If a cup of water spills on the floor, the water can’t unspill—that is, it’s inconceivable that each water molecule would exactly reverse its course to slip back into the cup. To do so would be to turn back time—something that, as far as we know, can’t be done. The water either spills or it doesn’t, but if it does, it’ll stay that way.
In that way, time as we experience it is asymmetric. We have memories of the past rather than the future, and spilled water doesn’t flow back to its cup, just as an arrow that has been let fly doesn’t return to its bow. In our everyday lives, the “arrow of time” goes only in one direction: forward.
“We know [this] is something that’s part of our common experience,” says Andrea Rocco, a theoretical physicist at the University of Surrey in England. But how exactly time’s arrow arises is less clear to physicists, in part because the math they use to describe most of the world makes no distinction between time that moves forward and time that moves backward; either direction is perfectly viable, as far as their equations are concerned.
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Relatedly, the concept of “time” becomes somewhat illusory in the absence of change. For instance, if our cup of water was held in stasis in a magic, perfectly insulated and physically impervious box floating in deep space, this “system” would seem the same whether it was examined five years ago or five millennia from now. So which way is time’s arrow flying inside the magic stasis box? For such isolated systems, time is thus considered to be symmetric; only when it is “open” to influence from the external environment is this symmetry broken, whether via water evaporating or the cup tipping over to spill its contents.
And yet open and isolated systems are inherently linked. Even if our cup of water was isolated from the external world, its molecules would still be randomly jostled by microscopic effects—changes that potentially break time’s symmetry, like the ticking of the cosmic clock. So why does this discrepancy exist, and what does it imply about the validity of the models physicists use to study the role of time in the reality we experience?
Different researchers have tackled these questions in different ways, but Rocco and his colleagues revisited some of the math behind the inconsistency to see if an alternative approach could resolve the apparent asymmetry. Their conclusions, recently published in Scientific Reports, detail the existence of not one but two opposing arrows of time within open quantum systems.
This is a bit like if our water cup were precariously balanced on a knife-edge: it could topple to spill down either side, each side being an opposite-facing arrow of time. But the cup falling one way versus the other doesn’t make the water spill differently. Either way, mathematically speaking, the end result is exactly the same—it preserves the symmetry for both possible instances. “In a sense, we are stuck in this universe in which time actually goes in one direction,” Rocco explains. “But the equations of motion that we are considering would have allowed the universe to go in the other direction.”
This way, the existence of both instances is a reflection of time symmetry, in contrast to the conventional understanding that the environment is imposing or “defining an arrow of time,” Rocco says. In other words, the researchers’ work suggests that two time’s arrows, rather than one, are a spontaneous feature of an open quantum system.*
The new work adds to some interesting questions about what physicists deem relevant in their studies of time. Michele Campisi, a theoretical physicist at the Italian National Research Council’s Nanoscience Institute, who was not involved in the study, commends the paper for its bold take but notes that it also implies a strange, subjective malleability to the origins of time’s arrow. The “hows” and “whys” of the way time flies are “a reflection of an approximation,” he says, dependent on a physicist’s preferred interpretation of quantum mechanics itself—of which there are several. One’s view of a quantum system is set to some degree by one’s expectations, he says. For instance, a more “global” view of events could also see a purported open system as just another part of a much larger, isolated one in which complications with time asymmetry wouldn’t occur at all.
Nevertheless, this paper demonstrates how our quest to understand the quantum realm is still far from complete, says James Cresser, a now retired professor of physics. “This [helps] shake up a commonly held idea that certain equations describing dissipative behavior are not time-reversal invariant and are therefore a theoretical indicator of a particular physical state of affairs,” Cresser says. (Cresser was thanked for “illuminating discussions” in the study and had taught its lead author Thomas Guff as an undergraduate, but he did not directly contribute to the work.)
For instance, the way water acts when it spills is akin to a type of dissipative behavior in quantum mechanics and thermodynamics called decoherence, in which a system progressively spreads out, or “decoheres,” and “loses” information. In this example, the information is the particular arrangement of water molecules previously inside the cup. Dissipative processes are considered asymmetric with regard to time because the initial configuration ends up irrelevant to the final state of affairs, explains Nicole Yunger Halpern, a physicist at the National Institute of Standards and Technology, who was not a part of the new study.
But even this kind of interpretation necessarily depends on our expectations of how a system must evolve as energy flows through it. For example, if we were to see two movies, one in which the water spills and another in which the water preternaturally returns to the cup, we’d be inclined to say that the second movie is illusory and impossible and that it is merely the first played backward. Thus, an asymmetric arrow of time is, in some ways, an “emergent phenomenon,” Yunger Halpern says. “Sometimes people call [this] a ‘psychological’ arrow of time.”
All that said, perhaps the concept of time—arrow or no—is nothing but “scaffolding” for the human brain to grasp at as we try to “label all the events that take place in the world around us,” Cresser says. “But the events themselves don’t rely on the scaffolding. And what we’re doing with these equations is applying one kind of temporal scaffolding as compared to another possible temporal scaffolding.”
In that case, our questions about time might never have answers—making them, well, timeless. “We are unavoidably buried in time—that is a profound part of our existence that we can never, ever escape,” Cresser says.
*Editor’s Note (2/27/25): This paragraph was edited after posting to better clarify Andrea Rocco’s comments about arrows of time.
