When Sheldon tries to "be the ball", he performs a Vulcan mindmeld on it from Star Trek (1966), one of his favorite series.
Before the scenes set in the bowling alley, when the atoms are shown rotating, one of the orbiting electrons transforms into a bowling ball.
A portion of this episode takes place in a bowling alley. Jim Parsons's first acting credit was a one-time appearance in the television series Ed (2000) which was mainly set in a bowling alley.