What makes us think we can actually detect gravitational waves?

Question

This refers to the discussion about gravitational waves for the YouTube video LIGO Gravitational Wave Observatory.

I have two questions:

1. When the gravitational wave passes through the space where the light is traveling, the light beam will itself be distorted as per the distortion of space (because the gravitational wave distorts everything in its path) and the slight change they expect to detect should be nullified. For instance, suppose the wave shrinks one of the pipes by half and increases the other by double, the waves inside would be distorted similarly, resulting in no overall change in the interference. Am I missing something here?

2. It takes a huge amount of energy to distort something (for example, a block of iron). If the gravitational wave distorts everything it passes through (such as the Earth, the Sun and space itself), it will lose its energy at a very high rate in trying to do this distortion (much more than what the inverse square law implies) when it passes through solid objects. The current understanding is that gravitational waves do not get effected by anything and pass through a solid as if was vacuum. How is this possible?

Answer 1

A gravitational wave will distort space-time and the light that is on a path affected by such a wave will be similarly affected, but it will still take longer (or shorter) to travel that path. Imagine a car travelling along the surface of a trampoline, a wave on the trampoline could cause its path to become longer, but it won't be impossible to detect whether that path was longer. The key is to monitor path lengths in two orthogonal directions and compare them continuously, a gravitational wave will make one shorter and the other longer for long enough to be detectable by a laser. The wavelengths won't necessarily be affected, but the time of flight and thus the returning phase of the waves will be, and that can be measured very precisely using interferometric techniques similar to a Michelson-Morley device.

As far as the energy to distort matter, that's irrelevant, it is space-time that is being distorted by gravitational waves, the energy calculations for compressing solid matter don't apply. Pick up a single coin, that coin is distorting all of space-time in, effectively, the entire Universe! Now move the coin around, now it's sending out gravitational waves which affect space-time in the entire Universe as well. Even, eventually, distant neutron stars or entire galaxies. Granted, for a single coin the perturbations are so tiny as to be utterly indetectable and inconsequential, but they still happen. Phenomena on a much larger scale such as closely orbiting neutron stars will send out much, much stronger gravitational waves, which we might be able to detect with sufficiently precise instruments. However, they still compress and expand the space-time all around us, but this is not a process that requires a continuous input of energy anymore than it takes a continuous input of energy to keep an object in orbit of another.