Quantum mechanics

In the classical world of "big things," variables like energy and momentum change smoothly and continuously. Quantum mechanics reveals that at the scale of atoms and subatomic particles, these quantities are "quantized"—they exist only in specific, discrete packets. This shift isn't just a minor correction; it is the foundational layer upon which chemistry, biology, and modern technology (like transistors and lasers) are built.

While classical mechanics works as a reliable approximation for the visible world, it fails entirely to describe the behavior of light and matter at the submicroscopic level. Quantum theory bridges this gap, showing that the "solid" reality we experience is actually a result of complex quantum interactions happening at scales invisible to the naked eye.

Unlike classical physics, which can predict exactly where a planet will be in a thousand years, quantum mechanics deals in probabilities. A particle’s state is described by a mathematical "wave function." This function doesn't say where a particle is; it provides "probability amplitudes"—complex numbers that, when squared via the Born rule, tell us how likely we are to find the particle in a specific spot.

The act of measuring a system fundamentally changes it. Before measurement, a system can exist in a "superposition" of multiple states at once. The moment an observation occurs, the wave function is said to "collapse" into a single, definite eigenvalue. This transition from a cloud of possibilities to a single fact remains one of the most debated and philosophically challenging aspects of the field.

One of the most famous demonstrations of quantum "weirdness" is the double-slit experiment. When light or electrons are fired at two slits, they create an interference pattern on a screen, behaving exactly like overlapping waves in a pond. However, they always strike the screen at discrete points, as if they were solid particles.

The truly strange part occurs when we try to detect which slit a particle passes through. The moment we observe the path, the interference pattern disappears, and the particles behave like classical "bullets." This wave-particle duality proves that the very presence of a detector—the act of gathering information—dictates how reality manifests.

Quantum entanglement occurs when two or more particles become so deeply linked that the state of one cannot be described independently of the others, regardless of the distance between them. Erwin Schrödinger called this the "characteristic trait" of quantum mechanics. If you measure the spin of one entangled particle, you instantly know the spin of its partner, even if it is light-years away.

This phenomenon was so unsettling that Albert Einstein famously doubted it, suggesting there must be "hidden variables" we simply couldn't see. However, subsequent experiments (most notably those testing Bell’s theorem) have consistently shown that nature is indeed non-local. This "spooky action" is now the engine behind emerging technologies like quantum computing and ultra-secure quantum cryptography.

In classical physics, if a ball doesn't have enough energy to roll over a hill, it stays on one side. In the quantum world, particles like electrons have a small but real probability of appearing on the other side of a "potential barrier" even without the energy to clear the top. This is called quantum tunnelling.

This isn't just a theoretical curiosity; it's a practical necessity. Tunnelling is what allows hydrogen atoms in the sun to overcome their natural repulsion and fuse, providing the energy for life on Earth. In technology, we exploit this effect in scanning tunnelling microscopes to see individual atoms and in flash memory and transistors to manage the flow of electricity at near-atomic scales.