Gravitational Waves

A History of Discovery

Hartmut Grote

• Publisher: CRC Press
• Year: 2019
• ISBN:
  9780429639876
• Edition: 1
• Topic: Physical Sciences
• Subtopic: Astronomy & Astrophysics

The historic detection of gravitational waves on September 14, 2015, prompted by the highly energetic fusion of two black holes, has made events in the universe "audible" for the first time. This expansion of the scientific sensorium has opened a new chapter in astronomy and already led to, among others, fascinating new insights about the abundance of black holes, the collision of neutron stars, and the origin of heavy chemical elements.

The history of this event, which is epochal for physics, is reconstructed in this book, along with a walk-through of the main principles of how the detectors operate and a discussion of how the search for gravitational waves is conducted. The book concludes with an update of the latest detections and developments to date and a brief look into the future of this exciting research field.

This book is accessible to non-specialist readers from a general audience and is also an excellent introduction to the topic for undergraduates in physics.

Features:

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• Provides an introduction to the historic discovery of gravitational waves

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• Explains the inner workings of the detectors and the search to find the waves hidden in the data

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• Authored by a renowned specialist involved in the ground-breaking discovery

Hartmut Grote is a Professor of physics at Cardiff University, UK. His main expertise is in experimental gravitational-wave physics, and he has worked on building and improving gravitational wave detectors for over 20 years. From 2009 to 2017, he was the scientific leader of the British-German gravitational-wave detector: GEO600.

Chapter 1

They exist, they don’t exist, they exist

1.1 Gravity: From Newton to Einstein

Gravity is considered the weakest of the physical forces, yet falling from a ladder onto the driveway would not be good for my health. When impacting the ground, it would be electromagnetic forces, the repelling of positive and negative charges, that would prevent my further falling through the asphalt: My body cannot easily penetrate it. The energy that would deform my body, however, is due to the gravitational force.

In addition to gravitational and electromagnetic forces, there are strong and weak nuclear forces that determine the stability and decay of atomic nuclei; however, they only act within a tiny distance from the nucleus. Although electromagnetic forces have a longer range than the strong and weak nuclear forces, they cancel out very quickly further away from the nucleus due to the equal amounts of positive and negative charges. At longer distances, gravitational forces dominate, creating an attraction between every kind of matter and energy known to us. In space, gravitation is the primary type of force that determines planetary motion, the life cycle of stars, and the evolution of the entire universe.

In the late seventeenth century, Isaac Newton formulated his laws of motion. With his meticulous quantitative analysis of how objects, or bodies of matter, move under the influence of force, he enabled unprecedented precision in the calculation of planetary orbits. In addition to these laws of motion, Newton also formulated a law of gravity that describes an attractive force between objects. According to this law, two bodies of matter attract each other with a force proportional to the mass of the two objects and inversely proportional to the square of the distance between them. Newton’s gravitational force works immediately and without delay, that is, instantaneously. Under this theory, even when I type on a keyboard or lift a glass, this is swiftly communicated to the whole universe, because when objects change their position in space, the direction and strength of their outgoing gravitational force changes.

If we sum up Newton’s law of gravitation and his laws of motion, we have the following chain of cause and effect: objects, such as our sun and the planets, exert instantaneously attractive forces which determine the way in which these objects move in space.

While this is the way Newton’s laws describe how gravity works, Newton himself was doubtful to a degree about this aspect of his theory. In a letter to Richard Bentley from 25, February 1693 Newton writes: It is inconceivable that inanimate Matter should, without the Mediation of something else, which is not material, operate upon, and affect other matter without mutual Contact. …That Gravity should be innate, inherent and essential to Matter, so that one body may act upon another at a distance [through] a Vacuum, without the Mediation of any thing else, by and through which their Action and Force may be conveyed from one to another, is to me so great an Absurdity that I believe no Man who has in philosophical Matters a competent Faculty of thinking can ever fall into it. Gravity must be caused by an Agent acting constantly according to certain laws; but whether this Agent [is] material or immaterial, I have left to the Consideration of my readers.

Regardless of this uncanny aspect of Newton’s theory, during the eighteenth century, with his precise predictions of planetary constellations that were repeatedly confirmed by observations, Newton’s theory became a triumph and it epitomized the power of the human mind.

