▁( 1 9 1 0 ) ▁for ▁example ▁used ▁for ▁this ▁purpose ▁( a ) ▁the ▁principle ▁of ▁relativ ity , ▁( b ) ▁hom ogene ity ▁and ▁is ot ropy ▁of ▁space , ▁and ▁( c ) ▁the ▁requirement ▁of ▁reci pro city . ▁Philipp ▁Frank ▁and ▁Hermann ▁Rot he ▁( 1 9 1 1 ) ▁argued ▁that ▁this ▁deriv ation ▁is ▁incomplete ▁and ▁needs ▁additional ▁assumptions . ▁Their ▁own ▁calculation ▁was ▁based ▁on ▁the ▁assumptions ▁that : ▁( a ) ▁the ▁Lor ent z ▁transformation ▁forms ▁a ▁hom ogeneous ▁linear ▁group , ▁( b ) ▁when ▁changing ▁frames , ▁only ▁the ▁sign ▁of ▁the ▁relative ▁speed ▁changes , ▁( c ) ▁length ▁contra ction ▁sole ly ▁depends ▁on ▁the ▁relative ▁speed . ▁However , ▁according ▁to ▁Paul i ▁and ▁Miller ▁such ▁models ▁were ▁ins u fficient ▁to ▁identify ▁the ▁invariant ▁speed ▁in ▁their ▁transformation ▁with ▁the ▁speed ▁of ▁light   — ▁for ▁example , ▁Ign at owski ▁was ▁forced ▁to ▁seek ▁rec ourse ▁in ▁elect rod ynam ics ▁to ▁include ▁the ▁speed ▁of ▁light . ▁So ▁Paul i ▁and ▁others ▁argued ▁that ▁both ▁post ul ates ▁are ▁needed ▁to ▁derive ▁the ▁Lor ent z ▁transformation . ▁However , ▁until ▁today , ▁others ▁continued ▁the ▁attempts ▁to ▁derive ▁special ▁relativ ity ▁without ▁the ▁light ▁post ulate . ▁ ▁Non - e uclidean ▁form ulations ▁without ▁imag inary ▁time ▁coordinate ▁M ink owski ▁in ▁his ▁earlier ▁works ▁in ▁ 1 9 0 7 ▁and ▁ 1 9 0 8 ▁followed ▁Po inc ar