Can LIGO actually detect gravitational waves?

[tar]

I am sorry for the misdirection. The validity of our gravity wave detection is in NO WAY challenged by an inability to read another GW embedded in the signal. There is very little chance that such a signal is even present (even if two rings cross paths it is not likely they do so at the same time...that is one ring could pass were another was or will be, but in the expanse of space, the chance of meeting is near nil), much less that it would be strong enough to register on the equipment. The use of gravity waves as plumbs of the space they transversed, is likewise lessened in likelihood.

"That's a speed, not a distance."

 

but the whole signal, the 20 revolutions prior the merge happened in a second so the path either took to get around each other could not be longer than 118,000 miles

 

divide that by pi and that by 20 and the diameter of the larger mass has to be less than that

Edited June 19, 2017 by tar

[imatfaal]

 

 

No assumptions are made. The interaction is modelled to find the form that the gravitational waves take. The waves are strongest in the (equatorial) plane of the orbits and weakest in the direction of the axis of the orbits. (This may complicated slightly by the spin of the black holes as I think it depends on the total angular momentum of the system, not just the axis of the orbits.)

 

(OK. A few assumptions are made in the analysis: that GR is correct, is the main one. Also that the orbits are nearly circular.)

 

You sure about the intensity variation Strange? Going back through my memory I seem to think that h_0 (on the axis of rotation) was strongest and that anywhere else you got a varying combo of h_+ and h_x both of which were related to h_0 by being multiplied by sines and cosines of angles of inclination (ie necessairly less than 1)

 

Unfo I cannot find any docs on this at present. My gut instinct is that you are correct - but memory is clear

[Strange]

so the strong wave would be in a plane less than 6 thousand miles thick, expanding out in that plane

 

 

No.

divide that by pi and that by 20 and the diameter of the larger mass has to be less than that

 

The larger mass had a diameter of about 200 km. So you seem to be out by a factor of 1,000.

 

You sure about the intensity variation Strange?

 

No!

 

I have just had another look at the parameter estimation paper but that just confused me. Maybe you can make more sense of it!

https://arxiv.org/abs/1602.03840

[swansont]

I am sorry for the misdirection. The validity of our gravity wave detection is in NO WAY challenged by an inability to read another GW embedded in the signal. There is very little chance that such a signal is even present (even if two rings cross paths it is not likely they do so at the same time...that is one ring could pass were another was or will be, but in the expanse of space, the chance of meeting is near nil), much less that it would be strong enough to register on the equipment. The use of gravity waves as plumbs of the space they transversed, is likewise lessened in likelihood.

"That's a speed, not a distance."

 

but the whole signal, the 20 revolutions prior the merge happened in a second so the path either took to get around each other could not be longer than 118,000 miles

 

divide that by pi and that by 20 and the diameter of the larger mass has to be less than that

 

 

0.6c * 1 sec / 20 = 9,000 km. (0.6c is 111,600 miles/sec)

 

divide that by 2π and you get ~1400 km in radius

 

We went through this a few pages back. You agreed the orbit was, at largest, a few thousand miles in diameter.

 

You sure about the intensity variation Strange? Going back through my memory I seem to think that h_0 (on the axis of rotation) was strongest and that anywhere else you got a varying combo of h_+ and h_x both of which were related to h_0 by being multiplied by sines and cosines of angles of inclination (ie necessairly less than 1)

 

Unfo I cannot find any docs on this at present. My gut instinct is that you are correct - but memory is clear

 

http://www.tapir.caltech.edu/~teviet/Waves/gwave_details.html

"The strongest radiation is along this rotation axis"

 

(This came up in another thread http://www.scienceforums.net/topic/93472-gravitational-lens-and-gravitational-waves-question/page-2#entry909493 )

 

 

Dipoles don't radiate along their axis, but quadrupoles do.

[tar]

​"If we integrate this flux over a sphere around the source, we get the total luminosity, or energy emitted per unit time. The result cannot depend on the TT quadrupole moment, since "tranverse" can only refer to a specific direction of propagation. Instead it depends just on the traceless quadrupole moment IT, whose components are:"

 

SwansonT,

 

So what does that mean? Is the energy of the strain propagated only edge on, only in the direction of the axis or both in some combination where being 45 degrees from either position you would get some lesser but calculable energy?

 

That is the luminosity seems to be figured on a sphere, but the wave propagates in certain directions, not all directions.

 

Regards, TAR

[swansont]

​"If we integrate this flux over a sphere around the source, we get the total luminosity, or energy emitted per unit time. The result cannot depend on the TT quadrupole moment, since "tranverse" can only refer to a specific direction of propagation. Instead it depends just on the traceless quadrupole moment IT, whose components are:"

 

SwansonT,

 

So what does that mean? Is the energy of the strain propagated only edge on, only in the direction of the axis or both in some combination where being 45 degrees from either position you would get some lesser but calculable energy?

