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. Human observed and look at nature and have some forms of explanation for how thing works. For example, Aristotle believed that all objects naturally come to rest; and they only move when a force is applied.

At some point, they began to ask 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 then 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 (independently with Leibniz), which, in my opinion, is one of the most useful inventions in mathematics, perhaps the best tool ever from the toolbox of mathematics to study physics as well as other engineering applications.

For a period of time, people believed that with a set of deterministic rules and given initial conditions, they could precisely predict the future behavior of a physical system. Based on this, the universe operates like a mechanical clockwork, and the law of causality suggests that its motion and state can be predictable. Inside this clockwork machine, everything is predetermined by precise physical laws. For example, using those rules, together with assumptions of continuity, they established a solid foundation for fluid and solid mechanics, as well as for other fields of physical science. They devised equations that successfully predict the dynamical behaviors of fluids and solids at the continuum scale by treating matters as homogeneous and continuous.

But as humans looked deeper into the worlds of very small things, they began to see strange behaviors in this mechanical clockwork picture. Experiments showed that matter at microscopic scales does not behave like a smooth continuum. For instance, matter is made of even smaller particles like electrons, protons, and neutrons. And particle sometimes behave like waves and waves sometimes behave like particles.

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 light also behaves like waves as shown in the double slit experiment. Niels Bohr proposed a new model of the atom that could explain the observation data very well. Later, Heisenberg showed that we cannot simultaneously know both the exact position and momentum of a particle with arbitrary precision, and Erwin Schrödinger came up with a wave equation to describe a quantum state of a physical system, and many others (e.g., Dirac, Feynman) continued to added more to the understanding of this microscopic world.

In this new framework, the world is no longer strictly deterministic in the classical sense. Even if the exact wavefunction of a system is known, one still cannot predict a single outcome with certainty. For instance, one can only predict probability of an electron appearing at certain locations around the nucleus. Nature itself contains uncertainty, not because of instruments or measurement or observation limit, but because this is how the microscopic world is structured. In other words, the world is no longer deterministic, but rather full of uncertainties.

The deterministic world of Newton is still incredibly accurate at large scales, e.g., planets move as predicted, bridges stand on the ground, airplanes fly over skies, cars move on the road, and many more. But under that smooth surface is a quantum world, where probability dictates what can and will happen, and reality is not fully defined until it is measured (and I still don’t understand any of this).