First, the good news for time travelers. Physicists have long recognized that nothing in the laws of physics specifically forbids time travel. As far as they can tell, these laws don’t care whether time is running forwards or backwards; they work just as well either way.

That recognition has spawned numerous studies, some of them surprisingly serious, to test the limits of causality. In this work, physicists have tried everything from bending the fabric of spacetime to exploiting quantum uncertainty to travel back and forth in time. They have even tested some of these ideas. But nothing seems to work. Indeed, some of the schemes require decidedly unphysical conditions that make them unlikely to ever be tested.

But the keenest enthusiasts always fall back on the notion that time travel is still not proven impossible.

Memory Loss

Now the bad news, which comes from Lorenzo Gavassino, a mathematician at Vanderbilt University in Nashville. Gavassino has discovered some previously unknown side effects of time travel.

He says the laws of physics may not forbid it but if it is possible, these laws lead to some outlandish consequences, one of which is that any human who made the journey would not be able to remember it. The laws of physics suggest this person’s memory would be wiped clean as soon as they returned to the present.

So how do the laws of physics lead to this disappointing conclusion? It turns out that just one law is responsible — the second law of thermodynamics, that the entropy, or disorder, of any system always increases over time.

Unlike all other laws, the second law distinguishes between time running forward and backwards. Eggs never unbreak and milk never unmixes from coffee and so on.

In a series of thought experiments, Gavassino has now shown that this has important consequences for a spaceship carrying a time traveler that follows a circular path through space time, in other words a journey back to the same instant in time.

A key feature of this circular journey is that the entropy must be the same at the beginning and at the end – because the traveler returns to their original state. So if the entropy increases over time, there must be a point in the circle where it is at a maximum before returning to its original value.

Gavassino says that the consequences for the time traveler in the spaceship passing beyond this point of maximum entropy are clear: “all thermodynamic processes (including biological processes such as memory formation and aging) are reversed,” he says. “Memories of an observer inside the spaceship are necessarily erased by the end of the journey.”

Gavassino’s breakthrough in this paper is to formalize this idea with the mathematics of quantum mechanics and spacetimes.

One particularly fascinating aspect of the paper involves the behavior of clocks during time travel. Gavassino demonstrates that clocks would not function as expected. For a clock to return to its starting point after a complete journey, it must tick at a frequency that produces a whole number of “ticks” during the trip.

This requirement can introduce subtle “defects” in clocks designed for standard linear time, making their measurements unreliable in a closed timelike curve. And since the same argument applies to the ordinary vibrations of molecules and atoms, this raises the possibility of widespread disruption to the ordinary existence of matter in a timelike curve.

Perhaps Gavassino’s most profound result is the erasure of memory, human, computer or otherwise. Gavassino models memory as an interaction between an object and a “memory-keeper.” He shows that memories created during the journey must be undone by the end, since the system must return to its original entropy state.

End Of The Loop

This phenomenon fundamentally alters the subjective experience of time for the traveler. “Any memory that is collected along the closed timelike curve will be erased before the end of the loop,” he explains.

Gavassino’s findings have significant implications for our understanding of time and causality. While the study does not determine whether time travel is possible, it sheds light on the strict conditions that must be met in such scenarios.

In a universe with close timelike curves, time travel would not resemble the freewheeling adventures of science fiction. Instead, travelers would confront a world governed by rigid self-consistency, erased memories, and disrupted causality.

Of course, wannabe time travelers will look for potential loopholes in Gavassino’s argument. One possibility is that while the second law of thermodynamics applies to a system as a whole, it need not necessarily apply to its component parts.

So there may be a way that some parts of a system could decrease in entropy while the rest increases in a way that ensures the total entropy follows the required conditions. Indeed, that’s how human memories form and are retained anyway. This could provide a way for humans and their memories to survive a trip round a closed timelike curve.

That’s tantalizing food for thought for potential time travelers. Of course, any actual time travelers among us will have long since concluded that Gavassino must have missed something somewhere.

Ref: Life on a closed timelike curve : arxiv.org/abs/2405.18640