How do gravitational waves differ from the expansion of the Universe?

[Andy DS]

TL;DR Summary

How do gravitational waves differ from the expansion of the Universe

How do gravitational waves in spacetime stretch and compress solid matter such as the LIGO experiment. I ask this because the expansion of spacetime of the Universe doesn't seem to have any effect on the small scale ie the solar system.

 

[osilmag]

I think I can explain if I understand your question correctly. Even though gravitation and the particle that goes with it is universal, there is a locality to it. An object will experience the ripples of a wave from a boat, but another object in a different body of water or far away will not experience that wave. So, the gravity acting at the edge of the universe will not affect our miniscule solar system inside the Milky Way galaxy.

 

[timmdeeg]

I ask this because the expansion of spacetime of the Universe doesn't seem to have any effect on the small scale ie the solar system.

This is correct and is true for gravitationally bound systems. The expansion of the universe has no effect on the tendency of gravitational waves to stretch and compress things because this is a local effect.
The global effect of the expansion of the universe is that gravitational waves like electromagnetic waves are observed redshifted far away from the source.

 

[Andy DS]

Thanks, but I'm not sure if I explained my query correctly, if gravitational waves from merging black holes stretch space time which has let's say infinite elasticity how does it manage to stretch the earth, which is much less elastic, to show up on the LIGO experiment. In other words do changes in the dimension of space time have an equal effect on the dimension of solid objects or does it depend on its elasticity.

 

[timmdeeg]

LIGO doesn't measure the stretching of earth, see Vibration Isolation.
I am not sure if gravitational waves stretch and compress the Earth to a certain extent, if at all then presumably much less than the distances between the isolated mirrors.

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[PeroK]

Thanks, but I'm not sure if I explained my query correctly, if gravitational waves from merging black holes stretch space time which has let's say infinite elasticity how does it manage to stretch the earth, which is much less elastic, to show up on the LIGO experiment. In other words do changes in the dimension of space time have an equal effect on the dimension of solid objects or does it depend on its elasticity.

The LIGO mirrors are incredibly sensitive to local changes in spacetime and hang by tiny glass threads. There's a video about this here:

https://www.ligo.caltech.edu/video/ligo20170216v

The gravitational waves are not "streching and compressing solid objects". They are changing the distance between extraordinarily sensitively balanced mirrors, that move at the smallest vibration.

The universal expansion depends on the overall density of matter across the universe generally. The solar system, compared to the universe as a whole, is dominated by matter and has settled into an equilibrium dominated by the gravity of the Sun and the other planets. And, solid objects on Earth are even less influenced by the factors that cause universal expansion.

The universe as a whole is much less dense and hence the dynamics are very different. Moreover, as the universe expands, its density decreases and this increases the infleunce of the vacuum energy (dark energy) and hence the expansion rate is increasing.

I can't see a meaningful comparison between expansion and gravitational waves.

 

[berkeman]

Whelp, thread locked temporarily for cleanup...

 

[PeterDonis]

Moderator's note: An off topic and misleading subthread has been deleted. Thread reopened.

 

[PeterDonis]

the expansion of spacetime of the Universe doesn't seem to have any effect on the small scale ie the solar system.

That is true, but gravitational waves are not the same thing as the expansion of the universe. The expansion of the universe, in this context, is best viewed as providing a "background" spacetime geometry, on which gravitational waves are localized fluctuations.

if gravitational waves from merging black holes stretch space time which has let's say infinite elasticity

There is a viewpoint in which spacetime can be viewed as a sort of elastic medium (among others, Sakharov, the famous Russian physicist, worked on this sort of model in the 1960s), but in this view, the elasticity is not infinite.

how does it manage to stretch the earth

As has already been noted, LIGO does not measure the stretching and squeezing of the Earth by gravitational waves. It measures the stretching and squeezing of the arms of a very precisely constructed and sensitive detector which, as has been noted, is carefully isolated from all other external sources of vibration, including the Earth.

There is another type of gravitational wave detector called a bar detector, originally invented by Weber and worked on several decades ago by a Russian team led by Braginsky (this work is described in the popular book Black Holes and Time Warps by Kip Thorne), which does measure the stretching and squeezing of a solid object (a large bar, usually of a metal like iron) by gravitational waves. Braginsky's work showed that this type of detector has serious limitations which probably make it unable to detect gravitational waves coming to Earth from distant sources, given the expected strength of those waves (now confirmed by LIGO). That limitation was one of the main reasons why LIGO used interferometer-type detectors.

 

[sophiecentaur]

Summary:: How do gravitational waves differ from the expansion of the Universe

How do gravitational waves in spacetime stretch and compress solid matter such as the LIGO experiment. I ask this because the expansion of spacetime of the Universe doesn't seem to have any effect on the small scale ie the solar system.

I'm basically an Engineer and I can't help interpreting this question in terms of AC vs DC measurement in the presence of noise. With nothing to compare local distances with and without Expansion then it seems that we have no chance of detecting it. With gravitational waves, we have changes with time so we can 'filter' the data and squeeze something out of what very sensitive equipment will show.
Is this nonsense or is it bringing the question into more familiar territory?

 

[Andy DS]

What I was trying to get to the bottom of is that, do the mirrors in the LIGO experiment actually move in response to gravitational waves or is that the time it takes the light to travel between them somehow modulated.

 

[Ibix]

What I was trying to get to the bottom of is that, do the mirrors in the LIGO experiment actually move in response to gravitational waves or is that the time it takes the light to travel between them somehow modulated.

You can interpret the LIGO measurements several ways - it's a matter of choice as long as you respect the invariant fact that the flight time of the light varies as the wave comes through. I think the most usual interpretation is to regard the distance between the mirrors as changing (whether you say the mirrors have moved or just that the distance changed is also a choice), but it's not obligatory. You can treat the speed of light as varying if you like, or if it makes some computation easier.

 

[PeterDonis]

do the mirrors in the LIGO experiment actually move in response to gravitational waves or is that the time it takes the light to travel between them somehow modulated.

These are not two different possible ways things could be. They are just two different descriptions of the same way things are. There is no such thing as "actually move"--"move" is frame dependent. So by an appropriate choice of coordinates, one can have the mirrors "moving" (spatial coordinates changing with time) and the coordinate speed of light constant, or one can have the mirrors "stationary" (spatial coordinates not changing with time) and the coordinate speed of light inside the apparatus changing with time.