I9    Gravitational  Waves

The immediate effect of the change of a gravitational field on distant objects is a particular problem of Newton's gravitational theory! If we quickly move a mass a few meters then the corresponding effect is immediately felt throughout the entire Milky Way. Time does not appear at all in Newton's force law! If we move a mass periodically back and forth, it creates an immediate force at arbitrary distances, that cause a small sample mass to vibrate. Any change in a gravitational field imparts an instantaneous transmission of energy and information across arbitrary distances! However, the STR sets with the speed of light an upper limit for any information transfer.

Einstein showed in 1918 that a change in the distribution of mass and therefore its impact on the structure of space-time according to GTR propagates at the speed of light. Thus two massive objects which are rapidly circling each other should emit gravitational waves which are transmitted at speed c throughout space.

The following visualization of gravitational waves was taken from http://lisa.jpl.nasa.gov/gallery

However, the effects on the structure of space-time, even from the most extreme sources, are extremely small. In 1987 in the Large Magellanic Cloud, a small companion galaxy of our Milky Way, a supernova explosion was observed (the explosion had taken place 160,000 years earlier ...). The ‘gravitational bolt’ on earth was a hundred times more intense than the radiation of the sun on the earth. However, it caused the distance from earth to sun to 'fluctuate' by only a few atomic diameters!

The length changes in the much shorter 'arms' of the existing detectors of such signals (300 m for TAMA300, 600 m for GEO600, 3 km for VIRGO and 4 km for LIGO) are correspondingly smaller. It has not yet been demonstrated that these facilities are capable of detecting these effects at all. Since early 2006 scientists have been waiting for the first signals. One is also dependent on the cooperation of several detectors: due to the enormous background noise, one can be reasonably certain a signal has been found, only when it has simultaneously been registered by multiple, widely separated detectors.

Satellite-based projects such as LISA have better chances of detecting a signal since the receiver is not exposed to terrestrial interference and since the arm length of the detectors can be tens of thousands of kilometers. More information can be found at the corresponding web-sites of NASA and ESA.

All ground based detectors have two arms perpendicular to each other. Gravitational waves are quadripole: If such a wave strikes perpendicular to the plane it affects 8 circularly arranged free falling test masses as shown above. First, the space in one direction is compressed and in the plane perpendicular to it expanded. Then the same happens in opposite directions. The metric of space-time ‘billows’ a little bit. This means that the elapsed time in the split halves of the laser beam in the two arms of the interferometer fluctuate for a short time at fixed mirrors. Therefore, when the two halves of the split beam are reunited the interference results no longer in permanent darkness (the default), but rather a brief flare becomes visible.

It is quite possible that tomorrow, for the first time, a gravitational wave will be clearly and directly demonstrated. This will require a bit of luck since supernova explosions, even in a large galaxy such as ours, do not occur every day. The last two were discovered by Tycho Brahe (1574) and Johannes Kepler (1604) – thus ringing the death knell on the idea of the immutability of the celestial sphere of fixed stars.

However, we have already had for a long time a very accurate indirect confirmation of Einstein’s gravitational waves. For more than 30 years, astronomers have measured the star system B1913+16. Two neutron stars of about 1.5 solar masses and a diameter of 20 km (!) orbit each other as shown in the picture above. A rotation takes less than 8 hours. Since this system radiates energy in the form of gravitational waves the two components must continually come closer. Thus, the orbital period gets shorter and shorter. This rotation can be measured very precisely, because the radio cone of one of the two stars passes the earth once each rotation: It is a pulsar. The decrease in the orbital period of 0.000,076,5 seconds per year, agrees with the prediction of GTR with an uncertainty of 0.2%. In 1993, R. Hulse and J. Taylor received the Nobel Prize in physics for the discovery and analysis of this double pulsar.

Recent findings on this topic are presented in [41]. The system PSR J0737-3039 A/B, described there, consists of two neutron stars, both of which are pulsars, and thus enable checking the predictions of GTR to an unprecedented accuracy.