 

That is the luminosity seems to be figured on a sphere, but the wave propagates in certain directions, not all directions.

 

Regards, TAR

 

 

The equations that follow the quoted bit tell you how the amplitude varies with angle.

[tar]

no doubt

 

I was not able to see it, and was hoping for an English translation.

Stange had said one of the GWs we saw was 30 degrees from edge on

which is also 60 degrees from axial

 

what percentage of the energy is going axially and what percentage is going edge on, in the case of GW150914?

I am trying to think in terms of radiation count, as if gravity was quantized into gravitons.

 

Some distant stars we "see" we piece together photon by photon over time. We have no such luxury in this case, as all the gravitons were released in particular directions within about a second.

Edited June 19, 2017 by tar

[imatfaal]

No!

 

I have just had another look at the parameter estimation paper but that just confused me. Maybe you can make more sense of it!

https://arxiv.org/abs/1602.03840

 

Gotta luv an honest answer.

...

http://www.tapir.caltech.edu/~teviet/Waves/gwave_details.html

"The strongest radiation is along this rotation axis"

 

(This came up in another thread http://www.scienceforums.net/topic/93472-gravitational-lens-and-gravitational-waves-question/page-2#entry909493 )

 

 

Dipoles don't radiate along their axis, but quadrupoles do.

 

Yes - that brings it all back. Robittybob questioning whether AstroKatie knew what she was talking about - seeing the female bit before the astrophysicist bit.

 

And I was looking at that very Caltech page a few days ago - must have sunk in without me realising. Thanks

---

 

I have just had another look at the parameter estimation paper but that just confused me. Maybe you can make more sense of it!

https://arxiv.org/abs/1602.03840

 

Using papers nomenclature

 

If we call [latex] A_{GW}[/latex] the maximum possible amplitude, the max amplitude at any time [latex]t[/latex] we denote as [latex] A_{GW}(t) [/latex]

 

and we call the angle that the observers line of sight makes with the axis of rotation [latex] \iota [/latex]

 

then we can say (ignoring the phase) that

 

[latex] h_+ = A_{GW}(t) \cdot (1+cos^2 \iota) \cdot (phase\ angle)[/latex]

 

[latex] h_x = A_{GW}(t) \cdot (-2 \cos{\iota}) \cdot (phase\ angle) [/latex]

 

[latex] (1+cos^2 \iota)\ and\ (-2 \cos{\iota})[/latex] are the important bits which show how the amplitude varies with elevation. Both will be at a maximum when [latex] \cos{\iota} [/latex] is equal to 1 or -1 and that will be the case when \iota = 0 or \pi - ie when you are on the axis

 

Because of the way the phase and magnitude are set when [latex] \iota [/latex] equals zero (ie along axis of rotation) the gravitational waves are not only most intense they are circularly polarized (along the line of propagation the peaks of the waves would trace a helical path - I guess a double helix).

 

When [latex] \iota [/latex] equals [latex] \pi/2 [/latex] (ie in the plane of rotation) the gravitations waves are linearly polarized ( along the line of propagation the peaks would trace straight lines

 

When [latex] \iota [/latex] is between the two values the waves would be elliptically polarized (which is kinda mixture of both)

[tar]

Well thank you Imatfaal. I do comprehend English words better than Greek letters standing for whole bunches of English words. But I still have the percentage question. The highest amplitude waves are going out, in a equatorial disk, the thickness initially of the diameter of the larger BH, whereas the axial power is going out at a max amplitude in exactly polar directions which I suppose is in two directions something like a barbershop pole coming out top and bottom, with two spirals on it, but the diameter of the orbit that put out the wave. Drawing a hypothetical sphere around the event, most of the power would hit the equator, not the poles. I am visualizing a couple degree size moon being the area of half the power going polar and a degree wide band on the horizon going 360 degrees around, putting maybe 100 times more power out on the equator than on the axis.

If you were under water, had a stick and you put it straight above your head and turned around in a little circle it seems that would take a lot less energy than holding the stick out making a big circle... but maybe I am thinking about conservation of angular momentum which probably does not apply here.

[imatfaal]

Well thank you Imatfaal. I do comprehend English words better than Greek letters standing for whole bunches of English words. ...

 

Obviously not that well - because your conclusion was this "The highest amplitude waves are going out, in a equatorial disk," which is the exact opposite of what I was explaining. The highest amplitude are axial - ie at the poles not on the equator.

 

the thickness initially of the diameter of the larger BH

Do you have any conception of the scales we are talking about? And we are dealing in mathematically ideals - the lowest amplitude linearly polarized radiation is on the plane of orbit; in reality you get what you get and any observations will have errors so high that plane or band are immaterial.

