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If the thief went to heaven that very day, then Jesus lied. Jesus wasn't in heaven that very day. The fact is, on the third day after He'd been raised from the dead and Mary saw Him in the garden, what did Jesus say to her? He said "don't cling to me for I HAVE NOT YET ASCENDED TO MY FATHER." Jesus Himself said He wasn't in Paradise on the same day that He died, so again, no matter what way you look at it, Jesus wasn't telling the thief that they would be together on that same day.
danschance who I quoted likes to say paradise is somewhere else and likes to base things on opinnion.