Why is Eid celebrated after the new moon is sighted?

After a month long fasting, Muslims all over the world celebrate Eid, that marks the end of the Holy Month of Ramadan. Muslims exchange new clothes, sweets, wishes and monetary gifts on the occasion. They are also encouraged to forgive and forget all past animosity on this day and great each other. 

According to Islamic traditions, the new moon cycle marks the end of the Islamic month of Ramadan and the arrival of the Shawwal.  It is believed that a new lunar month begins with the physical sighting of a sliver of the new moon.

Although, Eid is supposed to be celebrated after the new moon is sighted but due to the geographic positions and atmospheric factors Muslims in many parts of India celebrate Eid a day after Saudi Arabia. Only Muslims in Kerala follow Riyadh while celebrating Eid.