Lecture06_SR5

# Lecture06_SR5 - 1 Spacetime Vectors Relativistic Motion...

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2 Spacetime Vectors Relativistic Motion Examples Summary
3 The values ct, x, y, z can be regarded as the components of a vector in spacetime, a 4-vector The components of same vector can be expressed in a different frame of reference

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4 Define t = BC + CP x = OA + AB What is the map between the two different frames of reference? t' x' C B A Q BC = (v/c) x/c CP = QP/ γ t x P O OA = OQ/ γ AB = vt x' = OQ t' = QP X = OP
5 S frame S frame Lorentz Transformation

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6 Like vectors in 3-D space, one can add, scale and take the dot product of 4-vectors. However, the dot product of two 4-vectors A and B must be defined differently: This is the only way to make the dot product Lorentz invariant , that is, have the same value in all inertial reference frames
7 Hint: Show that X 2 = ( ct ) 2 ( x 2 + y 2 + z 2 ) X 2 = ( c t ) 2 ( x 2 + y 2 + z 2 ) is equal to

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9 According to the Principle of Relativity , the laws of physics should be the same in all inertial frames. In particular, this should be true of the 2 nd law of motion : However, this law cannot be exact because it predicts that velocities can be arbitrarily large t' x' t x P O B Q

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10 But, if Newton’s 2 nd law of motion is expressed the way Newton did originally: then the 2 nd law holds true in special relativity provided that… t' x' t x P O B Q
11 …we define momentum as follows t' x' t x P O B Q

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12 p = γ ( u ) m u implies where The expression:
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