In the early nineteenth century, however, a deviation of Uranus (the next planet beyond Saturn) from its calculated orbit had been observed. If Newton’s theory was correct, there was only one good explanation for this deviation—there must be another, previously unknown, planet influencing the orbit of Uranus. Independently of one another, the French mathematician and astronomer Urbain Jean Joseph Le Verrier and the Englishman John Couch Adams calculated the position of the unknown planet. Le Verrier asked Johann Gottfried Galle, an astronomer at the Berlin Observatory, to search in the section of the sky where his calculations had indicated its location. A short time later, Galle and his co-workers discovered the planet. Galle wrote to Le Verrier, Monsieur, the planet whose position you have calculated actually exists! A new planet had been found, for which Le Verrier later suggested the name Neptune.

The fact that a planet was discovered by a mathematical prediction was, once again, a grandiose confirmation of Newton’s theory of gravitation. However, there was another problem—the innermost planet in the solar system, Mercury, also showed a deviation from its Newtonian calculated orbit. After each orbit around the sun, the perihelion, the point in the Mercury track when it is closest to the sun, will shift, moving a little further in space. In one hundred years this shift adds up to 574 arc seconds. (An arc second is one part in 3600 of a degree.) In Newtonian theory, most of this shift could be explained by the influence of the other planets. However, there remained almost 8 percent (45 arc seconds) that were unexplained. After his triumphant prediction of the existence of Neptune, Le Verrier was now convinced that this anomaly of the Mercury track was caused by yet another unknown planet called Vulcan. It was a big mystery as to why this planet that must have its orbit so close to the sun had not already been observed.

More than fifty years later, only Albert Einstein was able to solve this riddle. In 1905, Einstein proposed a new theory of space and time, which follows from two assumptions: (1) Light always travels at the same speed, regardless of the speed of the source of the light or the speed of the observer. (2) The laws of physics in uniformly moving reference systems (systems that are not accelerated, also called inertial systems) are always the same; this is the principle of relativity formulated by Galileo. From these assumptions, the Special Theory of Relativity emerged, resulting in a close intermeshing of space and time, expressed by the concept of space-time. One consequence of the Special Theory of Relativity was the concept that nothing, including information, could travel faster than the speed of light. Among other considerations, this radically new idea led Einstein to the conclusion that not only space and time, but also Newton’s law of gravitation required a revision because according to Newton, the gravitational force spread instantaneously and with infinite speed. Up until now, instantaneous effect of gravity at any distance had not been called into question by most physicists. However, in light of the Special Theory of Relativity, it was no longer conceivable, and Einstein set to work to develop a new, more compatible theory of gravitation that would eventually become the General Theory of Relativity. Special Relativity is called ‘special’ because it only deals with inertial systems and in particular does not include a description of gravity. The new theory of gravitation, on the other hand, was given the name General Relativity because it also describes gravitation.

For Einstein, the central, motivating factor in the development of a new theory of gravitation was the apparent indistinguishability of acceleration and gravitational attraction. An astronaut in a windowless rocket has no way of knowing if she is sitting in the stationary rocket on the ground, waiting for takeoff, or if she is in an accelerating rocket in interstellar space. In both cases, her body would be pressed into the seat with the same force. Admittedly, this is a somewhat bizarre example, because an astronaut would probably always know where she is, but it is typical of the thought experiments that Einstein often employed. The indistinguishability of acceleration and gravitational attraction is also called the (strong) principle of equivalence, and Einstein called this idea the happiest thought of my life.

After several years of laborious work, Einstein’s thought experiments eventually led to the General Theory of Relativity, published on November 25, 1915. Figure 1.1 shows the beginning of this article. The hallmark of the new theory is that space itself must be considered deformable, whereas previously it had been considered immutable and flat, at least by Newton. More precisely, not only is space deformable, but space-time is deformable. (The unity of space and time previously introduced by the Special Theory of Relativity.) The potential deformation of time sounds very strange. This refers to a dilation of time, which means, for example, that clocks in a curved space do slow down. As a result, we simply often speak of the curvature of space and ignore the role of time, with the awareness that time is always dilated in curved space. What causes the curvature of space? Mass in the form of either matter or energy. Both the sun and an apple bend the surrounding space. Since the mass of the sun is larger than that of an apple, the curvature caused by the sun is also larger.

