Gravitational Waves Explained

Gravitational Waves

Ever since the dawn of human civilization, we have wondered about the celestial bodies that illuminate the night sky. If we look back into the history of mankind, several philosophers belonging to different civilizations had a diverse perspective on the existence and motion of these heavenly bodies. While some of them suggested that planets and stars are part of god’s realm and follow some “natural motion,” others proposed that these bodies revolve around the earth. Later in the 1500s, astronomers like Gallielio and Brahe discovered that the earth and other planets revolve around the sun, whose motion was later calculated by Kepler in 1609. In 1686, Sir Isac Newton described the cause of this motion as the Universal Law of Gravity in his famous book “Principia de Mathematica.” The law states that every object that has mass, from an apple that falls from the tree to the moon that orbits the earth, has a gravitational field associated with it, which interacts with the gravitational field of other objects and pulls each other together. He also explained that this influence of one body on the other varies proportionally to the product of their masses and inversely to the square of the distance among them; however, he did not describe how the effects of gravity instantly transfer from one place to another. In simple terms, Newton’s theory of gravity explains that there exists an attractive force among two massive bodies and what is the strength of that force, but it fails to explain what causes this force to act instantly at a distance. The Universal Law of Gravitation set a mark in human understanding of the universe and was efficient to successfully land the first humans on the surface of the moon; however, the enigmatic nature of its existence pertained until 1916, when Albert Einstien first published the General Theory of Relativity (GTR).

The essence of GTR lies in the idea of considering space and time, not two separate entities, but a unified attribute of the universe called the space-time continuum. In general relativity, gravity is described as the way in which matter behaves as a result of distortions in the space-time continuum. For instance, when you throw a ball in an upward direction, it falls back because the mass of the earth has altered the geometry of the space-time continuum around it in such a way that the ball’s straight-line motion appears as a projectile going up and down. To better understand this motion, draw a vertical straight line on a sheet of paper and consider that sheet as a space-time continuum. Folding the sheet in half would symbolize the similar trajectory of a ball moving upward in a curved space-time continuum. Another apt analogy can be thought of as follow: consider a circular sheet of fabric tightly held from all sides. If you place a heavy ball in the center of this fabric, it will distort the fabric’s otherwise flat surface into a conical shape; now, if you throw a marble on this surface, it will follow a specific trajectory due to the curvature created by the heavier ball in the center. It is important to note that the analogies mentioned above only symbolize the concept of curved space-time in 2-Dimensions and 3-Dimensions, respectively, and these are not entirely accurate as space-time is a 4-Dimensional entity, with three dimensions of space and one of time, which can be understood by employing the rigorous mathematics of Einstein’s field equation and Riemannian Tensor Geometry.

Field Equations

In a nutshell, the mass of the object curves the space-time continuum, and this curvature guides the motion of other matter present in its vicinity. As matter moves, it changes the curvature of space-time in the form of waves, much like the ripples produced by a boat circling in a water body. “Gravitational waves” is the name given to these ripples in the space-time continuum that spread out across the universe, traveling at the speed of light. Albert Einstien first predicted the existence of Gravitational waves in 1916 in his paper on the General Theory of relativity; however, he also proposed that these waves are too weak to be ever detected, even when produced by the motion of the heaviest celestial bodies known at that time. Almost 100 years later, on September 14, 2015, researchers successfully detected the first direct evidence of gravitational waves. This discovery earned three scientists, Rainer Weiss, Kip Thorne, and Barry Barish, the 2017 Nobel Prize in Physics. Let’s expand our knowledge about gravitational waves, starting with their discovery.

