*Originally published in the 2*^{nd }*issue of The Warwick Engineer.*

Imagine this: you somehow build a time machine and go back in time to murder your grandfather before he meets your grandmother. As a result, you will have never existed. However, if you were never born, you would not have been able to engineer a time machine to go back and kill your grandfather, which means that you would be born, and so on.

Originally proposed by French journalist Rene Barjavel in his novel “*Le Voyageur Imprudent” *(1993), this paradox has been a mainstay of philosophy, physics and the entire *Back to The Future* trilogy. However, this paradox is not only restricted to the the above described scenario, in fact, it regards the inconsistency presented by the fact that if If time travel were possible then a time traveller could both have and lack a given ability on a given occasion. Even more broadly, it concerns any action that annihilates the cause or means of traveling back in time.

Therefore, a good question to ask oneself would be: is then time travel feasible? That is to say, is it possible to time travel without incurring into paradoxes?

In order to address this question, we first ought to acknowledge the fact that as long as travelling forward in time is concerned, we are all experiencing it. Not only that but we could fast forward by being in a spaceship that travels at high speed and then return to Earth to find everyone much older. So the question, can be narrowed down to: is it possible to travel back in time without incurring into paradoxes?

This is where things start to get interesting and where speculations start to emerge. As a matter of fact, according to Einstein’s general theory of relativity, it could be possible to warp the space-time continuum to an extent where space-time is bended back to itself via an extremely powerful gravitational field. In so doing, it would be possible to create a closed-timelike-curve or CTC.

**Closed Timelike Curves**

** **Loosely speaking, a CTC is a solution to the general filed equations of Einstein’s general theory of relativity generated by applying a method called frame dragging. An example of such an object, would be the Van Stockum’s 1937 solution, which represents an infinitely long cylinder made of rigid and rapidly rotating dust. The rotating dust particles would then drag inertial frames so strongly to induce space-time to bend back to itself; thus generating a closed-timelike-curve.

Nevertheless, physicists like Stephen Hawking seem to abhor CTCs. The reason being that if an object were to travel thought a closed-timelike-curve, it would inevitably generate inconsistencies within casual relationships.

In a model presented by David Deutsch in 1991 nonetheless, it would be possible to avoid those paradoxes if the objects travelling thought a CTC are considered at a quantum scale. The rationale behind it is fairly straightforward: at a quantum level, a given fundamental particle does not follow strict deterministic principles, it rather obeys by the low of probability. Consequently, it is normal to think about a particle as having a certain probability of being in state A and another of being in state B.

**Deutch’s Model and The Grandfather’s Paradox**

In a recent paper published by Martin Ringbauer et al. in *Nature Communications* in 2014, it was investigated how Deutch’s model would deal with the grandfather’s paradox. Their findings can be summarized in the following way:

Instead of having a human travelling back in time via a CTC to prevent his or her own birth by killing their grandfather, suppose that a fundamental particle traverses a CTC to flip a switch that would turn either on or off the machine which generated it. In so doing, the particle itself has a given probability of having been emitted by the machine or not. This implies that the existence of the the particle is not deterministic but probabilistic.

We have seen before that the problem with the grandfather’s paradox is that the person travelling back in time would not posses the same properties once they came back from the journey. However, a particle generated by the machine with a probability of ½ would enter the CTC and come out of it with a ½ probability of turning off the machine and therefore being born with *½ *chance of traveling back to flip the switch. Drawing the parallel with the human case, the time traveler would be born with a ½ probability of murdering their grandfather giving their grandfather a ½ probability of being killed by them. Thus escaping the paradox by giving a solution in probabilistic terms which would not create scenarios where cause and effect break down.

Time travel is still a topic overflowing with speculations. Howbeit, given the recent development, its feasibility is far from being a subject to leave to science fiction lovers. Further, the implications arising form the studying of theoretical existence of CTCs have profound practical implications in quantum computing. In fact, as shown by S.Aaronson and J. Watrous in 2008, if closed-timelike-curves were to exists, quantum and classical computing would be equivalent and thus have the same power of complexity class. This would imply that quantum computers may no longer represent the next generation of supercomputers.

In spite of this, studying time travel and the associated concept of CTCs, could shed new light on the underlying principles which govern our universe and ultimately our lives.