 

 

 

whereas the axial power is going out at a max amplitude in exactly polar directions which I suppose is in two directions something like a barbershop pole coming out top and bottom, with two spirals on it, but the diameter of the orbit that put out the wave.

What the hell is axial power? Could you go away and read a primer on Gravitational waves? And again with the scale thing - who cares? Mathematically it is the axial direction that matters and observationally everything is too blurred to be important one way or another.

 

 

 

Drawing a hypothetical sphere around the event, most of the power would hit the equator, not the poles. I am visualizing a couple degree size moon being the area of half the power going polar and a degree wide band on the horizon going 360 degrees around, putting maybe 100 times more power out on the equator than on the axis.

I can dig out the equation which gives you the power for a given area -ie dE / dA dt but it is complex . But no - for any given area the closer the the poles the more the energy transferred per second. IF you take a big area near the plane and a small area near the poles then yes more power at the plane - but for equal areas no.

 

 

 

If you were under water, had a stick and you put it straight above your head and turned around in a little circle it seems that would take a lot less energy than holding the stick out making a big circle... but maybe I am thinking about conservation of angular momentum which probably does not apply here.

 

Angular momentum does apply here - gravitational waves rob the system of angular momentum as well as energy. this is what first allowed us an indirect confirmation of their existence - the taylor hulse binary .

 

But I am not getting into discussing hokey analogies - this is heavy duty physics; Einstein can get away with homespun thought experiments because he understood the real theory - but you cannot really work in the opposite direction

[tar]

imatfaal,

 

"Obviously not that well - because your conclusion was this "The highest amplitude waves are going out, in a equatorial disk," which is the exact opposite of what I was explaining. The highest amplitude are axial - ie at the poles not on the equator."

 

 

I thought your equations meant the highest amplitude H+ would be at the equator and the highest amplitude Hx would be at the poles, and my question was simply in GW150194 what percentage of the energy went out the top and bottom and what percentage went out on or near the equatorial disk.

 

Regards, TAR

[Mordred]

No I posted previously h+ is positive polarity and h× is cross polarity.

[tar]

OK I really do have to reread a bunch of stuff, I am completely confused. I thought, in the LIGO chart, the amplitude up on the black lines was considered H+ and the amplitude down was considered Hx. I was trying to visualize what that meant, in regards, to the merger and am now completely clueless.

 

What was that about space squishing along one arm of the LIGO while stretching on the other? Are not H+ and Hx inversely related on the 90 degrees? The amplitude of the one high while the other low?

better yet, I will bow out...this stuff is obviously way beyond me

Edited June 19, 2017 by tar

[Mordred]

Ok with electric field polarity is the vectors of charge.

 

With magnets polarity is vectors of poles (north, south)

 

Both above cases are dipolar.

 

GW is quadrupole instead of two vectors you have 4 (per wave cycle).

 

These occur regardless of propogation direction. They do not describe the direction the wave is travelling in. Though using the above one can calculate direction of travel.

 

Lets try this. Take a telegraph machine. Each bip on your morse code is a chirp. Each chirp will be dipolar (neg to positive and positive to negative). The signal still radiates outward depending on the emiiter antennae. Omnidirectional vs directional)

 

Now apply that to a GW wave each chirp corresponds to a change in angular momentum of the two BH's. A consequence of the conservation of angular momentum. The loss momentum is your GW wave. The chirp rate depends on the orbit changes.

 

Each chirp will have a quardupole polarity.

Here is the chirp mass formulas for a binary system (specifically).

 

https://en.m.wikipedia.org/wiki/Chirp_mass

 

See image 5 for how a GW transverse polarity wave propogates in 3d. ( best image I could find) though still misleading somewhat all images tend to be in GR lol

http://www.thephysicsmill.com/2016/03/06/direction-ligos-gravitational-waves/

Edited June 19, 2017 by Mordred

[swansont]

OK I really do have to reread a bunch of stuff, I am completely confused. I thought, in the LIGO chart, the amplitude up on the black lines was considered H+ and the amplitude down was considered Hx. I was trying to visualize what that meant, in regards, to the merger and am now completely clueless.

 

What was that about space squishing along one arm of the LIGO while stretching on the other? Are not H+ and Hx inversely related on the 90 degrees? The amplitude of the one high while the other low?

 

 

Amplitude is how big the excursion is. The direction is irrelevant. Stretching vs compression is not big vs small; the amplitude is how much you have of each as measured from some equilibrium point.

