Interaction of gravitational waves with matter

[Paul Colby]

Hello,

Lately I've been trying to understand the interaction of gravitational
waves with matter. In an article outlining a simplified treatment of a
Weber Bar detector a model of matter was used which approximates the bar
as a series of mass slabs connected by springs each obeying Hook's
law. The 4-acceleration of each slab is given by the geodesic equation
equated to the force exerted by each spring (scaled by the slab mass).
It seems clear to me that one is assuming in this model that the
"springs" or = inter atomic potentials are unaffected by the change in
geometry. What I find puzzling is that these potentials are
electrostatic in origin so shouldn't the electric fields be effected by
the geometry change to the same level as the mass geodesics of the
slabs?

Thanks
Paul Colby

[Anon E. Mouse]

Extending the reasoning of your thoughts one might expect that the
degree of coupling between a spatial distortion wave and matter might be
better observed by means of an amorphous mixture such as a plain carbon
microphone circuit, or a common resistor.

In these materials a series of boundary conditions exist which might
tell a tale about a transiting wave more clearly than a rigid body does.

Alternatively piezo electric materials with asymmetric crystal lattice
like quartz are known to be highly sensitive to mechanical stress or
strain and having a specific crystal orientation might have an innate
ability for directional sensitivity.

Another alternative would be to attempt to sense the passing temporal
distortion. In this case a AC transient induced in a high voltage DC
antenna wire would be telling and directional. Faraday shielding could
be used to reduce RF signal noise and running the circuit as a
comparator between a HV DC antenna and a ground potential antenna of
identical design could also be used to distinguish temporal distortion
waves from ordinary electromagnetic waves.

AAG

[Jonathan Thornburg [remove -animal to reply]]

I think your question is (almost?) the same as that posed (& answered)
in the delightful paper

Peter R. Saulson
"If light waves are stretched by gravitational waves, how can we
use light as a ruler to detect gravitational waves?"
American J. Physics volume 65 number 6, June 1997, pages 501-505
http://dx.doi.org/10.1119/1.18578

There seems to be a free copy of this online at
http://gw.aei.mpg.de/images/Saulson_1997AmJPhys_65_501.pdf

ciao,

--
-- "Jonathan Thornburg [remove -animal to reply]" <jth...@astro.indiana-zebra.edu>
Dept of Astronomy & IUCSS, Indiana University, Bloomington, Indiana, USA
"Washing one's hands of the conflict between the powerful and the
powerless means to side with the powerful, not to be neutral."
-- quote by Freire / poster by Oxfam

[Paul Colby]

On 2012-01-18 14:45:26 -0800, Anon E. Mouse said:

> Another alternative would be to attempt to sense the passing temporal
> distortion. In this case a AC transient induced in a high voltage DC
> antenna wire would be telling and directional. Faraday shielding could
> be used to reduce RF signal noise and running the circuit as a
> comparator between a HV DC antenna and a ground potential antenna of
> identical design could also be used to distinguish temporal distortion
> waves from ordinary electromagnetic waves.
>
> AAG

I've looked at a number of high frequency GW detection schemes one of
which is a statically charged coaxial cable wound into a helical form. The
first order interaction of a transverse traceless GW with a static
electric field
generates EM radiation at the frequency of the GW. These kind of GW antenna
may be effectively shielded from RFI. Using reciprocity one may compute
the directivity and conversion efficiency. What I get is,

V_g = (V_o / lambda_g) eta_r Int(dR/ds . h . dR/ds e^{ -i k R(s) + gamma s)ds

or on resonance,

V_g ~ V_o h (L / lambda_g)

where

h = metric strain ~10^-28 (at high frequency like 100
MHz this is
an enormous GW flux)
V_g = received voltage
V_o = DC voltage from inner to outer conductor ~10^5
lambda_g = wavelength of gravitational wave ~1 meter
L = length of coaxial line ~100ft
R(s) = helical coaxial path

One may compute the ratio of the received RF power to the incident
GW flux in watts/meter^2 to obtain a conversion area or cross section
for the antenna. These numbers are typically 10^-10 Barns (a Barn being
10^-28 meter^2) which is too small for me to consider doing.

Recently I've looked at simple high voltage capacitors where the recieved
voltage is,

V_g = h(t) V_o / epsilon_r

The nice thing about the capacitor configuration is it operates down to
very low frequencies where h is expected to be much larger. Unfortunately,
there are still a substantial number of zeros in the signal to noise.

All this is nice except it doesn't address my initial question which is why
is one able to ignore the direct effect of metric shear on the electric fields
within matter in the standard treatment of say the Weber bar?

[Paul Colby]

On 2012-01-19 04:48:35 -0800, Paul Colby said:

> All this is nice except it doesn't address my initial question which is why
> is one able to ignore the direct effect of metric shear on the electric fields
> within matter in the standard treatment of say the Weber bar?

I'm learning that being able to neglect internal E-fields in the bar follows
from an equivalence principle argument. There is a nice Dover book
"Classical Field Theory" by Davison E. Soper that is devoted to writing out
all the relavent interaction terms. For the GW wavelengths involved the
Hook law approximation for matter is well motivated.