## Wednesday, April 25, 2007

### History of gravitational waves

Daniel Holz discusses some history of gravitational waves. Click the animation above to get to his article. Note that my animation (LM) showing how space gets stretched in the presence of such a wave is rotated by 45 degrees relatively to Dan's animation (DH): they are two different "linear" polarizations. If you take the combinations
• LM + i DH, LM - i DH,
you will obtain a different basis of the so-called circular polarizations. In the corresponding pictures, an ellipse would simply rotate around, in one direction or the other.

In my wave, if you label the plane as x-y and the wave moves in the third, z-direction, it is the component g_{xy} of the metric tensor that fluctuates around zero. In Dan's wave, g_{xx} and g_{yy} fluctuate around one (in the East Coast convention); the two components oscillate in the opposite directions so that g_{xx} g_{yy} remains constant, equal to one. In the linearized approximation, it's equivalent to keeping g_{xx}+g_{yy} constant.

Einstein apparently knew about gravity waves as early as in 1918: he used linearized general relativity, the same modern approach that a particle physicist or string theorist would use today. It had to be very clear that the diffeomorphism symmetry wasn't enough to make all these waves unphysical - removable by pure gauge transformations - because the number of polarizations simply grows like D^2 or so with the dimension D while there are only D parameters in a diffeomorphism.

Nevertheless, there were doubters who argued that gravity waves shouldn't exist. It was a very stupid opinion that can mostly be blamed on the spiritual power of Mach's principle. According to Mach's (and Leibniz's) philosophy, empty space should be really empty - only relative positions of objects make sense - which means that an empty space shouldn't allow any gravity waves. General relativity however implies something completely different.

Gravitational waves are known to exist because certain binary stars lose exactly as much energy by emitting them as general relativity predicts. The 1993 physics Nobel prize has been given for this observation: the period of the pulsar orbit decreases by mere 75 microseconds every year but it can be measured. The energy carried by gravitational waves is quantized into "E=hf" Planck's units, just like for electromagnetic waves, and the quanta are called gravitons. Of course, individual gravitons haven't yet been seen, unlike photons, because they are too weakly interacting.

In perturbative string theory, gravitons are particular vibrations of a closed string with low enough energy so that it can give a massless spinning boson.