[aramis720]

Diving back into this topic after I've had a chance to review in detail various papers that address the question (how can LIGO detect gravitational waves when any distortion of the interferometer arms would seem to be in principle undetectable b/c the detecting device is distorted by exactly the same amount as the waves sought to be detected) and I find the answers unconvincing. The easiest to follow and the latest paper that I've found so far is Faraoni 2007:

 

https://link.springer.com/article/10.1007%2Fs10714-007-0415-5?LI=true

 

After reviewing Faraoni 2007 and these other papers (including Melissinos 2003 and Garfinkle 2005) it seems that this alleged detection of GWs by LIGO is incorrect. Check out the Faraoni paper and let me know what you think. Basically it presents a number of mathematical steps for calculating the changes in the interferometer arm lengths and light waves, from GWs, that rely on a number of assumptions that shift the calculations one way or the other and then the paper pronounces "Presto! We've shown that we can in fact detect GWs because there's a different effect on light than on the arms from the GWs," but the allegedly differential effect found seems to me to be entirely a consequence of the simplifying assumptions, which in one case are thought to be negligible and in the other significant. The basic problem remains: how could GWs be detectable, in principle, by a device that occupies a slice of spacetime that is being waved to exactly the same degree by the GWs sought to be detected?

I've attached Faraoni 2007 with my highlights.

[Mordred]

Here is the arxiv copy of that paper. It is well written. (I've studied it before numerous times 🙄

 

https://arxiv.org/abs/gr-qc/0702079

 

However you should note that paper shows that the arms and lasers are not affected equally. Which allows the detection.

 

"The gravitational wave treats in a different way" the wavelength of light and the length of the interferometer's arm. Physically, the interferometer works by measuring the differential stretching of the x and y arms while the high frequency light wave essentially experiences no inhomogeneities in the medium".

 

The differential stretching is the quadrupole action.

Edited July 2, 2017 by Mordred

[aramis720]

Yes I read the paper through and attached my highlighted version. My point was that the mathematical treatment of the physical effects in one case (the arms) interprets the GW effect as "negligible" while the effect on the light beam is considered significant, but both outcomes are a result of simplifying BUT OPPOSITE assumptions. And as I've stated too many times already this makes no sense bc the light waves and the arms occupy the same space. There is no principle offered for why the effect should be different on the two different physical phenomena. Rather, it seems to be a rather veiled attempt at incorrect mathematical sleight of hand to create an effect that logically can't exist. Do you see my point? Or am I misreading the paper?

[Mordred]

The key point is you have a difference of two seperate field interactions.

 

Treat the arms as a matter field with its own coupling constants. Then treat the photon or electromagnetic field with its own coupling constants.

 

The differences (differentials between these field intaractions can be measurable).

Then add on top of the above differences in polarity via the quadrupole nature of spin 2. The differences between x and y arms.

 

Mathematically speaking, which at this level heuristic explanations do not work well is quite detectable.

 

One of the calibration tests of lead weights previously mentioned, demonstrates the degree of variations.

 

That is the trick different fields exhibit different medium like reactions to types of fields. It is the differences we look for. (more often than not under symmetry relations described as anistropies) anistropy being in essence a non uniform relation.

 

It is challenging to recognize these differences without the mathematical background but it is the differences in information exchange between each type of field both within each field and how each field interacts with other fields that is detectable.

 

Reread the articles you mentioned and look for the differences of information/interaction exchange vs matter and radiation type fields. All interactions generate interferance. The nature of different interferences between different field compositions is important.

Seek the differences at every geometric event ( coordinate) at a moment in time not every location responds identically

 

The paper you mentioned describes two key dynamics. Differences in how two medium like fields interact. But also polarity differences of the two arms via spin 2 vs frequency of wave relations.

 

Key note those variations has a term under physics ... the quantity of Strain. not easily described for GW waves...at least not heuristically under math easily.(granted knowing how the math applies being essential). Particularly with different fields/mediums.( yes there is a distiction)

Edited July 2, 2017 by Mordred

[aramis720]

Mordred wrote:

 

The key point is you have a difference of two seperate field interactions.

Treat the arms as a matter field with its own coupling constants. Then treat the photon or electromagnetic field with its own coupling constants.

The differences (differentials between these field intaractions can be measurable).
Then add on top of the above differences in polarity via the quadrupole nature of spin 2. The differences between x and y arms.

Mathematically speaking, which at this level heuristic explanations do not work well is quite detectable.

One of the calibration tests of lead weights previously mentioned, demonstrates the degree of variations.

That is the trick different fields exhibit different medium like reactions to types of fields. It is the differences we look for. (more often than not under symmetry relations described as anistropies) anistropy being in essence a non uniform relation.

It is challenging to recognize these differences without the mathematical background but it is the differences in information exchange between each type of field both within each field and how each field interacts with other fields that is detectable.

Reread the articles you mentioned and look for the differences of information/interaction exchange vs matter and radiation type fields. All interactions generate interferance. The nature of different interferences between different field compositions is important.
Seek the differences at every geometric event ( coordinate) at a moment in time not every location responds identically

The paper you mentioned describes two key dynamics. Differences in how two medium like fields interact. But also polarity differences of the two arms via spin 2 vs frequency of wave relations.

