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

2014
journal article
article
cris.lastimport.wos2024-04-09T22:27:33Z
dc.abstract.enWe 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.pl
dc.affiliationWydział Fizyki, Astronomii i Informatyki Stosowanej : Instytut Fizyki im. Mariana Smoluchowskiegopl
dc.contributor.authorArodź, Henryk - 127144 pl
dc.date.accessioned2015-03-19T13:25:39Z
dc.date.available2015-03-19T13:25:39Z
dc.date.issued2014pl
dc.description.number5pl
dc.description.publication1pl
dc.description.volume35pl
dc.identifier.articleid055015pl
dc.identifier.doi10.1088/0143-0807/35/5/055015pl
dc.identifier.eissn1361-6404pl
dc.identifier.issn0143-0807pl
dc.identifier.urihttp://ruj.uj.edu.pl/xmlui/handle/item/3986
dc.languageengpl
dc.language.containerengpl
dc.rightsDodaję tylko opis bibliograficzny*
dc.rights.licencebez licencji
dc.rights.uri*
dc.subject.enLorentz transformationspl
dc.subject.enLorentz grouppl
dc.subject.encomposition of velocitiespl
dc.subtypeArticlepl
dc.titleDidactic derivation of the special theory of relativity from the Klein–Gordon equationpl
dc.title.journalEuropean Journal of Physicspl
dc.typeJournalArticlepl
dspace.entity.typePublication
cris.lastimport.wos
2024-04-09T22:27:33Z
dc.abstract.enpl
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.
dc.affiliationpl
Wydział Fizyki, Astronomii i Informatyki Stosowanej : Instytut Fizyki im. Mariana Smoluchowskiego
dc.contributor.authorpl
Arodź, Henryk - 127144
dc.date.accessioned
2015-03-19T13:25:39Z
dc.date.available
2015-03-19T13:25:39Z
dc.date.issuedpl
2014
dc.description.numberpl
5
dc.description.publicationpl
1
dc.description.volumepl
35
dc.identifier.articleidpl
055015
dc.identifier.doipl
10.1088/0143-0807/35/5/055015
dc.identifier.eissnpl
1361-6404
dc.identifier.issnpl
0143-0807
dc.identifier.uri
http://ruj.uj.edu.pl/xmlui/handle/item/3986
dc.languagepl
eng
dc.language.containerpl
eng
dc.rights*
Dodaję tylko opis bibliograficzny
dc.rights.licence
bez licencji
dc.rights.uri*
dc.subject.enpl
Lorentz transformations
dc.subject.enpl
Lorentz group
dc.subject.enpl
composition of velocities
dc.subtypepl
Article
dc.titlepl
Didactic derivation of the special theory of relativity from the Klein–Gordon equation
dc.title.journalpl
European Journal of Physics
dc.typepl
JournalArticle
dspace.entity.type
Publication
Affiliations

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