It turns out that energy is not conserved globally in General Relativity.
https://math.ucr.edu/home/baez/physics/Relativity/GR/energy_...
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It turns out that energy is not conserved globally in General Relativity.
https://math.ucr.edu/home/baez/physics/Relativity/GR/energy_...
The objects don't move. The space between them stretches and compresses.
Now, if the gravitational wave moves through a large massive object like a star or planet, the electromagnetic forces of the "stuff" in the object will cause it to resist this stretching or compressing. I think this does cause a very very very tiny "backreaction" to the gravitational wave, weakening it slightly.
Nope. This is a common misconception.
The difference between gravitational waves and gravity is a little bit like the difference between electromagnetic waves (emitted by an accelerating charge) and the electrostatic force (caused by a net charge at rest).
It's not possible to detect the effect of a charge far away, but easy to detect the propagating electromagnetic wave (light, ratio, etc).
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...)
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.
> 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.
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).
"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.
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...
Sounds like early-stage Quora.
And you have to maintain water in the tower in order to keep the water distribution system pressurized.
Also, why should self-driving be a government priority?
Uhhhh, gonna have to disagree there.
In fact, I would argue that multiplication being associative shows that this distinction is meaningless.