What the Aharonov-Bohm effect shows — electromagnetic potentials have physical effects even where fields are zero

What the fractional quantum Hall effect shows — emergent particles with fractional charge

Fractional quantum Hall effect demonstrates emergent particles with fractional electric charge

What gauge symmetry is — local phase transformations that leave physics invariant, the basis of all fundamental forces

Gauge symmetry: Local phase transformations preserving physics, underlying fundamental forces

What Bose-Einstein condensation demonstrates — macroscopic quantum coherence at ultralow temperatures

Bose-Einstein condensation shows macroscopic quantum coherence at temperatures near absolute zero

What the Casimir effect demonstrates — quantum vacuum fluctuations create measurable force between conducting plates

Casimir effect: Quantum fluctuations induce attractive force between parallel plates

Why the Dirac equation has negative energy solutions — interpreted as positrons, confirmed by Anderson in 1932

Dirac equation predicts negative energy states, later identified as antiparticles, positrons, by Anderson's experiments

How the Higgs mechanism works — spontaneous breaking of electroweak symmetry gives W and Z bosons their mass

Higgs field's non-zero vacuum expectation value breaks symmetry, endowing W and Z bosons with mass