Now Time Travel Can Be Paradox-Free, Thanks To Math

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It’s a worry of time travelers everywhere. What if they go back in time and do something terrible, like prevent their parents from meeting or killing their grandfather? Such a time-traveling “oops” could prevent them from ever being born. Therefore, they would have never existed to travel back in time in the first place.

This “grandfather paradox” has had want-to-be time travelers scratching their heads ever since we dreamed of traveling back in time. Does this mean that time travel is not possible? Does it mean that each decision we make creates several different branching worlds? This conundrum may have been cleared up (at least mathematically) by fourth-year undergraduate student Germain Tobar of the University of Queensland.

Time Travel and Philosophy

One way to solve the grandfather paradox? Time travel isn’t possible at all.

This is probably the easiest, yet least fulfilling, of potential solutions. Time travel isn’t possible, let’s wash our hands of any possibility and forget about it. And this very well may be the case.

However, in general relativity, things called closed time-like curves can exist, and are a way to solve general field equations. It’s like stepping on a train, taking a wonderful trip through the mountains, and returning to the same spot you left off, both in space and in time. That means the moment where you step off the train is both in the past and future of when you got on the train in the first place. In a closed time-like curve, an object returns to the same place and time that it was in the past, completing a loop. It’s unclear if closed time-like curves exist in our universe, but if they do, mathematically, they would allow for time travel.

Then there’s option two. In this quantum mechanical model, each choice opens up another universe. If time travelers changed something in the past, they would enter another parallel universe. The original timeline would still exist, one among many branching worlds. In such a model, it might be very hard for time travelers to return to the universe they came from.

Finally – time travel is possible, but time travelers can only do certain things. A time traveler who went back in time, for example, could not kill Hitler, no matter what he tried. This raises all sorts of philosophical problems – does the time traveler still have free will? It’s difficult to say time travel is possible while simultaneously destroying freedom of choice.

Paradox-Free Time Travel While Preserving Freedom of Choice

That’s where young physicist Germain Tobar steps in.

Under the supervision of physicist Dr. Fabio Costa, Tobar came up with a way to mathematically preserve freedom of choice, while allowing for paradox-free time travel.

For example, let’s imagine there is a scientist in a laboratory with a time-traveling coin. The coin enters the laboratory at some point in the past as “heads” and leaves at some point in the future as “tails”. Tobar’s model fixes the boundary conditions – the point in time where the coin enters and leaves the laboratory – as always heads and tails. Then, his model allows the state of the coin to change when it is in the laboratory. Since the initial and final state of the coin is fixed, a paradox is avoided. However, anything can happen to the coin when it is in the laboratory. “For example,” says Tobar, “she [the scientist] can decide to always flip the coin, or always prepare heads regardless of what she got… it can flip, it can hit other coins, and so on.” But no matter what she did or how hard she tried, each time the coin time-travels through her lab, it will always leave as “tails”.

Let’s take another pertinent example. “Say you traveled in time, in an attempt to stop COVID-19’s patient zero from being exposed to the virus,” Costa says. “However if you stopped that individual from becoming infected – that would eliminate the motivation for you to go back and stop the pandemic in the first place.”

In Tobar’s model, no matter what you did, the virus would still escape somehow. “You might try and stop patient zero from becoming infected, but in doing so you would catch the virus and become patient zero, or someone else would,” says Tobar. “No matter what you did, the salient events would just recalibrate around you.”

That means that you have complete freedom of choice, but no matter how hard you tried, you could not stop COVID-19 from escaping.

But this is good news for Marty McFly in Back to the Future. Nothing he did could prevent his parents from falling in love and getting married, and eventually, allowing Marty to be born. Other things might change, like how they met, or what his father ate for breakfast that morning. But nothing could change their eventual meeting.

This doesn’t necessarily rule out other models of time travel, for example, a quantum mechanical one. “Some of the quantum approaches would indeed invoke the existence of multiple universes, which interact through the time machine, possibly creating alternate timelines,” says Tobar. Instead, Tobar and Costa’s model is classical and shows that if only one universe exists, it is possible to allow for paradox-free time travel.

This work has other implications as well, including the unification of quantum theory with general relativity. “One of the main issues is that, in such a theory, time seems to disappear, making the traditional, temporal view of dynamics unsuitable,” says Tobar. “Our work presents a different way to look at physical laws, which could find applications in theories of quantum gravity.”

Could closed time-like curves, and potentially time machines, exist in our Universe?

“Proposals so far involve exotic matter (with negative or infinite energy), and we don’t know if such matter exists in our universe,” says Tobar. “An interesting consequence is that the CTCs [closed time-like curves] would only exist after a certain point in time, which means it would not be possible to time travel to before the first time machine was created. This would explain why we haven’t seen any time traveler from the future yet.”

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