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”.gravitational wave 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.

  • Sean

    You would have gotten a kickback, except that you neglected to cite my post on Einstein vs. Physical Review. I’d love to help you out, but rules are rules.

  • daniel

    Damn. Missed that one. Isn’t there some sort of statute of limitations? Have all the good posts been done?

  • Sean

    No, and yes.

  • George Musser

    Can I trouble you with a separate question about gravitational waves? Alternative theories of gravity predict non-transverse polarization. Why is that? Would it mean the graviton is not spin-2, or not only spin-2?


  • PK

    I do not for a moment want to imply that I doubt the existence of gravitational waves, but I am not sure about your last argument. For waves to really propagate they should fall off as 1/r, with r the distance from the observer to the source. I think that a mere kick of the bowling ball will have a 1/r^2 effect. It is the oscillatory quadrupole moment that sets up a resonance and creates the propagating wave, right?

  • Sean L.

    The quadrupole moment doesn’t have to oscillate, it just has to have a nonzero second derivative. And, indeed, it has one during the kick.

  • PK

    Yes, that makes sense. Thanks!

  • Scott H.

    There were ways to rewrite the coordinate systems such that the waves appeared to disappear.

    Not quite: You can make the wave disappear locally (e.g., within some region), but not globally. Eddington’s comment had more to do with the fact that you can choose coordinates so that all gravitational degrees of freedom appear to radiate. The 1922 paper in which Eddington makes this comment shows that only a subset of those degrees of freedom are in fact radiative in all coordinate systems; the remaining degrees of freedom can be made to “propagate” at whatever speed you like depending on how you tweak your coordinates. (Hence “speed of thought.”) Eanna and I present a version of this calculation in more modern notation in our review.

  • Paul Valletta

    There is the fact that a simplified model for gravitational waves, has to include every gravitational source? does one filter out all unwanted gravitational signals, with so many source’s in our Universe?

    Could it be there are so many source’s, individual identification become’s near immpossible?

  • Scott H.

    Hmm. My last attempt to post this got eaten….

    FYI, the material covered in that paper by Dan Kennefick has now been turned into a book. All of this stuff was based on his PhD thesis — the paper is a highly condensed version, the book is an expanded version.

  • Sean

    George (#4) — it could mean either that there are new graviton-like particles other than the usual massless spin-2 graviton, or that the usual graviton is not massless. One of the fun things about field theory is that different degrees of freedom can re-arrange themselves into different “particles,” depending on what phase the theory is in. The classic example is the Higgs mechanism, in which you go from a massless spin-1 gauge boson (2 polarizations) and one spin-0 boson (1 polarization) before symmetry breaking, to just a single massive spin-1 boson (3 polarizations) after symmetry breaking.

    (In a sense, we have already detected some components of the Higgs boson — they’re the longitudinal polarizations of the W’s and the Z!)

    Here is an example of a spin-0 (“longitudinal”) graviton polarization:

    Rather than distorting the shape of the ring of particles, it expands or contracts it.

    The reason why these new polarizations keep showing up is that it’s very difficult to modify GR at long wavelengths without introducing new degrees of freedom. Almost a theorem that you can’t do it, but there are always loopholes.

  • mollishka

    Eddington sure did a whole lot of quipping.

  • daniel

    Scott, Sean, Sean L., thanks for the clarifications! Paul Valletta, I’m not sure I entirely understand your question. You might be asking about the issue of confusion noise–when there are so many different sources that it becomes impossible to disentangle them, and you’re just left with an incoherent mess. This then raises the effective noise floor in the representative frequency regime, degrading your sensitivity. Such confusion noise is indeed expected to happen with galactic stellar-mass binaries and LISA. Fortunately there are large fractions of frequency-space where the binaries are sufficiently separated (in frequency) that they can be easily distinguished and identified. Another interesting question is why the night sky isn’t as bright as the surface of the Sun, known as Olbers’ paradox. A similar question can be asked of gravitational-wave sources: why isn’t the sky uniformly bright in gravitational-wave sources? This in fact is perhaps even more compelling, since GW sources aren’t opaque to GWs, so you can’t clump them and have them block each other. However, the same reasons that solve the electromagnetic Olbers’ paradox apply to gravitational waves: gravitational redshift and a finite age to the Universe prevent the infinities. Note that Olbers’ paradox is a stunningly simple and elegant argument that the Universe cannot be infinite, static, and Newtonian.

  • Paul Valletta

    Daniel, thanks for the concise explanation, especially as my question was vaguely defined.