Figure 1.1 The beginning of Einstein’s famous article about the field equations of General Relativity. The paper was published in the proceedings of the Royal Prussian Academy of Sciences on November 25, 1915.

The curvature of space, caused by matter, results in all objects in this space experiencing a force in the direction of the curvature. In this theory, space serves as a kind of mediator and carrier of information between objects and thus instantaneous action at a distance is no more required. This is in contrast to Newton’s theory where space does not play such a role.

To summarize, in the General Theory of Relativity we have the following chain of cause and effect: matter or energy curve space and the curved space determines the way objects move. In the catchy words of the physicist John Archibald Wheeler: Matter tells space-time how to curve and space-time tells matter how to move. Gravitation is contained in the geometry of space itself. This structure is also reflected in the Einstein field equations, which state that mass (or energy) and space curvature are directly related.

In the early stages of the development of his new theory, Einstein, together with his friend Michele Besso, calculated the effect of the sun-curved space on the perihelion shift of Mercury’s orbit. In another November 25, 1915, publication, he writes: The calculation provides for the planet Mercury a progression of 43” (arc seconds) in a hundred years, while astronomers specified 45 (±5)” as an unexplained remnant between observations and Newtonian theory. This means full agreement. Einstein’s new theory yields the value that was actually observed by astronomers, for which there had previously been no explanation! A short time later, Einstein notes in a letter to Arno Sommerfeld on December 9, 1915: The result of the perihelion shift of Mercury fills me with great satisfaction. Great to see how the pedantic accuracy of astronomy helps us, which I used to make fun of in the past! By solving this puzzle of astronomy that had persisted for more than fifty years, Einstein continues to make his mark and his peers are forced to seriously consider his new theory.

Bending of starlight confirms the new theory

The smallest energy unit of a beam of light, called a photon, has no mass at rest (it cannot exist at rest), but light can be assigned a mass through the equivalence of mass and energy, a consequence of the Special Theory of Relativity. If a light beam passes another object, like a star, the beam is slightly deflected. The Special Theory of Relativity allowed for this prediction, due to the attraction between objects demanded by Newton’s law of gravitation. In the November 25, 1915, publication, Einstein corrected this earlier prediction of light deflection; he found that the deflection of light is twice as large using the General Theory of Relativity.

Some time after this prediction, it became clear that the bending of starlight could possibly be observed in the vicinity of our sun. Comparing the apparent positions of stars that are visible close to the sun with their apparent positions when viewed at positions in the sky far away from the sun would reveal the bending of light if those positions were found to be different. A total solar eclipse is required for this method, in order to be able to see any stars visible in the vicinity of the sun. Figure 1.2 shows a cartoon of the bending of starlight at the sun.

Figure 1.2 The bending of light at gravitating objects like the sun leads to a shift in the perceived position of a star. (Illustration: Josh Field.)

The total solar eclipse of May 29, 1919, seemed particularly suitable for this measurement, since the sun would be in front of a group of bright stars, called the Hyades. In two famous expeditions to observe this eclipse, the Briton Sir Arthur Stanley Eddington and his colleagues measured the deflection of starlight by the sun. To increase the chance of success, one team, led by Eddington, ventured to the small island of Principe, off the coast of west Africa, whereas the other expedition, led by Andrew Crommelin, was sent to Sobral in northern Brazil. Figure 1.3 shows the telescopes of this expedition, set up in Sobral.

Figure 1.3 The telescopes that observed the 1919 total solar eclipse in Sobral, Brazil. This expedition used two telescopes, one equipped with a 10-inch lens (to the left) and one with a 4-inch lens (to the right). The image of the sun is reflected by moveable mirrors into the telescopes that lie horizontally within the hut. (Image courtesy of SCMG Enterprises Ltd.)

On the day of the eclipse, the weather was mostly cloudy in Principe, and only just when the t...

Table of contents

• Cover
• Half Title
• Title Page
• Copyright Page
• Dedication
• Contents
• Preface
• Acknowledgments
• Chapter 1: They exist, they don’t exist, they exist
• Chapter 2: They exist, they don’t exist
• Chapter 3: Michelson’s legacy: the interferometer
• Chapter 4: Interferometers around the world
• Chapter 5: Data analysis and Big Dog
• Chapter 6: They exist!
• Chapter 7: Future developments
• Literature
• Bibliography
• Index