where is the time interval for an observer ( e.g. ticks on his clock ) â `` this is known as the proper time , is the time interval for the person moving with velocity v with respect to the observer , is the relative velocity between the observer and the moving clock , is the speed of light .
where Î '' t is the time interval between two co-local events ( i.e. happening at the same place ) for an observer in some inertial frame ( e.g. ticks on his clock ) â `` this is known as the proper time , Î '' t ' is the time interval between those same events , as measured by another observer , inertially moving with velocity v with respect to the former observer , v is the relative velocity between the observer and the moving clock , c is the speed of light , and