A True Paradox Question.?

First of the the 'space time continuum' is a bit to treky. Second, the example is a contradiction. It begs the question, because for the ball to be there in the first place it would have had to already (as in past tense) been placed there, which you conclude in the example. The conclusion presupposes it's truth, all your scientist has done in not doing the time transfer is changing the premise that puts the ball there in the first place, in which case he didn't have anything to decide.