The study of closed timelike curves (CTC’s) provides valuable insight into particles that can loop back on themselves, breaking free of linear time.
“One aspect of general relativity that has long intrigued physicists is the relative ease with which one can find solutions to Einstein’s field equations that contain closed timelike curves (CTCs)—causal loops in space–time that return to the same point in space and time.”

The Science

Closed timelike curves are a necessary concept to understand this experiment.
CTCs are used to simulate powerful gravitational fields, like the ones produced by a spinning black hole, that could theoretically (based on Einstein’s theory of general relativity), warp the fabric of existence so that space-time bends back on itself. This creates a CTC, almost like a pathway to travel back through time.
The source of time travel speculation lies in the fact that our best physical theories seem to contain no prohibitions on traveling backward through time. The feat should be possible based on Einstein’s theory of general relativity, which describes gravity as the warping of spacetime by energy and matter. An extremely powerful gravitational field, such as that produced by a spinning black hole, could in principle profoundly warp the fabric of existence so that spacetime bends back on itself. This would create a “closed timelike curve,” or CTC, a loop that could be traversed to travel back in time. (source)

Experimenting With CTC’s

Single particles of light (photons) to simulate quantum particles travelling through time were just used by scientists from the University of Queensland, Australia. They showed that one photon can pass through a wormhole and then interact with its older self. Their findings were published in Nature Communications. 

Much of their simulation revolved around investigating the “grandfather paradox,” a hypothetical scenario in which someone uses a CTC to travel back through time to murder her own grandfather, thus preventing her own later birth.

The Grandfather Paradox in Quantum Physics

Instead of a human being traversing a CTC to kill her ancestor, imagine that a fundamental particle goes back in time to flip a switch on the particle-generating machine that created it. If the particle flips the switch, the machine emits a particle—the particle—back into the CTC; if the switch isn’t flipped, the machine emits nothing.