# Detecting Gravitational Waves: Is My Understanding Wrong?

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• wvphysicist
In summary, the equivalence principle does not say that the geometry of spacetime is the same everywhere, and gravitational waves can cause different distortions at different points in spacetime. This is how gravitational wave detectors like LIGO work.
wvphysicist
Something is wrong in my understanding of Relativity. There is an equivalence idea running around, which says that gravity and the distortion of space time by gravity waves acts the same way on all things. That would mean that all objects and light and space experience the same distortion from a gravity wave. Then the tunnel in the LIGO machine and the space in it and the laser beam must all distort the same amount. If there is no difference in these distortions than a gravity wave antenna cannot work. But it has. So where have I been misinformed?

wvphysicist said:
Then the tunnel in the LIGO machine and the space in it and the laser beam must all distort the same amount. If there is no difference in these distortions than a gravity wave antenna cannot work. But it has. So where have I been misinformed?

This is discussed here too:

wvphysicist said:
There is an equivalence idea running around, which says that gravity and the distortion of space time by gravity waves acts the same way on all things.

That's not what the equivalence principle says. It says (at least this is one way of putting it) that a freely falling object's path through spacetime depends only on the geometry of spacetime, not on the object's shape or composition. But it does not say that the geometry of spacetime is the same everywhere, nor does it say that that geometry is static and unchanging. Gravitational waves are distortions in the spacetime geometry, and those distortions vary in both space and time. So two objects that are not at the exact same point in space will be acted on differently by gravitational waves. That is how GW detectors work.

vanhees71
I find it actually quite strange when I try to visualize it. The mirrors in LIGO are made inertial along the beam direction by a very clever suspension system. As the GW passes the mirrors don't "move" in a classical sense of gaining kinetic energy relative to their initial position. It's the distance between mirrors that changes as the wave passes. Hope I haven't butchered this too badly.

Paul Colby said:
As the GW passes the mirrors don't "move" in a classical sense of gaining kinetic energy relative to their initial position. It's the distance between mirrors that changes as the wave passes

This is one way of looking at it, but it's worth pointing out that it's coordinate dependent. The coordinates that are usually used to describe GW detectors like LIGO put all of the effects of the GW into the transverse metric coefficients; that is, each of the detector masses and mirrors are at fixed coordinates, but the metric varies with time so the physical distance between objects at fixed coordinates changes. (If you think about it, you will see that this also means the coordinate speed of light changes.)

It is perfectly possible to adopt different coordinates, in which the masses/mirrors do move, in the sense of changing spatial coordinates with time. It just turns out that coordinates like these would be harder to work with mathematically, so they aren't used.

## 1. What are gravitational waves and how are they detected?

Gravitational waves are ripples in the fabric of spacetime, predicted by Einstein's theory of general relativity. They are caused by the acceleration of massive objects, such as black holes or neutron stars. They can be detected using specialized instruments called interferometers, which measure the tiny distortions in space caused by passing gravitational waves.

## 2. How do scientists confirm the existence of gravitational waves?

The existence of gravitational waves was first confirmed in 2015 by the Laser Interferometer Gravitational-Wave Observatory (LIGO) when they detected ripples in space caused by the merging of two black holes. This was followed by several other detections of gravitational waves, providing strong evidence for their existence.

## 3. Can gravitational waves be detected with the naked eye?

No, gravitational waves cannot be detected with the naked eye as they are very small distortions in space that require highly sensitive instruments to measure. The distortions caused by gravitational waves are on the order of 10^-18 meters, which is much smaller than the diameter of an atom.

## 4. Why are gravitational waves important to study?

Gravitational waves provide a new way of observing and understanding the universe. They can reveal information about the most violent and energetic events in the universe, such as the collision of black holes or the explosion of stars. They also provide a new tool for testing Einstein's theory of general relativity and our understanding of gravity.

## 5. What is the potential impact of detecting gravitational waves?

The detection of gravitational waves has already had a significant impact on the field of astrophysics and will continue to do so in the future. It has opened up a new window for observing the universe and has the potential to reveal new insights into the nature of space, time, and gravity. It may also lead to new technologies and advancements in our understanding of the fundamental laws of the universe.

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