Problems
For Discussion section week of Aug 26, 2009
Problem 1: Galilean Relativity. Although some of this in the book... try not to look at it!! Newtons laws are said to be invariant under so-called Galilean relativity, while Maxwells are invariant under special relativity. Galilean relativity involve coordinate transformations that you are intuitively using in every day life, despite being unaware of it. What does it mean to say Newtons laws are invariant to a Galilean coordinates transformation? Its just the statement that you can use F = ma in any inertial coordinate frame without modifying the equation. Galileo put it best when he commented that his pendulum experiments could have been done on a steady sailing ship and he would have gotten the same results, hence the name Galilean. Lets explore this further. a. Jack, standing on a stationary ship, , S uses coordinates (x, t) to describe an event. Jane in a passing ship, S , moving in the positive x-direction with speed v , is using coordinates (x , t ) to describe the same event. Assume their origins coincide at t = t = 0. Write down the transformation, i.e., the relation between (x, t) and (x , t ). Use intuition from everyday life, no special relativity for slow moving ships... b. Jacks people will try to measure the length of Janes (moving) ship using two simultaneous events occurring at: (x1 , t1 ) (x2 , t2 ) such that t1 = t2 and x1 is noting the position of one end of the ship, while x2 is noting the position of the other end. In Janes frame her ship is not moving. She will observe these two events separated by a distance x2 x1 . What is this distance? Now use the transformations to gure out what t2 t1 must be and x2 x1 must be.
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