Rethinking the Arrow of Time After Reading About Deng's Fields Medal
When I saw the news that Yu Deng received the 2026 Fields Medal, I became curious about the mathematics behind his work.
His research is mathematical rather than philosophical. Roughly speaking, it strengthens the connection between microscopic Newtonian mechanics—where countless individual particles interact—and the Boltzmann equation, which describes the statistical evolution of a gas. It is a remarkable mathematical achievement, but what fascinated me wasn't the proof itself.
Instead, it made me think again about one of the oldest questions in physics:
Where does the arrow of time come from?
The story we usually hear
A common explanation goes something like this.
At the microscopic level, the fundamental laws of mechanics are (approximately) time-reversal symmetric. If every particle's velocity were reversed perfectly, the particles would retrace their trajectories.
But at the macroscopic level, things become irreversible.
Heat flows from hot objects to cold ones. Perfume spreads through a room. A gas expands instead of spontaneously gathering back into one corner.
From this perspective, the arrow of time is said to emerge from statistical mechanics.
Whether this is exactly how physicists would phrase it is another question, but it is certainly a popular way of explaining the relationship between microscopic and macroscopic physics.
My intuition is slightly different
I'm not a physicist, so what follows is not a claim about established physics.
It's simply an intuition that has gradually formed while thinking about these ideas.
My intuition has three parts.
1. Time exists regardless of scale
I don't think time suddenly appears when enough particles are put together.
Time already exists in Newtonian mechanics. Newton's equations evolve with respect to time.
What seems absent is not time itself, but a preferred direction encoded in the equations.
Those are different statements.
Saying
"The microscopic equations do not distinguish a preferred direction"
is not obviously the same as saying
"There is no arrow of time at the microscopic level."
The first statement concerns the mathematical laws.
The second is a much stronger statement about reality.
2. The arrow of time is relational
When I say the arrow of time is a convention, I do not mean it is an arbitrary human invention like choosing whether maps point north or south.
Humans are physical systems.
Our brains form memories.
Our neurons interact.
Our bodies exchange energy with the environment.
Everything happening inside us is part of the same universe whose arrow we are trying to understand.
So when I say "future," I simply mean the direction in which my own physical system forms memories, records interactions, and evolves.
The convention is therefore physical, not merely linguistic.
It is the shared orientation adopted by interacting subsystems within the same universe.
An observer does not stand outside reality and assign an arrow.
The observer is part of the system whose arrow is being discussed.
3. The arrow is fundamentally statistical
This is the idea I find most interesting.
Suppose we temporarily forget about atoms and molecules.
Instead, imagine one million computational processes.
Each process has an internal state.
Each process can interact with nearby processes according to deterministic rules.
Every interaction updates the participating states.
The update rules themselves might be perfectly reversible.
Now imagine recording the complete state of every process over time.
Initially, information might be highly localized.
Perhaps only a handful of processes contain meaningful structure.
As interactions continue, information spreads.
Correlations become increasingly complicated.
Patterns diffuse across the entire network.
The exact microscopic evolution may remain reversible.
Yet if someone hands me a series of snapshots from the simulation without timestamps, I suspect I could often guess their temporal order.
Why?
Not because the local update rule tells me.
But because the statistics of the entire system tell me.
The system develops large-scale asymmetries that become increasingly obvious when many interacting components are considered together.
Why small systems feel different
Now imagine performing the same thought experiment with only two interacting processes.
A single interaction often looks equally reasonable in either temporal direction.
If I reverse the interaction, it still satisfies the same local rule.
Nothing about those two isolated processes strongly tells me which direction should be called "forward."
This is why I suspect the interesting distinction is not really "microscopic versus macroscopic."
Instead, it is whether the system contains enough interacting degrees of freedom for its temporal direction to become statistically inferable.
With very few interacting components, there simply isn't enough statistical structure.
With millions of interacting components, statistical regularities become difficult to ignore.
The local rules may remain reversible.
The collective behavior becomes direction-revealing.
What Deng's work made me appreciate
The Fields Medal was awarded for deep mathematics, not for explaining the philosophy of time.
But reading about Deng's work helped me appreciate something I hadn't fully appreciated before.
His work rigorously connects reversible microscopic dynamics to the Boltzmann equation over long times.
That doesn't prove why time has an arrow.
It doesn't solve the philosophical question.
But it strengthens the mathematical bridge between local reversible interactions and global statistical evolution.
To me, that's where the interesting questions begin rather than end.
A speculation
So here is my current intuition.
Perhaps the arrow of time is neither hidden inside every microscopic interaction nor magically created only at the macroscopic scale.
Perhaps it is something we can infer from sufficiently rich collective behavior.
A single interaction rarely tells us much.
Millions of interacting components do.
The arrow may therefore be less like an extra physical force and more like a statistical property of complex systems.
If this intuition is correct, then the concept is not limited to gases.
Any sufficiently large system—physical, biological, computational, or social—might exhibit a detectable temporal orientation whenever information spreads, correlations accumulate, and local interactions collectively produce asymmetric statistical structure.
I don't know whether this idea is ultimately correct.
But I think it is a fruitful way to think about time.
At least for me, Deng's work served as a reminder that sometimes the deepest questions are not answered by changing the laws themselves, but by asking what becomes visible once enough interactions are considered together.