Another reason that Hamlet is not present in Act 4 is the fact that Act 4 primarily consists of the consequences of his action in Act 3: killing Polonius. We see the fall-out of Hamlet's mistake. After losing her father, Ophelia goes truly insane and eventually drowns, unable to save herself from the overwhelming "sea of troubles" that engulfs her. Laertes vows revenge on the murderer of his father, and first turns on Claudius before Claudius turns him on Hamlet. Hamlet, of course, must leave Denmark, and Claudius has now ordered his execution, since after Hamlet's act of killing Polonius, Claudius knows that Hamlet had attempted to kill him. Act 4 is the act where so much is set in motion. Forces position themselves to act, so that Act 5 results in the catastrophe promised in great tragedies. Even though Hamlet is not present in much of the act, many of the events in act 4 are the direct result of his previous action.
One of the main reasons is that Hamlet is physically gone. He is sent off to England by Claudius, ostensibly to pick up some debt they owe to Denmark but those who receive him have orders to kill him, and Rosencrantz and Guildenstern go along for the ride to make sure the deed is done.
Figuratively, it serves as a sort of transition for him. As he truly leaves the scene, he views Fortinbras' army and expounds on his feelings of jealousy for the man that can push so great an army for what appears to be little reason. He decides that he too will be a man of action, and this time abroad serves to demonstrate that as he engineers the deaths of Rosencrantz and Guildenstern and returns to Elsinore ready to rock and roll.