Why Einstein’s theories of relativity make time travel possible

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Everyone has moments they’d like to erase from the past. These could be minor issues like a poor test result or a disagreement with friends, or significant events like the 2019 outbreak that initiated the COVID pandemic.

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In the realm of science fiction, time travelers are common, but we have yet to meet one in reality. Nevertheless, fields such as physics, mathematics, and philosophy have been investigating the concept for decades.

Albert Einstein’s special and general theories of relativity, published in 1905 and 1915, form the foundation for most theories about potential time travel. These theories revolutionized our understanding of the universe. Einstein proposed that time and space are not fixed; they can stretch or compress based on circumstances. This means a steel rod’s length or the duration of a second can vary based on the situation.

This idea is relatable—an hour at work might seem endless, while an hour with friends feels fleeting. However, Einstein focused on time’s actual duration, not its perception. For instance, according to relativity, a second on Earth differs from a second on an orbiting satellite.

Travel into the Future thanks to Rapid Movement

Einstein’s special theory of relativity allows for time travel into the future. He discovered that moving clocks tick slower. If you travel on a spaceship for a five-year journey at 97 percent of the speed of light, 20 years will have elapsed on Earth by your return. This is why, after 11 months on the International Space Station, NASA astronaut Scott Kelly is 13 milliseconds younger than his twin who stayed on Earth.

Time’s passage isn’t only influenced by motion; gravity and acceleration also play a role. Einstein’s insights revealed that gravity is a geometric effect, with mass and energy curving spacetime, which dictates the path of massive objects. Imagine stars creating depressions in spacetime, attracting other massive objects like planets.

Massive objects also cause time to slow in their vicinity due to their spacetime warping. This concept is featured in Christopher Nolan’s film Interstellar, where a character near a black hole ages only a few months, while decades pass for his daughter on Earth.

Journeys into the Past

The equations of general relativity theoretically allow for backward time travel through closed timelike curves. These curves enable a journey back to a starting point in spacetime. Dutch mathematician Willem Jacob van Stockum first recognized this potential in 1937.

The gap of over 20 years between the development of general relativity and this discovery is due to the theory’s numerous solutions, each describing a different universe.

When Einstein introduced his theory in 1915, researchers quickly pursued solutions resembling our universe. However, this task is challenging due to complex calculations and uncertainties about our universe’s properties, such as its shape and mass distribution.

The Einstein field equations, central to general relativity, are differential equations. They describe how functions change based on various factors, like how space curvature changes over time and space. These equations are summarized as: G_μν + Λg_μν = 8πG/c⁴× T_μν.

The left side of this equation addresses space geometry, with Λ as the cosmological constant accounting for the universe’s accelerating expansion. The right side relates to matter, explaining how massive objects move and influence space. These variables involve complex expressions, including derivatives.

An Equation with Many Solutions

The challenge is identifying a specific geometry (represented by a metric like g_μν, which defines spacetime geometry) and mass distribution (T_μν) that satisfy the equation. Astronomer Karl Schwarzschild was among the first to find a solution in 1916, describing empty spacetime around a stationary, massive object. This solution helps calculate gravity near planets, stars, or black holes.

In 1963, mathematician Roy Kerr extended Schwarzschild’s approach to rotating masses. Kerr’s solution exhibits remarkable properties, allowing for travel along closed, timelike curves, theoretically enabling backward time travel. However, this occurs only in an unstable region of Kerr spacetime, prone to collapse with minor changes.

While the Kerr solution likely describes spacetime outside rotating black holes, it fails near them, precisely where timelike curves might exist.

Interestingly, the Kerr universe isn’t the only solution to Einstein’s equations that permits backward time travel. Next week, we will delve into other solutions to the special and general theory of relativity, exploring their unique perspectives on the universe, time, and space.

This article originally appeared in Spektrum der Wissenschaft and was reproduced with permission. It was translated from the original German version with the assistance of artificial intelligence and reviewed by our editors.