APOD: LIGO Detects Gravitational Waves (2016 Feb 11)

[Chris Peterson]

I'm not talking about damping. Parts of the system move. That means work is done. That means energy is required, and the only source of that energy is the gravitational waves. They have to leave the interaction slightly less energetic than when they began. Energy is conserved, after all. And the mechanical energy spent in moving the LIGO components (not to mention the Earth itself) ends up as heat. What else could it end up as?

And when a comet comes in from the Oort cloud it speeds up. That means work is done. That means energy is required, and the only source of that energy is the potential energy in the Sun's gravitational field. Energy is conserved, after all.

But when that comet exits the Solar System it slows down thereby giving back that energy to gravitational potential energy. The only way for LIGO to accurately track the ripples in the gravitational wave is for it left motionless and still after the wave has pass...meaning no permanent energy absorbed and no heat.

Sure. Gravity is a conservative force, so the net work done in moving a particle (or to a close approximation, a large body) along a closed path is zero. But in this case, we're talking about a mechanical strain in a non-elastic body (the arms of LIGO or the Earth itself). That's not a conservative force, so the net work is greater than zero, and the gravitational wave must lose energy.

[Chris Peterson]

Here's an experiment. Two relatively stationary light detectors far away from significant gravitational fields are pulsed from an orthogonal again relatively stationary light source to establish a common time reference at/for the detectors. A high velocity rocket with a light pulse emitter travels down an imaginary line connecting the two detectors. The pulse trips the detectors measuring the elapsed time therefore the speed of light. Compare that to when the rocket was stationary or after the rocket passes. Simple eh? Today's optical emitters/detectors are capable of doing this, already found them. It could be done on Earth, however some theorists may claim Earth's local environment contaminated the result. It would be crazy never to attempt this.

It would be a crazy waste of resources to do this, and would provide no real boost to any scientific career. So don't hold your breath. As has already been pointed out, there are a dozen other measurements that have been made which would have been different were the speed of light anisoptropic or really, anything other than current GR and SR describes.

[daddyo]

LIGO was $600 million, all the science preceding effectively priceless, what's one more nail in the coffin experiment? What if it discovers something slightly different, or wholly unexpected, it's a new test never done before. It also would appeal to many of the public who fund a great deal of scientific research. I wish scientists didn't have to care about their careers since this is a direct conflict of scientific fact finding.

[alter-ego]

...
I'm not talking about damping. Parts of the system move. That means work is done. That means energy is required, and the only source of that energy is the gravitational waves. They have to leave the interaction slightly less energetic than when they began. Energy is conserved, after all. And the mechanical energy spent in moving the LIGO components (not to mention the Earth itself) ends up as heat. What else could it end up as?

...
The only way for LIGO to accurately track the ripples in the gravitational wave is for it left motionless and still after the wave has pass...meaning no permanent energy absorbed and no heat.

I think both of are basically right. It comes down to just how much energy do ripples in space-time lose through interaction with matter?

The absorbed fraction of incident GW energy is exceedingly small, but in in Thorne's work (below), he does discuss equivalent gravitational wave heating and absorption within a homogenous, viscous fluid. Wrt detection, a GW propagating on axis toward 2 LIGO detectors diametrically located on opposite sides of the Earth, a differential strain at between the two detectors will be immeasurable, but non-zero. Also the sensitivity to GW absorption is most sensitive high space-time curvature, i.e. mass alone is not really the right parameter to think about, it's density. So considering the strongest absorption cases consisting of quadrupolar mass distributions (most real objects are modeled well this way), objects fall into a simple order: black holes have the highest absorbed fraction, then neutron stars, then white dwarfs, then stars, then planets (Earth). Thorne estimated maximum absorbed power for the special cases where an ideal single-frequency quadrupolar resonance frequency is powered by a GW having the exact, narrow-band frequency. Thorne estimated a normal-density star, say the Sun, to absorb ≈ 10^-6 that of an equivalent mass BH. Similarly, the Earth absorbs ≈10^-10. To quote Thorne's unpublished Gravitational Radiation, Sec. 5E, Interaction of Waves with Matter:

Thus, although, in principle, gravitational waves could be attenuated significantly
by a medium of quadrupolar oscillators, in realistic situations the attenuation length greatly
exceeds the radius of curvature R produced by the oscillators; and thus, as in the case of a
viscous medium, attenuation cannot be astrophysically important.

