Time travel has always been fascinating to everyone, and it has been tackled in every possible way by science fiction. A concept of Einstein’s general relativity called Closed Timelike Curves (CTCs) offers the possibility to travel backwards in time. Time traveling has raised various paradoxes, such as the grandfather paradox: a man travels back in time and kills his grandfather, preventing his own birth (implying that he could not have traveled back in time after all). A team of researchers has recently proposed a new theory that can resolve the grandfather paradox.

A closed timelike curve is a particular kind of worldline, the unique path of an object through spacetime: in that particular case, the object returns to its starting point, thus allowing a time traveller to interact with their own past.

Seth Lloyd from MIT, along with scientists from the Scuola Normale Superiore in Pisa, Italy,  the University of Pavia in Pavia, Italy, the Tokyo Institute of Technology, and the University of Toronto, explore a new quantum formulation of CTCs. They have published their study in a recent issue of Physical Review Letters.

In their theory, the CTCs behave like ideal, noiseless quantum channels that displace systems in time without affecting the correlations with external systems. To remain self-consistent (in other words, to avoid paradoxes), CTCs are post-selected (they are then called P-CTCs), which also allows them to be simulated experimentally. There is an important difference between this theory and another proposed by David Deutsch: in Deutsch’s theory, to avoid paradoxes, the time traveler is traveling to a past different from his own – here, the time traveler must travel to his own past.

The researchers have also reported the results of an experiment demonstrating their theory’s resolution of the grandfather paradox.

For their demonstration, the grandfather paradox is implemented through a quantum teleportation circuit: a “living” qubit (a unit of quantum information, described by a quantum state in a two-state quantum mechanical system) goes back in time and tries to “kill” itself (i.e. a bit in the state 1 flips to the state 0). They stored two qubits in a single photon: one of them represents the forward-traveling qubit, the other the backward-traveling qubit. The P-CTC starts from two systems prepared in a maximally entangled state, and ends by projecting them into the same state.

The qubits are then entangled, and their states are measured by two probe qubits. A “quantum gun” is later fired at the forward-traveling qubit in order to rotate its polarization (the rotation depends on the gun’s accuracy, which can be varied), and the state of the probe qubits is measured: if the two probe qubits are in the same state, then the quantum gun has failed to flip the polarization and the photon “survives”. If the probe qubits are not in the same state, then the photon has “killed” its past self. It turns out that the time travel occurs only when the quantum gun misfires, i.e. when the photon “survives”.

Although the experiment is not performed, the team shows that P-CTCs also solve another time travel paradox, the unproven theorem paradox:  a time traveller reveals the proof of a theorem to a mathematician, who includes it in the same book from which the traveller has learned it – how did the proof come to existence?

Unfortunately, as CTCs have never been observed (they might even not exist at all), it is impossible to know whether they are described by their theory.



Seth Lloyd, et al. “Closed Timelike Curves via Postselection: Theory and Experimental Test of Consistency.” Physical Review Letters 106, 040403 (2011). DOI:10.1103/PhysRevLett.106.040403