Problem_1.1H - if F is appropriately defined in terms of F...

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Problem 1 COVARIANCE Consider the Galilean Transformation ' , ' x x Vt t t = - = , and the Lorentz Transformation 2 2 ' ( ), ' ( ), 1/ (1 ) x x Vt t t Vx V = Γ - = Γ - Γ ≡ - , where we have used c=1 units. These transformations connect two frames moving with V w.r.t. each other. Note that the motion of any mass m (rest mass) can be parameterized as x(t), x’(t), or t’(t). 1. Show that Newton’s equations / , / dx dt u mdu dt F = = are covariant under GT. You may assume that F is a given constant. You may define F’ in terms of F appropriately so as to accommodate covariance. 2. Show that Newton’s equations are not covariant under LT, even
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Unformatted text preview: if F is appropriately defined in terms of F and V . (Find explicitly the equation in the unprimed frame if NE apply in the primed lab frame, or vice-versa.) 3. By contrast, show that Einsteins equations 2 2 / , [ ]/ , 1/ (1 ) dx dt u md u dt F u = = =-are covariant under LT. [Covariance is defined as the equations look the same. i.e., both physicists agree on the type of all operations needed to describe motion under F .]...
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This note was uploaded on 12/29/2011 for the course PHYSICS 601 taught by Professor Hassam during the Fall '11 term at Maryland.

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