Philosophy of Time: Time’s Arrow

Author: Dan Peterson
Categories: Metaphysics, Philosophy of Science
Word Count: 999

In our experience, some sequences of events always happen in the same order. For instance, after pouring cream into coffee, the cream and coffee are separated. When stirred, they mix together. The opposite sequence of events, stirring cream out of coffee, never happens. But why?

This example suggests that time has an “arrow,” or special direction, that explains the unique time-ordering of such sequences and distinguishes the past from the future. We can imagine time being symmetric, meaning that the past and future are mirror images of each other. But time’s arrow suggests that time (in our universe, at least) isn’t like that, so time’s arrow is sometimes called a temporal asymmetry.

Many processes exhibit this arrow, such as the following, among many others:^[1]

• causes’ coming before, never after, their effects;
• remembering the past but not the future;
• Our always expanding, never shrinking universe.

Time’s arrow may seem strange for two reasons. First, though space is similar to time, at least in how it’s treated by some contemporary physical theories, space doesn’t seem to have an arrow: time’s arrow requires that causes always come before their effects, for instance, but there’s no “space’s arrow” that requires causes to come to the left or right of their effects.

Second, not all sequences of events are like stirring cream into coffee. Consider a pendulum like this:

A video of such a pendulum and the same video run in reverse look almost^[2] the same: you can’t tell which is which! So we need an explanation for why some sequences of events, like stirring cream into coffee, exhibit a temporal asymmetry while others, like the pendulum, don’t.

Here we’ll consider philosophers’ attempts to explain time’s arrow, which typically identify its source in one of three places: the laws of nature, the initial conditions of our universe, or the nature of time itself.

1. Laws of Nature

Laws of nature^[3] are features of our universe that allow us to predict or explain one state of affairs by reference to another. Some are temporally asymmetric,^[4] meaning that one particular temporal “direction” is singled out as special by the laws. One such law is the second law of thermodynamics,^[5] which says that, for closed systems, a physical quantity called “entropy” always increases over time, explaining why heat flows from hot objects to cooler ones. This temporally asymmetric law tells us something about the future (namely, its higher entropy) that isn’t true of the (lower entropy) past.

If some laws of nature are temporally asymmetric, then perhaps we can use these laws to explain where the arrow of time comes from. Processes like stirring cream into coffee are governed by the time-asymmetric laws of thermodynamics while processes like the pendulum are governed by the time-symmetric laws of Newtonian mechanics.

However, the “laws of nature” explanation isn’t always satisfying, as we can see in the case of stirring cream into coffee. The laws of thermodynamics which govern this process are themselves dependent on a more fundamental theory, statistical mechanics,^[6] whose laws don’t exhibit the same time-asymmetry. Put differently, the laws of statistical mechanics don’t seem to distinguish between the past and the future. If we rely on laws of nature to explain our arrow of time, then we may find ourselves needing to explain why thermodynamic laws are temporally asymmetric when more fundamental laws aren’t,^[7] which may be just as difficult to explain as time’s arrow.

2. Initial Conditions

If the arrow of time cannot be explained by time-asymmetric laws of nature, another reasonable explanation might rely on the initial conditions of the system being considered. Consider a game of pool: if I show you a pool table where the cue ball is on one end of the table and the other balls are in a triangle on the opposite end, you know that we are witnessing the beginning of a game.

You know that the game of pool hasn’t started yet, not because the laws that govern the balls on the pool table make this configuration impossible later on, but because this highly ordered state of the pool table is extremely unlikely given those laws late in the game.

Some philosophers believe that the universe, like a pool table, started off in a highly organized state that can help explain time’s arrow. This position is called the Past Hypothesis.^[8] Its proponents argue that it can explain not just many, if not all, of the phenomena we’ve previously discussed, but also the time-asymmetry of laws like the second law of thermodynamics.

However, some worry that the Past Hypothesis, in focusing on the large-scale behavior of the universe, lacks the resources to explain a local, or small-scale, arrow of time: e.g., the mere fact that the entropy of the universe as a whole is bound to increase in the next minute doesn’t guarantee that the entropy of my coffee must do so.

3. Spacetime Structure

Our final proposal suggests that the best explanation for the arrow of time is an asymmetry in the nature of time itself.^[9] So the answer to the question “Why is there an arrow of time but not an arrow of space?” is that the 4-dimensional spacetime we live in has a temporal, but not a spatial, asymmetry baked into it. Time’s arrow may be a fundamental fact about our universe that can’t be explained further.

