In reading about Feynmans functional aproach to QM it is obvious that in summing over all paths we also consider paths with v>c. This troubles me because it is possible to set a Lagrangian and a time interval for wich the non-relativistic classical path has the particle travelling at v>c. Take for instance the lagrangian of the free fall. Taking sufficiently far apart endpoints it is clear that we can have the particle arriving at v>c. I have tried bypassing this problem by using the relativistic action and some how shortening the spatial integration limits in each time slice so as to not sum over supraluminal paths, but have been unsuccessful. Any solution to this problem? I am aware of possible answers like " oh, don't worry about those paths, they cancell out". Please if you are tempted to say this, add a non-heuristic proof to your assertion. Happy New Year!