Time dilation - Revision history

71.203.227.52 at 13:09, 12 January 2015

2015-01-12T13:09:32Z

← Older revision		Revision as of 15:09, 12 January 2015
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en>Sethur2: /* Time dilation due to relative velocity symmetric between observers */ Fixed: "C => B and C => B" to "C => B and B => C"

2014-02-24T14:43:25Z

Time dilation due to relative velocity symmetric between observers: Fixed: "C => B and C => B" to "C => B and B => C"

← Older revision		Revision as of 16:43, 24 February 2014
Line 1:		Line 1:
	~~{{multiple issues\|~~		Hola! I am Dalton. Acting should be a thing that Now i'm totally addicted to. My carry is now in Vermont and I don't design on changing it. I am a cashier. I'm not awesome at webdesign but you may be want to check my website: http://circuspartypanama.com<br><br>Also visit my homepage [http://circuspartypanama.com clash of clans hack no survey no download]
	~~{{Technical\|section=\|date=July 2009}}~~
	~~{{Expert-subject\|Physics\|date=July 2009}}~~
	~~{{Unreferenced\|date=July 2009}}~~
	}}

	~~In [[physics]], the '''trinification model''' is~~ a ~~[[Grand unification theory\|GUT]] theory.~~

	~~It states~~ that ~~the [[gauge group]] is either~~

	~~:<math>SU(3)_C\times SU(3)_L\times SU(3)_R</math>~~

	or

	~~:<math>[SU(3)_C\times SU(3)_L\times SU(3)_R]/\mathbb{Z}_3</math>;~~

	and that the fermions form three families, each consisting of the [[Representations of Lie groups/algebras\|representations]] :<math>(3,\bar{3},1)</math>, <math>(\bar{3},1,3)</math> and :<math>(1,3,\bar{3})</math>.

	~~This includes the right-handed neutrino, which can account for observed neutrino masses (but has not yet been proved~~ to ~~exist)~~. ~~See [[neutrino oscillation]]s.~~

	~~There~~ is ~~also a <math>(1,3,\bar{3})</math>~~ and ~~maybe also a <math>(1,\bar{3},3)</math> [[scalar field]] called the [[Higgs field]] which acquires a VEV~~. ~~This results in~~ a ~~[[spontaneous symmetry breaking]] from~~

	~~:<math>SU(3)_L\times SU(3)_R</math> to <math>[SU(2)\times U(1)]/\mathbb{Z}_2</math>~~

	~~and also,~~

	~~:<math>(3,\bar{3},1)\rightarrow(3,2)_{\frac{1}{6}}\oplus(3,1)_{-\frac{1}{3}}</math>,~~

	~~:<math>(\bar{3},1,3)\rightarrow2\,(\bar{3},1)_{\frac{1}{3}}\oplus(\bar{3},1)_{-\frac{2}{3}}</math>,~~

	~~:<math>(1,3,\bar{3})\rightarrow2\,(1,2)_{-\frac{1}{2}}\oplus(1,2)_{\frac{1}{2}}\oplus2\,(1,1)_0\oplus(1,1)_1</math>,~~

	~~:<math>(8,1,1)\rightarrow(8,1)_0</math>,~~

	~~:<math>(1,8,1)\rightarrow(1,3)_0\oplus(1,2)_{\frac{1}{2}}\oplus(1,2)_{-\frac{1}{2}}\oplus(1,1)_0</math>,~~

	~~:<math>(1,1,8)\rightarrow 4\,(1,1)_0\oplus 2\,(1,1)_1\oplus 2\,(1,1)_{-1}</math>~~.

	~~See [[restricted representation]].~~

	~~Note that there are~~ '~~''two''' [[Majorana spinor\|Majorana]] neutrinos per generation (which is consistent with [[neutrino oscillation]]s). Also, a copy of~~

	~~<math>(3,1)_{-\frac{1}{3}}</math> and <math>(\bar{3},1)_{\frac{1}{3}}</math>~~

	~~as well as~~

	~~<math>(1,2)_{\frac{1}{2}}</math> and <math>(1,2)_{-\frac{1}{2}}</math>~~

	~~per generation decouple~~ at ~~the GUT breaking scale due~~ to ~~the couplings~~

	~~<math>(1,3,\bar{3})_H(3,\bar{3},1)(\bar{3},1,3)<~~/~~math>~~

	~~and~~

	~~<math>(1,3,\bar{3})_H(1,3,\bar{3})(1,3,\bar{3})<~~/~~math>~~.

