▁to ▁show ▁" in ▁the ▁way ▁of ▁cre ative ▁power ▁of ▁discovery ", ▁but ▁it ▁offered ▁not ational ▁advantages ▁in ▁some ▁cases , ▁particularly ▁in ▁the ▁law ▁of ▁velocity ▁addition . ▁( So ▁in ▁the ▁years ▁before ▁World ▁War ▁I , ▁the ▁accept ance ▁of ▁the ▁non - E uclidean ▁style ▁was ▁approximately ▁equal ▁to ▁that ▁of ▁the ▁initial ▁spac etime ▁formal ism , ▁and ▁it ▁continued ▁to ▁be ▁employed ▁in ▁relativ ity ▁text books ▁of ▁the ▁ 2 0 th ▁century . ▁ ▁Time ▁d ilation ▁and ▁tw in ▁par ado x ▁Ein stein ▁( 1 9 0 7 a ) ▁proposed ▁a ▁method ▁for ▁detect ing ▁the ▁trans verse ▁Do pp ler ▁effect ▁as ▁a ▁direct ▁consequence ▁of ▁time ▁d ilation . ▁And ▁in ▁fact , ▁that ▁effect ▁was ▁measured ▁in ▁ 1 9 3 8 ▁by ▁Herbert ▁E . ▁I ves ▁and ▁G . ▁R . ▁St il well ▁( I ves – St il well ▁experiment ). ▁And ▁Lewis ▁and ▁Tol man ▁( 1 9 0 9 ) ▁described ▁the ▁reci pro city ▁of ▁time ▁d ilation ▁by ▁using ▁two ▁light ▁clock s ▁A ▁and ▁B , ▁travel ing ▁with ▁a ▁certain ▁relative ▁velocity ▁to ▁each ▁other . ▁The ▁clock s ▁consist ▁of ▁two ▁plane ▁mirror s ▁parallel ▁to ▁one ▁another ▁and ▁to ▁the ▁line ▁of ▁motion . ▁Between ▁the ▁mirror s ▁a ▁light ▁signal ▁is ▁b oun cing , ▁and ▁for ▁the ▁observer ▁rest ing ▁in ▁the ▁same ▁reference ▁frame ▁as ▁A , ▁the ▁period ▁of ▁clock ▁A