Like “initial conditions” explanations, one advantage of this strategy is that a temporal asymmetry in spacetime itself could explain temporal asymmetries in the laws of nature: the laws of nature that are temporally asymmetric are responsive to this temporal asymmetry while those that are temporally symmetric aren’t.

Of course, this “feature of spacetime” explanation for temporal asymmetry may also leave us wondering why some laws, but not all laws, reference this fundamental temporal direction.

4. Conclusion

Time’s arrow calls out for explanation, but it remains unclear whether it tells us something important about how matter and the laws that govern it behave or about time itself, independent from matter.

Notes

^[1] Price (1996) and Dainton (2001) provide fairly exhaustive lists of differences between past and future attributable to time’s arrow.

^[2] I say “almost” here because, eventually, dissipative forces like friction lead to the pendulum’s motion changing. However, in a video of a few seconds, these dissipative forces would be unobservable to the naked eye. For those readers concerned that the existence of dissipative forces undermines this example, we can make the point a different way by noting that some laws of nature are temporally asymmetric while others are not, as I discuss in section 2.

^[3] For more on what philosophers mean by laws of nature, see Laws of Nature by Michael Zerella.

^[4] What it means for a law of nature to be temporally asymmetric is something a bit more specific than what most philosophers mean when they say that a sequence of events is temporally asymmetric – it’s a well-defined, formal property of the laws and the equations that describe them. Without getting too technical, we can define this property for our purposes as follows: take any physically possible sequence of events consistent with a particular law of nature. That law is temporally asymmetric if, when we reverse that sequence of events, the result is a sequence that is inconsistent with the law of nature in question.

^[5] Thermodynamics is a branch of physics that deals with concepts like heat, temperature, energy, and work. Classical thermodynamics emerged in the 19th century as the first sophisticated physical science to unite these disparate concepts, and work in classical thermodynamics fueled, and was fueled by, the industrial revolution.

^[6] Statistical Mechanics is a branch of physics that, like thermodynamics, deals with concepts like heat, temperatures, energy, and work; however, statistical mechanics advances our understanding of these concepts by treating them as features of large groups, called ensembles, of very small particles or systems. For more, see Eastman (2015).

^[7] For those readers knowledgeable about fundamental physics, specifically quantum field theory: you may object here that the fundamental laws of nature are time-asymmetric because the laws of physics are invariant not under T-symmetry, which represents time-reversal, but CPT symmetry, which is a charge-parity-time reversal symmetry. However, appealing to T-violations in quantum field theory doesn’t help those who want to rely on the second law of thermodynamics to explain the “cream into coffee” arrow of time because the phenomena which violate T-symmetry, namely weak interactions between leptons and quarks, aren’t the underlying physical phenomena responsible for the large-scale thermodynamic behavior of systems like a cup of coffee. So there is still a further fact that needs to be explained for those who want to rely on time-asymmetric laws of nature to explain all of the temporally asymmetric phenomena we care about, at least given our current best physical theories.

^[8] So named by Albert (2000).

^[9] Chapter 4 of Maudlin (2007) lays out a case for this position.

References

Albert, David. (2000). Time and Chance. Cambridge, MA: Harvard University Press.

Dainton, Barry. (2001). Time and Space.  McGill and Queens University Press.

Eastman, Peter. (2015) Introduction to Statistical Mechanics. Stanford University. Accessed July 2023

Maudlin, Tim. (2007). The Metaphysics Within Physics. Oxford University Press.

Price, Huw. (1996). Time’s Arrow and Archimedes’ Point. Oxford: Oxford University Press.

Sklar, Lawrence. (1977). Space, Time, and Spacetime. Berkeley, CA: University of California Press.

Related Essays

Philosophy of Space and Time: Are the Past and Future Real? by Dan Peterson

Time Travel by Taylor W. Cyr

Laws of Nature by Michael Zerella

PDF Download

Download this essay in PDF. 

About the Author

Dan Peterson is a visiting assistant professor of philosophy at Morehouse College. He received his Ph.D. from the University of Michigan and specializes in the philosophy of physics, philosophy of science, and formal epistemology. He has research and teaching interests in metaphysics, philosophy of religion, philosophy of education, and ethics. He is also the co-founder of Mind Bubble, an educational nonprofit in Atlanta that provides local students with free tutoring and educational workshops. DanielJamesPeterson.com

Follow 1000-Word Philosophy on Facebook, Bluesky, Instagram, Twitter / X, Threads, and LinkedIn, and subscribe to receive email notifications of new essays at 1000WordPhilosophy.com.