole, but without the black hole. This, he argues, opens the door to the possibility of creating a time loop you could step into. Critics have pointed out that Mallet’s solution still contains a singularity, so it isn’t a valid physical solution, but Mallett argues the singularity in his solution is an artifact that doesn’t affect the physics.

Even if Mallett is right, his time machine would not allow you to travel anywhere in time. The CTCs could only form in the span of time in which the time machine existed. So you can only go back as far as the moment the time machine was turned on, and you could only travel from the future in which it was still on. In other words, if you wanted to travel 10 years back in time, you’d have to turn on your time machine, keep it running continuously for 10 years, so that you could climb into the machine and arrive when you started. To go back to the future you’d simply have to hang around for another 10 years.

Of course the real question is whether it is possible to distort space and time strongly using only laser light, and whether that distortion could be made into a time machine. Mallet has proposed an experiment to test his model, but so far it hasn’t been performed. Until that happens (and succeeds) time travel is still very hypothetical.

In the end, time will tell.

Tomorrow: Warp Drive. NASA is rumored to be working on it, does that make it so? Find out tomorrow.

  1. Mallett, Ronald L. “The gravitational field of a circulating light beam.” Foundations of Physics 33.9 (2003): 1307-1314. ↩︎