#### From Einstein’s theory of relativity to the remarkable discovery of gravitational waves, a century-long ride.

__Intro__

100 years after it was first published, Einstein’s theory of relativity has emerged copiously triumphant in the wake of the recent direct detection of gravitational waves. Einstein said that everything is relative. Gravity isn’t exactly a downward force, time is not absolute and it’s all about ‘spacetime’. Was Isaac Newton entirely mistaken?

We hear ‘general relativity’ and we think ‘ E=mc^{2 }’, Albert Einstein’s gift to humanity. The general theory of relativity was published by Albert Einstein in 1916. A century later, in late 2015, the very first direct detection of the ‘gravitational waves’ as predicted by general relativity has ensued. Thanks to the brilliant LIGO team & the experiment, we now have the final proof for the ultimate prediction made by Einstein.

__Relativity: A refresher__

What is the theory of relativity? Subsequently, what is general and special relativity? An attempt to understand these concepts will require one to abandon predetermined notions regarding what gravity is and the concept of time as an absolute unit for all.

To begin with, Einstein stated that the laws of physics are same everywhere in the universe and so the properties of gravity would be universally identical and light would behave similarly for all observers anywhere. This universal property of physics implies that every observer in the universe will perceive space and time differently and personally. To put this into perspective, what might be 1 second for an observer crossing a black hole’s event horizon will be millions of years for us. Hence, it’s all relative.

Special theory of relativity: Since all the motion is relative and nothing is absolutely at rest but only relatively, there is no absolute frame of reference that exists but rather subjective ones. Special theory of relativity only describes the relative motion between two inertial (non-accelerating/constant) frames of reference. The general theory goes on to describe the relative motion of any sort.

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What does E=mc^{2} really mean?

Instead of thinking of matter and energy as two different things, Einstein viewed them as one single entity. The principle of mass-energy equivalence emerged from the special theory of relativity and states that energy equals mass times the speed of light squared. As the speed of light is quite high, this implies that a small amount of mass will contain a very large amount of energy. Additionally, ‘mass’ is just a property exhibited by ‘energy’.

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Einstein’s theory of general relativity explains “gravity” in terms of space & time or, rather, the theory describes the motion of objects in accordance with a “curved” spacetime. Additionally, the Newtonian description of gravity is rather incomplete. Trivially described, Einstein’s general theory of relativity states that objects, like Earth for e.g., “move” freely under their own inertia through curved space-time. Hence, the feeling of “falling down” that we attribute towards gravity is just the shortest path (geodesic) that we follow on a warped spacetime.

It is essential to realize that our current perception and understanding of ‘spacetime’ as an entirely separate entity will severely limit our capacity to comprehend how it works. For example, when I say “move” through spacetime, it does not refer to motion as we know it because it is not the kind of 3-D space we imagine in which motion exists (like we walk down a street as time evolves) but a 4-D entity.

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Curved spacetime?

Instead of imagining a universe where events occur in __space__ at certain points in __time__, try to think of “spacetime” as a dynamic entity. This fabric of spacetime is distorted by mass (or matter) that it contains and this distortion tells the matter how to move & evolve. The distortion caused in the fabric defines its __curvature__ and the shortest path between two points in this __curved spacetime__ is called a “geodesic”.

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Since their publication in 1915, the calculations and predictions laid out by Einstein have proven to be correct time & again. Several classical tests like the gravitational redshift of light, deflection of light by the Sun etc. and modern ones like gravitational lensing, gravitational time dilation are existing evidence that Einstein was right. One of the major predictions of his mathematics is gravitational waves and their formation & propagation through spacetime due to highly energetic cosmic events. September of 2015 was the final milestone as a direct detection of G-waves reinstated that Einstein’s equations make music and not noise.

__Relativity and everyday life__

All of this makes for a really good read until you begin the question the implications of these theories in everyday life. Is it required to think of the Einsteinian model of gravity when the Newtonian gravity model has been working just fine since centuries. Since we cannot see or feel the effects of relativity, does it really make any difference?

This might have been true before the human species decidedly ventured into space. With large distances and speeds, relativistic effects like time dilation can accumulate progressively and hence, must be accounted for. The GPS navigation system consists of 24 satellites orbiting at an altitude of roughly 20,000 kilometres. These GPS satellites have orbital periods of almost 12 hours and orbital speeds of about 3.9 km/s! Therefore, the effects of special and general relativity are noticeable and are erroneous for the system.

