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## Homework Statement

There are two stars A and B relatively at rest in the universe with the proper length of 12 ly.

A person is traveling at the speed 0.8c relative to the stars along the extended line of stars A & B (towards A).

When the person gets to the midpoint between A & B, he sees a light pulse from stars A and B respectively.

## Homework Equations

How many years ago does he claim the Star A emits the light pulse? (18 years)

Using Lorenz's transformation equation, t = G [ t' + vx'/c

^{2}]

What was the time difference for A when the person's time has elapsed these 18 years?

## The Attempt at a Solution

After length contraction, 12 ly => 7.2 ly for the person.

3.6 ly / (c-0.8c) = 18 years.

By using the Lorenz's transformation equation from the person's R.F. to A's R.F., the result is not 6 ly / c = 6 years as I expected.

Primed variables are with respect to the person, while the unprimed ones are to the Star A.

t = G [ t' - vx/c

^{2}]

G=0.6

t

_{f}= 0.6 [ t'

_{f}- 0.8c*3.6ly/c

^{2}] = 0.6t'

_{f}- 1.728y

t

_{i}= 0.6 [ t'

_{i}- 0.8c*( 3.6ly + 0.8c*18y)/c

^{2}] = 0.6t'

_{i}- 8.64y

t

_{f}- t

_{i}= 0.6( t'

_{f}- t'

_{i}) - 1.728 + 8.64

= 0.6*18y + 6.912y = 17.712y (Relative to Star A.)

Star A would claim that the light pulse only travels 6 years from himself to the person who's in the midpoint.

Why is it not 6ly/c= 6y?? (Relative to Star A.)

This is the discrepancy I'm asking about.

**What's wrong??**

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