by alter-ego » Sat Feb 20, 2016 7:18 am
Chris Peterson wrote:...
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?
neufer wrote:
...
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unpublished Gravitational Radiation, Sec. 5E, Interaction of Waves with Matter: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 ≈ 10
31 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 ~10
43, or T = 10
43G. 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.
[quote="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?
[/quote]
[quote="neufer"]
...
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.[/quote]
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 [u]incident[/u] 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[sup]-6[/sup] that of an equivalent mass BH. Similarly, the Earth absorbs ≈10[sup]-10[/sup]. To quote Thorne's [url=http://www.its.caltech.edu/~kip/scripts/PubScans/Kip-GravRadNewWindow89.pdf]unpublished Gravitational Radiation, Sec. 5E, Interaction of Waves with Matter[/url]:[quote]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, [color=#0000FF]attenuation cannot be astrophysically important[/color].[/quote]
In his analysis for an inhomogeneous elastic medium (weakly absorbing case, not quadrupolar), he estimates the GW absorption length to be ≈ 10[sup]31[/sup] meters for Earth-like matter.
For some intuitive insight, I find it helpful realizing that space-time is [i]very[/i] 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 ~10[sup]43[/sup], or T = 10[sup]43[/sup]G. 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.