# Time Travel, Without the Pesky Paradoxes

Time travel is a staple of science fiction, and not without reason. Who wouldn’t want to go back in time to explore history, or save the world from catastrophe. Time travel has also been deeply studied within the context of theoretical physics because it tests the limits of our scientific theories. If time travel is possible, it has implications for everything from the origin of the universe to the existence of free will. One of the central problems of time travel theory is that it gives rise to logical paradoxes. But a couple of researchers think they have solved the pesky paradox problem.

Before getting into the details of their work, let’s talk about what time travel means in the context of theoretical physics. In general relativity, there is no great cosmic clock representing the time or age of the cosmos. Time is not absolute but relative. The rate at which time flows for an object depends on how it is moving relative to another object. Each of us experiences time in a unique way. This means the position of an object is defined by its position both in space and time. This is why time is sometimes referred to as the fourth dimension, and while you can’t take the idea too literally, a four-dimensional space decent way to visualize spacetime.

As you move through space, you also move through time. In physics, this means we can draw a line through spacetime that represents your path or motion through space and time. This is known as your timelike curve. Your entire life can be traced as a single line from your glorious birth to your inevitable demise. This is pretty simple in special relativity, but in general relativity, things get complicated. In relativity, gravity is caused by the warping of space and time. As John Wheeler once put it: Matter tells spacetime how to curve, and spacetime tells matter how to move. Because of gravity, your timelike curve can be bent and twisted.

So what if you could bend your timelike curve so that it looped back on itself. This would be a closed timelike curve (CTC). It would mean that no matter what, your path and your life choices would inevitably return you to the place and time of your birth. Congratulations, you have somehow traveled back in time. In theoretical physics, if time travel is possible, it must be possible to create a CTC.

It turns out that general relativity allows for closed timelike curves to exist. In 1949 Kurt Gödel devised a rotating universe that has CTCs and is perfectly allowed by relativity. Even though we don’t live in Gödel’s universe, later work showed how CTCs could be created within our universe. There are aspects of particle physics and quantum theory that probably make time travel impossible. Still, as far as general relativity goes, time machines are possible.

So let’s assume for a moment that we can make a time machine. We now have a paradox problem. Suppose I travel back to 1955 and prevent my Dad from asking Mom to go to the Enchantment Under the Sea dance. They don’t have their first kiss, fall in love, or get married, which means I never get born. But if I’m never born, then I couldn’t break up my parents. Does that mean I was born? But then…oh dear. Back to the Future is just one example of the grandfather paradox. Since time travel allows you to disrupt the cause of your journey, there is no consistent timeline you can follow.

One solution to this paradox is to assume that a chain of events will always prevent a paradox. Science fiction author Larry Niven called this the law of conservation of history, but in physics, it’s known as the Novikov self-consistency principle, after Russian physicist Igor Dmitriyevich Novikov. He demonstrated that you can always define a paradox-free solution to any situation. A strange result of this principle is that you can, in some ways, have a self-causing effect. For example, you can go back in time to introduce your parents to each other. If you didn’t travel to the past, you would have never been born, but you did, so here you are.

While the self-consistency principle does solve the paradox, many people don’t like it because it means you can’t change your mind after the past is written in stone. You were born, so you absolutely must travel back in time to introduce your parents. You cannot change your mind and decide not to go back. Your future is as written in stone as the past. So much for free will.

But free will is an illusion, right? After all, our brains and bodies are made of the same stuff as planets and stars and follow the same physical laws. We have no more free will than a tossed ball. The story of our life isn’t a diary we write every day. It is a book printed and bound by the physical laws of the cosmos long before you were born. While that may be true, it seems odd that time travel would prevent even the illusion of choice. Given human nature, surely some time traveler would try to create a paradox to see what happens.

Here enters this new paper. Rather than looking at the physics of time travel, it explores the mathematical consistency of it. The authors examine whether you can have a closed timelike curve and still have complex dynamics. Put another way, can you travel back in time and yet have at least the illusion of free will. The authors found that you can, but in a surprising way.

They found that CTCs allow for complex systems because the constraint of a time loop doesn’t uniquely define a single path. Instead, there are multiple ways to form the CTC. So a time traveler would always have options to choose. If you were born because “future you” set your parents up on a date, then that will happen, but you are free to choose other things about your life. Maybe you travel back in time in your 50s rather than your 20s. Perhaps you try to break them up and fail. All sorts of things could happen. The point is you are both bound to close the loop and free to make other choices. If time travel exists, it doesn’t kill free will.

Of course, nothing in this work proves that time travel is possible, only that it can be dynamically consistent. If you do ever find yourself traveling to the past, you can rest assured that the story of your life is not yet finished.

Reference: Germain Tobar and Fabio Costa. “Reversible dynamics with closed time-like curves and freedom of choice.” Classical and Quantum Gravity 37.20 (2020): 205011