In the definition of a \u00ab speed \u00bb by a coordinate ratio, v=x\/t for example, relative between Galilean frames of reference, the velocity of light is an unattainable upper limit (for material objects).<\/p>\n\n\n\n
But is this physical?<\/p>\n\n\n\n
Relativity uses the concept of 4-velocity where the dynamic parameter is the proper time that we will denote T.<\/p>\n\n\n\n
Let\u2019s stay in RR, where we can integrate the \u00ab dt \u00bb in \u00ab t \u00bb, \u00ab dx \u00bb in \u00ab x \u00bb, \u00ab dS \u00bb in \u00ab S \u00bb and \u00ab dT \u00bb in \u00ab T \u00bb (it is linear) and consider only 2 parallel inertial frames of reference of relative velocity v = x\/t<\/p>\n\n\n\n
This gives: t= x\/v.<\/p>\n\n\n\n
The spacetime interval S, we have:<\/p>\n\n\n\n
S\u00b2 = c\u00b2T\u00b2 = c\u00b2t\u00b2-x\u00b2<\/p>\n\n\n\n
This gives c\u00b2T\u00b2= c\u00b2x\u00b2(1\/v\u00b2-1\/c\u00b2 ),<\/p>\n\n\n\n
With y = cste and z = cste, the 4-vector U\u00b5<\/sup>={dt\/dT, dx\/dT, 0, 0}<\/p>\n\n\n\n For the spatial component let us set : V = dx\/dT = X\/T<\/p>\n\n\n\n By setting the 4-speed: V = x\/T<\/p>\n\n\n\n We obtain:<\/p>\n\n\n\n V\u00b2 = v\u00b2 \/(1-v\u00b2\/c\u00b2)<\/p>\n\n\n\n Which can be > c, if v is very close to c.<\/p>\n\n\n\n Let\u2019s take the example v = 0.99 c we obtain:<\/p>\n\n\n\n V= 7c, approximately.<\/p>\n\n\n\n Since the proper time is the parameter that physically measures the time of the observer who follows this geodesic having a speed close to that of light, in the reference frame of the inertial observer of reference that we can, arbitrarily consider at \u00ab rest \u00bb, we see that this \u00ab velocity \u00bb of 7c has a physical character.<\/p>\n\n\n\n In one year of his own time, which also measures his aging, he travels a distance of 7 light years in the \u00ab rest \u00bb frame of reference.<\/p>\n\n\n\n This, illustrated by the \u00ab paradox \u00bb of the Langevin traveler (twins), is its mathematical foundation.<\/p>\n","protected":false},"excerpt":{"rendered":" In the definition of a \u00ab speed \u00bb by a coordinate ratio, v=x\/t for example, relative between Galilean frames of reference, the velocity of light is an unattainable upper limit (for material objects). But is this physical? Relativity uses the concept of 4-velocity where the dynamic parameter is the proper time that we will denote T. Let\u2019s … Continuer la lecture de « Faster than light! 13\/12\/24 »<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-3291","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/vous-avez-dit-bigbang.fr\/index.php?rest_route=\/wp\/v2\/pages\/3291","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/vous-avez-dit-bigbang.fr\/index.php?rest_route=\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/vous-avez-dit-bigbang.fr\/index.php?rest_route=\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/vous-avez-dit-bigbang.fr\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/vous-avez-dit-bigbang.fr\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=3291"}],"version-history":[{"count":1,"href":"https:\/\/vous-avez-dit-bigbang.fr\/index.php?rest_route=\/wp\/v2\/pages\/3291\/revisions"}],"predecessor-version":[{"id":3292,"href":"https:\/\/vous-avez-dit-bigbang.fr\/index.php?rest_route=\/wp\/v2\/pages\/3291\/revisions\/3292"}],"wp:attachment":[{"href":"https:\/\/vous-avez-dit-bigbang.fr\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=3291"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}