The discovery of gravitational waves offers a new way of looking at the universe. Who knows what we will discover?

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On 11 February 2016, it was announced by the Laser Interferometer Gravitational-Wave Observatory (LIGO) collaboration that gravitational waves had been discovered, finally confirming a century old prediction. This was very exciting, and the story was big news, making the front page of national newspapers and magazines, with even President Obama tweeting about it. The history of gravitational waves up to their discovery is rather interesting, so I thought I’d share some of it here.

What are gravitational waves?

Our currently accepted theory for the description of the laws of gravity is Einstein’s general theory of relativity, which celebrated its one hundredth birthday last November. Over the last century, it has shown itself to be one of the most mathematically elegant physical theories. Its formulation completely changed the way we think of gravity. Before Einstein, the accepted theory was Newton’s universal law of gravitation, which he published in 1687. It stated that gravity was a force: two objects with mass experience a mutual attraction, exactly like two magnets attracting each other.

Relativity turned this picture on its head, and said that gravity wasn’t actually a force; rather, it was a result of energy and mass causing spacetime to curve. Objects would travel on the path of shortest distance in this curved space. These would no longer be straight lines, they would now be curved. Such paths are known mathematically as geodesics. This alternative view leads to a range of predictions which weren’t possible in the Newtonian picture, for example: light can be deflected by gravity, black holes can exist and large masses can slow down time.

Gravitational waves are one of these predictions of general relativity which wouldn’t be possible without this viewpoint of a curved spacetime. A gravitational wave is a wave in the fabric of spacetime itself. Mathematically, this means that the components of the metric describing spacetime obey the wave equation, one of the most useful equations in applied mathematics. It is given by the following differential equation

\begin{align}

\frac{1}{c^2}\frac{\partial^2 h}{\partial t^2}=

abla^2 h.

\end{align}

Here $c$, which is the speed of light, is also the speed of the gravitational wave, and $

abla^2$ is known as the Laplacian, and is given by the sum of the second order spatial partial derivatives. The solutions to this equation (h) are waves, such as $\sin$ functions, telling us that the vacuum of space temporarily stretches in one direction, while contracting in another. Thus, if you have a ring of particles, and a gravitational wave passed through them, they would look something like this:







GIF used with kind permission from M. Pössel/Einstein Online.

Einstein vs Peer Review

It was Einstein himself, 100 years ago in 1916 shortly after the publication of his general theory of relativity, who originally realised these ripples in spacetime were a prediction of his theory. Einstein realised that the waves would be very small, and so there would be no hope of detecting them any time soon.

However, later in his life, Einstein started to have doubts. One of the fundamental concepts of relativity is that physics should be coordinate independent: you should be able to choose whatever system of coordinates you like (for example Cartesians or polars), and end up with the same results. Einstein thought these gravitational waves may just be an artefact of a poor choice of coordinate system, and perhaps if a better system was chosen the waves would disappear. Einstein was wrong.

Einstein wrote a paper with a collaborator Nathan Rosen, where they claimed to have disproved the existence of gravitational waves. They sent their paper for publication to the American journal Physical Review in 1936; but the journal’s editor read the paper with suspicion. It appeared that Einstein had made a rather elementary mistake when working in curved spacetime: he had simply chosen a bad coordinate system. The editor sent the paper to an expert reviewer to confirm his suspicions, and these comments were sent back to Einstein.

Einstein was rather taken aback by the idea that he should be subjected to peer review. He withdrew his paper from the journal, sending the following slightly passive aggressive letter to the editor:

“Dear Sir, We (Mr. Rosen and I) had sent you our manuscript for publication and had not authorized you to show it to specialists before it is printed. I see no reason to address the—in any case erroneous—comments of your anonymous expert. On the basis of this incident I prefer to publish the paper elsewhere. Respectfully, A. Einstein”

Einstein later submitted the paper to another journal (although in fairness to Einstein, he substantially revised the paper, and instead of claiming a disproof of the existence of gravitational waves, he actually proposed a new type of cylindrical gravitational wave). For more on this story, I recommend reading this excellent article “Einstein versus the Physical Review”

False detections

Research in general relativity was not very active between 1930–1960. The theory was thought of as mathematically elegant, but niche, and in practice it was often too difficult and cumbersome to perform calculations with.

But in the 1960s, a new wave of post-war scientists led a resurgence of interest in the field, and gravitational waves came to be accepted as real physical phenomena. Soon the race to detect them began.

One of the pioneers of gravitational wave detection was Joseph Weber, an American physicist. He created various experiments that attempted to detect these waves, and one of his detectors was even sent up to the moon on Apollo 17 in 1972. He claimed to have detected gravitational waves with his experiments many times, which led to much controversy. Numerous attempts to replicate Weber’s findings were made, but no one else could find a signal. Weber started to develop a dodgy reputation in the scientific community, and aggressive exchanges were had both in conferences and journal letters.

However, these days Weber is viewed in a better light. Although his experimental apparatus was not sensitive enough to detect anything, he pioneered ideas used in later detection attempts. Today he is regarded as the founder of the field of gravitational wave detection.

The discovery

This brings us to the modern day and the LIGO experiment. LIGO currently consists of two detectors in the US: one in Washington and one in Louisiana. Each detector consists of two 4km long tunnels at right angles to each other, and down each tunnel a beam of light is transmitted. The light then hits a mirror at the end of the tunnels, and is reflected back to the start. Any time delay between the two beams of light returning could be due to space distorting in one of the directions, ie. a gravitational wave.

The idea is simple, however in practice it is incredibly hard to make the detector sensitive enough to detect the waves above background noise. Many years have been spent eliminating every other possible source of interference. The detector is currently able to operate at an extraordinary degree of sensitivity, detecting changes in length at a scale of 1/1000th of the width of a proton, about $10^{-18}$m, which makes LIGO the most sensitive ruler ever made!

Finally, this February, 100 years on from Einstein’s original prediction and after months of rumours and speculation, the first detection of gravitational waves was announced. (Although the news embargo on the announcement was broken by one member of the LIGO collaboration who had the announcement printed on a cake.) A signal was detected in both detectors. Moreover, advanced numerical simulations tell us that the shape of the wave observed corresponds to that occurring when two black holes merge.

I went to a talk recently by one of the collaborators on the LIGO paper and the future looks exciting. We’re expecting more detections over the next year, and very soon another detector will come online, which will enable us to do full blown gravitational wave astronomy. With this third detector, physicists will be able to triangulate the signal, so we will know exactly where in the universe the waves have come from. (The paper announcing the detection has over 1000 co-authors. The audience attending this talk were mainly maths professors, who seemed far more interested in the logistics of writing a paper with a 1000 other people rather than the discovery of gravitational waves themselves.) In future there are plans to build and send a gravitational wave detector into space.

When astronomers first looked at light in the X-ray spectrum, they discovered a lot about the universe that we could not see simply by looking at the visible spectrum. With gravitational waves, we have a new way of looking into the universe. Who knows what we will discover?