# lorentz invariance

11. ### I Motivation for the usage of 4-vectors in special relativity

I recently had someone ask me why we use 4-vectors in special relativity and what is the motivation for introducing them in the first place. This is the response I gave: From Einstein's postulates( i.e. 1. the principle of relativity - the laws of physics are identical (invariant) in all...
12. ### B About the Lorentz invariance of Planck constant

Is it proved experimentally that the planck constant is invariant in the moving system? If that experiment exists, would you show me that in detail?
13. ### Lorentz invariance of the Minkowski metric

I understand that in order to preserve the inner product of two four vectors under a change of coordinates x^{\mu}\rightarrow x^{\mu^{'}}=\Lambda^{\mu^{'}}_{\,\, \nu}x^{\nu} the Minkowski metric must transform as \eta_{\mu^{'}\nu^{'}}=\Lambda^{\alpha}_{\,\...
14. ### Huygens principle in odd/even dimensional flat space

A well known math theorem says that - if the spatial dimension is odd - D'Alembert equation gives rise to a solution containing a term which is completely supported on the light cone. A mathematical wrap up could be the following: "in dimension 3 (and in fact, for all odd dimensions), the...
15. ### Searching for a function that vanishes only when x^mu = y^mu

Hi all, Just doing some hobby physics while I put off working on my research. In one dimension, the function $$f(a,b)=[1-\exp(-(a-b)^2)]$$ vanishes when a=b. In Minkowski spacetime though, such a function is not so easy to find (if you require Lorentz invariance). If...