lecture4 - 1 PHY3221 Detweiler Lecture#4 Relativity Lorentz...

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Unformatted text preview: 1 PHY3221 Detweiler Lecture #4 Relativity Lorentz transformation A coordinate rotation: t = t x = x cos θ + y sin θ y =- x sin θ + y cos θ z = z Notice that distance is conserved under a coordinate rotation rotation: x 2 + y 2 = ( x cos θ + y sin θ ) 2 + (- x sin θ + y cos θ ) 2 = x 2 cos 2 θ + 2 xy cos θ sin θ + y 2 sin 2 θ + x 2 sin 2 θ- 2 xy cos θ sin θ + y cos 2 θ = x 2 (cos 2 θ + sin 2 θ ) + y 2 (sin 2 θ + cos θ ) = 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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lecture4 - 1 PHY3221 Detweiler Lecture#4 Relativity Lorentz...

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