"Will the LIGO Experiment Work?"
Cino
An ambitious experiment to detect gravitational waves from distant
astronomical sources is currently in preparation (Laser Interferometric
Gravitational Observatory - LIGO). A typical source for such waves would be
two stars circling each other in close proximity. It is proposed to detect
these waves by means of a two axis laser array to measure the relativistic
effects of
the waves as they pass by. It is postulated that these waves will cause the
distance between the ends of the array, as sensed by Laser inteferometry, to
be moved by the "distortion of space" as they pass the Earth. It is expected
that this movement will be detectible by an interference pattern observable
in Laser signals sent between the ends of the arrays. Calculations have
shown that the gravitational wave produced by a massive star in close orbit
about another should contain enough energy to be readily detectible by this
method. What does not seem to be mentioned is the fact that LIGO is only
capable of detecting longitudinal waves. In addition in none of these
reports does mention seem to have been made of the fact that such waves must
always be generated as multiple waves which cancel completely for
longitudinal waves and cancel in the far field for transverse waves.
Considering the distances involved and the size of the LIGO array, all such
observations will be made as distant far field observations.
The generation of multiple waves (e.g.- two for a binary system)
results from the fact that, as is the case with a single gravitational
object, the center of gravity of a gravitationally coupled multiple object
must remain stationary as its component parts move with respect to each
other. As a result, the gravitational wave (as seen at an "infinite
distance") from one of the objects in a binary system will be equal in
amplitude and opposite in phase to the gravitational wave from the other.
The net gravitational radiation from the pair will consist of both
longitudinal and transverse waves which are equal in amplitude. The
longitudinal waves will be opposite in phase and should therefore cancel
completely. The transverse waves will have a very small phase angle between
them equal to the radius of the orbit(so) involved divided by the distance
to the source.
The transverse waves are only observable if the two objects can be
resolved as separate objects (near field radiation). If they cannot be so
resolved (far field radiation) by the gravitational wave detector, they will
be impossible to detect because the detector will experience only the static
field from their common center of gravity. The cyclical field which for
which detection was hoped for will cancel. A further complication in the
detection of the transverse wave is the fact that they will not produce a
'stretching" of the local horizontal, they will produce a "tilting" of the
local vertical. The LIGO array should not capable of detecting the effect
even if it has sufficinet amplitude.
The longitudinal waves emanating from the center of gravity of the
emitting system always produce far field radiation which cancels completely.
An additional complication results from the fact that any residual component
of the gravitational radiation is attenuated not only by the expected
inverse square law, it suffers an additional attenuation in proportion to
the cube of distance rather than the square of distance do the transverse
waves. It would seem reasonable to assert that there are no longitudinal
waves for LIGO to detect.
Gravitational waves certainly do exist, we live on a world with an
enormous gravity wave detector, the oceans. The tides in the ocean are
produced by the Moon's gravitational field. The time of high tide advances
about an hour a day. This advancement can be considered to be the output of
a gravity wave detector, but, that gravity wave would be undetectable at
interplanetary distances because the gravitational waves from the Earth and
the Moon would cancel each other virtually completely! The writer has
received arguments that the fact that binary stellar systems are observed to
lose energy over time due to radiation of gravitational energy to the
Universe shows that the limitation described does not occur and that
gravitational waves will therefore be
detectible. Such an argument is faulty. The radiating objects are embedded
in the Universe and, as a result, all of the radiated gravitational energy
is absorbed as "near field" radiation. It is only the shrimpy detectors that
man is capable of building which will have difficulty in detecting
transverse gravitational waves. (In addition to the expected attenuation in
wave strength imposed by the inverse square law, the energy received by the
far field detector represented by the LIGO array will be reduced in
proportional to the square of the ratio of the orbital radius of the sources
divided by the distance to the sourced. Rotsa Ruck Fellows!
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Bogdan
of waves (ie, caused by just the rotation binary system). Instead it
is supposed to be looking for more "point-like" phenomena like star
collisions, collapses and supernovae. See http://en.wikipedia.org/wiki/LIGO#Mission
These phenomena cause primarily longitudinal (actually, spherical)
waves. For instance, a (non-rotating) supernova causes rapid, large
changes in the radial distribution of matter around the center of
mass, both by throwing large amounts of matter away (the ejecta) and
condensing a large mass in a very small space (a neutron or black
hole). (I don't know which of the two phenomena has a larger effect
gravity-wise, though I suppose the collapsing does because it's
quicker). The same happens when a normal star hits a degenerate one
(much of the mass is quickly condensed, some of it is quickly
ejected).
A rotating system complicates things, but in the far-field this effect
is still present. (It might be amplified/attenuated in some
directions, I don't know.) An impact between two collapsed stars also
changes the distribution. In the far field, it looks as their combined
mass is quickly collapsed in a denser object. Angular momentum will
also contribute if its distribution changes a lot (imagine two
oppositely-rotating objects impacting to an approximately non-rotating
one), though I have no idea how that looks in the far-field.
At lower scales, I'm told that even a neutron-star star-quake could
cause detectable gravity waves (also of the spherical kind). They may
be more common, though.