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WeekProb_Aug_26

# WeekProb_Aug_26 - in a passing ship S moving in the...

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Discussion Problems For section week of Aug 26, 2009 Problem 1: Galilean Relativity. Although some of this in the book. .. try not to look at it!! Newton’s laws are said to be invariant under so-called “Galilean relativity”, while Maxwell’s 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 Newton’s laws are invariant to a Galilean coordinates transformation? It’s just the statement that you can use ~ F = m~a 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. Let’s explore this further. a. Jack, standing on a stationary ship, S , uses coordinates ( x, t ) to describe an event. Jane
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Unformatted text preview: 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. Jack’s people will try to measure the length of Jane’s (moving) ship using two simultane-ous events occurring at: ( x 1 , t 1 ) ( x 2 , t 2 ) such that t 1 = t 2 and x 1 is noting the position of one end of the ship, while x 2 is noting the position of the other end. In Jane’s frame her ship is not moving. She will observe these two events separated by a distance x 2-x 1 . What is this distance? Now use the transformations to ﬁgure out what t 2-t 1 must be and x 2-x 1 must be. 1...
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