Key note those variations has a term under physics ... the quantity of Strain. not easily described for GW waves...at least not heuristically under math easily.(granted knowing how the math applies being essential). Particularly with different fields/mediums.( yes there is a distiction)

 

aramis720 responds:

 

Ok, indulge me here please. Here are the key passages from Faraoni 2007.

 

He discusses three recent explanations for why LIGO could in theory detect GWs, including Saulson 1997, a presentation by Kip Thorne, and Garfinkle 2005. He ends up concluding that Thorne's version is accurate and he provides what he considers to be a solid mathematical foundation for it. Here's his comment about Thorne:

 

"'…the influence [of the GWs] on the light is negligible and it is only the mirrors that get moved back and forth and the light’s wavelength does not get changed at all …'. However, substantiating Thorne’s answer with a clear mathematical argument is not entirely trivial, as is shown in Sect. 3."

 

 

He then attempts to demonstrate that indeed it is the mirrors that move and the light's wavelength doesn't change under the influence of GWs. In section 3, he states, with respect to the motion of the mirrors (p. 682):

 

"Under the assumption λgw >> L the spatial dependence of hαβ can be neglected and ... Therefore, in the approximation used, the laser photons do not suffer spatial deflections to first order."

 

He adds at p. 683:

 

"In the approximation λgw >> L the temporal variation of h11 (t) during the short time ≈ 2L it takes for the light to travel to the mirror and back is negligible and δλ [is approx. equal to] 0 in this approximation."

 

And with respect to the mirror positions and arm lengths, Faraoni states the effect is "different from zero" (p. 683):

 

"In the approximation λgw >> L the time dependence disappears and del x/L = h+(t = 0)/2, Eq. (4.2), which is different from zero..."

 

But one could just as well argue that this "different from zero" result should also be considered negligible in the approximation lambda >> L. No numbers are offered in this paper with respect to the negligibility decisions.

 

More importantly, we are back to my OP question: WHY would the GW have any effect on the arm length and the mirror positions when the GW is distorting spacetime to exactly the same degree that would make it in principle undetectable?

 

I also note that the explanations offered in this forum have changed remarkably as the discussion has progressed, beign initially focused on the notion that it is in fact the change in phase that is detectable.

 

If we're focusing now on the Thorne/Faraoni explanation, a quite different explanation than the earlier explanations, we seem to have a major problem in explaining at the level of basic physics and logic why there would be a differential effect on the mirrors and the light. You mention differential field effects, but what is the basic rationale that undergirds the different mathematical treatment here? WHY would these fields be affected fundamentally differently? Why are the coupling constants different? In terms of fields and distortions of spacetime a good metaphor is the sagging or bulging sheet (which is spacetime). If the GW is defined as a distortion of the sheet, the fields that occupy spacetime are influenced the same way by such distortions, as a matter of principle.

 

Suggesting that it is the TT gauge approach that is the source of the difference just substitutes a different set of assumptions without explaining the basic physical differences (it seems to me). Again, light and the physical arms are occupying exactly the same physical space that is being distorted by the GWs. The mathematical explanations offered by Faraoni don't really attempt to address why the different simplifying assumptions are warranted in each case and he doesn't recognize in the paper that the different assumptions lead to opposite effects and it is ONLY these different simplifying assumptions that lead to the differential effects. He states at the end of the paper (p. 684):

 

"Physically, the interferometer works by measuring the differential stretching of the x and y arms while the high frequency light wave essentially experiences no inhomogeneities in the 'medium' in which it propagates—the gravitational wave—because the wavelength λgw of the gravitational wave is so much larger than the wavelength of light. This conclusion agrees with Thorne’s qualitative answer to the objection."

 

As we know from the alleged detection events, the physical effect being measured is very small indeed -- that's why it's taken so long to get a clear signal (albeit a false positive, it seems to me). So with a very small signal attempting to be detected, it seems a bit strange to argue for negligibility ("essentially experiences no inhomogeneities") of physical effects resulting from the GWs with respect to wavelength, but for non-negligible effects with respect to distortion of the mirror positions and the arm lengths. Particularly when the physical rationale for why the mirror positions would be affected has simply not been offered anywhere.

Edited July 2, 2017 by aramis720

[Mordred]

ok Everyone is making this far more complex than it really is.

 

Lets look specifically at the belief that the structure of the arms (matter field) will move the same as the laser.

 

Let me ask you if you apply a force of value x when you multiply this with different mass values will the acceleration be the same?

[latex] f=ma[/latex]

 

The structure of the arms is far more massive than photons so why believe they would move identically? that one formula alone should tell everyone that would be impossible?

 

Even under freefall systems massless objects will follow a different spacetime path than massive objects. null geodesic vs spacetime geodesics.

