(d) Use the inverse Lorentz transformation equation to show that at t' = 0 in the rocket frame t

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(d) Use the inverse Lorentz transformation equation to show that at $t' = 0$ in the rocket frame the clocks along the positive $x$ axis in the laboratory frame appear to be set ahead of those in the rocket frame, with clocks farther from the origin set farther ahead; and that clocks along the negative $x$ axis in the laboratory frame appear to be set behind those in the rocket frame, with clocks farther from the origin set farther behind, according to the equation (47) $t = \pm x' \sinh \theta_r = \pm x' \beta_r/(1 - \beta_r^2)^{1/2}$ The fact that neither of two observers in relative motion agrees that the reference event and the reading of zero time on all clocks of the other frame occur simultaneously is called the relative synchronization of clocks.

          (d) Use the inverse Lorentz transformation equation to show that at $t' = 0$ in the rocket frame the clocks along the positive $x$ axis in the laboratory frame appear to be set ahead of those in the rocket frame, with clocks farther from the origin set farther ahead; and that clocks along the negative $x$ axis in the laboratory frame appear to be set behind those in the rocket frame, with clocks farther from the origin set farther behind, according to the equation
(47)
$t = \pm x' \sinh \theta_r = \pm x' \beta_r/(1 - \beta_r^2)^{1/2}$
The fact that neither of two observers in relative motion agrees that the reference event and the reading of zero time on all clocks of the other frame occur simultaneously is called the relative synchronization of clocks.

(d) Use the inverse Lorentz transformation equation to show that at t' = 0 in the rocket frame the clocks along the positive x axis in the laboratory frame appear to be set ahead of those in the rocket frame, with clocks farther from the origin set farther ahead; and that clocks along the negative x axis in the laboratory frame appear to be set behind those in the rocket frame, with clocks farther from the origin set farther behind, according to the equation
(47)
t = ± x' sinh = ± x' /(1 - ^2)^1/2
The fact that neither of two observers in relative motion agrees that the reference event and the reading of zero time on all clocks of the other frame occur simultaneously is called the relative synchronization of clocks.

Added by Rebecca C.

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