What is the best 3D description of Gravitational waves?

[swansont]

I was just repeating what the wikipedia article said "If R is much greater than a wavelength,....". I had not specifically tested this aspect. https://en.wikipedia.org/wiki/Gravitational_wave#Wave_amplitudes_from_the_Earth.E2.80.93Sun_system

 

 

Yes, you repeated it. But you apparently didn't process what the information meant. That's a crucial step to understanding.

[Robittybob1]

 

 

Yes, you repeated it. But you apparently didn't process what the information meant. That's a crucial step to understanding.

What did you think it meant?

[swansont]

What did you think it meant?

 

 

 

"We couldn't see the 3D structure as the equations were simplified and only worked where R is much larger than the wavelength."

 

To me that says you concluded you can't use the equations to deduce the solution. But you could, since the equations are valid. We are much further than a few wavelengths from the event. For almost all places in the universe, you can do this. You just can't if you are very close to the event.

 

As for the link about the earth-sun system, I have no idea what to make of that. I don't recall that being part of the discussion at all. It's just another random shift of the discussion that you seem to introduce at odd intervals.

[Robittybob1]

Tha

 

 

 

 

"We couldn't see the 3D structure as the equations were simplified and only worked where R is much larger than the wavelength."

 

To me that says you concluded you can't use the equations to deduce the solution. But you could, since the equations are valid. We are much further than a few wavelengths from the event. For almost all places in the universe, you can do this. You just can't if you are very close to the event.

 

As for the link about the earth-sun system, I have no idea what to make of that. I don't recall that being part of the discussion at all. It's just another random shift of the discussion that you seem to introduce at odd intervals.

That was because to simplify the equation they use the barycenter as the point source of the GWs. So unless you happen to agree that GWs are sourced from the barycenter I don't think we can deduce any 3D structure from that.

 

That was where the equations are found in that link that is all.

Edited April 1, 2016 by Robittybob1

[swansont]

Tha

 

That was because to simplify the equation they use the barycenter as the point source of the GWs. So unless you happen to agree that GWs are sourced from the barycenter I don't think we can deduce any 3D structure from that.

 

That was where the equations are found in that link that is all.

 

 

If you are far enough away, it doesn't matter. That's the whole point. The waves would look the same. You don't use approximations unless they give you the right answer.

[Robittybob1]

 

 

If you are far enough away, it doesn't matter. That's the whole point. The waves would look the same. You don't use approximations unless they give you the right answer.

The right answer to those equations is not the 3D structure but the strain at a large distance from the barycenter.

Edited April 1, 2016 by Robittybob1

[swansont]

The right answer to those equations is not the 3D structure but the strain at a large distance from the barycenter.

 

 

That's what the wave is: the strain at any point. You can determine the 3D solution just by putting on different values for the variables. And it's not particularly large distances, astronomically speaking. A 30 Hz oscillation has a wavelength of 10000 km. That's smaller than the earth.

[Robittybob1]

 

 

That's what the wave is: the strain at any point. You can determine the 3D solution just by putting on different values for the variables. And it's not particularly large distances, astronomically speaking. A 30 Hz oscillation has a wavelength of 10000 km. That's smaller than the earth.

Have you seen the error bars for the estimated distance to GW150914. If we knew the distance down to the last 10,000 km we wouldn't be having this debate.

 

Primary black hole mass 36þ5 −4M⊙ Secondary black hole mass 29þ4 −4M⊙ Final black hole mass 62 þ4 −4M⊙ Final black hole spin 0.67 þ0.05 −0.07 Luminosity distance 410 þ160 −180 Mpc Source redshift z 0.09þ0.03 −0.04

Luminosity distance 410 þ160 −180 Mpc massive uncertainty there.

[swansont]

Have you seen the error bars for the estimated distance to GW150914. If we knew the distance down to the last 10,000 km we wouldn't be having this debate.

Luminosity distance 410 þ160 −180 Mpc massive uncertainty there.

 

 

We're 1.3 billion light years away.

 

But that's not even the point. The equations are valid outside of a tiny sphere, regardless of our distance. Knowing the exact distance is entirely beside the point. We know we're much further than a few wavelengths distant, and that's all that matters. I hope you understand that despite the uncertainty in the distance, we know that it didn't happen within our solar system, right? So the equations are going to work just fine.

[Robittybob1]

 

 

We're 1.3 billion light years away.

