  A Fermi arc is a disconnected segment of a Fermi surface observed in the
pseudogap phase of cuprate superconductors. This simple description belies the
fundamental inconsistency in the physics of Fermi arcs, specifically that such
segments violate the topological integrity of the band. Efforts to resolve this
contradiction of experiment and theory have focused on connecting the ends of
the Fermi arc back on itself to form a pocket, with limited and controversial
success. Here we show the Fermi arc, while composed of real spectral weight,
lacks the quasiparticles to be a true Fermi surface. To reach this conclusion
we developed a new photoemission-based technique that directly probes the
interplay of pair-forming and pair-breaking processes with unprecedented
precision. We find the spectral weight composing the Fermi arc is shifted from
the gap edge to the Fermi energy by pair-breaking processes. While real, this
weight does not form a true Fermi surface, because the quasiparticles, though
significantly broadened, remain at the gap edge. This non-quasiparticle weight
may account for much of the unexplained behavior of the pseudogap phase of the
cuprates.
