Question

what will happen if every states follow local time

Answer 1

There would be confusions regarding time whenever you travel between states. National recordings would get the additional task of time stamping according to Local times...etc. In short, it would increase the tasks of especially time bound national workers in solving time related problems. But on the other hand it would benefit astronomers and space observatories and few other domains of the economy. 
But the dominating negative effect will be the reduced productivity due to time barriers (limits) and more time related delays in many places.
I hope my perspective helps.

Answer 2

The basis of time zones was to divide Earth into sections of longitude 15 degrees each. That would allow for 24 zones to represent 24 hours in the day (one rotation of Earth). However, in the United States, the borders were usually drawn to follow state lines, or natural landmarks and county lines. There are even a few instances of counties split into two time zones.