There’s a "ghost" energy field out there that quantum particles can't even feel—they just breeze right through it like nothing is there.
arXiv · March 13, 2026 · 2603.11183
Why it matters
For decades, it was assumed that any real physical field would leave a unique signature on the energy levels of particles passing through it. This study disproves that theory by proving the existence of a complex energy field that perfectly mimics a total vacuum, making it impossible to detect through standard quantum measurements.
From the abstract
Using numerical certification, we prove the existence of a nontrivial real-valued two dimensional periodic potential whose associated discrete Schrödinger operator is Fermi isospectral to the zero potential. This provides a negative answer to a question posed by the third author concerning the rigidity of Fermi isospectrality in dimension two. This example also disproves a conjecture of Gieseker, Knörrer, and Trubowitz in the 1990s stating that for any nontrivial real-valued periodic potential i