In his analysis for an inhomogeneous elastic medium (weakly absorbing case, not quadrupolar), he estimates the GW absorption length to be ≈ 10³¹ meters for Earth-like matter.

For some intuitive insight, I find it helpful realizing that space-time is very stiff, but not infinite as the Newtonian metrical space is. This indicator is the coupling coefficient between Einstein's curvature (G) and stress-energy (T) tensor. The coupling factor ~10⁴³, or T = 10⁴³G. The equivalent Newtonian factor is infinite. Though very large, this finite coupling factor is what permits speed-of-light GW to exist. Also, this factor implies a "stiffness" that far, far exceeds ordinary matter stiffness. So when a GW comes rumbling through, matter is slave to the ripples of space-time - matter is literally transparent resulting in a non-zero, but exceedingly small loss of GW energy. So whatever dampening forces that exist within matter, a miniscule amount local heating should occur (e.g. LIGO's fused silica end-mirror suspension fibers), but with insignificant reduction of the GW strain which the detectors measure.

[neufer]

I'm not talking about damping. Parts of the system move. That means work is done. That means energy is required, and the only source of that energy is the gravitational waves. They have to leave the interaction slightly less energetic than when they began. Energy is conserved, after all. And the mechanical energy spent in moving the LIGO components (not to mention the Earth itself) ends up as heat. What else could it end up as?

And when a comet comes in from the Oort cloud it speeds up. That means work is done. That means energy is required, and the only source of that energy is the potential energy in the Sun's gravitational field. Energy is conserved, after all.

But when that comet exits the Solar System it slows down thereby giving back that energy to gravitational potential energy. The only way for LIGO to accurately track the ripples in the gravitational wave is for it left motionless and still after the wave has pass...meaning no permanent energy absorbed and no heat.

Sure. Gravity is a conservative force, so the net work done in moving a particle (or to a close approximation, a large body) along a closed path is zero. But in this case, we're talking about a mechanical strain in a non-elastic body (the arms of LIGO or the Earth itself). That's not a conservative force, so the net work is greater than zero, and the gravitational wave must lose energy.

One must clearly differentiate between the quasi free arms of LIGO (made up of disconnected mirrors) and connected non-elastic (i.e., DAMPED) bodies such as the Earth itself. The Earth is much less free to move under the influence of gravitational waves than are the arms of LIGO but it is able to absorb some of the gravitational energy and transform it to heat (through damping). Think of the known tidal heating of Jupiter's Galilean satellites due to hourly gravitational tidal distortions. If Galilean like satellites had orbited the binary black hole GW150914 they would, in addition, be tidal heated by millisecond gravitational tidal distortions from the merger.

1) Free motion such as the LIGO arm oscillations & comet trajectories do not constitute a permanent transfer of gravitational energy to kinetic energy and heat. Such free motions simply map out the curves in space time.

2) Restrained motion such as the muted tidal response of single non elastic bodies (e.g., Weber bars, Io) do constitute a permanent transfer of gravitational energy to kinetic energy and heat.

[Chris Peterson]

1) Free motion such as the LIGO arm oscillations & comet trajectories do not constitute a permanent transfer of gravitational energy to kinetic energy and heat. Such free motions simply map out the curves in space time.

I'm unconvinced. Any macroscopic body, made up of bound atoms, should deform as a gravitational wave passes through it at c (which is much higher than the speed of sound in that body). And no such body is perfectly elastic. The mirror does not move as a single entity and eventually return to its original position. It is also deformed. Just because it is suspended in some way doesn't mean it is perfectly free.

2) Restrained motion such as the muted tidal response of single non elastic bodies (e.g., Weber bars, Io) do constitute a permanent transfer of gravitational energy to kinetic energy and heat.

As noted above, I don't see any difference between the mirrors in LIGO and a Weber bar. Both are restrained.

In any case, aside from details about whether and to what degree individual bodies transform gravitational waves into heat or other forms of energy, my response to the original question remains valid- some gravitational wave energy is lost to interactions with matter, which results in a degree of attenuation. The magnitude of that attenuation is almost certainly too small to be of physical consequence except by the most extreme analysis, but that doesn't mean it isn't real.

[bystander]

LIGO-India Gets Green Light
California Institute of Technology | LIGO | 2016 Feb 18

Following this month's announcement of the first observation of gravitational waves arriving at the earth from a cataclysmic event in the distant universe, the Indian Cabinet, chaired by Prime Minister Shri Narendra Modi, has granted in-principle approval to the Laser Interferometer Gravitational-wave Observatory in India (LIGO-India) Project. The project will build an Advanced LIGO Observatory in India, a move that will significantly improve the ability of scientists to pinpoint the sources of gravitational waves and analyze the signals. Approval was granted on February 17, 2016. ...

