Chapter1_2 - rotation in 3-dimensional space r R r ′ = r r where R is the rotation matrix Invariance under Time Translation In empty space there

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PHY3063 R. D. Field Department of Physics Chapter1_2.doc University of Florida Euclidean Geometry in Empty Space The homogeniety and isotropy of euclidean space can be express by three invariance principles ( i.e. symmetries of empty space): Invariance under Translation: In empty space there is no difference between the frame O and the frame O' where O and O' are related by C z z B y y A x x + = + = + = ' ' ' where A, B, and C are constants. Invariance under Rotation: In empty space there is o difference between the frame O and the frame O' where O and O' are related by a
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Unformatted text preview: rotation in 3-dimensional space r R r ′ = r r where R is the rotation matrix. Invariance under Time Translation: In empty space there is no difference between the frame O and the frame O' where O and O' are related T t t + = ' where T is a constant. Symmetries imply conservation laws and vice-versa! Experimental observation! No preferred origin! No preferred direction! No origin of time! Leads to linear momentum conservation! Leads to angular momentum conservation! Leads to energy conservation!...
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This note was uploaded on 05/29/2011 for the course PHY 3063 taught by Professor Field during the Spring '07 term at University of Florida.

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