to justify giving mass to a would-be massless particle, scientists were forced to do something out of the ordinary. they assumed that vacuums (empty space) actually "had" energy, and that way, if a particle that we think of as massless were to enter it, the energy from the vacuum would be transferred into that particle, giving it mass. a mathematician named jeffrey goldstone proved that if you violate a symmetry (for example, a symmetry with a rubik's cube would be if you state that the corners must always be rotated 0 or 3 times to be solvable (it works)), a reaction will occur. in the case of the rubik's cube, the cube will become unsolvable if violated. in the case of the higgs field, something named after jeffrey goldstone (and another scientist who worked with him named yoichiro nambu) is produced, a nambu-goldstone boson. this is an excited or energetic form of the vacuum, which can be graphed revealing that shown above. this was first explained by peter higgs.