Why Doesn’t Time Run Backward? Entropy and the Arrow of Time

Pour milk into a cup of coffee, and the white swirls gradually spread until the whole cup is the same color. But if you keep waiting, will the milk gather itself back together?

You can play a video backward. The cup in front of you has no rewind button. It is familiar enough, yet a little strange when you stop to think about it.

Let’s explore why time does not seem to run backward through the idea of entropy. No equations this time. At the end, we will take a small step into science fiction.

The arrow of time in a cup of coffee

Play a video of milk mixing into coffee backward, and white swirls emerge from the mixture before gathering into a separate patch of milk. You could probably tell which way the video was playing without being told.

This direction that distinguishes past from future is called the “arrow of time.” The direction associated with processes such as mixing and cooling is the thermodynamic arrow of time. Physicist Sean Carroll also uses coffee and milk to explain its connection with entropy. Carroll’s explanation in Caltech’s magazine (PDF)

Does entropy mean “messiness”?

Entropy is sometimes described as disorder. But it is not a matter of whether something looks tidy or messy to us.

From a statistical perspective, we ask how many different microscopic arrangements and motions of molecules can correspond to the same state on a larger scale. Entropy is related to the number of those possibilities. OpenStax: entropy on a microscopic scale

To get a feel for the difference, imagine six coins laid out in a row. There is only one arrangement with all six showing heads. There are twenty arrangements with three heads and three tails, depending on which coins show heads.

This is an analogy about counting possibilities, not a model of molecular motion. It shows how something we describe as one overall state can contain many different arrangements. In matter made up of enormous numbers of molecules, the differences in the number of possibilities become enormous too.

Staying mixed is overwhelmingly more likely

Keeping milk and coffee neatly separated puts tight restrictions on where their molecules can be. A mixed state allows vastly more arrangements.

As the molecules move and collide, the liquids mix. For an everyday-sized cup, spontaneously returning to the original separated state is so unlikely that we would not expect to see it happen. This gives us a way to understand why mixing is irreversible on that scale. The Feynman Lectures: irreversibility

In thermodynamics, the entropy of an isolated system—one that exchanges neither matter nor energy with its surroundings—does not decrease. This is the second law of thermodynamics, expressed as a macroscopic law that averages over microscopic fluctuations.

The important point is to consider the surroundings as well as the object itself. A freezer can turn water into ice, but it uses electricity and releases heat outside while doing so. Looking only at the decrease in the water’s entropy does not establish a violation of the second law. MIT: entropy changes in a system and its surroundings; OpenStax: refrigerators and heat pumps

Is reversing motion the same as traveling into the past?

Could we simply reverse every molecule’s motion? In Newtonian mechanics, when forces depend only on position, reversing the velocities of all the particles gives a mathematical solution in which they retrace their paths.

That does not mean every physical process can easily be reversed, or that people can travel into the past. There is a gap between individual motions having time-reversed solutions and a whole cup naturally returning to its unmixed state. The Feynman Lectures: reversibility in mechanics

Freezing water again does not take it back to the same moment yesterday. Recreating a similar state and rewinding time are different things.

A question that remains: the beginning of the universe

This does not solve every mystery of time. Another important part of understanding the arrow of time is the starting point: the past was in a state of lower entropy.

Why, then, did the universe begin in such a special state? That question leads into cosmology. Simply saying that entropy increases does not answer it. Carroll discusses this problem and the lack of an agreed explanation in his own account. Carroll on the arrow of time (2004)

Where does science fiction put the “what if”?

Let’s leave the scientific explanation here and try a fictional thought experiment.

Suppose a device could restore just one room to the state it was in ten minutes earlier. The air, the coffee on the desk, and the body of the person inside all return to their earlier states.

If the person’s memories return too, how would they know they had used the device? If their memories remain, what exactly is the device restoring, and what is it leaving alone?

This is not an explanation of a feasible machine. Adding conditions to the phrase “rewind time” creates reasons for a character to struggle or make a choice. Part of the pleasure of exploring science is discovering more questions to ask in a story.

What would you want to keep, and what would you want to undo?

If this topic interests you, you might also enjoy this novel.