Time travel has been a subject of countless human narratives, ranging from ancient Hindu myths to modern science fiction such as the famous H.G. Well’s *The Time Machine*. While many fictional accounts assume the possibility of time travel, they often also reveal the paradoxical nature of the idea itself.

For example, many fictional stories share a common narrative about the way present changes once someone has travelled back in time. Let us take someone who has travelled back in time and decided to kill their grandfather before he had any kids – for one reason or another. If the time traveler succeeded, then who is one of their parents, namely the one who was their grandfather’s child? How come is the time traveler alive, if his prior line of descendance has been cut?

The paradox is known by the name of the Grandfather paradox. This and other unsolved logical puzzles such as the Unproved theorem paradox – where a mathematician reads a nice proof of a theorem, goes back in time and tells it to the person who wrote the book – seem to disprove the very logical possibility of time travel.

However, it is common knowledge among physicists that laws of general relativity do allow the possibility of time travel. The idea was formulated in 1948 by Kurt Gödel, the logician and mathematician mostly known for his Incompleteness theorems. Gödel discovered that if spacetime is modelled as a certain type of 4-dimensional geometry (including time as the fourth dimension), the unique pathway travelled by a material particle might close up and form a loop. The loop was given a name of *closed timelike curve* (CTC) and it implies a theoretical possibility for some particals to go back in time.

It is important to note that CTCs emerge in some accounts of general relativity and not in others. In other words, the existance of CTCs is a mathematical possibility, but as of now there is no proof of their physical existence, which according to some scholars will be ruled out by future developments in quantum gravity.

Despite that, CTCs do emerge in a variety of contexts in physics, and a British physicist David Deutsch has created a theory of CTCs where consistency conditions are layed out. Deutsch has managed to describe how particles would act if they were travelling in closed timelike curves.

Recently Deutsch’s theory has been subject to some criticisms, mostly because it invokes the many-worlds interpretation of quantum mechanics in order to avoid inconsistencies such as the Gradfather and the Unproved theorem paradoxes.

Seth Lloyd, a self-described “quantum mechanicist” at at Massachusetts Institute of Technology, and his colleagues presented a modified idea of time travel where no traveller can alter the past. In Deutsch’s model, the quantum state travelling across CTC must retain all of its features in the consistency with the rest of the non-closed spacetime. Lloyd’s model differs in that a system exiting a CTC after safely travelling back in time must no longer be consistent with the world of the future but rather with the world of the past where it arrived. However, the system itself either reaches the destination in exactly the same state or it does not go anywhere at all.

What this amounts to is that no time traveller will be able to kill their grandfather no matter how hard they try, simply due to the consistency restraints on the closed timelike curves.

The idea is based on an already existing notion of quantum teleportation by means of which qubits can be transmitted from the sender to the receiver faster than the speed of light if the two are entangled. Lloyd’s time travel is in a sense an entangled communication channel between the future and the past. The difference is that in Lloyd’s and his colleagues’ account, is that the teleported state must be allowed to be *post-selected*. Post-selection is a method in computation where only certain results are accepted, and thus it ensures that no inconsistencies take place.

The question remains, however, whether quantum physics allows post-selected computations. It is a hot topic in today’s quantum computing because if post-selection was possible, then quantum computers would be even more powerful than it is usually thought, allowing only those computations that yield post-selected results and thus saving immeasurable amounts of power.

**Reference:**

*Is Time Travel Possible? Testing the ‘Grandfather Paradox’, *Seth Lloyd at Santa Fe Institute, YouTube link.