A subsurface safety valve features no flow tube to operate the flapper and optionally an equalizing valve in the flapper, if used. It relies on magnetic force that is selectively created to draw the flapper to the open position. A torsion spring can close the valve when the field is removed. Optionally, the fields can be set up to pull and push the flapper open or to do either one. The optional equalizer valve can also be operated by a force field, preferably magnetic.