[neufer]

I don't see any difference between the mirrors in LIGO and a Weber bar.

The LIGO mirror arms were designed to accurately map out the space time ripples in the 0.03 second "chirp" and then come to a rest. LIGO tracks space time strain without ever permanently absorbing it.

High "Q" Weber bars were designed to be set ringing (at their own natural frequency) for an extended period of time by the passage of the 0.03 second "chirp." Their damped oscillations eventual decay away into piezoelectric energy, sound & heat. Some of the space time strain was absorbed by the bar's own mechanical strain.

[Chris Peterson]

I don't see any difference between the mirrors in LIGO and a Weber bar.

The LIGO mirror arms were designed to accurately map out the space time ripples in the 0.03 second "chirp" and then come to a rest. LIGO tracks space time strain without ever permanently absorbing it.

I'd say without absorbing much of it. I am unable to see how it would be possible to make a structure that absorbs none of it. It must deform, and it's not perfectly elastic.

BTW, as a separate issue, I'm not sure its physically possible to even detect a gravitational wave- by any mechanism- without extracting energy from it.

[neufer]

I don't see any difference between the mirrors in LIGO and a Weber bar.

The LIGO mirror arms were designed to accurately map out the space time ripples in the 0.03 second "chirp" and then come to a rest. LIGO tracks space time strain without ever permanently absorbing it.

I'd say without absorbing much of it. I am unable to see how it would be possible to make a structure that absorbs none of it. It must deform, and it's not perfectly elastic.

BTW, as a separate issue, I'm not sure its physically possible to even detect a gravitational wave- by any mechanism- without extracting energy from it.

Sure...but the energy loss is much much smaller that the temporary kinetic energy of the oscillating mirrors (which quickly come to complete rest unlike the ringing Weber bars). One should not confuse the temporary kinetic energy of oscillating LIGO mirrors with permanently absorbed energy any more than one should confuse the temporary kinetic energy of comet with permanently absorbed energy. They are both temporary energy transfer events involving relatively little heat generation.

[Chris Peterson]

I'd say without absorbing much of it. I am unable to see how it would be possible to make a structure that absorbs none of it. It must deform, and it's not perfectly elastic.

BTW, as a separate issue, I'm not sure its physically possible to even detect a gravitational wave- by any mechanism- without extracting energy from it.

Sure...but the energy loss is much much smaller that the temporary kinetic energy of the oscillating mirrors (which quickly come to complete rest unlike the ringing Weber bars). One should not confuse the temporary kinetic energy of oscillating LIGO mirrors with permanently absorbed energy any more than one should confuse the temporary kinetic energy of comet with permanently absorbed energy. They are both temporary energy transfer events involving relatively little heat generation.

To be clear, I'm not confusing the two. I have no doubt that much of the force present is conservative, and no net work is performed. Nor that where work is performed, in deforming bodies, that the heat generation is significant.

[neufer]

Click to play embedded YouTube video.

[alter-ego]

...
1) Free motion such as the LIGO arm oscillations & comet trajectories do not constitute a permanent transfer of gravitational energy to kinetic energy and heat. Such free motions simply map out the curves in space time.

It is true LIGO has gone to the next level of sensitivity and via the quadruple end-test-mass (ETM) suspension system, the mirrors are a closer approximation to ideal free-falling test particles. However, I think the principle of mapping the ripples in space-time with even less energy absorption will likely be acheived with e-LISA. e-LISA will likely be the best approximation to ideal GW detector test particles since they will be in orbit (free-falling) and truly unconstrained. The physical deformation of the satellites themselves might be the only sources for absorption, and given a peak sensitivity ~10mHz (1/10,000 LIGO frequency) any component satellite (quadrupolar) resonances for GW absorption will likely be less than LIGO. (The suspension wires and fibers have about 10 resonances in the 100Hz to 10kHz range)

All Test Masses (Input and End) have the same suspension design

[neufer]

http://www.cbs.com/shows/the-late-show- ... late-show/

[neufer]

http://www.ted.com/talks/allan_adams_wh ... 2016-02-18#

[neufer]

Click to play embedded YouTube video.

The Nobel Prize committee are known for waiting a long time before they award the prize to the person(s) behind a breakthrough discovery.

Peter Higgs might disagree.