 

But that's not even the point. The equations are valid outside of a tiny sphere, regardless of our distance. Knowing the exact distance is entirely beside the point. We know we're much further than a few wavelengths distant, and that's all that matters. I hope you understand that despite the uncertainty in the distance, we know that it didn't happen within our solar system, right? So the equations are going to work just fine.

exactly - it was a long long way away.

Edited April 1, 2016 by Robittybob1

[swansont]

exactly - it was a long long way away.

So the equations are valid. You keep agreeing with me, and yet come to the opposite conclusion. The equations tell you the behavior of the waves throughout almost the entire universe. How can you possibly say that you can't find the 3D structure of the waves?

[Robittybob1]

So the equations are valid. You keep agreeing with me, and yet come to the opposite conclusion. The equations tell you the behavior of the waves throughout almost the entire universe. How can you possibly say that you can't find the 3D structure of the waves?

So you would swear that each wavefront is a complete sphere around the barycenter? From one peak intensity to the next how do you get the next pulse in your model? That is the bit that is stumping me.

[Strange]

So you would swear that each wavefront is a complete sphere around the barycenter? From one peak intensity to the next how do you get the next pulse in your model? That is the bit that is stumping me.

 

See imatfaal's excellent breakdown in post #110 (http://www.scienceforums.net/topic/94060-what-is-the-best-3d-description-of-gravitational-waves/?p=913689)

 

Rob

 

1.That last section of the equation gives you a nice oscillation (it is a pretty standard expression in waves) this is what it looks like

 

http://www.wolframalpha.com/input/?i=cos%5B2*(sqrt((6.67e-11)*(1.3e32)%2F(100000%5E3)))(t-4e16)%5D

 

[latex] \cos\left[2\omega(t - R/c)\right] [/latex]

 

That describes each "pulse" (sine wave).

[swansont]

So you would swear that each wavefront is a complete sphere around the barycenter? From one peak intensity to the next how do you get the next pulse in your model? That is the bit that is stumping me.

How do you get the next pulse in a water wave?

 

The wavefront is just an arbitrary point on a cycle, typically the positive peak. But it's an oscillation.

[Robittybob1]

 

See imatfaal's excellent breakdown in post #110 (http://www.scienceforums.net/topic/94060-what-is-the-best-3d-description-of-gravitational-waves/?p=913689)

 

 

That describes each "pulse" (sine wave).

That is as measured by the observer at R. I want to know if you think all parts of the wave at a distance of R from the barycenter are going to have the same intensity at any one "t"? If that was so the GW would be a pulsing signal. I have never seen that description before.

[swansont]

That is as measured by the observer at R. I want to know if you think all parts of the wave at a distance of R from the barycenter are going to have the same intensity at any one "t"? If that was so the GW would be a pulsing signal. I have never seen that description before.

Look at the data in the paper. It's a sinusoidal oscillation. Pulsing.

[Robittybob1]

How do you get the next pulse in a water wave?

 

The wavefront is just an arbitrary point on a cycle, typically the positive peak. But it's an oscillation.

That would depend on the wave generator. If you threw a pebble into the water you would get rings from one point but it soon fades away. There so many situations really.

Look at the data in the paper. It's a sinusoidal oscillation. Pulsing.

I have never denied that at one point in space e.g. at the LIGO that you wouldn't get a "sinusoidal oscillation. Pulsing."

You would get the same pulsing from spherical and spiral 3D structure but those that go for the spherical have to have a pulsating source. In other words you would have to say the source of the GWs is pulsing, and I haven't seen it described that way. Would you say the source is pulsating?

[swansont]

That would depend on the wave generator. If you threw a pebble into the water you would get rings from one point but it soon fades away. There so many situations really.

 

Yes, it does depend on the generator, but why focus on something irrelevant? A pebble is a single impulse, but even that creates more than one cycle. And it fades away, but gravitational waves aren't subject to the dissipative influences you have on a water wave, so again, perhaps focusing on the irrelevant bits is not the best strategy here.

Would you say the source is pulsating?

No, I'm a physicist. I'd use the vocabulary of physics.

[Robittybob1]

Yes, it does depend on the generator, but why focus on something irrelevant? A pebble is a single impulse, but even that creates more than one cycle. And it fades away, but gravitational waves aren't subject to the dissipative influences you have on a water wave, so again, perhaps focusing on the irrelevant bits is not the best strategy here.

