▁define ▁the ▁reci pro cal ▁ ▁see ▁velocity ▁addition ▁formula . ▁ ▁Occ urrence ▁Following ▁is ▁a ▁list ▁of ▁formula e ▁from ▁Special ▁relativ ity ▁which ▁use ▁ ▁as ▁a ▁sh orth and : ▁ ▁The ▁Lor ent z ▁transformation : ▁The ▁simplest ▁case ▁is ▁a ▁boost ▁in ▁the ▁x - direction ▁( more ▁general ▁forms ▁including ▁arbitrary ▁directions ▁and ▁rot ations ▁not ▁listed ▁here ), ▁which ▁describes ▁how ▁spac etime ▁coordinates ▁change ▁from ▁one ▁in ert ial ▁frame ▁using ▁coordinates ▁( x , ▁y , ▁z , ▁t ) ▁to ▁another ▁( x , ▁y , ▁z , ▁t ) ▁with ▁relative ▁velocity ▁v : ▁ ▁Cor oll aries ▁of ▁the ▁above ▁transformations ▁are ▁the ▁results : ▁ ▁Time ▁d ilation : ▁The ▁time ▁( ∆ t ) ▁between ▁two ▁t icks ▁as ▁measured ▁in ▁the ▁frame ▁in ▁which ▁the ▁clock ▁is ▁moving , ▁is ▁longer ▁than ▁the ▁time ▁( ∆ t ) ▁between ▁these ▁t icks ▁as ▁measured ▁in ▁the ▁rest ▁frame ▁of ▁the ▁clock : ▁▁▁ ▁L ength ▁contra ction : ▁The ▁length ▁( ∆ x ) ▁of ▁an ▁object ▁as ▁measured ▁in ▁the ▁frame ▁in ▁which ▁it ▁is ▁moving , ▁is ▁shorter ▁than ▁its ▁length ▁( ∆ x ) ▁in ▁its ▁own ▁rest ▁frame : ▁ ▁App lying ▁conservation ▁of ▁momentum ▁and ▁energy ▁leads ▁to ▁these ▁results : ▁ ▁Rel ativ istic ▁mass : ▁The ▁mass ▁m ▁of ▁an ▁object ▁in ▁motion ▁is ▁dependent ▁on ▁ ▁and ▁the ▁rest ▁mass ▁m 0 : ▁▁ ▁Rel ativ istic ▁momentum :