Here is an explanation of the "Famous Violinist Problem," an argument which, in my opinion, puts the final nail in the coffin of anti-abortion rhetoric.
In her thought experiment we are asked to imagine a famous violinist falling into a coma. The society of music lovers determines from medical records that you and you alone can save the violinist's life by being hooked up to him for nine months. The music lovers break into your home while you are asleep and hook the unconscious (and unknowing, hence innocent) violinist to you. You may want to unhook him, but you are then faced with this argument put forward by the music lovers: The violinist is an innocent person with a right to life. Unhooking him will result in his death. Therefore, unhooking him is morally wrong.
However, the argument does not seem convincing in this case. You would be very generous to remain attached and in bed for nine months, but you are not morally obliged to do so. The parallel with the abortion case is evident. The thought experiment is effective in distinguishing two concepts that had previously been run together: “right to life” and “right to what is needed to sustain life.” The fetus and the violinist may each have the former, but it is not evident that either has the latter. The upshot is that even if the fetus has a right to life (which Thompson does not believe but allows for the sake of the argument), it may still be morally permissible to abort. Theorizing about thought experiments usually turns on the details or the patterns of specific cases.