By Harrison D.M.
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About the Author
Andrew Thomas studied physics within the James Clerk Maxwell development in Edinburgh college, and bought his doctorate from Swansea college in 1992. he's the writer of the what's fact? site (www. whatisreality. co. uk), essentially the most renowned web pages facing questions of the basics of physics. it's been referred to as “The top on-line advent to quantum theory”.
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Additional resources for About Mass-Energy Equivalence
45) 0. 41) in the form and put m = k, i = j to get which is equivalent to Eq. 45). 1 Write down the equations of a null geodesic in the space· time given by the line-element ds 2 = dt 2 - 2ex1 dt dx2 - (dxl)2 + ! l (x2)2 ez"l] 2 constant, where ~ dxz - [(x2)2exl ~ + 2e-"'1) dt ~ is an affine parameter. ') ds = 0 ds ds gik - - where s is the proper length parameter, gives the usual geodesics. 3 Two metrics g 111 ;k and g 121 ;k on a given space-time give the same geodesic curves. Show that their respective Christoffel symbols r il)i kl and r IZ)i kl satisfy a relation of the form where Vk are the components of a vector.
35) This process of symmetrization can be extended to more than two indices. Thus for any tensor of rank n, we define sik s 1 at P 2, say. 8) If we consider a family of cunes, all starting from P1 and ending at P 2 we get different values of s(P1 , P 2 1 ~). We shall look for that curve for which s(P1 , P 2 1')is stationary. 9) This i'l the classh,;al Euler-Lagrange problem and the solution h 43 SPACE-TIME CURVATURE given by the Euler-Lagrange equation. Writing Bq. 8) in the form s 1 =f 0 F(xi, xi) dA. , the Euler-Lagrange equation is d (oF)_ oF_ 0 dA. 11) = (gik x 1 x~<)i we have oF --: ox' = -1 gik X. k • -oF. 12) x" x' = 0.
About Mass-Energy Equivalence by Harrison D.M.
1 at P 2, say. 8) If we consider a family of cunes, all starting from P1 and ending at P 2 we get different values of s(P1 , P 2 1 ~). We shall look for that curve for which s(P1 , P 2 1')is stationary. 9) This i'l the classh,;al Euler-Lagrange problem and the solution h 43 SPACE-TIME CURVATURE given by the Euler-Lagrange equation. Writing Bq. 8) in the form s 1 =f 0 F(xi, xi) dA. , the Euler-Lagrange equation is d (oF)_ oF_ 0 dA. 11) = (gik x 1 x~<)i we have oF --: ox' = -1 gik X. k • -oF. 12) x" x' = 0.