	~~Note that calling the [[Representations of Lie groups/algebras\|representations]] things like~~ <~~math~~>~~(3,\bar{3},1)~~<~~/math~~> ~~and (8,1,1) is purely a physicist's convention, not a mathematician's convention, where representations are either labelled by~~ [~~[Young tableau]]x or [[Dynkin diagram]]s with numbers on their vertices, but still, it is standard among GUT theorists.~~

	~~Since the [[homotopy group]]~~

	~~<math>\pi_2\left(\frac{SU(3)\times SU(3)}{[SU(2)\times U(1)]~~/~~\mathbb{Z}_2}\right)=\mathbb{Z}<~~/~~math>,~~

	~~this model predicts [[Magnetic monopole\|monopoles]]. See [['t Hooft-Polyakov monopole]].~~

	~~This model is suggested by [[Sheldon Lee Glashow]], [[Howard Georgi]] and [[Alvaro de Rujula]], in 1984~~. ~~This is one~~ of ~~the [[maximal subalgebra]] of E6, whose matter representation 27 has exactly the same representation as above.~~

	~~==References==~~
	~~{{Reflist}}~~

	~~[[Category:Particle physics]~~]

en>Gob Lofa: /* Overview */

2014-01-28T16:10:12Z

Overview

← Older revision		Revision as of 18:10, 28 January 2014
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			In [[physics]], the '''trinification model''' is a [[Grand unification theory\|GUT]] theory.

			It states that the [[gauge group]] is either

			:<math>SU(3)_C\times SU(3)_L\times SU(3)_R</math>

			or

			:<math>[SU(3)_C\times SU(3)_L\times SU(3)_R]/\mathbb{Z}_3</math>;

			and that the fermions form three families, each consisting of the [[Representations of Lie groups/algebras\|representations]] :<math>(3,\bar{3},1)</math>, <math>(\bar{3},1,3)</math> and :<math>(1,3,\bar{3})</math>.

			This includes the right-handed neutrino, which can account for observed neutrino masses (but has not yet been proved to exist). See [[neutrino oscillation]]s.

			There is also a <math>(1,3,\bar{3})</math> and maybe also a <math>(1,\bar{3},3)</math> [[scalar field]] called the [[Higgs field]] which acquires a VEV. This results in a [[spontaneous symmetry breaking]] from

			:<math>SU(3)_L\times SU(3)_R</math> to <math>[SU(2)\times U(1)]/\mathbb{Z}_2</math>

			and also,

			:<math>(3,\bar{3},1)\rightarrow(3,2)_{\frac{1}{6}}\oplus(3,1)_{-\frac{1}{3}}</math>,

			:<math>(\bar{3},1,3)\rightarrow2\,(\bar{3},1)_{\frac{1}{3}}\oplus(\bar{3},1)_{-\frac{2}{3}}</math>,

			:<math>(1,3,\bar{3})\rightarrow2\,(1,2)_{-\frac{1}{2}}\oplus(1,2)_{\frac{1}{2}}\oplus2\,(1,1)_0\oplus(1,1)_1</math>,

			:<math>(8,1,1)\rightarrow(8,1)_0</math>,

			:<math>(1,8,1)\rightarrow(1,3)_0\oplus(1,2)_{\frac{1}{2}}\oplus(1,2)_{-\frac{1}{2}}\oplus(1,1)_0</math>,

			:<math>(1,1,8)\rightarrow 4\,(1,1)_0\oplus 2\,(1,1)_1\oplus 2\,(1,1)_{-1}</math>.

			See [[restricted representation]].

			Note that there are '''two''' [[Majorana spinor\|Majorana]] neutrinos per generation (which is consistent with [[neutrino oscillation]]s). Also, a copy of

			<math>(3,1)_{-\frac{1}{3}}</math> and <math>(\bar{3},1)_{\frac{1}{3}}</math>

			as well as

			<math>(1,2)_{\frac{1}{2}}</math> and <math>(1,2)_{-\frac{1}{2}}</math>

			per generation decouple at the GUT breaking scale due to the couplings

			<math>(1,3,\bar{3})_H(3,\bar{3},1)(\bar{3},1,3)</math>

			and

			<math>(1,3,\bar{3})_H(1,3,\bar{3})(1,3,\bar{3})</math>.

			Note that calling the [[Representations of Lie groups/algebras\|representations]] things like <math>(3,\bar{3},1)</math> and (8,1,1) is purely a physicist's convention, not a mathematician's convention, where representations are either labelled by [[Young tableau]]x or [[Dynkin diagram]]s with numbers on their vertices, but still, it is standard among GUT theorists.

			Since the [[homotopy group]]

			<math>\pi_2\left(\frac{SU(3)\times SU(3)}{[SU(2)\times U(1)]/\mathbb{Z}_2}\right)=\mathbb{Z}</math>,

			this model predicts [[Magnetic monopole\|monopoles]]. See [['t Hooft-Polyakov monopole]].

			This model is suggested by [[Sheldon Lee Glashow]], [[Howard Georgi]] and [[Alvaro de Rujula]], in 1984. This is one of the [[maximal subalgebra]] of E6, whose matter representation 27 has exactly the same representation as above.

			==References==
			{{Reflist}}

			[[Category:Particle physics]]

87.113.169.218: /* Simple inference of time dilation due to relative velocity */ correction / clarification of language used

2012-08-29T20:08:10Z

Simple inference of time dilation due to relative velocity: correction / clarification of language used

New page

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