Dumb, but earnest question: if space itself changes, how can the distance change? What is the distance a measure of, if not space itself? What's the yardstick, speed of light?
Gravitational waves really do change the time it takes for light to travel between two points. We use light travel-times to measure distances, thus we say that the distance between the points has changed.
If it feels counterintuitive for spacetime to be changing, that's good. It is outside our human experience and perception. The strongest gravitational waves ever observed by scientists passed through everyone who was alive in 2015. None of those people noticed before the instruments registered a detection.
IIRC, the reason no one noticed is that even the strongest gravitational waves are only going to "stretch" space by something less than the diameter of a hydrogen atom.
Edit: from wikipedia LIGO page: "(interferometers) are capable of detecting a change of less than one ten-thousandth the charge diameter of a proton"
I dont know why I remember the human hair analogy, perhaps I am confusing it with something else?
If the yardstick is light-speed, is there any meaningful distinction between saying that space itself changed and that there are local perturbations to the speed of light?
The thing I struggle with is that we normally think of things occupying space. If space itself gets distorted, then the size of those things should change, too. Or is that mental model a useful but ultimately incorrect way to think about the world?
When the light merges back together, if the two paths traveled took exactly the same distance (or an even multiple of the wavelength at least), then the beams add together constructively and you put back together the light from the laser.
But if one path becomes longer or shorter the other, the light is out of phase with itself (peaks of the waves no longer line up with each other) and you can detect the interference between them.
LIGO can detect a change in distance of less than one ten-thousandth the charge diameter of a proton.
https://en.wikipedia.org/wiki/LIGO#/media/File:Gravitational...