Will the LIGO Experiment Work?
Cigamtp
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 shoud 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!
The source material for this posting may be found in "Gravity" (1987),
"The Einstein Hoax" (1997), and "Corrections to Residual Errors in Special
Relativity (1999) located at http://www.members.aol.com/einsteinhoax/site.htm.
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