Jump to content

Shifting LIGO to the binary. Thought experiment.


Robittybob1
 Share

Recommended Posts

If we took the LIGO right up to the binary the end of arm that pointed toward the barycenter would experience the greatest G force so the test particles would move apart particularly when they were in the eclipsed position.

 

There was another thought experiment where we brought the LIGO right inside the orbiting binary.

 

"Then, if the infall could take longer to allow us time to take the LIGO further and further away from the BBH but staying on the angular momentum vector, this toing and froing should continue."

 

(The Hulse Taylor binary pulsar is expected to take several hundred thousand years to merger, so we can allow infall and bring the LIGO back to Earth in time to see the last second of the merger.)

 

What sort of gravity wave patterns would we get from placing the LIGO in different orientations near or inside a BBH or binary pulsar?

 

If then we withdraw the LIGO at ever increasing distances from the BBH what effects does this cause?

Edited by Robittybob1
Link to comment
Share on other sites

I don't think there is an easy answer to the question. The waveforms close to the binary (and even more so inside the orbit) would be extremely complex. Different components of the gravitational waves fall off at different rates so we see relatively simple.

Link to comment
Share on other sites

I don't think there is an easy answer to the question. The waveforms close to the binary (and even more so inside the orbit) would be extremely complex. Different components of the gravitational waves fall off at different rates so we see relatively simple.

Could we make the distances great enough so the whole problem can be dealt with by Newtonian Gravity, in fact why not use the dimensions of a known binary pulsar? https://en.wikipedia.org/wiki/Hulse%E2%80%93Taylor_binary

The pulsar and its neutron star companion both follow elliptical orbits around their common center of mass. The period of the orbital motion is 7.75 hours, and the two neutron stars are believed to be nearly equal in mass, about 1.4 solar masses.

 

The LIGO mechanism would need to be modified to operate in the weightlessness of space. mirrors are set up so both arms can be crossed at their midpoints. There would need to be frictionless movement of the mass within the arm.

We measure the pressure of the test mass on the ends of the arm.

 

 

Let the star be exactly equal in mass. And let the orbit be circular. So the barycenter is exactly in the center of the two masses and ligo arms are centered on that too. Let the LIGO be stationary and the stars are moving around it.

If the first arm (arm1) was centralised on the barycenter.

 

Wouldn't the two test masses be attracted toward ends of the arm1 and register maximum pressure when the stars are inline with arm1. The pressure will be least when the stars are orthogonal to the first LIGO arm1.

The same applies to the second arm (arm2) but the pressure is recorded at 90 degrees to arm1

.

Edited by Robittybob1
Link to comment
Share on other sites

Could we make the distances great enough so the whole problem can be dealt with by Newtonian Gravity, ...

.

 

How many posts on gravitational waves? Newtonian gravity is instantaneous and there is no gravitational radiation within it - you need GR and the speed limit on gravitational propagation to get waves

Link to comment
Share on other sites

 

How many posts on gravitational waves? Newtonian gravity is instantaneous and there is no gravitational radiation within it - you need GR and the speed limit on gravitational propagation to get waves

Keep the idea of "speed of propagation" but think in terms of gravity like Newton did. I only went down that track to overcome Strange's objection in #2 quote:

"The waveforms close to the binary (and even more so inside the orbit) would be extremely complex. Different components of the gravitational waves fall off at different rates so we see relatively simple"

 

There had to be some way to simplify the situation of the thought experiment, and that was to slow down the orbital rate and increase the distance so that Newtonian gravity would give a good approximation for I'm only looking at which way (way = direction and strength) that the test masses would be moved by gravity at this stage.

Remember that change wave diagram. Even at mundane speeds you can get waves.

Edited by Robittybob1
Link to comment
Share on other sites

So you want to simplify the situation to the point you can use a theory that doesn't generate gravitational waves (and then make some ad-hoc assumptions to add them back in)/

 

Any gravitational waves generated that way will be purely fictional and have no connection to the gravitational waves that actually exist. As such, they would not provide any sort of answer to your original question. You might as well just keep it really simple and make up the answer you want.

 

So, the only way you are going to get any sort of realistic answer is by doing the full analysis. (And note that LIGO is quite possibly larger than the system generating the waves! But presumably you could use a much smaller detector as the waves would be much greater in magnitude.)

Link to comment
Share on other sites

I'm only looking at which way that the test masses would be moved by gravity at this stage.

 

You could use Newtonian gravity to answer that (incorrectly). In which case, they would be in a stable orbit like any other pair of masses.

 

But, of course, they would not be creating gravitational waves, which is why the orbit is stable.

And LIGO would detect nothing because there would be no gravitational waves.

Link to comment
Share on other sites

 

You could use Newtonian gravity to answer that (incorrectly). In which case, they would be in a stable orbit like any other pair of masses.

