Question

PROBLEM #2: Consider the metric: and vector: a) Compute the length-squared of the vector v. b) Using Mathematica, make a ContourPlot of the length of the vector in the x,y space. Comment about the result. Note, for this one, just focus on the first quadrant; I'll explain in class. c) Can you think of a physical example where this is the appropriate metric to use to measure distance??? There are more than one answer, but the more nat ural the better; think creatively)

Answer 1

The matric is g mu v = (1 1 1 1), and vector is v = (x y) a) Vertical-bar Vertical-bar v Vertical-bar Vertical-bar ^2 = g mu v v^2 v^2 = u^' v^' + v^2 u^2 = x^2 + y^2 b) ln[phi) = contour plot[x^2 + y^2, {x, 0, 5}, {y, 0, 5}]