The difficult childhood of gravitational waves

By Daniel Holz | April 25, 2007 9:52 am

Gravitational waves were born from the mind of Einstein in 1918. He noticed that his brand-spanking-new field equations for the general theory of relativity had a simple wave solution in the weak field regime. These solutions represent propagating waves in the fabric of spacetime, traveling at the speed of light. In another fit of creative nomenclature these were dubbed “gravitational waves”. For a ring of particles floating in space, a passing gravitational-wave will cause them to oscillate (image at right stolen from the Wikipedia entry). For an introduction to the theory behind gravitational waves, I highly recommend chapter 7 of a certain textbook. (Sean, I get a kickback, right?)

Sadly, gravitational waves have had a fairly rough childhood. First came the doubters. There was much debate within the community as to whether gravitational waves truly existed. It might sounds strange that, given an equation describing their existence, gravitational-waves could nonetheless be questioned by large numbers of physicists. However, general relativity can be tricky, and it’s not always straightforward to understand what it’s trying to tell us. In this particular case, the question was whether or not gravitational waves were a gauge artifact. It can sometimes get confusing as to whether an effect is truly physical, or is just a byproduct of the coordinate system one has chosen. For example, look at the latitute/longitude coordinate system on the Earth. This system gets weird at the poles, where suddenly the longitude is no longer well defined (there are an infinite number of valid longitudinal coordinates for the same point). The North and South poles are somehow special, and if all you had were the coordinates, you might be afraid to take a walk there. Who knows what lurks at the singularities?! Needless to say, the problem is with the coordinates, and not with the poles themselves. (Although nowadays you might be afraid to head to the North Pole because you might end up under water. But don’t worry, Bush has it under control.)

Another example of the trickiness of coordinates, drawn from general relativity, is the black hole. In the canonical Schwarschild coordinates describing a black hole, it looks like terrible things (e.g., singularities) happen at the event horizon [or Schwarschild radius, which represents the ‘surface’] of the black hole. But these are a problem with the coordinates. In truth, nothing particularly weird happens as you cross the surface of a black hole (besides gravitational lensing causing the sky to appear bent and warped). This can be seen by writing the exact same spacetime in different coordinates (e.g., Kruskal coordinates), where everything becomes well behaved (except for the singularity itself). No big deal crossing the event horizon (though all hell breaks loose as you approach the singularity). A similar confusion resided in the nature of gravitational waves. There were ways to rewrite the coordinate systems such that the waves appeared to disappear. Sir Arthur Eddington supposedly quipped that gravitational waves travel at “the speed of thought” (referring to a subset of waves which indeed are coordinate artifacts). In addition, many of the early calculations were done in the linearized, weak-field regime, where simplifying assumptions are made regarding the strength of gravity. Calculating the presence of waves in the full-blown theory is not nearly as straightforward. In Einstein’s original work he presented the “quadrupole formula”, which describes the energy loss due to gravitational-wave emission from a binary system, and which is actively used to this day. But the weak-field assumptions neglect self-gravity, which could be important in a binary system. Roughly 20 years after his initial proposal of gravitational waves, Einstein submitted a paper to the Physical Review with the title “Do Gravitational Waves Exist?”, with the answer “No”. (There’s a general rule that all paper titles in the form of a question have a negative answer.) The father disavowed his own children. We all make mistakes. (In this case, the referee rejected the paper. Einstein took great offense, and never again submitted to Physical Review. The referee was right. Einstein was wrong.) It took another 40 years or so for the community to develop a full understanding of how gravitational-waves fit into general relativity. They are now considered an essential component of the theory. A very interesting discussion of this history can be found in a paper by Daniel Kennefick.

One way to think about the necessary existence of gravitational-waves is through the following thought experiment. Imagine that you are on one side of a room, and that on the other side is a very massive object (e.g., a plutonium bowling ball). The lights are off in the room, but fortunately you are carrying a very sensitive gravitometer, so that you notice the force of gravity due to the massive ball: your gravitometer points right at the bowling ball. Now let us assume that Mark sneaks in, and gives the ball a good (preferably relativistic) kick. Since the ball has moved, the gravitational field should register the change. Newton tells us that the gravitometer would instantly adjust. But from relativity we know that nothing travels faster than the speed of light (including information), and therefore we need ‘something’ to go from the accelerating bowling ball to our gravitometer, to tell it that the bowling ball has indeed moved. This is a gravitational wave! It carries with it the information about the accelerating mass, rushing out at the speed of light to announce the motion of the bowling ball to the entire Universe. Also notice that, were the bowling ball to suddenly contract, but remain spherical and conserve mass, then the gravitometer wouldn’t register a change. From this, we conclude that spherically symmetric variations don’t emit gravitational waves. As with most hand-wavy arguments, there are some important details being glossed over here (e.g., near vs far-field effects; Scott and Eanna have a nice review). But it makes a compelling case that something akin to gravitational waves must exist for general relativity to be self-consistent.

In a following post I’ll discuss the next sordid chapter in the history of gravitational waves.

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