 

But, of course, they would not be creating gravitational waves, which is why the orbit is stable.

And LIGO would detect nothing because there would be no gravitational waves.

Because the BHs or masses are orbiting they are accelerating. (Due to the curved motion) Would the test masses cause fluctuating pressure on the ends of the celestial LIGO? (C.LIGO set-up as described above.)

We are not asking about gravity waves.

"And LIGO would detect nothing because there would be no gravitational waves." So did you try and answer the question? "It would detect nothing".

 

A detection in this thought experiment was increased or decreased pressure on the end of the C.LIGO arm.

 

Are you saying the test mass would not change the pressure it exerted on the end of a C.LIGO arm either inside or outside the orbits of the binary BHs?

Edited by Robittybob1
Link to comment
Share on other sites

So you trying to detect changes in gravity by it stretching the arm of the experiment by varying amounts?

 

It would be straightforward to calculate the changing (Newtonian) force of gravity at some point near the pair of objects. You could do this in a spreadsheet as previously suggested (in one of your other threads). It is a pretty straightforward application of Newton's law and vector addition.

 

If you wanted to convert this to what would happen to a LIGO type instrument (although I'm not sure why you would) you would have to make some assumptions about the mass and stiffness of the structure to work out how much it would be affected. This would effectively be a tidal effect over the length of the arm. I'm not sure what this would tell you beyond the changing force of gravity that would make the extra complexity worthwhile.

Edited by Strange
Link to comment
Share on other sites

So you trying to detect changes in gravity by it stretching the arm of the experiment by varying amounts?

 

It would be straightforward to calculate the changing (Newtonian) force of gravity at some point near the pair of objects. You could do this in a spreadsheet as previously suggested (in one of your other threads). It is a pretty straightforward application of Newton's law and vector addition.

 

If you wanted to convert this to what would happen to a LIGO type instrument (although I'm not sure why you would) you would have to make some assumptions about the mass and stiffness of the structure to work out how much it would be affected. This would effectively be a tidal effect over the length of the arm. I'm not sure what this would tell you beyond the changing force of gravity that would make the extra complexity worthwhile.

That is sort of what I was getting at. With the quadrupolar waves there seems to be varying amounts of movement of the test particles around the ring. With the circular polarisation pattern the points (using the points of the compass to describe where I'm looking) at NE SE SW NW points move less than the points N, E ,S and W.

Does that mean if I wanted to spread the effects throughout space that the whole effect wouldn't be reduced at the inverse square law with distance?

http://www.johnstonsarchive.net/relativity/gravwavepic.html

 

Some of the animations on this site really show this up http://www.universetoday.com/127255/gravitational-waves-101/

Could Newtonian gravity ever create wave patterns like that?

Link to comment
Share on other sites

Well you can't place magnetic points to gravity waves. There is certainly directional properties.

 

Yes gravity waves decrease with distance.

 

Gravity waves aren't part of Newtonian gravity

Edited by Mordred
Link to comment
Share on other sites

Th

 

Well you can't place magnetic points to gravity waves. There is certainly directional properties.

Yes gravity waves decrease with distance.

Gravity waves aren't part of Newtonian gravity

They are not magnetic but points (just compass points). I could have used the clock face but there was no hour number that represented NE, SE, SW or NW it was going to get too complicated to say "half past one" for NE etc.

https://en.wikipedia.org/wiki/Gravitational_wave#/media/File:Quadrupol_Wave.gif

 

Are the effects of gravity waves spread out through space evenly in all directions? If they were linear polarized I would say they are not evenly spread.

With the setup as described you would see periodic strains on the test masses in the Celestial LIGO. Did you not see that?

 

OK with traditional Newtonian gravity the effects were thought of as instantaneous but the generator of these instantaneous effects still had to go through the motions. That becomes a major difference in that under Newtonian Gravity the merger happened as the signal was received by LIGO rather than 1.3 billion years later.

But that wasn't what I was thinking about in the thought experiment, I was thinking whether we would see the polarization pattern and then work out how much force we would see back on Earth using Newtonian gravitational force calculations.

Edited by Robittybob1
Link to comment
Share on other sites

I think you better study the term polarization.

 

For example a star emits electromagnetic radiation in all directions but this has transverse polarization.

 

"Polarization (also polarisation) is a property of waves that can oscillate with more than one orientation. Electromagnetic waves such as light exhibit polarization, as do some other types of wave, such as gravitational waves. Sound waves in a gas or liquid do not exhibit polarization, since the oscillation is always in the direction the wave travels"

 

https://en.m.wikipedia.org/wiki/Polarization_(waves)

Another good example may be a omnidirectional antenna. It emits the signal in all directions. The polarizations suuply the data.

Link to comment
Share on other sites

I think you better study the term polarization.

 

For example a star emits electromagnetic radiation in all directions but this has transverse polarization.

