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When we say waves, we usually imagine soothings like a sin wave, with a crest and a trough. But we can't use the same logic with gravitational waves, can we? Because if gravitational waves had a crest, would that not mean that space-time is being curved one way (down lets say) and another way later (up lets say). Would this not mimic negative mass?

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First of all, gravitational waves are waves in 4 dimensions, 3 of space and one of time. So, they do 'ripple' as a rubber sheet or any other 2 dimensional surfaces.

As for imagining gravity waves, we can't directly. Visualizing anything 4 dimensional is beyond human comprehension. But we can try and imagine it's effects on other objects, like we can't imagine curvature of spacetime, but we can imagine it's effects, that is gravity.

So, let's say a gravity wave passes through an object. As it is a disturbance in spacetime itself, the object's length, width and height vary (get longer and shorter) as the waves passes through it. If the object has a clock with it, the duration that the clock measures would start oscillating, getting longer and shorter.

That's the closest you can get to imagining gravity waves. If you found yourself in the path of one, this is what would happen. In fact, LIGO does the same. Only usually the varying of space and time is so low, that we can't even notice it.

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