Visual-effects supervisor John Gaeta and the Manex team reframed the problem. Instead of forcing one camera to travel fast enough, they built an array of still cameras around the action. The production used up to 120 still cameras for the effect, with motion-picture cameras helping connect the normal-speed action around it.
The still cameras were triggered in sequence, so neighboring viewpoints captured neighboring moments. Put together, those frames could behave like a virtual camera moving around action that was progressing at a radically different speed.
Digital interpolation and compositing helped connect the photographed views and complete the environment. The result was not simply a frozen subject seen from many angles; the shot could move through both space and time in a way a single physical camera could not.
Time-slice techniques existed before The Matrix. What the film did was push the idea into dynamic moving action, popularize Bullet Time, and make the technique serve the story: as Neo begins bending the rules of the Matrix, the camera appears to bend the rules of ordinary photography too.