Didactic derivation of the special theory of relativity from the Klein–Gordon equation

Bibliographic description

punktacja MNiSW [2014 A]: 15

title:	Didactic derivation of the special theory of relativity from the Klein–Gordon equation
author:	Arodź Henryk
journal title:	European Journal of Physics
volume:	35
issue:	5
date of publication :	2014
article ID:	055015
ISSN:	0143-0807
eISSN:	1361-6404
DOI:	10.1088/0143-0807/35/5/055015
language:	English
journal language:	English
abstract in English:	We present a didactic derivation of the special theory of relativity in which Lorentz transformations are 'discovered' as symmetry transformations of the Klein–Gordon equation. The interpretation of Lorentz boosts as transformations to moving inertial reference frames is not assumed at the start, but it naturally appears at a later stage. The relative velocity v of two inertial reference frames is defined in terms of the elements of the pertinent Lorentz matrix, and the bound _{\|v\|<c} is presented as a simple theorem that follows from the structure of the Lorentz group. The polar decomposition of Lorentz matrices is used to explain noncommutativity and nonassociativity of the relativistic composition ('addition') of velocities.
keywords in English:	Lorentz transformations, Lorentz group, composition of velocities
number of pulisher's sheets:	1
affiliation:	Wydział Fizyki, Astronomii i Informatyki Stosowanej : Instytut Fizyki im. Mariana Smoluchowskiego
type:	journal article
subtype:	academic paper

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