The rules of reality at the smallest scales. Provably correct. Makes no intuitive sense. The most precisely tested theory in all of science.
Quantum mechanics is the fundamental theory describing the behavior of matter and energy at atomic and subatomic scales. It is the most precisely tested theory in scientific history — predictions match experiments to one part in a trillion. It also says that particles exist in superpositions of multiple states simultaneously, that observation affects reality, that information can be instantaneously correlated across any distance, and that the universe is fundamentally probabilistic. If you understand quantum mechanics and are not confused, you haven't understood it.
In classical physics, things are either waves or particles — water waves vs. billiard balls. In quantum mechanics, everything is both simultaneously. An electron shot at a screen with two slits creates an interference pattern — as if it passed through both slits at once as a wave. But when you detect which slit it passes through, the interference pattern disappears and it behaves like a particle.
The act of measurement forces the quantum system to "choose" a definite state. Before measurement, the electron literally has no definite position — it exists as a probability wave described by the wavefunction. This is not a limitation of our measurement — it is how reality works at this level.
A quantum system exists in multiple states simultaneously until measured. Schrödinger's cat — alive AND dead — is an illustration of this applied to macroscopic scales. At quantum scales it is literal, not metaphorical.
Two particles can be "entangled" — measuring one instantly determines the state of the other, regardless of distance. Demonstrated over thousands of kilometers. Einstein called it "spooky action at a distance" and spent years trying to disprove it. He was wrong.
Heisenberg: you cannot simultaneously know both the exact position and exact momentum of a particle. More precisely you know one, less precisely you can know the other. This is not a measurement limitation — it is a fundamental feature of reality.
Particles can pass through barriers they classically shouldn't have enough energy to cross. How the Sun burns (protons tunnel through the electromagnetic barrier to fuse). How transistors at small scales sometimes fail. How some enzymes work in biology.
Uses superposition and entanglement to perform certain computations exponentially faster than classical computers. Qubits exist in superposition of 0 and 1 simultaneously. Not faster at everything — extraordinary for specific problems (cryptography, simulation).
What causes wavefunction collapse? Why does measurement force a definite outcome? Multiple interpretations exist (Copenhagen, Many-Worlds, pilot wave) and we cannot currently distinguish between them experimentally. This is genuinely unresolved.
The Schrödinger equation is to quantum mechanics what Newton's second law (F=ma) is to classical mechanics — it describes how the quantum state of a system changes over time. The wavefunction ψ contains all information about a quantum system.
Quantum mechanics describes the very small with extraordinary precision. General relativity describes gravity and large-scale spacetime with extraordinary precision. They are the two most successful theories in physics. They are mathematically incompatible.
When you try to apply quantum field theory to gravity, you get nonsense — infinite answers called divergences that can't be renormalized away. A complete theory of "quantum gravity" — unifying these two frameworks — does not exist. String theory and loop quantum gravity are attempts, but neither is confirmed. This is the deepest open problem in theoretical physics.