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Unformatted text preview: 1 PHY3221 Detweiler Lecture #4 Relativity Lorentz transformation A coordinate rotation: t = t x = x cos + y sin y =- x sin + y cos z = z Notice that distance is conserved under a coordinate rotation rotation: x 2 + y 2 = ( x cos + y sin ) 2 + (- x sin + y cos ) 2 = x 2 cos 2 + 2 xy cos sin + y 2 sin 2 + x 2 sin 2 - 2 xy cos sin + y cos 2 = x 2 (cos 2 + sin 2 ) + y 2 (sin 2 + cos ) = x 2 + y 2 . This might seem obvious because the mathematics just confirms your everyday experiences. The Galilean transformation: t = t x = x- vt y = y z = z Inverse transformation: t = t x = x + vt y = y z = z The Lorentz transformation: t = t- vx/c 2 p 1- v 2 /c 2 x = x- vt p 1- v 2 /c 2 y = y z = z 2 Inverse transformation: t = t + vx /c 2 p 1- v 2 /c 2 x = x + vt p 1- v 2 /c 2 y = y z = z Notice that in the limit that v/c 0, but v remains finite, the Lorentz transformations approach the Galilean transformation. So, only when v is comparable to...
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This note was uploaded on 12/15/2011 for the course PHY 3221 taught by Professor Chan during the Spring '08 term at University of Florida.
- Spring '08