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Chapter1_all

Chapter1_all - PHY3063 R D Field The Scope of PHY3063...

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PHY3063 R. D. Field Department of Physics Chapter1_1.doc University of Florida The Scope of PHY3063 Physics: To devise concepts and laws that can help us to understand the universe ( i.e. nature)! speed size seed of light in vacuum c 10 -10 m 10 -14 m Quantum Physics PHY3063 Relativity Physics PHY3063 Classical Physics Everyday world Relativistic Quantum Physics ??? Atomic Size Nucleus Size Classical (or Newtonian) Physics based on: (1) Motion of a particle can be described by position as a function of time. (2) Space is three dimensional. (3) Space is Euclidean. (4) Time is absolute. a b c α β γ Laws of Plane Geometry a 2 + b 2 = c 2 α + β + γ = 180 o d Circumfrence C = π d π = C/d = 3.1415927… Do the laws of plane geometry hold in our world?

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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 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!
PHY3063 R. D. Field Department of Physics Chapter1_3.doc University of Florida Galilean Transformation Consider two frames of reference the O-frame (label events according to t,x,y,z) and the O'-frame (label events according to t',x',y',z') moving at a constant velocity V, with respect to each other at let the origins coincide at t= t' = 0. In the Galilean transformations the O and O' frames are related as follows: z z y y t V x x t t = = + = = z z y y Vt x x t t = = = = Velocity Transformation: z z y y x x v dt dz dt dz dt dz v v dt dy dt dy dt dy v V v V dt dx dt dt V dt dx dt dx v = = = = = = = = + = + = + = = ' ' ' ' ' ' ' ' ' ' Acceleration Transformation: z z y y x x a dt z d dt z d dt z d a a dt y d dt y d dt y d a a dt x d dt x d dt x d a = = = = = = = = = = = = 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 ' ' ' ' ' ' ' ' ' y x z y' z' x' V Event O: (t,x,y,z) O': (t'.x',y',z') O O' x' x Vt' Time is absolute! Classical velocity addition formula! Acceleration is a Galilean invariant!

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PHY3063 R. D. Field Department of Physics Chapter1_4.doc University of Florida Postulates of Classical Physics Consider two frames of reference the O-frame (label events according to t,x,y,z) and the O'-frame (label events according to t',x',y',z') moving at a constant velocity V, with respect to each other at let the origins coincide at t= t' = 0. Let the force F act on a mass m in the O-frame
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Chapter1_all - PHY3063 R D Field The Scope of PHY3063...

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