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SURREY, England — Most of us take for granted that time flows in one direction. We remember the past but can’t recall the future. Photos yellow with age but never spontaneously restore themselves. Coffee cools down but never randomly heats up. This one-way flow of time, known as time’s arrow, seems fundamental to how our universe works. But new research suggests that, at the quantum level, time’s flow may not be as rigid as we assume.

The study, published in Scientific Reports, reveals that in the microscopic realm of atoms and subatomic particles, the equations describing their behavior remain symmetric in time, meaning they can, in theory, evolve both forward and backward simultaneously.

Lead author Dr. Andrea Rocco, an associate professor in Physics and Mathematical Biology at the University of Surrey, explains this paradox with a familiar example: “One way to explain this is when you look at a process like spilt milk spreading across a table, it’s clear that time is moving forward. But if you were to play that in reverse, like a movie, you’d immediately know something was wrong – it would be hard to believe milk could just gather back into a glass.

“However, there are processes,” Rocco continues, “such as the motion of a pendulum, that look just as believable in reverse. The puzzle is that, at the most fundamental level, the laws of physics resemble the pendulum; they do not account for irreversible processes. Our findings suggest that while our common experience tells us that time only moves one way, we are just unaware that the opposite direction would have been equally possible.”

To investigate this mystery, Rocco and her team examined open quantum systems—small collections of quantum particles that interact with their surroundings. Previous theories suggested that these systems pick up a preferred direction of time, like a leaf carried by a river’s current. However, through detailed mathematical analysis and computer modeling, the team discovered that quantum systems don’t necessarily pick a single direction. Instead, their equations naturally preserve time symmetry, allowing them to evolve both forward and backward.

Their approach involved two key assumptions: treating the environment surrounding the system in a way that allowed a focus solely on the quantum system itself and assuming that the environment—like the entire universe—is so vast that energy and information dissipate into it without returning.

What they found was surprising. Even after applying these assumptions, the mathematical equations describing the system’s behavior remained symmetric with respect to time—meaning they worked equally well whether time moved forward or backward.

“The surprising part of this project was that even after making the standard simplifying assumption to our equations describing open quantum systems, the equations still behaved the same way whether the system was moving forwards or backwards in time,” says Thomas Guff, the postdoctoral researcher who led the calculations. “When we carefully worked through the maths, we found that this behavior had to be the case because a key part of the equation, the ‘memory kernel,’ is symmetrical in time.”

Guff also highlighted an intriguing mathematical detail: “We also found a small but important detail which is usually overlooked – a time-discontinuous factor emerged that keeps the time-symmetry property intact. It’s unusual to see such a mathematical mechanism in a physics equation because it’s not continuous, and it was very surprising to see it pop up so naturally.”

At the heart of this discovery is something called the “Markov approximation”—a mathematical technique physicists use to simplify complex quantum systems. Conventional wisdom held that this approximation naturally broke time symmetry, forcing quantum systems to evolve in only one temporal direction. The new research challenges this idea, showing that when properly formulated, the Markov approximation actually preserves time symmetry.

While this doesn’t mean we’ll suddenly start remembering the future or watching eggs unscramble themselves, it suggests that at a fundamental level, nature may be more temporally ambidextrous than previously thought. The asymmetry we experience in daily life likely emerges from the collective behavior of countless interacting particles rather than from any fundamental law.

Rather than time being like a river that only flows in one direction, it may be more like an ocean with complex currents moving in multiple directions. On a macroscopic level, we are simply carried along by one particular current, which gives us our sense of time’s arrow.