i am reading Lillian R. Lieber's book on the einstein theory of relativity and i am a bit confused on page 65. she wants to take the equations:(adsbygoogle = window.adsbygoogle || []).push({});

x=x'cosθ - y'sinθ

y=x'sinθ + y'cosθ

and compare them to:

x'=β(x-vt)

t'=β(t-vx/c^{2})

she takes c as one so:

x'=β(x-vt)

t'=β(t-vx)

she solves for x and t and gets:

x=β(x'+vt')

t=β(t'+vx')

then she replaces t with iτ and t' with iτ' and she gets:

x=β(x'+vt')

iτ = iβτ' + βvx'

x=β(x'+vt')

τ=βτ' + iβvx'

next is the part i am confused about. she sets β = cosθ and -iβv = sinθ. this nicely turns the Lorentz equations into:

x=x'cosθ - τ'sinθ

τ=x'sinθ + τ'cosθ

what i don't understand is how did she choose -iβv = sinθ? it works out all nicely in the end but how did she know that sinθ had to equal -iβv? was it arbitrary as a result of trial and error or did she use β = cosθ in order to figure out that -iβv = sinθ?

**Physics Forums - The Fusion of Science and Community**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Question on lorentz transformation equations

Loading...

Similar Threads - Question lorentz transformation | Date |
---|---|

I Question about derivation of lorentz transformation | Feb 24, 2017 |

Quick question about relative velocity in Lorentz Transform | May 9, 2015 |

Question about v in Lorentz Transformation equation | Jan 16, 2014 |

Lorentz transformation question | Aug 29, 2013 |

Question about Lorentz Transforms | Mar 2, 2013 |

**Physics Forums - The Fusion of Science and Community**