The Discovery of Gravitational Waves

Although gravity is the oldest known force to mankind, it is also the weakest among the other three fundamental forces of nature, the electromagnetic force, weak nuclear force, and strong nuclear force. Whilst every object that accelerates under the influence of gravity (even the apple falling from the tree and the moon orbiting the earth) generates gravitational waves in the fabric of space-time (analogous to an electric charge radiating EM waves when accelerated under the influence of EM force), these waves are too small to be detected by the most sensitive detectors ever made by the human beings. For several years, such complexities led many scientists, including Einstien himself, to doubt the existence of gravitational waves. Eventually, in 1974, astrophysicists Russell Hulse and Joseph Taylor discovered a binary pair of neutron stars 21,000 light-years from the earth. Seven years later, after tracking the radio emissions of one star in the pair for years, Taylor and two other colleagues (Joel Weisberg and Lee Fowler) noted that the time it takes for the two stars to orbit each other was decreasing exactly in a way that general relativity predicted if the two stars were radiating gravitational waves. Later this discovery did not only earn the Nobel Prize in Physics in 1993 but also initiated the hunt for better instrumentation for the detection of gravitational waves. Analyses of other binary neutron star systems confirmed this effect, firmly concluding that gravitational waves were not just theoretical; however, these findings were not direct confirmations of gravitational waves but the confirmation of effects that could only be explained by the existence of gravitational waves. These findings also confirmed that detectable gravitational waves could only be produced by cataclysmic astronomical events, such as colliding black holes, supernovae (massive stars exploding at the end of their lifetimes), and colliding neutron stars; however, even such events create gravitational waves that impact our detectors on Earth by an amount thousand times smaller than the size of a proton. Another problem was identifying such events, as these are rare, scattered across the universe, and possibly billions of light-years away.

When gravitational waves travel, they stretch the space-time in one direction and compress it in the direction perpendicular to the stretching. The idea was to detect the stretching and compression of something in the space-time fabric, which would confirm the existence of gravitational waves. In 1960, Joseph Weber at the University of Maryland made the first effort to build detectors for gravitational waves, using large cylinders of aluminum that would vibrate in response to a passing gravitational wave; however, this research didn’t produce any fruitful result other than pointing the scientist to look for something much more sensitive to gravitational waves. During the 1960s and 1970s, several scientists proposed the idea of using interferometry for the detection of gravitational waves. The idea of using a laser interferometer for this seems to have been floated independently by various people, including M. E. Gertsenshtein and V. I. Pustovoit in 1962, and Vladimir B. Braginskiĭ in 1966. The prototypes based on laser technology were developed in the 1970s by Robert L. Forward and Rainer Weiss. After several advancements in the prototype’s sensitivity and noise cancellation efficiency, it finally became the Laser Interferometer Gravitational-wave Observatory (LIGO), a marvel of precision engineering that made the first direct discovery of the gravitational waves on September 14, 2015.

barish-thorne-weiss

The Role of LIGO in detecting Gravitational Waves

Laser Interferometer Gravitational-Wave Observatory (LIGO) is one of the most sophisticated and precise instrumentation present on our planet. It is an always-running experiment (closed only for degradation or maintenance) with a central goal of directly detecting the cosmic gravitational waves and developing these observations as an astronomical tool to enhance our understanding of the universe. This instrument works by splitting and recombining a beam of light and creating a pattern (called an interference pattern) that can be studied and analyzed. In this case, the patterns can reveal information about gravitational waves. The current LIGO facility consists of two almost identical observatories situated in the United States of America, the LIGO Livingston Observatory in Livingston, Louisiana, and the LIGO Hanford Observatory, on the DOE Hanford Site, located near Richland, Washington. These observatories are 3030 km apart on the surface of the earth, while a straight line distance below the surface is 3002 km. This distance provides a fairly enough time difference of 10 milliseconds for a gravitational wave to hit the two observation sites. The time difference provides necessary data for the determination of the source of gravitational waves using the trilateration technique. Each of the observatories is a huge L-shaped facility with 4 km long ultra-high vacuum tubes established perpendicular to each other.

