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# Lecture10 - Lecture 10 Notes 95.658 Spring 2012...

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Lecture 10 Notes, 95.658, Spring 2012, Electromagnetic Theory II Dr. Christopher S. Baird, UMass Lowell 1. Pre-Einstein Relativity - In the science world, Einstein did not invent the concept of “relativity,” but instead created a more accurate physical theory to describe the concept of relativity. - “Relativity” is the concept of how the physics in one frame of reference relates to the physics in another frame of reference. - The most common and useful relationship that can exist between two frames of reference is that one frame of reference is moving with a constant velocity compared to the other. There are other relationships, such as an accelerating frame, a rotating frame, or a stretching frame in comparison to the other frame. But these types are more complex and should be handled later. - For the purpose of definitions, let us always say one frame of reference is at rest and call it the “lab frame” K and the other frame of reference that we call the “moving frame” K ' always moves at a velocity v relative to the lab frame. Frame K has coordinates ( x , y , z , t ) and K ' has coordinates ( x ', y ', z ', t '): - Mathematically, the concept of relativity involves answering the question: If we know the physics equations in K , what must we do to them to make them still hold in K '? - This question was first answered in Galilean-Newtonian mechanics. It was observed that Newton's second law ( F = m a ) held exactly the same form in every inertial (non-deforming, non-accelerating) reference frame. F x = m d 2 x dt 2 and F x ' = m ' d 2 x ' dt ' 2 so that: m d 2 x dt 2 = m ' d 2 x ' dt ' 2 - Galilean-Newtonian mechanics also assumed universal time, in other words all clocks run at the same speed in all frames and at all points in space. This leads to t = t ' and dt / d x = 0. It also assumed universal mass so that m = m ' and dm / d x = 0, leading to: d 2 x dt 2 = d 2 x ' dt 2 - This observation leads directly to Galilean relativity, or the Galilean concept of how to transform v K K'

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equations from one frame to the next. - Simplify to one dimension and integrate both sides of the equations, being careful to keep integration constants: d x dt = d x ' dt A x = x ' A t B - The constant B simply tells us where the spatial origins are set at t = 0. We can easily get B = 0 be aligning both origins at the same point at t = 0. x
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Lecture10 - Lecture 10 Notes 95.658 Spring 2012...

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