SEP predicts that in the cold dark matter (CDM) scenario that the internal dynamics of the galaxy should not depend appreciably on even strong external gravitational fields so that rotational velocities should not change. The reason is that in CDM dark matter is concentrated around the galaxy: the only effects would be tidal forces plus the Newtonian acceleration of the galaxy which does not depend on its mass. The observations suggest that this is actually not the case, and this is seen as a support for MOND and in conflict with CDM and also with GRT if SEP is assumed.
In the TGD framework the flat velocity spectrum of distant stars around the galaxy is due to a long cosmic string carrying dark matter and energy containing tangles in which strings have thickened and partially decayed to ordinary matter. This also explains why galaxies form linear structures. These are not local objects so that SEP does not apply to them. Hence there need not be any actual violation of SEP. The long string as a non-local object would react to the external forces which its own mass and rotating stars would experience the net gravitational force caused by the environment as entities in empty space since there would be no cold dark matter present now.
There would be a strong dependence of the effects on the direction of external gravitational fields when they are caused by a single object rather than being an average effect of the environment. If the external gravitational field is in the direction of the string, there would be an acceleration to this direction since the cosmic string does not cause gravitational field in this direction. This would sharply distinguish between halo models and TGD predicting the possibility of free flows of matter along long strings. If the external gravitational field is transversal there would be smaller perturbation reducing the transverse radial gravitational force of the cosmic string and attracting it.
In the recent study, the effect of gravitational fields caused by the environment of the galaxy was studied. These fields represent the sum of environmental gravitational fields. The first estimate is that the gravitational attraction of the environment boils down to a radial central force transversal to the cosmic string weakening the gravitational force caused by the long string. This would give rise to the reduction of the effective value of string tension T and indeed reduce the rotational velocity (v2 ∝ TG). What about CDM model? Due to the presence of dark matter halo, the effect of external fields would be a considerably weaker tidal effect in the CDM model at the distances considered (near the boundary of the visible galaxy).
For a summary of earlier postings see Latest progress in TGD.