Gravitational Waves

Last Thursday, or early Friday morning in Australia, the LIGO (Laser Interferometer Gravitational-Wave Observatory) Scientific Collaboration announced “the first direct detection of gravitational waves and the first observation of a binary black hole merger” (which produced the waves).


LIGO Livingston Interferometer. (Credit: Caltech/MIT/LIGO Lab)

They have released several papers on and the main paper was accepted by journal Physical Review Letters.

This is the abstract of that paper:

On September 14, 2015 at 09:50:45 UTC the two detectors of the Laser Interferometer Gravitational-Wave Observatory simultaneously observed a transient gravitational-wave signal. The signal sweeps upwards in frequency from 35 to 250 Hz with a peak gravitational-wave strain of 1.0 × 10-21. It matches the waveform predicted by general relativity for the inspiral and merger of a pair of black holes and the ringdown of the resulting single black hole. The signal was observed with a matched-filter signal-to-noise ratio of 24 and a false alarm rate estimated to be less than 1 event per 203 000 years, equivalent to a significance greater than 5.1σ. The source lies at a luminosity distance of 410[+160,-180] Mpc corresponding to a redshift z = 0.09[+0.03, −0.04] . In the source frame, the initial black hole masses are 36[+5, −4]M⊙ and 29[+4, −4]M⊙, and the final black hole mass is 62[+4, −4]M⊙, with 3.0[+0.5, −0.5]M⊙c2 radiated in gravitational waves. All uncertainties define 90% credible intervals. These observations demonstrate the existence of binary stellar-mass black hole systems. This is the first direct detection of gravitational waves and the first observation of a binary black hole merger.

The absolutely amazing thing about these discoveries is that they all have roots in the general theory of relativity created mainly by Albert Einstein exactly 100 years ago. It is a centenary of belief in the full implications of his theory, carried from one physicist to the next like parent to child, which has brought about this magnificent discovery.

Einstein himself had a rocky history with gravitational waves and black holes. He published a paper in 1916 where he first predicted the existence of gravitational waves, then published a paper in 1918 in which he corrected errors in that paper and clarified his analysis, then in 1936 with a young collaborator Nathan Rosen (who also collaborated with him on the famous EPR paper which aimed to show that quantum mechanics is incomplete, and a paper introducing idea of wormholes) he wrote a paper refuting the existence of gravitational waves, then in 1937 he rewrote and published that paper with a more rigorous analysis that showed that gravitational waves actually exist. The interesting matter here is that the 1936 paper was rejected from the prestigious journal Physical Review because it had an error in its analysis. Einstein then became angry at the journal since, in his words “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”. Back then the system of peer review was fresh so Einstein did not expect any hurdles in publication. He decided to get it published in another journal but luckily he found the error himself before that happened, so the 1937 paper predicts gravitational waves. He boycotted publishing in Physical Review after that incident. Einstein published a paper in 1939 where he gave an argument that black holes do not exist.

So then there are two ironies associated with Thursday’s discoveries. One is that the LIGO team decided to announce the discovery of gravitational waves only after it was accepted by peer-reviewed Physical Review Letters, which is the opposite of Einstein’s action to avoid publishing in Physical Review because its editors sent his paper for peer-review. The other is that the discovery was made with gigantic Michelson interferometers with arms more than 4km long. The original Michelson interferometer of 1887 was much smaller, with arms about 1m long, and it provided the key piece of evidence for Einstein’s special theory of relativity precisely because it was not able to detect an ‘aether’, a medium that was thought by other physicists at the time to allow the propagation of light.


LIGO Interferometer (Credit: Wikipedia)

Slightly over a decade ago, around 2005, I was eager to learn about relativity and I found a website called Einstein@Home that allowed internet users anywhere in the world to offer computational power to assist in LIGO to find gravitational waves. I immediately signed up and it was a nice feeling to be part of the international effort. Looking at the website today I’ve noticed it says ‘Exciting news: Gravitational Waves detected!’ but then it says on the same page ‘Did Einstein@Home play any role in this? No, it didn’t. The signal in the instrument lasted only about 1/4 of a second. It’s not a continuous-wave signal like the type that Einstein@Home has been searching for.’ So the discovery was a detection of only a particular type of gravitational wave of very short time scale. Nevertheless this opens up hope for finding continuous-waves, indeed it has begun a new chapter in astronomy on how to observe the universe at all.

It should be noted that LIGO’s interferometers are said to be the most precise rulers ever created. LIGO is capable of measuring changes of order of magnitude better than one in ten thousandth the effective diameter of a proton (to 10-18 metres). The level of precision of Advanced LIGO, the detector currently used, has been achieved not only due to research in relativity and general interferometer engineering but crucially in quantum optics and theory of quantum measurement (namely into quantum radiation pressure and shot noise, and in future detectors quantum ‘non-demolition’ measurements that evade back action will be important as well as squeezed states).

Finally it is expected a Nobel Prize will come out of this discovery. Peter Higgs and Francois Englert shared the 2013 Nobel Prize for predicting the ‘Higgs boson’ in the 1960’s , an elementary particle discovered by CERN’s Large Hadron Collider in 2012. The 1993 Nobel Prize was awarded to Russell A. Hulse and Joseph H. Taylor Jr. for discovering a new type of pulsar which was used to indirectly show the existence of gravitational waves. The 2014 or 2015 Nobel was tipped to go to BICEP2 team for discovering a signature in the cosmic microwave background of gravitational waves from ‘inflationary’ expansion of spacetime in the early universe, except their results were found to be inconclusive. The 2016 Nobel Prize could go to the LIGO team as a whole or perhaps to Kip Thorne and Rai Weiss for leading the project right from the start. Einstein will have to skip this one.

Einstein’s 1918 paper:

In his seminal 1918 paper on gravitational waves Einstein derives their existence by considering what small (linear) gravitational fluctuations are possible in a region of spacetime without a gravitational field (Minkowski spacetime). It is shown that the fluctuations behave a wave equation in the same sense as light (electromagnetic waves) or sound (pressure waves). The speed of the waves is the speed of light. Using local energy and momentum conservation a formula is derived for the energy and momentum associated with the fluctuations and then it is shown that for a mass point at rest the energy and momentum ‘radiated’ both equal zero. He then shows that for a wave propagating along an axis there are two types of polarisations of the fluctuations but both are directed perpendicular to the axis. Using momentum and energy constraint the energy radiated in the fluctuations (waves) is expressed in terms of the rate of change of momentum distribution (specifically moment of inertia) of the masses producing the waves. Importantly, the distribution must have a changing second time derivative of quadrupole moment; a spherically symmetric or dipole distribution cannot produce gravitational waves. Again using energy momentum conservation the energy absorbed by the wave by a mechanical object is calculated. Finally Einstein replies to a criticism of Levi-Civita that his energy-momentum conservation formula is not valid in all coordinate systems (not covariant).

Indeed the discovery this week was based on the conclusion from this paper that a changing second time derivative of quadrupole moment of masses is required . Massive objects orbiting each other possess this property so the phenomenon of black holes orbiting each other and then merging fits this category.


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One Response to Gravitational Waves

  1. Pingback: Gravitational Waves – No. 2 | Exploring The Unexplored

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