 

So why would anyone think the arms will move identically to the lasers.? How can it? The GR formulas and Newton formulas both show this isn't the case. (this isn't a freefall system so were not factoring out mass as per freefall)

 

Simply apply f=ma. a Newton offorce hits a 1 kg object and a 2 kg object. The second object will have half the acceleration of the first object.

 

Now apply that to the arms which is far more massive than the laser beams.

 

Lets just use a force on the x direction. Force can be anything, the arm in the x direction will move different than the arm in the y direction. Simple vector addition tells us that.

 

So now lets look at the detector design.

 

The detector sends a beam of known frequency. The detector splits this frequency to two identical frequencies and sends them down each arm.

 

Then after being reflected back the two beams are recombined. The recombined beams (two identical frequencies) will contructively interfere. The sum of the two beams will equal the original frequency.

 

Now change one axis but not the other by some arbitrary force. The length of one arm is no longer identical to the length of the other arm.

 

What does this do to the beams. Well tge amplitudes of each frequency signal will no longer be in the identical phases.

 

1 beam will be phase shifted, while the other beam won't. (Does not matter if this is due to GW waves or not any force or vibration will do the same).

 

As the arm lengths or spacetime paths of the two beams are not identical in one arm compared to the other arm. The two signals will be out of phase.

 

When you recombine two signals out of phase you get destructive interference. The signal will be less than the original.

 

Like I stated the type of force makes no difference, 1 arm will not move identical to the other arm because of the Direction of force.

 

In a GW wave this becomes more pronounced. You have multiple vector components in a quadrupole wave.

 

At one instance of your cycle x+ and x- will spread out while y+ and y- contracts. Then half a cycle later the above reverses

 

It would impossible for both arms to move identically. So you will get destructive interferences simply by the differences in length of each arm. (For the lasers each laser will follow a different length of geodesic. The GW wave cannot and will not affect the two geodesics identically. For precisely the same reasons above.

 

The vector direction of the GW wave will have a different influence of two lasers at two angles. (Simple vector addition tells us that)

 

If its that simple why would anyone assume we can't detect a GW wave? Simple they forget to apply the vector addition components. The beam recombination allows us to see the miniscule variations in length on recombination. Regardless of cause of the variations of length.

 

As for a single arm and a laser beam. well the arm is a rigid object, the laser beam is not. So why would they move the same? Under spacetime contractions and expansion in this case. Every point will have different densities so the amount of curvature at each point will be different.

 

A wave itself has different curvature values at each point of the wave. It would be impossible for every point of an object to be influenced identically. (again for the same reasons above. the vector components vary.

 

A field wave has different vector components at every coordinate. When you move that wave through another field. Every coordinate of those fields will have different vector components.

 

It would be impossible for the entire LIGO apparatus to move identically in the same vector value. That is a misconception that every coordinate would be affected identically. It is an impossible misconception. The vector components will vary at every coordinate.

 

(that is what the differential accelerations of the above paper is referring to) The vector components at each coordinate cannot be identical so the sum of vectors at each coordinate cannot be identical. Those differences may be miniscule but our detector is designed to detect these miniscule variations in its design. It does so by looking for the time delays due to changes in spacetime paths of the two frequencies upon recombination.

 

constructive vs destructive interference and the amount of interference. Neither arm can possibly be affected identically (vector components will vary at every coordinate).

 

Lol just like gravity varies at every coordinate around Earth, move another gravitational field variation through that varied gravitational field and every coordinate will move differently at any moment in time. You want a simple way to see this. Watch two water waves collide. Does the resulting waves have the same vector values at every coordinate? of course it doesn't so why would anyone think the LIGO detector would be any different?

 

This is what is shown on those formulas. Every coordinate will vary differently at every coordinate as it must when you have 1 anistropic field moving through another anistropic field.

 

Here is an at home visual aid. Take two clear plastic sheets. Draw on each sheet a graph from a central point assign a different field value at each coordinate.

 

Label sheet a [latex]\eta_{\mu\nu}[/latex] the other sheet [latex]h_{\mu\nu}[/latex] don't worry about what vectors you place at each coordinate. (just make sure they vary)

 

Now slide one sheet over the other sheet in any direction and sum those vectors at each coordinate.

 

The sum of vectors at each coordinate will vary. (lol in a sense GR 1 oh 1) handy tools those plastic sheets with a dry eraser marker. If the two sheets have differences in geometry you need a transformation between the two sheets. if your using the Newton approximation that transform isn't needed.

 

(lol a smart lazy person will just draw vector arrows at coordinate on each sheet) then vector sum them with a ruler and compass at each coordinate). Easy way to model how one field affects another at every coordinate at a given moment in time.

