Tuesday, 13 March 2018

homework and exercises - Derivation of Lorentz Transformations


How can I derive the Lorentz transformations? I don't want to use hyperbolic functions and the fact that the light waves travel by forming spherical wavefronts. Is there a way to derive the Lorentz transformations applying the conditions I have mentioned. I was unable to understand the method given in Landau and lifshitz deeply. That's why I want a method other than the one using hyperbolic functions



Answer



Here's a derivation that uses very basic properties of space and time (isotropy, homogeneity, the fact that two Lorentz boosts should compose into another valid Lorentz boost, etc.). The constant maximum speed through space (i.e., the speed of light) is a derived property, not an assumption.


One more derivation of the Lorentz transformation - Jean-Marc Levy-Leblond


Here's a similar one that uses linear algebra after deriving the fact that the transform is linear, with similar results.


Nothing but relativity - Palash B. Pal



These kinds of group-theory-based derivations go back to Vladimir Ignatowski in 1910.


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