Would you use the pebble analogy to describe the production of GWs? I have always likened it to the waves of water from a two head rotating garden sprinkler.

But that too was only a 2D description and I was trying to develop the 3D description.

[swansont]

Would you use the pebble analogy to describe the production of GWs?

Only as a very rough analogy. They're both waves, but not a lot in common beyond that.

 

I have always likened it to the waves of water from a two head rotating garden sprinkler.

Which was shown to be wrong.

[Robittybob1]

Only as a very rough analogy. They're both waves, but not a lot in common beyond that.

 

 

Which was shown to be wrong.

Was it? I can't recall that. Time to recap the thread if I'm starting to forget.

[Strange]

That is as measured by the observer at R. I want to know if you think all parts of the wave at a distance of R from the barycenter are going to have the same intensity at any one "t"?

 

The height of the wave depends on distance, time and the angle of the observer:

 

3. This is to do the overall strength [latex] \frac{G^2}{c^4}\, \frac{2 m_1 m_2}{r} [/latex]

 

 

 

If that was so the GW would be a pulsing signal. I have never seen that description before.

 

I don't know what you mean. It IS a pulsing signal. A sine wave. At any position in space, you will see a sine wave. The intensity depends on your distance and the angle.

Would you use the pebble analogy to describe the production of GWs?

 

A better analogy might be a (food) mixer with two paddles rotating around a common centre - and also each rotating. This would produce all sorts of complex motion in the water nearby but a few metres away, you would just see ripples spreading out in a circle.

 

I'm not sure what you are failing to see here. You mentioned a spiral. These equations do not describe a spiral. If that were the case then the [latex]\theta[/latex] term would have to appear in the final part of the equation in order to describe a change of phase as you change your angle wrt the source.

[Robittybob1]

 

The height of the wave depends on distance, time and the angle of the observer:

....

I'm not sure what you are failing to see here. You mentioned a spiral. These equations do not describe a spiral. If that were the case then the [latex]\theta[/latex] term would have to appear in the final part of the equation in order to describe a change of phase as you change your angle wrt the source.

The height (amplitude) of the wave depends on distance, time and "the angle of the observer". Let's define angle of observer. I take the to be the angle of the orbital plane to the observer, and that angle isn't going to change whether the wave generator is a point source or a line between two bodies.

A point source will give off waves that if looked at from a 2D perspective are circles (and I think if and if only if the point source pulsates.

A line between the two massive bodies rotated will produce 2 waves per rotation and the waves will be a spiral.

 

The equations give the amplitude of the wave at distant point in space "R" from the source. It is sinusoidal in nature because of the succession of wave crests coming from the generator. How do you get the barycenter (your point source) to produce a succession of waves.

The small r term only makes sense if the are two bodies in binary orbit. #59 for r is derived from the omega equation.

If it was a point source what difference would the r term make?

Obviously the omega has a bearing on the frequency of the wave fronts, but how do you get successive wavefronts from a point source?

 

 

3 equations:

\omega=\sqrt{G(m_1+m_2)/r^3}

 

h_{+} = -\frac{1}{R}\, \frac{G^2}{c^4}\, \frac{2 m_1 m_2}{r} (1+\cos^2\theta) \cos\left[2\omega(t - R/c)\right]

 

 

h_{\times} = -\frac{1}{R}\, \frac{G^2}{c^4}\, \frac{4 m_1 m_2}{r}\, (\cos{\theta})\sin \left[2\omega(t-R/c)\right]

Edited April 2, 2016 by Robittybob1

[Strange]

A line between the two massive bodies rotated will produce 2 waves per rotation and the waves will be a spiral.

 

Citation needed. That does not seem to be what your equations say.

The small r term only makes sense if the are two bodies in binary orbit. #59 for r is derived from the omega equation.

If it was a point source what difference would the r term make?

 

That equation only tells you orbital frequency. It says nothing about gravitational waves.

 

Obviously the omega has a bearing on the frequency of the wave fronts, but how do you get successive wavefronts from a point source?

 

The equations you are using are approximations based on a point source. It assumes that the gravitational waves come from that point source but says nothing about how they arise (because at the distance these equations are valid, the nature of the source doesn't matter too much).

[swansont]

how do you get successive wavefronts from a point source?

It's a sine wave. It goes up and then down, and then up and down, over and over again. The part where it's up is the wave front. You get successive wave fronts because the source keeps generating them.