100 years of General Relativity part 7: Gravitational Waves, a New Window to the Universe

Friends,

This is the seventh and last part of the VERITAS series on General Relativity. Just to remind our readers: We are doing this series on Einstein’s Theory of Relativity to celebrate the 100th Anniversary of General Theory of Relativity. If you have missed any of the first six parts, you can read them here:
https://unvarnishedveritas.wordpress.com/tag/100-years-of-general-relativity/

In the previous parts we have studied the basic ideas behind special and general relativity. We discussed how gravity bends space time and slows down time. We have also explored one of the most interesting and astonishing results of relativity: black holes. And then we applied general relativity to the whole universe to understand how it evolved after Big Bang and how it may end up billions of years from now. If you have not read the previous parts, I suggest you read them before reading this one.

In this article we will discuss Gravitational waves which are a consequence of Einstein’s theory of General Relativity and were predicted by him in 1916. Gravitational waves have recently been detected for the first time- an event that made headlines in scientific journals and also in newspapers. We will also discuss the implications of this discovery and why this discovery is of immense importance to science and technology.

In the earlier episodes of this series we saw that according to General Relativity, Gravity is a distortion in space-time caused by objects with mass. What happens when this mass moves? The distortion moves too. Now imagine what will happen if the mass accelerated? According to General Relativity, a massive accelerating body would create ripples in space-time or gravitational waves that travel at the speed of light. In other words, waves of distorted space would move from the accelerating body outwards and travel in all directions at the speed of light. Though these were predicted in 1916, they had never been detected till September 2015.

Any accelerating body will produce gravitational waves. So, I, you, our cars, our pets, every object that we know produces gravitational waves when accelerated. However most of these gravitational waves are so weak that there is no hope of detecting them. Let’s look at objects/phenomenon that generate powerful gravitational waves. The most powerful gravitational waves would be generated by colliding black holes, supernovas( the collapse of stellar cores), coalescing neutron stars(when two neutron stars come together to form one), coalescing white dwarf stars, the wobbly rotation of imperfectly shaped neutron stars and the remnants of gravitational radiation created by Big Bang.

Here are some properties of gravitational waves:

1) Gravitational waves can theoretically have any frequency. The frequency depends on the kind of acceleration that the cause of these waves undergoes. Astrophysical sources are likely to produce waves that have a frequency ranging from 10^-16Hz to 10^4 Hz. Higher frequencies would come from waves that were created by Big Bang.
2) When gravitational waves pass an observer, he will notice that the distance between objects increase and decrease at the frequency of the wave. This happens because gravitational waves are waves of distortion of space. We will see how this effect was used to detect these waves.
3) Unlike electromagnetic radiation, gravitational waves interact very weakly with matter. So they travel through the universe virtually unchanged. This is a very important property and we will discuss this later in this article.

Now lets understand how gravitational waves can be detected and the technique used for the first detection that happened in sept 2015. The amplitude of the waves that reach earth are so small that detecting and measuring them is a very complex engineering task. Let’s take an example to show you how tiny are the wave amplitudes that reach earth. Let’s take a binary star system- a binary star system is two stars that revolve around each other. So these stars are being accelerated as they revolve around each other. To make the acceleration larger, let’s make one of these stars a Pulsar. So we have a “normal” star revolving around a Pulsar. This system would produce gravitational waves of an amplitude of 10^-26 m on Earth. Detecting a wave of such a small amplitude would take an engineering marvel.

So we need to do two things to detect gravitational waves: we need to find a way to detect extremely small amplitudes and we need to find stronger sources of gravitational waves. Merging black holes may produce gravitational waves that may have an amplitude of 10^-20 m on Earth. Since these may the most powerful sources of gravitational waves, we need to be able to detect amplitudes of this order of magnitude to claim that we have found gravitational waves.

The property of gravitational waves that we can use for their detection is that when gravitational waves pass an observer, he will notice that the distance between objects increase and decrease at the frequency of the wave. See the following animation from Wikipedia:

gravitationalwave_pluspolarization
( if you see a static image and not an animation, please click this link to see it: https://en.wikipedia.org/wiki/Gravitational_wave#/media/File:GravitationalWave_PlusPolarization.gif)

Imagine a set of particles set into a circular ring. When there are no gravitational waves passing the ring, it appears perfectly circular. However, when gravitational waves pass through the ring, the space in which the ring resides gets distorted and exhibits an “oscillation” like the one depicted in the animation. Now, what you see in this animation is hugely exaggerated. The effect is so small that it is extremely difficult to observe. And that brings us to the marvellous experiment that actually observed these waves.

