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John Stanly

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GR has just been explained to me in a lecture and I'm a little confused about a few things. I've been running through a few scenarios in my head and I don't see how they can occur without a paradox.

One scenario is if you have two spaceships traveling parallel to each other at relativistic speeds in opposite directions a large distance away from one another, both with light clocks visible to the other. From my understanding, if one spaceship views the other spaceship's light clock it will see fewer ticks than on their own light clock. But if the other spaceship was doing the same thing they too would notice the other spaceship going slower.

For arguments sake, let's say that both spaceships believe that for every 10 ticks of the other spaceship's clock, their clock ticks 20 times. To me, this fits all of the constraints of GR, but it doesn't make sense to me then how both spaceships could be going slower than the other.

Could someone just clarify this for me?

Thanks,

John