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# Help - Contraction Problem - I'm getting contradictory outcomes

Sun 5 Oct, 2014 06:50 pm
I have a basic Special Relativity problem that shows seemingly contradictory results depending which inertial frame you observe from Here's the problem...

You have 2 identical spaceships approaching each other (let's say in the horizontal direction) at a relative speed of 0.8c where the rest length of each ship is 900m.

That is, you have a ship 1 moving from left to right and ship 2 approaching from right to left closing in on each other.

(so each ship as observed from the other ship is 540m long at 0.8c)

Now we also have a big ring with an inside rest diameter of 1000 m traveling alongside ship 2 just above ship 2 and matching it's speed...the ring is orientated so that it's diameter is parallel to the horizontal axis so from the other ship the diameter is contracted to 600m dia.

Now as the ships pass each other, both ships add a vertical component to their speed to pass through the ring.
<------ ======== Ring
ship 1 ------> <------ ship 2

As observed from ship 2 (the one moving at same speed at the ring right to left) the ring is 1000m in dia and ship 2 sees it's own length as 900 m and so passes through unscathed.

ALSO as observed from ship 2, ship 1 is 540 m in length and so it too passes through the ring unscathed...so far so good.

Next we look at what happens form ship 1's point of view...

Observed from ship 1, ship 2 is 540 m long and the ring diameter is 600m long...so ship 2 STILL passes through the ring unscathed.

BUT ship 1 sees its OWN length as 1000 m compared to the ring's contracted dia of 600 m and in trying to pass through, collides with the ring and is destroyed!

From ship 1's inertial frame it cannot pass through the ring but from ship 2's inertial frame ship 1 CAN pass through the ring..

How is this contradiction explained?

Thanks Much

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