Hoping to rebound from their divisional loss to the Jets, the Dolphins stayed at home for a Week 4 AFC East duel with the New England Patriots on Monday night.  Miami delivered the opening punch in the first quarter as quarterback Chad Henne hooked up with wide receiver Davone Bess on a 19-yard touchdown pass.  In the second quarter, the Patriots answered with kicker Stephen Gostkowski making a 23-yard and a 30-yard field goal. New England took the lead in the third quarter as wide receiver Brandon Tate returned the second half's opening kickoff 103 yards for a touchdown, followed by running back BenJarvis Green-Ellis' 12-yard touchdown run.  The Dolphins responded with Henne completing a 28-yard touchdown pass to running back Ricky Williams, but the Patriots came right back with quarterback Tom Brady's 11-yard touchdown pass to wide receiver Danny Woodhead.  New England would continue its dominance on special teams in the fourth quarter as cornerback Kyle Arrington returned a blocked field goal 35 yards for a touchdown.  Afterwards, the Patriots sealed the win as safety Patrick Chung returned an interception 51 yards for a touchdown. With the loss, Miami went into its bye week at 2-2.. How many yards longer was Brandon Tate's special teams touchdown when compared to the longest field goal?