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 long time, people believed that if we have a set of rules and we know the initial conidtions, then we can predict what a physical system will do in the future. So the universe is like a big mechanical clock, everything just follow the rules and nothing is really random. Inside this clockwork machine, everything is predetermined by precise physical laws, and it works pretty well. People used this idea to build the foundation for fluid and solid mechanics and many other fields too. They wrote down equations that can predict how fluids and solids behave, just by assuming matter is smooth and continuous (and these equations are still everywhere today).

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 very small scales does not really behave like a smooth continuum anymore. For instance, matter is made of even smaller particles like electrons, protons, and neutrons, or even smaller sub-atomic particles. 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 picture, the world is not deterministic anymore like we used to think. Even if we know the wavefunction of a system perfectly, we still cannot say for sure what will happen. We can only talk about probability, like the chance of finding an electron somewhere around the nucleus. And people think this uncertainty is not because our instruments are bad or our measurement is not good enough. It is just how the small world is. So nature itself is full of uncertainty.

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 everything is just probability, and things are not really decided until you measure them (and I still don’t understand any of this).