One of the most prominent features of LIGO is its precision in the detection of gravitational waves. There are several factors, called noise in technical language, that can hamper the LIGO’s effort to make its sensitive detection. Noise can be considered as physical vibrations from the environment (from cars driving on nearby roads to the earthquakes and waves crashing on distant ocean shores), fluctuations within the laser itself, even molecules crossing the path of the laser. Over a thousand scientists have worked for decades to overcome these problems. This work can be summarized into three central advancements that the current LIGO incorporates

  • The 4km beam tubes are kept under ultra-high vacuum, which prevents sound waves and temperature changes from altering the path of the laser light.
  • The mirrors at each end are held in place by a very complex seismic isolation system to counteract any vibrations using both electromagnetic and hydraulic systems.
  • There is a specific reason for building two almost identical observatories 3003 km apart. One interferometer can only tell that a potential gravitational wave has been detected, and at least two detectors are required to be certain that it is not random noise. Because gravitational waves move at the speed of light, when a potential gravitational wave has been detected, we can check that the same signal arrived at the next detector with the right time difference (a few milliseconds). The detectors are sensitive enough to be affected by events like a tree falling or someone dropping a hammer. The tiny likelihood of this same event happening in different places, with the correct time delay, means that these detections can be safely discarded.

Although the Hanford and Livingston detectors are essential to LIGO’s operation, there is also an important partnership between LIGO and a network of other gravitational wave observatories and researchers around the world. Most prominently, LIGO closely collaborates with Virg, a 3 km gravitational wave interferometer near Pisa, Italy. The quest for gravitational waves would be greatly aided by this partnership. The question now left is why scientists are so fascinated with gravitational waves that they are willing to spend billions of dollars on such projects. To understand this, let’s discuss the importance of gravitational waves.

LIGO_measuremet

LIGO measurement of the gravitational waves at the Livingston (right) and Hanford (left) detectors.

Why are Gravitational Waves Important

For centuries, the light was the only source of information that humans had to understand the mysteries of the Universe. Scientists have relied exclusively on the EM radiations coming from the distant stars, planets, and other celestial objects for the understanding of their distance from us, their chemical composition, and their fundamental nature. The discovery of gravitational waves has launched a new era in astronomy where scientists can understand the behavior of some of the most mysterious heavenly bodies, such as black holes, which do not emit any light. More significantly, since gravitational waves interact with matter very weakly (unlike electromagnetic radiation, which can be absorbed, mirrored, refracted, or bent), they pass through the Universe almost undetected, providing us with a direct view of the gravitational-wave Universe. The waves carry information about their origins, which is free of the distortions or alterations suffered by EM radiation as it traverses intergalactic space. With this recent detection, astronomers have been able to combine gravitational waves with more traditional ways of observing the universe, helping to untangle mysteries about the dense, dead objects known as neutron stars. Since gravitational waves can freely travel through matter, gravitational-wave detectors, unlike telescopes, are pointed to observe the entire sky rather than a single field of view. LIGO has lifted a veil of mystery from the Universe, paving the way for groundbreaking new physics, astronomy, and astrophysics science. Some detectors are more sensitive in certain directions than others, which is one of the reasons why having a network of detectors is advantageous. Although it is not completely certain yet, there is a possibility to calculate the properties of the primordial gravitational waves from measurements of the patterns in the microwave radiations and use those calculations to learn about the early universe.

stellar Graveyard

This graphic shows the masses of black holes detected through electromagnetic observations (purple), black holes measured by gravitational-wave observations (blue), neutron stars measured with electromagnetic observations (yellow), and neutron stars detected through gravitational waves (orange). (Credit: LIGO-Virgo/ Northwestern U. / F. Elavsky & A. Geller )

