New study reexamines time symmetry in quantum systems

New research claims that quantum mechanical processes do not distinguish between forward and backward directions of time. But does it substantively alter our understanding of the universe?

Spilled milk doesn’t flow back into the jug on its own. However, if it did, no law of physics would be violated.  So then how does our sense of the unidirectional flow of time emerge from laws of physics that, themselves, have no preferred direction? How can these both be simultaneously true?

In classical physics, the arrow of time is explained by thermodynamics. However, this only works under the assumption of “molecular chaos”—an approximation introduced by Ludwig Boltzmann to show that particles don't acquire correlations after interactions. Under this assumption, when a system interacts with the environment—exchanging matter and energy—it evolves such that entropy, the amount of disordered energy, increases in the direction of past to future. This assumption is essential for the observed time asymmetry and underpins the “second law of thermodynamics.” 

This explanation holds for classical systems—those governed by Newton’s laws. However, the universe is fundamentally quantum mechanical, and Newton’s laws are only approximations for large systems. Unlike classical systems, the assumption of molecular chaos cannot be applied to quantum systems to enable an arrow of time. That's because quantum entanglement ensures that in every interaction, correlations build up between particles.

But suppose classical systems, which exhibit an arrow of time, emerge from quantum systems. How does the arrow of time (and the second law of thermodynamics) emerge from time-symmetric quantum mechanics where the assumption of molecular chaos is invalid? The answer is in decoherence. 

When large numbers of quantum particles interact and become entangled, the correlations between these particles quickly diffuse through the system until individual particles seem uncorrelated. At this point, decoherence has occured, entanglement is no longer observable, and the system has become classical. This process is why quantum computers are so hard to build and sustain—once the quantum bits interact with their environment, they lose their quantum nature. 

It's in this transition between quantum and classical via the process of decoherence that we can study the emergence of the classical world, and so, perhaps understand how the time symmetry of the underlying laws of nature can give rise to a universe with such an indisputable arrow of time. That was the goal of Thomas Guff, Chintalpati Umashankar Shastry, and Andrea Rocco from the University of Surrey. In a paper published in Scientific Reports on January 29, 2025, these scientists shared their surprising finding that suggests that even open quantum systems—those on the verge of transition to the classical—can exhibit the time symmetry of their underlying quantum laws. But does this mathematical observation lead to any fundamental understanding?

The arrow of time in open quantum systems

In a closed system—one that does not exchange matter and energy with its environment—there is no way to distinguish between forward and backward directions of time. To understand whether quantum mechanics does choose a direction, physicists’ study open systems—those that can freely exchange both matter and energy with the environment. Animal bodies are an example of open systems, taking in food and oxygen from the environment and releasing heat and carbon dioxide.

Schematic showing the concept behind the time-reversal transformation. The system and environment move backward in time. Credit: Guff, T., Shastry, C.U. & Rocco, A. Emergence of opposing arrows of time in open quantum systems.

In this new study, the researchers chose the simplest mathematical prototypes for open quantum systems and assumed that once mass, energy, and information left the system, it could not return from the environment.

Examining the Markov process

The team studied the “Markov process,” which posits that, at any particular moment, only the system’s present state determines its future state—irrespective of how it got to the present state. That is, there is no way the system’s past state affects it. For practical systems, theorists impose this “Markov approximation” on their mathematical description.

Diagram representing a two-state Markov process. [Credit: Joxemai4; Wikimedia Commons]

The authors investigated the equations that govern basic open quantum systems. These equations are popular in physics, and physicists have derived them assuming one arrow of time.

“We have relaxed this assumption,” said Andrea Rocco, one of the authors of the study, who is an associate professor in physics and mathematical biology and the head of the Quantum Sciences Research Group at the University of Surrey in the UK.

When the team performed the mathematics on this model interaction, they found that the equations were almost identical to the standard ones—but to make them fully match, you had to flip the notion of time. That is, even in the presence of decoherence, quantum mechanics allows the movie to be played forward and backward.

“This is surprising,” said Rocco. “One might expect that when a system interacts with an environment in which it can dissipate energy and information, an arrow of time should emerge naturally.”

Two arrows of time?

Since the authors conclude that both directions of time are permissible by the quantum mechanical equations, there is nothing inherently asymmetric in the laws of nature. That means that the second law of thermodynamics still holds. Once a state of minimum entropy has been chosen, whether the movie plays forward or backward, it will increase.

“This suggests that both directions of time are permissible and are not prohibited by the second law of thermodynamics once the arrow of time has been chosen or fixed a priori,” said Shrobona Bagchi, a postdoctoral research fellow at the Quantum Universe Center of the Korea Institute for Advanced Study in South Korea. Both directions of time result in decoherence, dissipation, and equilibrium for the open quantum system, and entropy reaches its maximum.

Deepak Dhar, a distinguished professor at the International Centre for Theoretical Sciences in India, notes that choosing a low-entropy initial condition is key. Whichever way time flows, entropy increases—a conclusion aligning with the authors’ findings.

“In general, the time-reversal symmetry is not preserved in quantum systems under Markov approximation, but there are some conditions if imposed then the dynamics can preserve the time-reversal symmetry,” agreed Sahil, a visiting postdoctoral fellow at the Institute of Mathematical Sciences in India. However, he added that the author’s findings depend on the Markov assumption. If the Markov assumption is relaxed, the system could have different dynamics that do not preserve the time-reversal symmetry.

Dhar adds that he was initially surprised by the authors’ claim but realized it aligns with “detailed balance,” the principle that each transition in a Markov process has an equally possible reverse transition. That principle maintains time-reversal symmetry.

“The Markov approximation is a special restriction on the open quantum system and its environment,” said Sahil.

Is it possible that the authors have simply rediscovered a known principle? In the abstract of their paper, “Emergence of opposing arrows of time in open quantum systems,” they wrote: “Our results show instead that the time-reversal symmetry is maintained in the derived equations of motion.”

“Then where is the arrow of time?” Dhar asked. “This is just using new bottles for old wine.”

No practical consequence—yet

While the authors acknowledge that their mathematical findings may not impact the world of everyday experience—“We happen to live in one of the two arrows of time, and we are just stuck in it,” said Rocco—the work adds a fresh perspective to ongoing debates in fundamental science. 

The results don’t hint that time travel is possible, or immediately shift the trajectory of quantum computing. The challenges caused by decoherence remain just as before, and researchers must continue seeking ways to scale quantum computers despite entropy and noise.

Still, even skepticism like Dhar’s—“I don’t think they have added much to the actual description…They have added to the confusion by introducing funny terminology”—is a sign that the study is provoking necessary discussion.

Whether one sees it as a bold reminder or a retread of a known principle, the study at least reaffirms that the arrow of time we observe may come down to initial conditions—rather than an absolute rule within quantum laws. And that realization nudges us one step closer to understanding the deep structure of reality.

Debdutta Paul is a freelance science journalist with a PhD in astrophysics and, until recently, was the science writer at the International Centre for Theoretical Sciences, running Synapse by ICTS. He has written for The Wire (India), The Hindu, Nature, The Swaddle, TheLifeofScience.com, and other publications. He lives in Bengaluru, India.