What if the speed of gravitational waves were different from the speed of light?

[parshyaa]

What would happened if the speed of gravitational waves were not equal to the speed of light . Please explain it with example of sun and Earth or any other but in easy way. With reference to general relativity.

 

[Nugatory]

What would happened if the speed of gravitational waves were not equal to the speed of light . Please explain it with example of sun and Earth or any other but in easy way. With reference to general relativity.

It's not mathematically possible, which makes it impossible to sensibly answer the question as asked: it's like asking what would happen if we could factor a prime number.

Light is electromagnetic radiation obeying the laws of electricity and magnetism; gravitational waves obey the laws of gravity.

Both sets of laws have the property that they are the same for all observers regardless of their speed (we don't see the laws of E&M or gravity changing with the seasons even though the Earth is moving in a completely different direction in June and December). One consequence is that waves obeying these laws must travel at the same speed for all observers; this is the basis of Einstein's theory of special relativity.

It turns out that there can only be one "same for all observers" speed; if you assume that there is more than one you end up with mathematical contradictions and an inconsistent theory. So, since there's only one possible speed, they both have to travel at that speed, and it's the same for both of them.

It's actually a historical accident that we even call $c$ "the speed of light". We measured how fast light moves centuries before the discovery of electromagnetic and gravitational waves, so when we found that the one and only "same for all observers" speed was equal to the already known speed of light it was natural to keep calling that speed "the speed of light".

 

[Khashishi]

Well, it would mean that general relativity is not correct. But so far, general relativity has passed many of our tests with flying colors, so I wouldn't bet on it.

 

[Recycler]

It would be interesting to observe a stellar object in the path of the gravitational wave that would display a visual result of the wave's passing through it.Then could we calculate the wave's speed of transmission using the distance between origin and impacted object?

 

[Khashishi]

The only thing we can detect with gravitational waves right now are colliding black holes. With the two LIGO observatories, we can't get a good measurement of where the gravitational waves are coming from, but when additional observatories come online we can do triangulation to find where they are coming from. Then we can compare with visual observatories.