 

A truly creative person could apply this methodology and animate the two fields as they cross each other over time. If you treat each each spacetime coordinate displacement as a vector you can even use this to model the geometry changes. (albiet through additional steps on applying the geometry changes to the coordinate grids.) Lol please keep in mind each sheet will subsequently get changed at each interaction. (good ole action reaction laws) This is only a rough back of envelop visual aid.

 

Orders of approximation the paper refers to see here.

 

https://en.m.wikipedia.org/wiki/Order_of_approximation

Edited July 2, 2017 by Mordred

[aramis720]

Mordred, your discussion reveals that you are thinking of the GW traveling through space (and I think this is the general conception among physicists), but as I've pointed out many times now GWs are defined as waves of space, not waves traveling through space, as described on p. 679 of the Faraoni paper. So, no, the arm lengths will not be affected differently in any detectable way because the space they occupy is being distorted in exactly the same way as the apparatus that occupies that space, regardless of the direction of the waves and the vectors at issue. Again, the key point: GWs are defined as waves of space itself. The only reason, it seems, that Faraoni and Thorne conclude that the mirrors move is because of the simplifying but opposite assumptions I discussed previously with respect to the mirrors and the wavelength of the light.

[beecee]

GWs are defined as waves of space, not waves traveling through space,

 

Yep, that's the way I understand it and I'm sure most understand it that have any interest in cosmology and GR.

 

 

So, no, the arm lengths will not be affected differently in any detectable way because the space they occupy is being distorted in exactly the same way

No, obviously the arms being at right angles to each other, will be affected differently as peaks and troughs pass through and obviously also then, the distance the laser has had to travel.

 

 

The only reason, it seems, that Faraoni and Thorne conclude that the mirrors move is because of the simplifying but opposite assumptions I discussed previously with respect to the mirrors and the wavelength of the light.

So you are claiming everyone else is wrong including probably the world's authority on BH's Kip Thorne?

So then obviously your next step is to gather all the evidence you have supporting your hypothesis, and submitting a paper for professional peer review.

Let us know how you go.

On another forum I once frequented, we also had one who was insisting that GW's as discovered, were not as reported and also his even more dramatic claims that GR was wrong, period!

During plenty of debate with this joker by other knowledgable people on that forum, I decided to get it from the horses mouth so to speak. I E-Mailed aLIGO and received the following reply.........

 

Dear Barry,

My name is Maximiliano Isi and I am a member of the LIGO Laboratory at the California Institute of Technology. I also happen to be the author of one of the papers cited at the end of your message. Thank you for your interesting email and apologies for the belated reply.

It is absolutely true that our observations do not allow us to fully rule out the existence of non-GR physics. This is just a consequence of the fact that experimental observations have the power to disprove theories, but not to prove them: scientific theories are falsifiable, but not demonstrable. The best we can do is to say that our measurements agree with GR up to some (high) confidence level. It is in that precise sense that we mean "Einstein was right" (a misleading phrase: we don't know whether GR is fully accurate, we just cannot prove it wrong with what we have seen).

We have several methods to make quantitative statements about the agreement between the GR prediction and the signals we measure, but I won't describe them here in detail. Note that in order to find signals in the detector noise we use templates that tell us what the waves look like, and those templates are the output of highly–advanced super-computer simulations of GR dynamics; this means that the signal cannot be too different from the GR prediction or we wouldn't have seen it at all!

Now, agreement with GR is not exclusive: an alternative theory might explain our observation just as well as GR or even better. Given any two competing theories (with different predictions), we can always ask which one is favored by our data, and we have well-established statistical methods to make quantitative statements to answer. Unfortunately, however, the mathematics of GW emission and propagation has only been worked out for very few of the viable alternatives to GR and in most of those cases the theories are similar enough to GR that the signals we'd expect to see are practically indistinguishable. The reason for this is that computing GW waveforms for interesting sources is an extremely complicated mathematical problem and (as mentioned above) it takes super-computers to do it even in GR, the theory we know best (and most alternatives are intrinsically more complicated).

So far this has all been about the relation between theory and experiment. However, most of the text in your message alluded to potential logical inconsistencies within GR itself. Since the main point relies on a thought experiment, let me begin to address this by clarifying that, although thought experiments can be a very useful tool, they are not proper logical arguments in themselves and do not formally tell us anything about the the validity of a theory. This is because natural language is too ambiguous to express formal statements: GR (as every other physical theory) is a mathematical framework and we need mathematics to discuss it properly. This is evident when you consider how both quantum mechanics and special relativity are full of paradoxes that seem to point to contradictions that go away when expressed mathematically. Paradoxes point to the inadequacies of our intuitions, not to those of the theory.

That said, I'd like to point out a few potential flaws in the argument presented in your email, without actually going into mathematical detail:

First, Feynman's sticky bead argument played an important role in re-igniting interest in GWs at a point in history when it wasn't clear whether they were real at all; however, the argument is not a core part of the GR framework and is usually not even referred to in modern treatments of the topic—our understanding of GR has come a long way since the 50's!

