The Minimum Length and the Surprises of Quantum Physics ⚡ экспресс
The subtle difference between Hilbert spaces for canonical and generalized momentum operators in the context of minimal-length theories has been clarified. It is shown that the existence of a minimal length permits the canonical momentum to have complex eigenvalues. A new method for generating quantum entanglement, stemming from this difference, is reported. These results illustrate how incorporating a fundamental minimal length into the description of quantum phenomena can be fruitful, revealing new facets of nonlocal correlations.
Spacetime at ultra-short distances resembles a digital screen: it's not smooth but made of tiny 'pixels.' This minimum length was calculated by Max Planck, and Heisenberg's uncertainty principle explains why the world cannot be continuous: precise measurement always distorts reality. This is how quantum discreteness of space arises. Physicists explored how this pixelation changes one of the fundamental properties of particles—momentum, the measure of their motion.
It turns out that in a pixelated world, momentum ceases to be sharp: it gains an 'imaginary,' fuzzy part—as if the particle simultaneously accelerates and fades. Such an effect is unthinkable in standard quantum mechanics, but it's natural when we look beyond the Standard Model and even into the physics of black holes, where similar ideas help solve the mystery of evaporation. But the most striking part is another surprise. The pixel structure itself can entangle particles. Normally, this requires a collision or joint creation, but here no action is needed: the discreteness of space acts like invisible glue, instantaneously linking quantum states. This spontaneous entanglement could be called a new face of the 'spooky action at a distance' that Einstein warned about.
🎯 If an atom were scaled up to the size of the observable universe, the minimum Planck length would be comparable to the height of a tree—just about ten meters.