2. Consider a frame of reference R at rest. We consider a particle, travelling at constant velocity v = (ez, Vy, v). We

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2 Consider A Frame Of Reference R At Rest We Consider A Particle Travelling At Constant Velocity V Ez Vy V We 1 (36.17 KiB) Viewed 52 times

2. Consider a frame of reference R at rest. We consider a particle, travelling at constant velocity v = (ez, Vy, v). We track its position with the tensor, [X] d () y(t) -(t) Consider a frame for reference R travelling at velocity u along the r direction. The Lorentz tensor AM, allows us to transform the tensor X* into Xwhich tracks the position of the particle from the point of view of Ř. It is given by -39 0 0 2 I-By 0 0 [A] - 0 0 10 0 0 0 1 with a = (1 – 34)-1/2 and 3 = u/c. (a) Use X" = A", X" to calculate the expression of 1, 1, y and as a function of B.,1,1.9 and . (8 marks) (b) The velocity of the particle along the r axis, measured from the frame of reference Ř, is given by i/i. Identically we have v: = </t. Express or/c as a function of v./c and u/c. Verify that if yr = c then = c. (10 marks)