The most accurate theory ever tested cannot tell you where an electron is
Quantum mechanics predicts an electron's magnetic behaviour to within one part in a trillion, yet refuses to say where that electron will turn up. It deals only in probabilities. Particles act like waves, slip through barriers they should not cross, and become so entangled that describing them separately stops making sense.
The theory grew from puzzles classical physics could not solve. Max Planck cracked the black-body radiation problem in 1900, and Albert Einstein's 1905 paper tied energy to frequency to explain the photoelectric effect. That early old quantum theory matured in the mid-1920s, when Niels Bohr, Werner Heisenberg, Erwin Schrödinger, Paul Dirac and Max Born, among many, turned it into a full theory. Classical mechanics survives as an approximation that works at everyday scales.
At its core is chance. A particle is described by a wave function assigning a complex number, a probability amplitude, to each point; squaring its size, the Born rule, gives the odds of finding the particle there. The Schrödinger equation carries those amplitudes forward in time. Energy, momentum and similar quantities come in discrete steps for bound systems, and the uncertainty principle forbids sharp predictions of position and momentum together.
The double-slit experiment shows the strangeness. Light through two slits builds up bright and dark interference bands, as waves would, yet it lands at the screen as individual points. Detect which slit each photon uses and the pattern vanishes. Electrons, atoms and molecules do the same. Tunnelling lets particles cross energy barriers that would trap them classically, enabling radioactive decay, fusion inside stars and scanning tunnelling microscopes.
Entanglement links interacting systems so tightly that only the whole can be described. Schrödinger regarded it as the feature that most sharply separates the theory from classical thinking, and it now powers quantum computing. Bell's theorem showed that broad families of hidden-variable theories, which hoped to restore certainty, clash with quantum physics. Why measurement produces definite outcomes remains fiercely debated, and applying the theory to people, as in the Wigner's friend puzzle, raises philosophical problems.
Source: Quantum mechanics
