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Time can advance back and forth at the same time in quantum mechanics.

Even time behaves “strangely” in the realm of quantum mechanics. This is shown by a new study published in the journal Communications Physics, in which the authors reached this conclusion when applying the idea of ​​quantum superposition states to the concept of entropy.

Published by a team from the Universities of Bristol, Vienna, Balearic Islands and the Institute of Quantum Optics and Quantum Information, the new study proposes to rethink how the flow of time is understood and represented in contexts of quantum laws.

Time in Quantum Mechanics

Entropy is a quantity of thermodynamics that measures the evolution of systems from a state of order to disorder, which is useful for showing the passage of time. In fact, entropy was a way of not only explaining the quantum changes of a system (set of particles, for example), but of proving time itself as physically real.

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According to the laws of thermodynamics, particles can be distributed at quantized energy levels (in “packets”), including translational, vibrational, rotational, and electronic. This means that during the evolution of that system, particles will gain new values, which scientists call “information”.

This information of a particle is never lost, even if the matter is transformed. For example, the particles on a burned sheet of paper will carry the information it had before the sheet burned. If scientists could study this information and control all the properties of the particles, it would be possible to turn carbon back into paper again.

However, it is technically impossible to reverse the entropy of a system — it always increases, never decreases. In other words, the disorder of these particles is always increasing, with new information. To cite one more example, ice cubes in a glass of water melt, this means that the entropy in this system increases. It is much easier to make ice melt than it is to freeze water.

The increase in entropy is therefore a process that occurs in only one direction, which seems to suggest that time itself can only advance towards the future. We can’t re-freeze the ice in the glass, any more than we can go back in time, as if we were rewinding a recorded video.

In other words, atoms can rearrange themselves, but that means that entropy increases whenever they get more disordered—water has more disordered atoms than ice, just as carbon has more disordered atoms than a sheet of paper. That’s why freezing water requires a lot of energy.

entropy and arrows of time

With entropy, we’re always seeing things happen in one direction—from an organized to disordered state—as time progresses. We can explain the past with the information in a system, but we cannot predict the future simply because entropy increases.

This implies a time always ahead, with no possibility of going back to the past, just as we cannot re-freeze the water or de-burn the sheet of paper. But what if time wasn’t a one-way street for particles in these systems?

For the authors of the new study, everything depends on the amount of entropy produced in an event. If it is small enough, there is a considerable likelihood of a reversal of a phenomenon. That’s because, in the quantum realm, the quantum superposition principle dictates that two superimposed states of a system are possible (yes, we can evoke Schrödinger’s cat).

According to the study, this principle can be applied to time arrows (which point the direction of time in a system where entropy increases). This implies “that quantum systems that evolve in either temporal direction can also evolve simultaneously along both temporal directions.

But why do we never find these superpositions of time streams? Well, the authors claim that they quantified “the entropy produced by a system that evolves in a quantum superposition of processes with opposing time arrows.” With this, they found that “this usually results in designing the system in a well-defined time direction, corresponding to the more likely process of the two.”

On the other hand, when it comes to small amounts of entropy, “one can physically observe the consequences of the system having evolved both back and forth in temporal directions at the same time.” Generally, time is an ever-increasing parameter, but the study shows “that the laws that govern its flow in quantum mechanical contexts are much more complex,” said Dr. Giulia Rubino of the University of Bristol, lead author of the study.

It may all seem pretty confusing, but entropy is an important concept for performance improvements in thermal machines and coolers, and the concept of overlapping time arrows can help improve this equipment. The article was published in Communications Physics.

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