# 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

• From what do you wish to derive the Lorentz transformations? Given the invariance of the spacetime interval, the derivation is a simple calculation. Given some other starting point (e.g. the invariance of the speed of light?) there calculation will look different. – WillO May 10 '16 at 22:03
• I want to derive the Lorentz transformations from any possible way but the hyperbolic functions...or ok can you please prove it from the invariance of speed of light – Shashaank May 10 '16 at 22:06
• You can't derive the Lorentz transformation from anything. They are a simple fit to experiments, just like the rest of physics. – CuriousOne May 10 '16 at 23:41
• @Shashaank : Hint: Start with the case of one space dimension. Setting $c=1$, a transformation in $SO(1,1)$ leaves the speed of light invariant if and only if it has $(1,1)^T$ as an eigenvector. Where can you go from here? – WillO May 11 '16 at 0:11
• PS: I think you can safely dismiss @CuriousOne's stated position (that logical or mathematical derivations are never part of physics --- so that, for example, the derivation of momentum conservation from translational symmetry is not physics) as too idiosyncratic to take seriously. – WillO May 11 '16 at 0:15