Lộc Lương

Once upon a time, when humans came down from living on trees to the ground (either on purpose or by supernatural will), they were curious about everything around them. They invented fire, developed civilizations, made wars, and built tons of beautiful wonders, and so much more.

At some point, they began asking deeper questions about nature and about where they lived. For a long time, they believed they lived on a flat surface and at the center of the universe. This idea survived for centuries—until some tough men resisted: “No, we are not at the center, and the Earth is not flat.” And people put them in jail for saying that.

Nicolaus Copernicus said that the Sun is at the center of the solar system. Galileo Galilei laid the groundwork for the laws of motion, which were later developed by Isaac Newton. When Newton discovered gravity and established the three laws of motion, they became fundamental to many achievements and tools we use today. Later, he invented calculus, which, in my opinion, is one of the most useful things ever invented in mathematics.

For a long time, scientists believed that with a set of deterministic rules and given initial conditions, they could precisely predict the future behavior of a physical system. The universe operates like clockwork, and the law of causality suggests that its motion is predictable. Using those rules, together with assumptions of continuity, they established a solid foundation for fluid mechanics and solid mechanics. They devised equations that successfully predict the dynamical behavior of fluids and solids at the continuum scale by treating materials as homogeneous and continuous, ignoring their atomic structure.

But as humans looked deeper—into atoms, into light, into the very small world—they began to see cracks in this clockwork picture. Experiments showed that nature at microscopic scales does not behave like a smooth continuum. Energy comes in discrete packets. Particles sometimes behave like waves. Waves sometimes behave like particles.

Then came a new revolution.

Max Planck came up with the idea that energy is quantized by solving the blackbody radiation problem. And then Albert Einstein showed that light itself can behave like particles. But it also behaves like waves (e.g., double slit experiment). Niels Bohr proposed a new model of the atom. And later, Werner Heisenberg and Erwin Schrödinger built the mathematical foundation of quantum mechanics.

In this new theory, the world is no longer strictly deterministic in the classical sense. Even if we know the exact wavefunction of a system, we still cannot predict a single outcome with certainty. For instance, we can only predict probability of an electron appearing at certain locations around the nucleus. Heisenberg showed that we cannot simultaneously know both the exact position and momentum of a particle with arbitrary precision. Nature itself contains uncertainty—not because of imperfect instruments or measurement, but because this is how the microscopic world is structured.

The deterministic world of Newton is still incredibly accurate at large scales, e.g., planets move as predicted, bridges stand, airplanes fly, cars move, and many more. But beneath that smooth surface is a quantum world, where certainty dissolves into probability, and reality is not fully defined until it is measured (and I don’t understand this).