Importantly, gravitational waves are not waves of Newtonian gravity. Gravitational waves do not "push and pull" along the direction of propagation. They stretch and compress space along axes perpendicular to the direction of propagation.
> E.g., if the moon suddenly lurched towards the Earth, we'd perceive an increase in gravity between the two. But that would be a semi-permanent change in the strength of that attraction between the two objects; not what I'd think of as a wave-like fluctuation.
Indeed, gravitational waves do not work this way.
Unfortunately it is hard to explain gravitational waves without significant math.
In fairness, even Einstein himself waffled over whether gravitational waves would be a real effect predicted by the theory. Then it took nearly a century to detect them experimentally, and there were plenty of doubters along the way.
The results one gets from intuition are generally incorrect in important ways. Here's a derivation of a wave equation from Einstein's field equations:
https://en.wikipedia.org/wiki/Linearized_gravity
A more helpful introduction for a layperson might be the paper titled "Gravitational Waves on the back of an envelope":
https://aapt.scitation.org/doi/10.1119/1.13627
But, infuriatingly, that paper does not seem to be open-access. Here's someone's scanned copy:
https://www.ru.ac.za/media/rhodesuniversity/content/mathemat...
This may be, likely is, a stupid question, but how do you measure this if space itself is stretched or compressed? Won't any yardstick lying in that space also be stretched or compressed? Or is it a matter of this distortion of space changing geodesics through it so light following a straight line will end up in a different place? It seems that LIGO uses interferometry to measure a change in distance between two points, though, and I don't understand how that can be measured if space is stretched, only if space is added. Perhaps that is the answer right there: when space is stretched dimensionless particles traveling through that space are not stretched, because they are dimensionless. Or perhaps better, objects in space stretch, but their momentum vectors don't stretch.
"If light waves are stretched by gravitational waves, how can we use light as a ruler to detect gravitational waves?" https://universe.sonoma.edu/moodle/pluginfile.php/89/mod_res...
The way I explain it: The light already inside the arm cavity is stretched. But newly entering light is not. We are basically using the light as clock to measure the length of the arm. When the arm is in the "stretched" state, light will take longer to make a roundtrip in the arm. It will accumulate slightly more phase, which is measured interferometrically.
It is important that the storage time of the light in the arm is short compared to the period of the gravitational wave.
I would say that we measure space in two different directions concurrently.
> and then looking for changes in the interference pattern between light moving along each of the dimensions
This is true, but I like to push back against the use of the phrase "interference pattern." We're not looking at a "pattern", which to me brings to mind a complicated interference pattern resolved spatially. We do not resolve the "interference pattern" spatially. We measure the amplitude (er, power) of the light coming out of the interferometer with a photodiode (a single pixel, if you will.)
> In practice, gravitational waves will come from all sorts of weird angles, but they will distort each of the two dimensions differently
This is true. The detector's sensitivity to waves coming from different directions is the "antenna pattern."
> t they will distort each of the two dimensions differently and allow us to figure what direction they were propagating by the interference pattern that's observed.
With a single detector, we cannot determine the direction in which a g.w. is propagating. With a single detector and a transient (short-lived) source, we cannot tell the difference between a loud source in a direction where the detector is not very sensitive versus a quieter source in a direction where we have good sensitivity.
With a network of detectors and/or signals that persist for a long time (compared to the rotation of the earth, etc) we can resolve the source direction.
This is an interesting idea, but I think it's not right.
To be honest, even as an experimentalist who worked on LIGO, I'm not sure how to treat the effect of the g.w. on photons in the arm. Instead I think of the entire arm cavity vacuum as a giant phase modulator.
Try sci-hub.
Is it possible to compress space?
The geodesic distance between inertial test masses increases and decreases.
Colloquially we say that space has stretched and compressed.
Geodesic distance can be measured by the time it takes light to travel between the points.
Inertial test masses can be simulated by hanging them from fine wires (LIGO) or by setting them up in an orbital constellation (LISA).
Space is a mathematical abstraction. You can do anything with, because it's just math. If you want to bend, curve, distort, rip space, or add more dimensions — go for it.
