Question

(4 marks) Derive the inverse Lorentz transformation for the partial deriva- tives, u a cat (5) (6) a ar a ду a дz a at a ar' a ay a az! a 7 at' (7) u (8) ar' Hint: you need to use the chain rule. (2 marks) Write down analogous expression to equations (5)-(8), assuming a Galilean transformation: x' = x -ut, y = y, z = z and t' = t.

Answer 1

c² 1 V1-27/12 Lorentz Transformation relm, t'=81t-uz) X'= 812-ut) where, 8= y'=y z = z ut relative speed between two systemo @t coa da ax' fa' + hot' da OX [8 (X-ut)] %&+ Oba [(t-4.)] fo!' -8 rue pot! Tox' 8 8 ( Tau! u for) =& proved ha t tot Iz de dyl + Toy! + gy Poz! a x' Fox' + ay dy ५ 24 a (y) toy! py - You! => proved

od otra' % 62 It otot dy d dz tor 92 az 8 1 => d (2) for 2 hoz ta' proved It Toz' + Jy Hon't t' at fot a x ta' + DE O DE [8/4 - ut)] Estonia [X(t - 4x)] %t' =- ru otore' => 1 tot ( pot' - uofon) proved. HI Galilean Rel? x = x-ul yl ay z = 2 tot. rel? of derivative as follows, Fox' Tox Hoy Hou' toz hoz tot - ud Answer tot Loo convinience poroof Hoxt as follows, 2x of at flot' dy! M di de by + for 0zl fra da 21 tida on (x-ut) Oton formed

dyl + dawor + be + (oy ०५ a (५) क Offy toy proved ना

9x? z %> 来 ht 02 多。 Toy' *2 ZZ T >> (4) 名: 今 %> Sh: proved

99 %. ә а Әь *g + Чо t toa at 10 О + 0. е 10. (+) əme! х/ о (– це )2 + āt Еф- ч ба'. => a e + 0 n proved