Comment by cobaltoxide | Hacker News Reader

Comment by cobaltoxide | Hacker News Reader

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Gravitational waves are waves of the metric tensor. Einstein's field equations provide the "restoring force."

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...

> 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.

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.

Here is an introductory paper on that exact topic:

"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.

On a similar note - if a huge gravity wave passed through the earth, say one that stretched the space I’m in by a factor of 10, would I feel anything?

> 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.

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.

The clever thing about interferometers is that they're actually measuring space and time in two different dimensions concurrently and then looking for changes in the interference pattern between light moving along each of the dimensions. Simplistically, imagine a gravitational wave propagating along one dimension of the interferometer (realistically gravitational waves will never be perfectly aligned with any direction of the interferometer). Space will be distorted in that dimension but not the other and we can notice the change in the resulting interference pattern. In practice, gravitational waves will come from all sorts of weird angles, but 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.

> The clever thing about interferometers is that they're actually measuring space and time in two different dimensions concurrently

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.

You might enjoy this video which goes into that question:

https://youtu.be/iphcyNWFD10

Sci Hub has it apparently: https://sci-hubtw.hkvisa.net/10.1119/1.13627

> But, infuriatingly, that paper does not seem to be open-access.

Try sci-hub.

> They stretch and compress space along axes perpendicular to the direction of propagation.

Is it possible to compress space?

(Not a native speaker).

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.

I appreciate what you’re trying to get at, but it’s not right. Gravitational waves exist in GR even in theories with no matter / Higgs.

The Higgs is a scalar field; gravitational waves are spin-2.

Thank you for pointing it out.

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.

I believe this answer is nonsense.

> 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).

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