View Full Version : Can gravitational waves be superposed?

philippeb8

2018-Jan-18, 04:55 AM

(I asked permission for this question beforehand but I'll make it quick nevertheless)

If we have two pairs of colliding black holes at the same time, will the gravitational waves we measure here on Earth be twice the amplitude?

If so then I thought Einstein said gravity cannot be superposed, in contrast with what Newton said.

Shaula

2018-Jan-18, 05:25 AM

If so then I thought Einstein said gravity cannot be superposed, in contrast with what Newton said.

Nope. See: https://en.wikipedia.org/wiki/Linearized_gravity#Linearized_Einstein_field_equat ions

In the weak field approximation GR is a linear system, that is how you recover Newtonian gravity as a weak field approximation of GR. It is only in the case of very strong fields that you have to take into account non-linear effects.

Edit: To make it clear this means that in the weak field approximation (which will cover your scenario) you can treat the system as linear and so add the gravitational wave amplitudes. Although as there is no requirement for them to be in phase you won't get twice the amplitude generally.

philippeb8

2018-Jan-18, 05:37 AM

Nope. See: https://en.wikipedia.org/wiki/Linearized_gravity#Linearized_Einstein_field_equat ions

In the weak field approximation GR is a linear system, that is how you recover Newtonian gravity as a weak field approximation of GR. It is only in the case of very strong fields that you have to take into account non-linear effects.

Edit: To make it clear this means that in the weak field approximation (which will cover your scenario) you can treat the system as linear and so add the gravitational wave amplitudes. Although as there is no requirement for them to be in phase you won't get twice the amplitude generally.

Ah... got it!

philippeb8

2018-Jan-18, 05:51 AM

Ah... got it!

(Everything is so clear in my head now, thanks CQ!)

tusenfem

2018-Jan-18, 05:56 AM

(I asked permission for this question beforehand but I'll make it quick nevertheless)

If we have two pairs of colliding black holes at the same time, will the gravitational waves we measure here on Earth be twice the amplitude?

If so then I thought Einstein said gravity cannot be superposed, in contrast with what Newton said.

If you ask me permission, you might have the decency to wait until I say yes or no!

Jens

2018-Jan-18, 09:51 AM

By the way, I think the question is about waves being superimposed, not superposing, which I guess means to really strike a pose.

Grey

2018-Jan-18, 05:27 PM

It's perhaps worthwhile to note that everything we know about how gravitational waves behave is from Einstein's general relativity. We've had some indirect measurements over time (for example, the observed loss of orbital energy over time in a binary pulsar system), and the recent (and impressive!) direct observations from LIGO. But we were able to build something to detect them precisely because they appear to behave exactly the way Einstein predicted they would. If there are any differences between how gravitational waves actually behave and Einstein's predictions (note that he thought it was purely academic; it sounds like he didn't think that we'd ever be able to actually observe them), we'll need even better tools than LIGO.

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