class30 - 1.3 Lorentz Transformation Since Galilean...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 1.3 Lorentz Transformation Since Galilean transformations are inconsistent with Einsteins postulate of the speed of light, we must modify them. Consider our two inertial frames S and S , and let the axes be parallel, with S moving w.r.t. S with a speed u in the x direction. The times t and t are zero when the origins coincide. For events with y = x 2 = 0, these should also have y = x 2 = 0 independent of the rest of the variables. Similarly for z = x 3 , and we get x 2 = x 2 and x 3 = x 3 (24) These are the same as the Galilean transformation. Along the x direction, we derive the most general linear transformation, x 1 = ax 1 + bt (25) At the origin of S , where x 1 = 0, we expect x 1 = ut . Substitute this initial condition in. 0 = aut + bt b =- au (26) and our general linear combination reduces to x 1 = a ( x 1- ut ) (27) By symmetry, we also have x 1 = a ( x 1 + ut ) (28) Now lets apply the second postulate of Special Relativity. If a pulse of light is sent fromNow lets apply the second postulate of Special Relativity....
View Full Document

Page1 / 3

class30 - 1.3 Lorentz Transformation Since Galilean...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online