Physical medium should be compressible, like any other medium. Higgs «field» (let's call it Higgium — Higgs+Vacuum) is presented everywhere, because Higgs boson gives mass to every particle in the Visible Universe and beyond, so it should conduct gravitational waves. As demonstrated by LIGO/VIRGO, gravitational waves causes distortions in light travel. These distortions can be explained as changes of conductivity in Higgium, which can be caused by changes in density, so yes, it can be waves of compression.
The Higgs is a scalar field; gravitational waves are spin-2.
Spin-0 particles are round particles, like o (like ball), or something that cannot rotate at all. Spin-2 particles are symmetrical particles, like 8 (like H2 molecule).
For spin-0, it can be changes in density only. For spin-2, it can be changes in orientation, in rotation speed, in rotation orientation, Dzhanibekov effect, wobbling, and some other if it has more complex shape, e.g. two spirals connected.
In general Einstein's field equations govern the dynamics of $g$, and if you take the first order behaviour in $\epsilon$ around $g_0$ as flat space, then you recover the wave equation for $h$ as in the article you linked, with propagation speed $c$ the speed of light. (There are some additional subtleties about choice of gauge, but this is not physical).
I'm not sure what you mean with your moon example.
Suppose the gravitational attraction between the earth and moon is 2e20 Newtons.
Now imagine something forces that attraction to strengthen from 2e20N to 3e20N. E.g. the Earth and moon get closer to each other, or the moon gets more massive somehow.
When we talk about "detecting gravity waves", I understand that to mean that on Earth we've managed to detect that increase from 2e20N to 3e20N.
My point was: perhaps that looks like the rising edge of a wave phenomenon, but it's not actually cyclic like I expect from a traditional "wave". So I couldn't understand why it's called a gravity wave.
In differential geometry, the device called a "metric" let's you define things like angles and distances on some space. This is generally denoted as g with the Greek letters mu and nu as subcripts. Just to give you a feel of what's going on, I'll leave out the subscripts, but what OP's saying is that
g = k + h
Anyway, what Gravity Waves boil down to are situations (read distributions of matter) that cause h to obey the wave equation. In other words, gravitational waves are spacetimes that have a component that waves "on top" of a given reference "background" spacetime. Of course, you could cherry pick your background such that anything looks like waves on top, but typically we choose the background to be Minkowskian (i.e. flat).
FWIW, the above perturbative approach is called Linearized Gravity and is kind of a (nice) hack to restrict study of the really hairy non-linear Einstein Equation to cases that are manageable.
> I understand that to mean that on Earth we've managed to detect that increase from 2e20N to 3e20N.
This not what how gravitational waves behave. This assumption is not correct and will confuse you.
Unfortunately, I don't know enough to explain the difference.
https://en.wikipedia.org/wiki/Gravity_wave
They have absolutely nothing to do with gravitational waves.
Nonetheless, in the gravitational wave community (i.e. LIGO) we don't usually ever talk about true "gravity waves" so we use the terms interchangably.
The exception is that "gravity waves" in the Earth and the atmosphere can couple to LIGO through ordinary Newtonian gravity, which is something we have to think about and exclude.
Electromagnetic waves are similar. The Lienard-Wiechert field formulas [1] have 2 terms. The first term describes the delayed field, and is proportional to 1/r^2, while the second describes waves and is proportional to 1/r.
[1] https://en.wikipedia.org/wiki/Li%C3%A9nard%E2%80%93Wiechert_...
I would add that considering counterfactual situations like "if the sun were to move instantly to the right" is of limited utility. That cannot happen (violates conservation of momentum). (Granted, other thought experiments have been quite influential in this field...)
Gravitational waves are also different from changes to the amount of gravitational force. This can be seen from the fact that gravitational waves affect the distances between objects, whereas the sun which exerts far more gravitational force has no measurable effect (at least, to my knowledge rotating objects don't change length noticeably).
When I think of waves, I think of systems governed by the wave equation [0].
But IIUC that requires a restoring force. I'm not sure what that would mean in the case of gravity.
E.g., if the moon suddenly lurched towards the Earth, we'd perceive an increase in gravity between the two. But that would be a semi-permanent change in the strength of that attraction between the two objects; not what I'd think of as a wave-like fluctuation.
[0] https://en.wikipedia.org/wiki/Wave_equation