 

"Polarization (also polarisation) is a property of waves that can oscillate with more than one orientation. Electromagnetic waves such as light exhibit polarization, as do some other types of wave, such as gravitational waves. Sound waves in a gas or liquid do not exhibit polarization, since the oscillation is always in the direction the wave travels"

 

https://en.m.wikipedia.org/wiki/Polarization_(waves)

Another good example may be a omnidirectional antenna. It emits the signal in all directions. The polarizations suuply the data.

This is the type of wave pattern that is coming from the binary https://en.wikipedia.org/wiki/Circular_polarization#/media/File:Circular.Polarization.Circularly.Polarized.Light_Right.Handed.Animation.305x190.255Colors.gif but there will be two of these per orbit.

 

I must admit I can't quite make a mental image of the gravitational wave surrounding a BBH. Do you have a mental image? Is it more like shells around an onion (spherical waves of polarized gravitational changes??) For to think of it as tubes of circularized polarization is alright in a small region but how do you get to fill the entire universe from those?

I'm looking for details on the way the gravitational wave spreads out from the binary source. All I know at present is that it is linearly polarized with the orbital plane and circularly polarized above and below the orbital plane. It might be safest to think it spreads the effects throughout the universe in an inverse square relationship, even though Katie Mack did tweet that the strength is greatest perpendicular to the orbital plane (so it varies in different directions).

Edited by Robittybob1
Link to comment
Share on other sites

Yes the strength varies so does the Hx and H+ polarization, however the polarization doesn't mean that the gravity waves isn't in all directions. Just as it doesn't determine direction of an EM wave in an antenna.

 

Your position to the wave can distinguish the alignment of the system by the differences between the h+ and hx polarizations.

Link to comment
Share on other sites

Yes the strength varies so does the Hx and H+ polarization, however the polarization doesn't mean that the gravity waves isn't in all directions. Just as it doesn't determine direction of an EM wave in an antenna.

 

Your position to the wave can distinguish the alignment of the system by the differences between the h+ and hx polarizations.

OK I'll just use the inverse square law, i.e. at twice the distance the force will be a quarter of the strength.

Link to comment
Share on other sites

OK I'll just use the inverse square law, i.e. at twice the distance the force will be a quarter of the strength.

 

You have posted 100s of messages on gravitational waves - have you even read the Wikipedia page? Gravitational waves are not Newtonian and are not force and as such they do not vary as the force varies; we talk about the amplitude (in terms of a strain) and the polarisation (in terms of + and x) of gravitational waves not the force. I get you cannot do the maths - it is very hard - but can you not read the Wikipedia page and do a bit of googling?

Link to comment
Share on other sites

And the amplitude decreases linearly with distance, not an inverse square law.

If you see a reference to that please let the forum know. That could be true if the force decreases by the inverse square law, that would mean force is affected by area and area is the multiplication of the x and y dimensions of that area. Amplitude could be measurement in the x or y dimension.

What is the equivalent to amplitude in Newtonian gravity?

In terms of GW what do you think the amplitude is measuring? Is it the way the the ring of test particles move? Is it they move less hence less amplitude? I have no problem with wave frequency as there are two wavefronts passing a point per orbit, and the wavelength is the speed of light divided by frequency, but what is the amplitude?

I think I see it now: a fluctuating force will have an amplitude and frequency.

 

In terms of GW what do you think the amplitude is measuring?

In post #18

 

.... Gravitational waves are not Newtonian and are not force and as such they do not vary as the force varies; we talk about the amplitude (in terms of a strain) and the polarisation (in terms of + and x) of gravitational waves not the force. ....

 

The thought experiment is to see how far we can look at the situation using Newtonian or Newtonian type concepts. I have been surprised how often the LIGO team used Newtonian type math to assist in their calculations.

I really want to know the connection of strain to the alignment of the binary bodies. Even using LIGO as it was designed if LIGO was right beside or inside the binary when does it register the maximum strain? At what position were the BH masses when the strain is maximum?

Edited by Robittybob1
Link to comment
Share on other sites

Is this the equation you are referring to? Kinetic Energy ~ MR^2/t^2 ~ Potential Energy ~ GM^2/R : (42) on page 9. I can't see the connection sorry.

Edited by Robittybob1
Link to comment
Share on other sites

Seriously?

 

Are you not aware that the amount of energy carried by a wave is related to the amplitude of the wave.

 

Those two formulas directly relate to the quoted posts.

Edited by Mordred
Link to comment
Share on other sites

Create an account or sign in to comment

You need to be a member in order to leave a comment

Create an account

Sign up for a new account in our community. It's easy!

Register a new account

Sign in

Already have an account? Sign in here.

Sign In Now
 Share

×
×
  • Create New...

Important Information

We have placed cookies on your device to help make this website better. You can adjust your cookie settings, otherwise we'll assume you're okay to continue.