Gravity May Shield Spacetime From Time Travel Paradoxes, But the Fix Brings Its Own Instability

The old rule of time travel goes like this: if you go back, you must not kill your grandfather before he has children. If he never has offspring, you are never born, and you can never make the trip. How the Universe would settle that contradiction is unknown. One possibility is that the laws of physics simply refuse to let the situation arise, which is the position Stephen Hawking took.

Hawking set out the idea in 1992 as his chronology protection conjecture, written to probe whether backward time travel is possible at all. It states that the laws of physics do not allow the appearance of closed timelike curves. His calculations supported it, but physicists have still not established that the Universe actually enforces it.

The difficulty lies in Einstein's general theory of relativity, our best description of gravity. It permits some strange arrangements of spacetime, among them closed timelike curves: paths that, in the mathematics at least, can carry a traveler back into their own past. Whether such paths could exist physically is a separate question. Hawking suspected quantum effects would prevent them from forming, but no one has conclusively identified the mechanism.

Two physicists at the University of New Hampshire, Moustafa Ismail and David Mattingly, asked whether gravity itself might supply the answer. If the mathematics of gravity allows time loops, a different formulation of gravity might forbid them. General relativity is the best framework for gravity, but it is not the only one.

In general relativity, spacetime has a geometry described by a metric, which fixes distances and intervals of time. A mathematical connection describes how directions change as you move through that geometry, and the two are tied together in a particular way. An alternative called metric-affine gravity loosens that tie, so the metric and the connection can act more independently. Ismail and Mattingly found their room to maneuver there.

Using it, they built a model in which spacetime has a built-in direction of time. Under the right conditions, time runs forward along every path a traveler could take, so looping back into one's own past becomes impossible. They named it Metric-Affine Gravity Imposing Chronology, or MAGIC.

The catch is a new kind of fluctuation. In general relativity, gravity fluctuates in two ways, matching the two ways gravitational waves stretch and squeeze space. MAGIC adds a third, a scalar mode. On the cosmological background the researchers studied, this mode suffers a gradient instability. Instead of traveling as stable waves, its disturbances can grow exponentially, with shorter wavelengths growing faster. In its present form, MAGIC therefore cannot give a stable description of the Universe, and that is the largest obstacle to making it a viable theory.

There are two smaller ones. First, MAGIC establishes the conditions for chronology protection only locally. To guarantee that time cannot loop back anywhere in the Universe, the researchers must assume something extra about the overall structure of spacetime, and they have not shown that this follows from the model. They can make MAGIC prevent time loops, but they have not shown that preventing them is built into it.

Second, the model is meant to stop the metric from breaking down in ways that would make spacetime impossible to describe, but that safeguard does not work in every circumstance. The researchers have not shown such breakdowns occur in MAGIC, but they have not ruled them out either.

MAGIC is not offered as a final answer. It is a demonstration of how chronology protection might be built into gravity, a step in a research direction rather than a working solution. The authors write that stabilizing the scalar without losing the timelike, closed projective mode is the natural next step toward a phenomenological completion. Stabilizing that mode, and showing the protection holds everywhere, is the work still ahead.