There is a long-standing debate about whether spin-charge separation is the root cause of the peculiar normal-state properties and high superconducting transition temperatures of the high-Tc materials. In the proposed state of matter, the elementary excitations are not electron-like, as in conventional metals, but rather the electron 'fractionalizes' to give excitations that are chargeless spin-1/2 fermions (spinons) and charge +e bosons (chargons). Although spin-charge separation has been well established in one dimension, the theoretical situation for two dimensions is controversial and experimental evidence for it in the high-Tc materials is indirect. A model with sharp experimental tests for a particular type of separation in two dimensions has recently been proposed. Here we report the results of those experimental tests, placing a conservative upper limit of 190 K on the energy of the proposed topological defects known as visons. There is still debate about the extent to which this experiment can settle the issue of spin-charge separation in the high-Tc copper oxides, because some forms of the separation are able to avoid the need for visons. But at least one class of theories that all predict a vortex-memory effect now are unlikely models for the copper oxides.