# Naked Science Forum

## Non Life Sciences => Physics, Astronomy & Cosmology => Topic started by: evan_au on 26/01/2017 10:46:08

Title: Why don't Gravitational Waves follow the "Inverse Square Law"?
Post by: evan_au on 26/01/2017 10:46:08
I was puzzled by comments from gravitational wave astronomers to the effect that gravitational waves decrease according to 1/distance.
• They claimed that if they increased the detector sensitivity of a gravitational wave detector by a factor of 4, they would be able to detect the same event out to 4 times the distance, or 64 times the volume of space.
• This is unlike an optical telescope, where if you increased the detector sensitivity by a factor of 4, they would be able to detect the same event out to twice the distance, or only 8 times the volume of space.

It seems that the behavior of gravitational waves is very different from light, gravity, neutrino intensity, etc, which all follow an inverse square law.
One article I read suggested that today's gravitational wave detectors measure "strain" or "stretch" caused by the gravitational waves, not the power of the gravitational wave. The power declines following an inverse square law, but the strain follows an inverse law. The power is proportional to strain squared.

What do you think?
Title: Re: Why don't Gravitational Waves follow the "Inverse Square Law"?
Post by: jeffreyH on 26/01/2017 18:46:35
The gravitational wave can be thought of as a two dimensional object if we slice a plane through it. So that we end up with an equation of the form Gm ln(r) where r will be the radial distance from the emitting object. I have not been rigorous in this assertion.
Title: Re: Why don't Gravitational Waves follow the "Inverse Square Law"?
Post by: yor_on on 31/01/2017 16:23:47
Evan, now you confuse me too :)
How the heck would they be able to 'observe' a gravitational wave at a further distance?
If they mean that the sensitivity increase that amount I think I can understand.
Title: Re: Why don't Gravitational Waves follow the "Inverse Square Law"?
Post by: evan_au on 31/01/2017 21:15:49
Quote from: yon_on
How the heck would they be able to 'observe' a gravitational wave at a further distance?
I think they mean it in terms of sensitivity and/or detector range.

Let's say we define a "standard event": say collision of two black holes, each of 10 solar masses, where we see the event edge-on. We detect this event with a signal:noise ratio of 25:1.

If you double the sensitivity of the detector, you would then be able to detect a "standard event" at twice the distance, still with a 25:1 SNR.

Of course, with a sample size of 2 gravity wave events (so far), we really don't know what a typical event looks like!
Title: Re: Why don't Gravitational Waves follow the "Inverse Square Law"?
Post by: yor_on on 31/01/2017 23:26:46
Ah, it got me confused, probably when reading the comparison made of increasing the sensitivity of a telescope.  Made me think of observing something from a distance, forgetting that it doesn't really matter, all observations are local, no matter if made by a telescope or by a gravitational detector. I's you observing the measurement.
Title: Re: Why don't Gravitational Waves follow the "Inverse Square Law"?
Post by: yor_on on 06/02/2017 14:40:29
Here is a really good description of Ligo, as well as of the foundation of 'gravitational waves' Evan. It's seldom I find something as good as this, so it's definitely worth reading. As well as thoroughly enjoying this comment. "Weiss was struggling to teach his course. An attempt to integrate Webers work hardly helped: It was hopeless. I couldnt understand what Weber was up to. Weiss turned to a particular aspect of general relativity[t]he only thing I really understood in the whole damn theoryand improvised: 'And so I gave as a problem, as a Gedanken problem, the idea' "

It's a lovely 'in depth' article with a lot of references. Across the Universe, by Steven wheeler. (http://inference-review.com/article/across-the-universe) to me it's a school example of how one should present an idea, no matter if physical or political, really impressive, makes me quite envious :)
=

keep spelling the names wrong, need new glasses.
Title: Re: Why don't Gravitational Waves follow the "Inverse Square Law"?
Post by: zx16 on 06/02/2017 22:52:16
The gravitational wave can be thought of as a two dimensional object if we slice a plane through it. So that we end up with an equation of the form Gm ln(r) where r will be the radial distance from the emitting object. I have not been rigorous in this assertion.
Or it could be that "gravitational waves" don't really exist.
Title: Re: Why don't Gravitational Waves follow the "Inverse Square Law"?
Post by: Bored chemist on 07/02/2017 22:32:33
Actually it's a moot point that light follows the inverse square law.
The power per unit area does.
But if you measured the electric field strength you would find (IIRC) it varies linearly with distance.
(the maths works out because the power is proportional to the square of the field strength. you can check it with this calculator)
http://www.qsl.net/pa2ohh/jsvpm.htm

Similarly, sound intensity falls as the square of the distance, but the amplitude (measured as displacement) doesn't.

It seems that what we measure in a gravity wave experiment is more akin to displacement than power.