At the end of 1990, Alcubierre moved to Wales to attend graduate school at Cardiff University, receiving his PhD degree in 1994 through study of numerical general relativity.

[4][9][10][11] After 1996 he worked at the Max Planck Institute for Gravitational Physics in Potsdam, Germany, developing new numerical techniques used in the description of black holes.

Since 2002, he has worked at the Nuclear Sciences Institute of UNAM, where he conducts research in numerical relativity, employing computers to formulate and solve the physical equations first proposed by Albert Einstein.

[12] The solitary wave solutions proposed by Alcubierre for the Einsteinian field equations may possibly prove general relativity consistent with the experimentally verified non-locality of quantum mechanics.

Miguel Alcubierre made a special appearance on the TV productions How William Shatner Changed the World[14] and Michio Kaku's Sci Fi Science: Physics of the Impossible,[15][16] in which his warp bubble theory was discussed.