Special relativity says that time appears to slow down for an observer in motion relative to a stationary one. This effect is known as time dilation. Furthermore, general relativity says time passes quicker when the observer is away from a massive astronomical body because the fabric of spacetime is less curved (or low gravity) when compared to being at close proximity. As the GPS satellites are away from the earth, time dilation would cause the atomic clocks to on the ground to fall behind the atomic clocks on-board the satellites. Additionally, the satellite atomic clocks would also appear to slow down since the satellites are at constant relative high speeds. Although opposite, these two effects are not enough to cancel each other out and need to be compensated for since they are cumulative.

The satellite clocks run ahead by about 38 microseconds per day and for a high precision system like the GPS navigation technology, such an accumulation of noise could throw the system out of whack. With navigational errors of approximately 10 kilometres within one day, the global positioning system would be rendered utterly unusable in hours.

__So what are G-waves?__

Gravitational waves are ripples manifested in the fabric of space-time because of large enough disturbances or some cataclysmic events in space, like colliding black holes or binary neutron star systems. The most common analogy (though unrealistic) is the ‘bowling ball on a trampoline’. The depression caused by the weight of the ball on the sheet depicts the distortion in the fabric of spacetime caused by a large enough astronomical body, like the Sun. Now, if you think about two bowling balls circling each other on a large enough trampoline, they will cause ripples propagating from the centre to the outside. This is essentially how G-waves can be explained. But unlike ripples travelling on a sheet, G-waves will “stretch & squeeze” the fabric of spacetime as it passes through, since it is a __quadrupole wave__.

It is really imperative to grasp that the fabric of spacetime will not resemble the rubber sheet even remotely. Because the fabric of space-time has four dimensions, an added dimension of time over the three conventional (and easily perceptible) dimensions of space. Furthermore, the planetary bodies are not exactly __on__ the fabric (like the bowling ball on the rubber sheet) but they are a part of the fabric. And this goes for any body with mass; stars, planets, you & me. So if you & I spin around each other as fast as possible, would we cause ripples or distortions in the fabric of space-time? Yes, of course! Could we detect these ripples? If anyone can, it is LIGO.

__What is the LIGO experiment?__

Laser Interferometer Gravitational-Wave Observatory (LIGO) is a very large scale experiment set up to detect gravitational waves. It was first in August 2002 that the initial LIGO (iLIGO) began its quest for the direct detection of gravitational waves and this continued till 2010 but there wasn’t a single detection made. At this point iLIGO was capable of detecting a change in the order of 1/1000^{th }the width of a proton! Admittedly, it does sound quite impressive but it also happens to be the minimum sensitivity requirement to have any shot at detecting a passing-by G-wave. To accomplish this, the LIGO experiment makes use of lasers.

A laser beam is shot through a beam-splitter into two 4-kilometre-long vacuum tubes (right-angled to each other) with a mirror at both the ends. The laser beam is bounced 400 times between the mirrors at either ends before it is brought back together. If there is no disturbance (G-wave or otherwise), the laser beam will undergo destructive interference when the two beams reunite and no signal is received. However, if a G-wave happens to pass by, it would shrink one of the arms and simultaneously lengthen the other causing unbalanced interference and a signal will be detected. Moreover, the signal caused by a passing gravitational wave (as opposed to other external disturbances like seismic activity) will have a very unique signature. As the stretch & squeeze of each arm will oscillate with time, the interference pattern will capture this information and will also reveal the wave’s directionality.

With no detection of G-waves until 2010, iLIGO concluded its initial operations. Between 2010 and 2014, iLIGO underwent some astonishing engineering & technological upgrades. In 2004, iLIGO obtained the approval to evolve into “Advanced LIGO” (aLIGO) with a 10x increase in the sensitivity of the instrument. aLIGO was installed and tested and it had by now surpassed the capabilities & sensitivity of iLIGO. With a 10x higher sensitivity, the aLIGO is not only capable of measuring much smaller changes in length but it can also observe a volume in space which is 1000 times larger than the iLIGO.

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__Advanced LIGO : QUICK FACTS__

- LIGO is the world’s largest and most sensitive interferometer.
- LIGO contains one of the largest and purest sustained vacuums (10
^{-9 }torr) on Earth, second only the Large Hadron Collider in Switzerland. - LIGO attempts to measure the smallest measurement ever attempted by Science (1/10,000
^{th }the width of a proton). - Although a space observatory, LIGO is blind to the electromagnetic spectrum as G-waves do not fall into this spectrum.
- LIGO has twin facilities in USA (LIGO Livingston & LIGO Hanford) which ensures that any G-wave detection can be precisely confirmed & tallied, ignoring local disturbances.

