The Arrow of Time — Why does time flow forward?
If the fundamental laws of physics are time-reversible,
why does entropy always increase?
Why do eggs break but never unbreak?
Time-symmetric. Every process can run backwards.
Time-asymmetric. Entropy always increases.
Newton's laws, Maxwell's equations, even quantum mechanics—all are time-reversal symmetric. If you film particles bouncing around and play the film backwards, the reversed motion is equally valid physics.
Intact Egg
Low Entropy
Broken Egg
High Entropy
Never Happens!
Yet the microscopic physics of egg molecules IS time-symmetric. So why don't eggs unbreak?
Boltzmann's key insight: It's about statistics, not strict impossibility.
Yes, entropy CAN decrease. But the probability is astronomically small. There are vastly more high-entropy states than low-entropy states. Systems almost always move toward the probable.
Boltzmann assumed particle velocities are uncorrelated before collisions. This "molecular chaos" hypothesis secretly breaks time symmetry— it's an assumption about initial conditions, not the laws themselves.
Poincaré showed systems DO eventually return to near-initial states— but the "recurrence time" for macroscopic systems exceeds the age of the universe by factors of 101023.
Information isn't destroyed—it becomes practically inaccessible. The precise reversal requires knowing ALL particle velocities perfectly. Any tiny error grows exponentially (chaos), preventing reversal.
Why was entropy LOW in the past? Because the Big Bang was an extraordinarily low-entropy state. The arrow of time points AWAY from this special initial condition. We don't ask "why does entropy increase?" but rather "why did the universe START with such low entropy?"
This shifts the paradox from physics to cosmology— the mystery of our universe's special beginning.