Question

Problem 3: (Total 20 points) Note: If you use the parameter, y, in any answer, you should give a clear definition of y. All the motions in this problem occur along the z-axis. a) For the following Lorentz transformation, what is the relative velocity (including the direction) between S and S'? What are the initial positions at $t = t' = 0$? (2 point) $z' = \gamma(z + vt)$; $ct' = \gamma(ct + vz/c)$. x and y do not change. Here $\gamma = 1/\sqrt{1 - (v/c)^2}$ b) Use the length contraction to derive one of the above Lorentz transformation equations between two inertial frames (S and S'). Note: the relative motion is along z not x. (6 points) c) Use this result to demonstrate that a simultaneous event at different locations in the S frame cannot be a simultaneous event in the S' frame if v is not zero. (2 point)

          Problem 3: (Total 20 points)
Note: If you use the parameter, y, in any answer, you should give a clear definition of y. All
the motions in this problem occur along the z-axis.
a) For the following Lorentz transformation, what is the relative velocity (including the
direction) between S and S'? What are the initial positions at $t = t' = 0$? (2 point)
$z' = \gamma(z + vt)$; $ct' = \gamma(ct + vz/c)$. x and y do not change. Here $\gamma = 1/\sqrt{1 - (v/c)^2}$
b) Use the length contraction to derive one of the above Lorentz transformation equations
between two inertial frames (S and S'). Note: the relative motion is along z not x. (6 points)
c) Use this result to demonstrate that a simultaneous event at different locations in the S
frame cannot be a simultaneous event in the S' frame if v is not zero. (2 point)

Problem 3: (Total 20 points)
Note: If you use the parameter, y, in any answer, you should give a clear definition of y. All
the motions in this problem occur along the z-axis.
a) For the following Lorentz transformation, what is the relative velocity (including the
direction) between S and S'? What are the initial positions at t = t' = 0? (2 point)
z' = γ(z + vt); ct' = γ(ct + vz/c). x and y do not change. Here γ = 1/√(1 - (v/c)^2)
b) Use the length contraction to derive one of the above Lorentz transformation equations
between two inertial frames (S and S'). Note: the relative motion is along z not x. (6 points)
c) Use this result to demonstrate that a simultaneous event at different locations in the S
frame cannot be a simultaneous event in the S' frame if v is not zero. (2 point)

Added by Linda E.

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