Carbon's third p-orbital contributes to its sp3 hybridization through a process called electron promotion, where one electron from the 2s orbital is excited to the 2p orbital, allowing for the formation of four equivalent bonds instead of just two. This promotion occurs before tetrahedral bonding, with the energy required for this process being compensated by the stability gained from forming multiple bonds. The discussion clarifies that while this concept is often used to explain bonding intuitively, it does not represent a physically observable process. Additionally, many elements, not just carbon, exhibit similar behavior in bonding, often existing in a state closer to an excited state when forming molecular bonds.