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__14__^{th}__ September 2015__

A few days before the first official aLIGO search was scheduled to begin, the LIGO team ran an engineering test and, unknowingly, marked September 14^{th} as one of the most iconic days in the history of mankind. Described as the greatest discovery of the century, the LIGO team successfully, for the first time, directly detected gravitational waves caused by two colliding black holes about 1.3 billion years ago!

First indirect detection: As any system generates gravitational waves, it also emits gravitational radiation. This leads to a loss in the orbital energy of the astronomical body as the waves radiate outwards. The orbital frequency of the binary neutron star system (PSR1913+16) has been observed since its discovery in 1974. The loss of orbital energy moves the stars closer decreasing their orbital period. The observed decrease of the orbital period over the past 35 years agrees with the energy loss through gravitational radiation predicted by general relativity to better than 1 percent accuracy. This marked the first * indirect detection* of G-waves by Russell Hulse and Joseph Taylor, awarded with the Nobel Prize in 1993.

__So, Is Issac Newton wrong?____ __

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“No one must think that Newton’s great creation can be overthrown in any real sense by this [Theory of Relativity] or by any other theory. His clear and wide ideas will for ever retain their significance as the foundation on which our modern conceptions of physics have been built.”

~Albert Einstein

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It is of course puerile to say that Newton was wrong since it was his equations that enabled humanity to send our own to the moon. It is perhaps more prudent to say that Newton’s original theories had certain shortcomings which Einstein recognized. He explained gravity and other Newtonian relationships using general relativity, with mathematical predictions and better precision than Newton ever had. Additionally, Newton was of the opinion that gravity was a constant and instantaneous force of nature and any information regarding a sudden change (in gravity) will in communicated with the entire system in an instant. This would imply that gravity travels faster than light which did not make sense and was something Einstein could not agree with as he saw the speed of light as a ‘cosmic speed limit’.

Although Newton understood very well how this “force” of gravity worked, he wasn’t sure what it was. When Einstein explained gravity as a purely geometric property of spacetime, his general theory of relativity not only explained everything that Newton had but also covered few things that Newton couldn’t; like what was the agent causing gravity? To quote Issac Newton, “Gravity must be caused by an agent acting constantly according to certain laws. But whether this agent be material or immaterial, I have left to the consideration of my readers.” Almost 300 years after Newton, Albert Einstein was successfully able to provide a better & wholesome understanding of gravity.

__Future of gravitational wave astronomy__

As aLIGO continues its operations, more detections of gravitational waves are expected in the coming months and years from far away cosmic events. Also, gravitational wave astronomy has begun to have an impact on the scientific community globally. Projects like LIGO-India (IndIGO), the Virgo interferometer in Italy, KAGRA in Japan etc. are working towards G-wave detection as well.

ESA’s Evolved Laser Interferometer Space Antenna (eLISA) is proposed to launch sometime in mid-2030s and it aims to accurately detect G-waves from a large volume of astronomical sources. eLISA will work just like LIGO but in space with an arm length of one million kilometres and hence, will be quite sensitive and capable of detecting much fainter signals. In addition to this, ESA’s LISA Pathfinder (LPF) was launched in December 2015 and has been sent to space to test the essential technology required to operate eLISA. The LPF is currently operating 1.5 million kilometres from the Earth (towards the Sun) and will acquire information about the geometry of the spacetime fabric by understanding the “path” of a specimen in pure gravitational free-fall. This is already the beginning of major steps in the field of G-wave astronomy.

__Last word__

The direct detection of these G-waves has been called the greatest discovery of the century. Although it is astonishing that Einstein’s predictions have proven to be correct 100 years after he made them, there is much more to the significance of this detection. Until now, we have been studying the universe through the electromagnetic (visible or invisible radiation) spectrum. However, gravitational waves do not fall into the electromagnetic spectrum at all. Hence, gravitational wave astronomy will provide a completely new way to look at the Universe, especially in terms of the things that we find most mysterious in the cosmos; like black holes, workings of supernovae or Dark energy.

I believe, not only is it about understanding the things that we already know from a better perspective but about discovering many celestial unknowns. It is an entirely new dimension of knowledge that we can now step into. Furthermore, it calls for a much deeper sense of curiosity and an initial acceptance of our ignorance as people of science (or not) to be ready for surprising discoveries, many scientific “firsts” and, specially, an influx of unexpected knowledge in the field of gravitational wave astronomy.

[author] Mannat Kaur, MSc Aerospace Engineering, Air Transport Operations, TU Delft [/author]