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Ala, compression and rarefraction at the peaks and troughs of the gravity wave, physically warp space-time as the wave transverses the fabric.
The tradional model of a wave that we all know and love (co/sin) isnt the best one to describe it, you really need to picture gravity waves as longitudinal waves, not transverse.
Sometimes, you ask the wrong questions and get bogged down, or resist accepting the answer because of your frustration. Then later on it just occurs to you "Oh... it's XYZ... Of course...". But try to explain your epiphany to someone else, and you can still spin your wheels even though it's now so clear to you.
Words are not enough! Welcome the Singularity where thoughts can be exchanged purely!!
Siftbot, we will join with you one day! :-)
Brian is stating that a wave is a disturbance (energy) moving and reshaping a particular medium in a particular direction. The wave bends and stretches water, for example, and tends to flow at certain speed and in a certain direction. That act of moving "through" the water is something entirely different, like a stick penetrating the medium/wave. Same with space-time. Space-time is the medium in which the wave occurs. Moving through space-time is more akin to what you and I are doing right now. At least that's my take on it.
Any movement on that sheet creates ripples in the fabric of space-time.