The Quantum Physics Problem No Computer Can Really Solve | Science For Sleep

Welcome to Physics With William — your calm place to unwind, relax, and gently drift into sleep while exploring one of the strangest limits hidden inside quantum physics. Tonight, we softly explore the spectral gap — the energy difference between a quantum system’s ground state and its first excited state. For many systems, knowing whether this gap exists can tell us something fundamental about the phase of matter and how the system behaves. But in certain quantum many-body models, something remarkable happens: there is no universal algorithm that can always determine whether the system is gapped or gapless. This is not simply a problem of computers being too slow. It is a form of undecidability — meaning that, in the most general case, the question cannot be solved by any algorithm at all. The result connects quantum physics to some of the deepest ideas in mathematics and computer science, showing that even perfectly stated physical questions can sometimes lie beyond the reach of computation. Take a slow breath, imagine a quantum system hiding a question that no machine can always answer, and let Physics With William carry you into calm — where even the limits of knowledge can feel quiet and still. Sources: Undecidability of the Spectral Gap — https://www.nature.com/articles/natur... Full Paper: Undecidability of the Spectral Gap — https://arxiv.org/abs/1502.04573 Undecidability of the Spectral Gap in One Dimension — https://discovery.ucl.ac.uk/id/eprint... Turing Machines — https://plato.stanford.edu/entries/tu... Review of Modern Physics: Quantum Many-Body Systems and Tensor Networks — https://journals.aps.org/rmp/abstract...