What Causes Gravitational Waves

In general, any mass moving under the influence of gravity (the curvature of the space-time continuum) produces gravitational waves of certain intensity; however, as discussed earlier, detecting the gravitational waves of lower intensities is almost impossible with the available technology. LIGO detects gravitational waves generated by some of the Universe’s most energetic events, including colliding black holes, merging neutron stars, exploded stars, and perhaps even the birth of the Universe itself. Detecting and analyzing gravitational waves allows us to study the Universe in ways never before possible, giving astronomers and other scientists their first glimpses of wonders that were previously obscure. Since the universe is plentiful of incredibly massive objects, the gravitational waves researchers mainly classify gravitational waves based on their source into four categories:

  • Continuous Gravitational Waves: Continuous gravitational waves are thought to be produced by a single spinning massive object like a neutron star. As this star spins, any bumps or imperfections in its spherical form will produce gravitational waves. If the star’s spin rate remains constant, so do the gravitational waves it emits, i.e, the gravitational wave has the same frequency and amplitude all the time. This is why they’re known as “Continuous Gravitational Waves.” Researchers have developed several simulations of what a continuous gravitational wave would sound like if the signal observed by LIGO is converted to sound.
  • Compact Binary Inspiral Gravitational Waves: Compact binary inspiral gravitational waves are produced by orbiting pairs of massive and dense (“compact”) objects like white dwarf stars, black holes, and neutron stars.  There are three subclasses of “compact binary” systems in this category of gravitational-wave generators, Binary Neutron Star (BNS), Binary Black Hole (BBH), and Neutron Star-Black Hole Binary (NSBH). As the orbiting objects move closer together, they orbit faster and faster, which means eventually, the objects will begin orbiting each other fast enough that the gravitational waves they emit fall within the sensitive range of LIGO.
    CIBS
  • Stochastic Gravitational Waves: According to astronomers, the Universe has so few major sources of continuous or binary inspiral gravitational waves that LIGO isn’t concerned with more than one moving through Earth at the same time (producing confusing signals in the detectors); however, they do believe that many small gravitational waves are constantly traveling through the Universe and that they are mixed at random. These small waves from all directions make up a “Stochastic Signal,” so-called because “stochastic” refers to a random pattern that can be statistically analyzed but not precisely predicted.
  • Burst Gravitational Waves: This category of gravitational waves belongs to the realm of unexpected physics, both because LIGO has yet to detect them and because there are so many unknowns that scientists have no idea what to expect! For example, we don’t always have enough information about a system’s physics to predict how gravitational waves from that source will appear. While this makes searching for burst gravitational waves difficult, detecting them has the greatest potential to reveal revolutionary information about the Universe.

Interesting Facts

  • The source of the first direct gravitational wave detected by LIGO on September 14, 2015, was a collision of two black holes that happened around 1.3 billion years ago when multicellular life was just beginning to form on the earth. This discovery is considered one of humanity’s greatest scientific achievements.
  • The distortion in the space-time continuum caused by gravitational waves is of the order {10}{-19} m, i.e., 10,000 times smaller than the radius of a proton. To detect these distortions, a light beam is bounced back and forth 400 times within the LIGO observatory’s 4-km arms, traveling up to 1600 km and allowing for a significant measurement.
  •  The mirrors that reflect the light weigh 40 kg (88 pounds) and hang by silica fibers in a complex suspension system.
  • LIGO detects such a small change in space-time that it can detect a lot of other vibrations too. For this reason, the speed limit at LIGO is 16 km (10 miles) per hour to minimize vibrations from nearby cars.
  • The recent discoveries at LIGO have shown another possible affirmation to one of Einstien’s predictions. When waves of different wavelengths pass through a physical medium, the rays of light diverge (this is how a prism creates a rainbow); however, Einstein’s theory of general relativity says gravitational waves ought to be immune to this sort of dispersion. The recent discoveries of black hole mergers have shown the potential to best support this theory so far.
  • By converting gravitational waves into sound waves, we can literally listen to the universe. The sound of two colliding black holes is something like a cosmic “chirp,” a kind of whooping sound that progresses quickly from low pitch to high.

 

Add Comment