Laser Interferometer Gravitational-Wave Observatory (LIGO) is one of the grandest and most ambitious experiments ever performed. There are two LIGO interferometers, one in Louisiana state in USA and the other in Washington state in USA. Each of these two observatories is shaped like a L with each arm of the L 4 km long. See the Wikipedia image below:

simplified_diagram_of_an_advanced_ligo_detector

In the above figure we see that light from a laser source hits a beam splitter and is split into two beams. Each of these beams travels along one of the arms of the L. As discussed earlier, each of these arms is 4 Km long. From the diagram it seems that the two light beams will reflect back after travelling the 4 km arms and meet again. But that is not the case. It is not shown in the diagram, but to improve the accuracy of the experiment, each beam is reflected 280 times before it is allowed to meet the other beam. The setting of the mirrors is such that when the two beams meet after having travelled a distance of 280X8 km, they will be completely out of phase ie, when the meet each other they neutralize each other( this is called destructive interference) and the photo detector is not “fired”. Now, lets see what happens if a gravitational wave passes through the observatory. Depending on the direction of propogation of the wave, one of the arms will become slightly shorter or longer than the other one. This is because the wave will cause a distortion of space and the length will change. This causes the two beams to loose their out of phase setting. They become slightly in-phase and thus do not cancel each other completely. And therefore the photodetector fires. Note that I have simplified the method of functioning of the observatory but the basic principle of the observatory is as described. The amazing thing is the accuracy with which it can measure the difference in length between the two arms and the amplitude of gravitational waves that can be detected. The LIGO can detect gravitational waves of amplitude 5 X 10^-22 m! That, I would say, is an astounding level of accuracy! But what happens if a LIGO detector experiences a vibration due to a seismic event on earth? That may also disturb the legs of the L and cause a wrong detection. And that is the reason why we have two LIGO detectors thousands of miles apart. Any gravitational wave reading at one LIGO must be followed by another reading at the second LIGO detector and the difference in time between these two detections must match the time required by light to travel the distance( gravitational waves travel at the speed of light).

An interesting thing about LIGO is that it is connected to Einstein and his ideas in many ways: LIGO is based on Michelson-Morley experiment performed in 1887. The results of this was used by Einstein to formulate Special Relativity. LIGO uses Lasers. The idea of lasers came from a 1917 paper by Einstein. LIGO uses a photo detector- and we know that Einstein explained photoelectric effect in 1905. And finally LIGO is used to detect Gravitational Waves which Einstein predicted in 1916.

On 14th Sept, 2015, LIGO detected the first gravitational wave. The characteristics of the waveform matched what Einstein had predicted exactly a 100 years earlier. Scientists analysed this signal and concluded that it was caused by the merger of two black holes. Scientists estimated that the black holes were about 29 and 36 times the mass of the sun and the event took place 1.3 billion years ago( light took 1.3 billion years to reach us). About 3 times the mass of the sun was converted into gravitational waves in a fraction of a second. There was a 7 ms difference between the detection at the two LIGO observatories. Scientists could use this information to determine the direction of the black holes relative to the earth. And then on 26th December 2015, another signal was detected at the LIGO detectors. This signal again came from the merger of two black holes, one 14 times the mass of the sun and the other 7 times the mass of the sun. The combined entity was a black hole of about 20 solar masses. Thus a mass of about 1 solar mass( mass of our sun) was shot outwards as gravitational waves. The event took place about 1.4 billion light years away.

Now, let’s understand why gravitational waves are important. First, gravitational waves was the only idea proposed by Einstein’s general theory of relativity that had still not been confirmed. And now we know that Einstein’s theory of general relativity was correct in all aspects. And the detection of gravitational waves exactly a 100 years after Einstein proposed his theory was a wonderful celebration of the 100th anniversary of the great theory. But there is a bigger significance of the detection. Gravitational waves opens up a new window to study the universe. Our current window to study the universe was opened when Galileo first looked at the night sky using a telescope. That changed the world! Since then scientists have relied on electromagnetic waves( light, radio waves, x rays etc) to study the universe. Electromagnetic waves have a problem: they interact with matter and this interaction can disrupt them or impede them. Gravitational waves pass through the universe without any obstacles. So, while light from distant stars may be blocked by interstellar dust or other objects, gravitational waves will pass through without problems. So we will be able to “see” more, much more. Also, not all objects and events emit electromagnetic radiation. For example, two colliding black holes do not emit electromagnetic radiation but they emit a lot of gravitational waves. So, we have found a new way to look at the Universe. And many people believe that this will make a huge impact on the evolution of science from now on.

Now that gravitational waves have been detected, and we know how to do it, I am certain that we will see many gravitational wave detectors come up all over the world. There is a proposal for two Gravitational wave detectors in Europe( Virgo and GEO600), Japan( KAGRA) and even one in India( INDIGO). And scientists will find ways to make the detectors more sensitive to be able to measure waves of even smaller amplitude. So, this is really the beginning of a grand new adventure to unravel the mysteries of the universe using gravitational waves. And this is a very exciting time to do physics!

And with this we end our celebration of the 100th anniversary of Einstein’s General Relativity. It really is an amazing theory and a tribute to human intellect. And people who think that science is just about cold hard logic and has nothing to do with beauty, should read this theory once because I believe that it is one of the most beautiful creations of the human mind.

“The most beautiful thing we can experience is the mysterious. It is the source of all art and science. He to whom this emotion is a stranger, who can no longer pause to wonder and stand rapt in awe, is as good as dead; his eyes are closed.” – Albert Einstein

kanwar

============= ============ =================== ============== ========= =====
Go wondrous creature, mount where science guides
go measure earth, weigh air, state the tides,
instruct the planets in what orbs to run
correct old time, regulate the sun
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