relativity_1 - PHY2061 R. D. Field PHY2060 Review...

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Unformatted text preview: PHY2061 R. D. Field PHY2060 Review Postulates of Special Relativity Consider two frames of reference the O-frame and the O'-frame moving at a constant velocity V, with respect to each other at let the origins coincide at t= t' = 0. Follow the path of a light ray that was emitted at the origin of the two frames at the instant they crossed. y Light Ray O: (t,x,y,z) O': (t'.x',y',z') y' V O O' x x' z' z inertial First Postulate of Special Relativity (“Relativity Principle”): • The basic laws of physics are identical in all systems of reference (frames) which move with uniform (unaccelerated) velocity with respect to one another. The laws of physics are invariant under a change of inertial frame. The laws of physics have the same form in all inertial frames. It is impossible to detect uniform motion. Second Postulate of Special Relativity (“Constant Speed of Light”): 2.99792458x10 • The speed of light in a vacuum has the same value, c, in all inertial frames. The speed of light in a vacuum is always independent of the Experimental velocity of the source of the light or the velocity of the observer. observation! The entire theory of special relativity is derived from these two postulates. Light Path in O-frame d = ct Light Path in O'-frame d ′ = ct ′ d ′ = x′ 2 + y ′ 2 + z ′ 2 (ct ′) 2 − x ′ 2 − y ′ 2 − z ′ 2 = 0 d = x2 + y2 + z2 (ct ) 2 − x 2 − y 2 − z 2 = 0 Must find the transformation that results in Invariant! (ct ) 2 − x 2 − y 2 − z 2 = (ct ′) 2 − x′ 2 − y ′ 2 − z ′2 Department of Physics relativity_1.doc University of Florida 8 m/s ...
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