The problem with the past
Einstein's general theory of relativity allows for some strange possibilities. The mathematics that describes gravity and the curvature of spacetime also contains solutions with "closed timelike curves" (CTCs). A CTC is a path through spacetime that loops back on itself, allowing an object or person to return to their own past and potentially create paradoxes, like the classic grandfather paradox.
Physicists have conceived of several theoretical ways to create these CTCs. These include the Gödel metric, based on a rotating universe, and immense, infinitely long spinning cylinders of matter called Tipler cylinders. More famously, in the 1980s, physicist Kip Thorne and his colleagues explored the physics of traversable wormholes. Prompted by a request from Carl Sagan for his novel Contact, Thorne's work showed that these spacetime tunnels could, in theory, be manipulated to connect two different places, but two different times. This proliferation of physically plausible and technologically impossible time machines created a serious problem for causality.
A cosmic protection agency
In a 1992 paper, Stephen Hawking proposed a solution he called the "Chronology Protection Conjecture". His idea posits that the laws of physics themselves intervene to prevent CTCs from forming on a macroscopic scale. He humorously suggested the existence of a "Chronology Protection Agency" that "makes the universe safe for historians".
The proposed mechanism relies on the interaction between general relativity and quantum mechanics. According to the conjecture, as one attempts to warp spacetime to create a time machine—for example, by manipulating a wormhole—the threshold to the past would be flooded with energy. Quantum vacuum fluctuations, the sea of virtual particles that exist even in empty space, would enter the time loop. These particles would circle through the wormhole endlessly, becoming real and accumulating an infinite amount of energy. This runaway energy density, technically a divergence in the expectation value of the renormalised stress-energy tensor, would create a gravitational field so intense that it would destroy the wormhole right at the moment it was about to permit time travel.
The conjecture remains unproven and is debated. Subsequent research has suggested that in some models, the energy buildup might not become infinite, potentially allowing for a time machine to form. The construction of a traversable wormhole in the first place requires a huge amount of "exotic matter" with negative energy density to keep it open, something which may not be physically possible in sufficient quantities. An alternative idea, Igor Novikov's self-consistency principle, proposes that time travel might be possible, but only in ways that are not paradoxical; any attempt to change the past would be guaranteed to fail.