How to See an Electron Tremble ⚡ экспресс
Zitterbewegung — the oscillatory motion arising from the Dirac equation — has remained unobservable for free electrons due to its scale on the order of the Compton wavelength. A relativistic vortex electron wave packet was constructed as a coherent superposition of positive and negative energy states, and its spatiotemporal dynamics were studied. It is shown that introducing orbital angular momentum makes it possible to multiply the ZBW amplitude compared to traditional Gaussian packets, while maintaining coherence. The resulting vortex states unify Gaussian and Bessel–Gauss models within a single formalism. This result opens new prospects for observing relativistic quantum effects in structured electron beams.
According to the laws of the microworld, an electron obeying the Dirac equation trembles even at complete rest. This is Zitterbewegung — an oscillation with an amplitude of trillionths of a millimeter, like a spinning top on an invisible axis. For nearly a hundred years, it couldn't be detected: the jitter is thousands of times smaller than an atomic nucleus.
Now researchers have found a way to blow it up. By passing electrons through a special "lens", the beam is twisted into a vortex — like water swirling down a drain — and two states are mixed: one with positive energy and one with negative. Negative energy isn't a trick; it's a door to the world of antimatter opened by Dirac: for a fleeting moment, the electron turns into a positron, and this transition rocks the particle. The two states add up like mutually reinforcing waves, making the oscillation noticeable.
If detectors register the trembling, we'll directly witness the link between quantum mechanics and the ultimate speed limit of the Universe. Vortex electrons might also help us probe the curvature of spacetime on a microscopic scale.
🎯 Beyond the jitter, the Dirac equation predicted antimatter. When Dirac first saw solutions with negative energy, he proposed that all negative-energy states are filled with electrons, forming a "Dirac sea", and the holes in this sea are positrons.