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## Main Question or Discussion Point

The question is in reference to calculating relativity of simultaneity. I am on the step where I take the time in Alice's frame from the front and from the rear clock and minus it to the get the total time. I end up with gamma squared etc (For more details see the picture below)

I have observer Bob who is stationary and who see Alice moving.

Now that I finished describing the question here is the question.

How does ## L' = (L_a) (v) ## etc become ## (L_b) (v) ## etc?

I start with the information L_moving because Alice is moving. I don't have Bob's frame. My point is I have L_moving not L_stationary. I am referencing to this formula ##L' = \frac L y ## In order to get L shouldn't I go ## L = L'Y ## but it looks like I go ## L' = \frac L y ##

picture below

When I say etc I am referring to ## \frac { (L_a) (V) (gamma^2) } { (c^2) } = \frac {(L_b) (V) (gamma^2) } {(gamma) (c^2)} . ##

I have observer Bob who is stationary and who see Alice moving.

Now that I finished describing the question here is the question.

How does ## L' = (L_a) (v) ## etc become ## (L_b) (v) ## etc?

I start with the information L_moving because Alice is moving. I don't have Bob's frame. My point is I have L_moving not L_stationary. I am referencing to this formula ##L' = \frac L y ## In order to get L shouldn't I go ## L = L'Y ## but it looks like I go ## L' = \frac L y ##

picture below

When I say etc I am referring to ## \frac { (L_a) (V) (gamma^2) } { (c^2) } = \frac {(L_b) (V) (gamma^2) } {(gamma) (c^2)} . ##

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