Here's a spaceship with Sally in the corner....

Sally is in the lower right corner of the spaceship with 2 flashlights. One flashlight is aimed straight up at a mirror which reflects the light back down towards Sally. This is a light clock with the light bouncing straight up and down. She has another flashlight aimed up and to the left towards a mirror. So this is another light clock but at an angle. The ship is moving to the right with velocity V according to John who is outside the ship. This ship's velocity is such that from John's point of view the light from the angled flashlight isn't going at an angle but is going straight up and down because the rightward velocity of the ship exactly matches the leftward movement of the light.

Upward flashlight: Sally sees the light up and down. John sees it at an angle.

Angled flashlight: Sally sees the light at an angle. John sees the light up and down.

The 2 situations are reversed.

If T and t represent time for the 2 different reference frames then using the pythagorean theorem we can derive 2 contradictory time dilation formulas:

delta T = delta t/((1 - (v/c)^2)^.5)

delta t = delta T/((1 - (v/c)^2)^.5)

Code:

```
/\ | -------------------> V
/ \ |
/ \ |
/ \ |
/ Sally John
```

Sally is in the lower right corner of the spaceship with 2 flashlights. One flashlight is aimed straight up at a mirror which reflects the light back down towards Sally. This is a light clock with the light bouncing straight up and down. She has another flashlight aimed up and to the left towards a mirror. So this is another light clock but at an angle. The ship is moving to the right with velocity V according to John who is outside the ship. This ship's velocity is such that from John's point of view the light from the angled flashlight isn't going at an angle but is going straight up and down because the rightward velocity of the ship exactly matches the leftward movement of the light.

Upward flashlight: Sally sees the light up and down. John sees it at an angle.

Angled flashlight: Sally sees the light at an angle. John sees the light up and down.

The 2 situations are reversed.

If T and t represent time for the 2 different reference frames then using the pythagorean theorem we can derive 2 contradictory time dilation formulas:

delta T = delta t/((1 - (v/c)^2)^.5)

delta t = delta T/((1 - (v/c)^2)^.5)

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