Abstract: The peculiar ultra-fast trembling motion of a free electron — the Zitterbewegung predicted by Erwin Schrödinger in 1930 when he scrutinized the Dirac equation — has been simulated using a single trapped ion. The Dirac equation, proposed by Paul Dirac in 1928 to describe the behaviour of relativistic quantum particles, merges quantum mechanics with special relativity. A number of peculiar effects emerge from the equation, including a rapid quivering motion or 'Zitterbewegung', well established in theory but difficult to observe in real particles. Christian Roos and colleagues have developed a proof-of-principle quantum simulation of the Dirac equation using a single trapped ion set to behave as a free relativistic quantum particle. The high level of control of trapped-ion experimental parameters in this system makes it possible to simulate and study Zitterbewegung and other textbook examples of relativistic quantum physics.