Why does Hamlet believe that altering "the murder of Gonzago" will provide proof of Claudius's guilt?"Hamlet"
Shakespeare's use of a play within a play reminds the reader of the much-used question "Does art imitate life, or does life imitate art?" In Hamlet's case, he strives to have art imitate life in order to pique the conscience of Claudius. Hamlet instructs the players to alter the drama, then he asks his friend Horatio to closely observe Claudius when one scene "comes near...the circumstance of my father's death."
In this scene Lucius, the nephew to the king of the play enters and says
Thoughts black, hands apt, drugs fit, and time agreeing,/Confederate season, else no creature seeing,...Thy natural magic and dire property/On wholesome life usurps immediately. (III, ii,234-238)
Then, Lucius pour poison into the ear of the "king." When this action occurs, King Claudius rises and Hamlet asks, "What, frighted with false fire?"
When the Queen notices Claudius's discomfiture she asks, "How fates my lord?" And, the King says, "Give me some light. Away!" Observing this reaction of the king, Horatio tells Hamlet, "I did very well note him." This reaction of Claudius is enough to convince Hamlet that his uncle is, indeed, guilty of slaying his father, King Hamlet.
Guildenstern and Rosencrantz are later sent to summon Hamlet to his mother's room. When they arrive, they inform Hamlet that Claudius is "in his retirement [from the play] imarvellous distempered" (III,ii,275). When Hamlet queries, "With drink, sir?" Guildenstern replies, "No, my lord, with choler." (III,ii, 276-277),confirming further Hamlet's suspicions.