Ψ|Ψ|² THE SCHRÖDINGER EQUATION
07 — Beyond Schrödinger

What comes after this equation

The Schrödinger equation describes non-relativistic quantum mechanics — particles moving much slower than light. It isn't the final word on physics, and it doesn't pretend to be. Here's what lies past its boundary.

Everything else on this site — Quantum 101, the experiments, the weird stuff — sits comfortably inside what the Schrödinger equation actually governs. The topics below don't. They're real, active physics, but they either extend the equation, replace it in regimes where it breaks down, or sit at questions physics hasn't answered yet.

Quantum Field Theory

The Schrödinger equation treats particles as fixed objects moving through space and time. It has no room for particles being created or destroyed — which happens constantly at high energies, where relativity matters and mass can convert into new particles. Quantum field theory replaces particles with fields as the fundamental objects: what we call a "particle" is just a localized excitation of its underlying field.

Dirac's equation, which predicted antimatter, was an early step toward this — a relativistic replacement for Schrödinger's equation. QFT is the fuller framework it eventually grew into, and it underlies the Standard Model of particle physics.

Quantum Information

Quantum information theory asks what quantum mechanics implies for information itself — how much can be encoded in a quantum state, how entanglement can be used as a resource, and what quantum systems can compute or communicate that classical systems fundamentally can't. It's the theoretical foundation underneath quantum computing, discussed on Quantum Made Real, and quantum cryptography, which uses measurement's disturbance of a quantum state to detect eavesdropping.

Quantum Gravity

General relativity describes gravity as curved spacetime; quantum mechanics describes everything else as discrete, probabilistic, and quantized. The two theories are individually extraordinarily well-tested, and nobody has yet found a way to combine them into one framework that works in every regime — particularly inside black holes and at the universe's earliest moments, where both gravity and quantum effects should matter at once.

String theory and loop quantum gravity are the two most developed attempts at an answer. Neither has experimental confirmation. This is genuinely open physics, not a settled result with unresolved details.

The Quantum-to-Classical Transition

If everything is fundamentally quantum, why does the everyday world look so reliably classical? Why don't chairs and cats show interference patterns? The mainstream answer is decoherence: large objects interact with their environment so constantly and thoroughly that their quantum superpositions wash out almost instantly, leaving behind what looks like ordinary, definite classical behavior.

Decoherence explains why superposition becomes practically unobservable at large scales — but it doesn't, by itself, solve the measurement problem covered on The Weird Stuff. Exactly how "practically unobservable" becomes "one definite outcome" is still argued about.