{"id":82343,"date":"2015-04-30T03:00:00","date_gmt":"2015-04-30T00:00:00","guid":{"rendered":"http:\/\/www.fyysika.ee\/?guid=188285b55fd7adb9a3c5700a5d22dc4b"},"modified":"2015-04-30T03:00:00","modified_gmt":"2015-04-30T00:00:00","slug":"non-linear-energy-conservation-theorem-in-the-framework-of-special-relativity","status":"publish","type":"post","link":"https:\/\/www.fyysika.ee\/?p=82343","title":{"rendered":"Non-linear energy conservation theorem in the framework of special relativity"},"content":{"rendered":"<p>In this work we revisit the study of the gravitational interaction in the context of the special<br \/>\ntheory of relativity. It is found that, as long as the equivalence principle is respected, a<br \/>\nrelativistic nonlinear energy conservation theorem arises in a natural way. We interpret that this<br \/>\nnonlinear conservation law stresses the nonlinear character of the gravitational interaction. The<br \/>\ntheorem reproduces the energy conservation theorem of Newtonian mechanics in the corresponding low<br \/>\nenergy limit, but also allows to derive some standard results of post-Newtonian gravity, such as the<br \/>\nformula of the gravitational redshift. Guided by this conservation law, we develop a Lagrangian<br \/>\nformalism for a particle in a gravitational field. We realize that the Lagrangian can be written in<br \/>\nan explicit covariant fashion, and turns out to be the geodesic Lagrangian of a curved Lorentzian<br \/>\nmanifold. Therefore, any attempt to describe gravity within the special theory, leads outside their<br \/>\nown domains t&#8230;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>In this work we revisit the study of the gravitational interaction in the context of the special<br \/>\ntheory of relativity. It is found that, as long as the equivalence principle is respected, a<br \/>\nrelativistic nonlinear energy conservation theorem arises in&#8230;<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_genesis_hide_title":false,"_genesis_hide_breadcrumbs":false,"_genesis_hide_singular_image":false,"_genesis_hide_footer_widgets":false,"_genesis_custom_body_class":"","_genesis_custom_post_class":"","_genesis_layout":"","footnotes":""},"categories":[178],"tags":[],"class_list":{"0":"post-82343","1":"post","2":"type-post","3":"status-publish","4":"format-standard","6":"category-rss-fuusikaharidus","7":"entry"},"_links":{"self":[{"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=\/wp\/v2\/posts\/82343","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=82343"}],"version-history":[{"count":0,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=\/wp\/v2\/posts\/82343\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=82343"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=82343"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=82343"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}