If you're a student I don't think you can fly without an FI. He doesn't have to be in the plane with you, of course, but even if he sends you solo you are actually flying under the priviliges of his license.
Also I don't believe a student can take passengers, and if the guy with a PPL is in the right hand seat then that's what he is.
And even if you could fly with just a PPL, he would have to log it as P1 so you wouldn't be able to log it at all, which I guess would defeat the object.
Not 100% sure if this is right, I'm sure someone will correct me if not.....