    Your explination raises some interesting points, one of which is if there is a another way to proceed? this linked paper is in research that may be beneficial?:

    Thanks again for making a very interesting subject so informative,pv.

  • Paul Valletta

    It may be interesting to veiw the co-ordinate diference’s by looking at the applet above, and the same applet on Lubos Motle’s site:

    if you use the sidebar slider to that only half the applet is visible, then the one that Sean placed clearly shows the individual particles expanding and contracting.

    The applet at Lubos’s site does not show this effect, by only showing half the applet at Lubos’s site, you get a different co-ordinate projection, one that is 1/4 rotated, and no expansion or contraction.

    I have asked Lubos to explain this defference,pv.

  • Ryan Scranton

    Ok, now that the physics stuff has been addressed, let’s get to the really interesting question. With that “speed of thought” quip and the “I’m trying to think of the other two” response to the reporter’s question about there only being 3 people in the world outside of Einstein who understand GR, Eddington has to be the reigning heavyweight champion in the field of being funny in the context of general relativity. It’s an obscure field of comedy, to be sure, but the mixture of humor and ego is a fine blend. So, my question to the field is this: who has the 21st century (or even late 20th century) got to compete with this titan of the tensor-based tee-hee?

  • http:/// Matti Pitkanen

    Gigantic values of the gravitational Planck constant bring in rather fascinating new elements to the notion of gravitational waves. Hence TGD based view about gravitational radiation differs in many respects dramatically from the classical view. A hugely scaled up version of the theory for the emission of radiation in atomic scale systems results.

    For details see the article at my blog.

    Matti Pitkanen

  • Paul Kamoda

    What I have read on GR and related articals. Leads me to think any experments or work on time traval is really playing around with Gravity or Anti-Gravity. Since Gravity has direct effect on speed of light and time. What I never hear is one reffering to the speed of light and time as here on earth, around or star, in our part of the galixie, and out local group. Speed of light and time is alway relative to gravity. So if fabic of gravity is flat and not bent do to an object or other mass then the much faster as will as time.

    Now if we could contral Gravity in say a bubble around a object, Then if object is standing still time pass more slowly if gravity in the bubble was increased. Same is true if gravity was less in the bubble time would pass faster by. Now if the object was moving at speeds that can be reached with a Ion rocket of 1/2 the speed of light and bubble is .1, .01 & so on we go faster then light related to out side the bubble but inside still be going 1/2 the speed of light. It could be some kind of warp field so to speak. As we would be warping Gravity.

    I think this could be done in the next 25 years if sience were to do a Mannhatten project on the control of Gavity. I do believe that the speed of light is the masurement of time. It is accepted and now proven black holes are real so then a white hole could be equelly there. also. If a gravity bubble of absolute zero was reached then the light speed would be infinit and time also. One could travel across the Universe in split second of time.

    It is just a thougth but if I am right the Star are not out of reach.

  • Binh

    I’m no scientist, so bear with me:

    My understanding is that gravity bends space-time, so my question is: why does gravity need waves?

    The image in my mind of how gravity works is a two-dimensional grid which becomes bent and distorted with the presence of a mass. In my analogy, the grid would now appear to have a third dimension kind of like this (very ugly) picture:

  • Coin

    There’s a general rule that all paper titles in the form of a question have a negative answer.

    Which is funny, because all political op-ed titles in the form of a question have a positive answer, usually before the end of the first paragraph.

  • Pingback: Einstein’s cosmic messengers | Cosmic Variance()

  • murray

    we need a good solid experimental proof that the speed of “propogation of gravity” is finite

    if it can not be prooved absolutely to be finite then we have to assume until proven otherwise that it is as Newton reluctantly accepted – infinite

    if we have to accept that it is “infinite” then we have to assume that, as nothing can travel faster than light, there is not traveling at all but that there is some form of physical connection – think of every mass in the universe embedded in a solid field – that can not, with current technology, be detected or, can be detected and is being detected, but can not be recognised for what it is

    if Gravity is the key then consider that red-shift is not the consequence of an expanding universe but of intergalactic light propegating at considerably higher speeds than within a higher gravity density region like a galaxy (

    The trouble with our current view of the universe is that our model is too good – it’s enough to explain enough to keep us happy – but it needs more attacking – we should always attack most fiercly those assumptions that form the foundations of our beliefs and the speed of light being constant is one of the biggest assumptions our thinking rests upon – if C was not a constant (except within a local gravity density) then we no longer need gravity waves, expanding universes, dark matter and a lot of other Ptolemy epicyclic solutions to our fundamental misunderstanding of the universe



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