Second, our intuitions about space and time do not jive well with GR. Because spacetime can be curved, the fact that circumference of the loop in the example decreases does not say much about the radius. For example, imagine you went in a circle around a massive object (say, Sun) and measured the distance travelled (call it c, for circumference), and then travelled radially inwards towards the center and measured that distance too (call it r, for radius), then you would find that c < 2*pi*r because the massive body curve the spacetime around it. This is all to say that a shrinking circumference does not imply a shrinking radius (at least not in all frames).

Third and last, it seems to be implied in the text you quote that the existence of longitudinal gravitational waves would be in conflict with GR; however, this is only true in a narrow sense that needs to be explained. According to GR, at any point in space-time one should be able to find a particular form of the GW equations (the technical term for this freedom in the eqs. is gauge, think of it as a frame of reference though it's not the same) in which the wave can be expressed as the combination of two independent polarizations transverse to the direction of propagation. Notice some key aspects of this statement: there is a specific choice of gauge (or frame of reference, if you wish) in which the equations take this particularly nice form, and that choice can only be defined locally (i.e. a choice that works nicely in one point in space, will be bad somewhere else). This means that if you choose an arbitrary frame of reference, chances are the wave will not look transverse, though you could always switch to the specific frame and gauge which will make the waves look nice at that point (this is the so called transverse-traceless gauge). The bottom line is that you might think that you have longitudinal waves, but you can always explain that as a combination of independent, transverse waves.

Finally, I would like to add a few words about Carver Mead's G4v theory. Unlike most alternatives to GR, Carver's theory makes markedly different predictions than GR with respect to the polarization content of GWs. However, the relative orientation of our detectors makes LIGO not really good at distinguishing different polarizations in transient (short-lived) signals like the ones we have observed so far. Furthermore, we don't have a full prediction of what the GW trace of the merger of two compact objects would look like in G4v (Carver is working on it), so we cannot make a statement about which theory, if any, is favored by the data. So we will have to wait for more detections and more theoretical work until we are able to make a statement about G4v.

Once again, thank you very much for a very thought-provoking email and for your interest in LIGO and gravitational waves in general. By all means, do let me know if you would like me to clarify any of the points above or if you have any questions.

Best,

Maximiliano Isi

--------------------

California Institute of Technology

LIGO Laboratory, MC 100-36

Pasadena, CA 9112

5

[aramis720]

beecee, I've mentioned a couple of times already in this thread that the chance of my being correct is very minimal. I'm not even a physicist, but I am trained as a scientist and critical thinker and have written some in the philosophy of physics. That said, I still haven't seen my concerns addressed well in this forum or elsewhere. You suggest, as have many others in this thread, that there is in fact a differential effect from GWs on the physical arms of the interferometer, based on the different directions of the arms.

 

But this is manifestly incorrect when we recognize that GWs are defined as waves of spacetime itself. So, as I've stated numerous times since my OP, this definition of GWs seems to render any detection of such waves by a physical apparatus in principle impossible simply because any distortion of spacetime itself will distort the physical apparatus occupying that slice of spacetime by exactly the same amount as the wave itself, in every direction. So the direction of the wave doesn't matter.

 

I'm not sure why this point isn't sinking in, but as I just mentioned to Mordred it seems that a lot of people continue to envision GWs as traveling through space rather than being waves of space itself.

 

Thanks for the post on GR but I'm not here challenging GR itself. I'm just asking about the LIGO experiment and GWs.

[beecee]

beecee,

 

I've mentioned a couple of times already in this thread that the chance of my being correct is very minimal. I'm not even a physicist, but I am trained as a scientist and critical thinker and have written some in the philosophy of physics.

Yes, just as Ocean waves are also "waves of the Ocean itself"

It appears your interpretation itself is wrong. It imo is manifestly wrong, to say that GW's, or ripples of the spacetime, [not space] will not affect two arms at right angles to each other differently. eg: If GW's were of greater magnitude, and one passed through me, I would appear stretched in one direction and squashed in the other...likewise at any one particular moment in time, one of the arms will appear longer [as judged by the laser] then the other arm.

I'm at a loss how you can see it any differently.

 

 

 

beecee, I've mentioned a couple of times already in this thread that the chance of my being correct is very minimal. I'm not even a physicist, but I am trained as a scientist and critical thinker and have written some in the philosophy of physics. That said,

You do have it over me then in that regard...I'm just a poor old retired Maintenance Fitter and Machinist. But one who has read up a fair bit on this subject and others associated with it.

All jokes aside, why not write or E-Mail aLIGO and ask for their opinion.

Edited July 3, 2017 by beecee