And Yet It Moves: Gravitational Waves

Author and artwork: Patrick Rhodes


“The moment he was set at liberty, he looked up to the sky and down to the ground, and, stamping with his foot, in a contemplative mood, said, Eppur si muove [And yet it moves], meaning the earth.” [1] Giuseppe Baretti, on Galileo Galilei

Galileo Galilei knew the Earth revolved around the Sun and that it wasn’t, as the Catholic Church would have him believe, some unmoving object around which everything else revolved. Despite religious pressure to acquiesce, he refused. Nearly 70 years prior to this “Galileo affair” [2] as it has come to be known, Copernicus had published the first mathematical, geometric system to place the sun at the center of the solar system in his widely circulated book entitled On the Revolutions of the Heavenly Spheres (1543). Galileo, using a new invention called a telescope [3], was able to confirm these mathematical computations through observation, albeit indirectly. Although he was later confined to his house by order of the church for challenging the Bible’s teaching in Chronicles 16:30, which states “the world is firmly established; it cannot be moved [4]”, he remained resolute, stating “and yet it moves”.

In effect, Copernicus and Galileo demonstrated a common approach to the accumulation of scientific knowledge, that is, through mathematical prediction and observation – and the obstacles that must be overcome to bring this knowledge to light. Likewise, gravitational waves were also predicted by mathematics, but in the early 20th century, nobody knew how to measure them. On Feb. 11, 2016, after a long struggle and costing over half a billion dollars, our perception of reality was fundamentally altered when gravitational waves were announced to have finally been directly observed

Prediction, Mathematics, Technology
Nearly two thousand years before Galileo Galilei (1564 − 1642 CE), a Greek astronomer of exceptional intelligence named Aristarchus (ca 310 − ca 210 BCE) proposed the first known model of a heliocentric universe – one in which the Earth traveled around the Sun. It was a radical idea and, like Galileo, he too found opposition to his ideas as they conflicted with the accepted geocentric (Earth-centered) theory which had been supported by such giants as Aristotle (384-322 BCE) and later by Ptolemy (ca 100 − ca 170 CE). As a result, Aristarchus was never able to overcome the prevailing thought of his day and the world remained burdened with an erroneous, geocentric view from which we wouldn’t recover for two millennia. 

Aristotle was among the first to “canonize” modern rhetoric in his treatise on the subject, the aptly named Rhetoric [5]

Fortuitously and beginning in the 16th century, scientists began to exert a much stronger influence upon society. The notion of quantifying natural phenomena such that it could be reduced to a set of numbers and equations, referred to as “mathematization”, was adopted, resulting in the Scientific Revolution [6]. While mathematization wasn’t a new concept per se, its scope and application increased dramatically during this period. At last, as a result of this revolution, Aristarchus’ idea of a heliocentric universe was finally validated through the hard work of the aforementioned Copernicus and Galileo (among others which are too many to mention here). People finally adopted the notion that the Earth does indeed “move”.

Figure 1 

The scientific revolution marched on, producing ever more efficient theories and elegant mathematics from which to quantify these natural phenomena. Calculus, the branch of mathematics which greatly streamlined and expanded the mathematical scope addressing rates of change (differential calculus) and area/volume (integral calculus) was developed during this time. Likewise, the branch of mathematics dealing with the collection, analysis and interpretation of numerical data – known today as statistics – was largely codified and expanded from the late 17th century through the 20th century. These mathematical advances, combined with Isaac Newton’s formalization of classical mechanics, allowed technology to be developed at a frenetic pace.

Einstein Predicts Gravitational Waves
Eventually, this explosion of scientific knowledge led to a “Golden Age” of physics during the early part of the 20th century, during which a young German patent clerk named Albert Einstein (1879 − 1955 CE) came to think much differently about the nature of the universe. Like Copernicus and Galileo before him, his ideas fundamentally challenged long-held beliefs. However, in this case, it wasn’t some religious ideal blocking his path, but rather science itself in the form of Newtonian physics. 

Newton’s ideas of a geometrically “flat” universe were mathematically sound, well-tested and had been widely accepted as scientific canon for over two hundred years. And yet, here was a man presenting a theory which radically challenged that understanding of reality. When Einstein proposed a more dynamic, “curved” universe in his theory of General Relativity in 1916, many scientists were rightly skeptical. After all, like all scientific theories, Einstein would have to show proof that his ideas – and the math behind them – were predictable and observable. This is, after all, how science works: new theories which propose to supplant current theories must be rigorously tested before they are adopted.

Einstein’s theory of Special Relativity was the simpler precursor to the much more mathematically intense General Theory of Relativity – one large difference between the two being that Special Relativity dealt mostly with constant velocities whilst General Relativity took acceleration into consideration, thereby enormously increasing its complexity

Einstein, working with other scientists and field personnel, spent the next several years testing his theory, which found resistance not only because of the exotic experimentation required, but because of political issues stemming from World War I. For some time, his research was very difficult to come by as he was German, hence, his work wasn’t allowed in the hands of the allies such as the UK and the US. There was one prediction made from his theory – gravitational waves – which wasn’t able to be tested during this time. Mercifully, it wasn’t because of any political strife or nationalism, but rather because the advanced technology required to observe these waves simply did not exist. In fact, it would take nearly one hundred years after the publication of General Relativity to verify this claim. In order to understand what gravitational waves are and thus, the importance of their observation, a little theoretical ground must be traversed.

One of the properties of mass, according to the theory of General Relativity, is that it will “warp” the fabric of space-time around itself – the very reality in which we live. That is, an object with mass will – in relation to how massive it is – “draw in” space-time around itself, pulling nearby objects towards itself (and vice versa). In effect, this is a new way of describing gravity [7]. Further, the more massive an object is, the more it will pull in space-time around itself, including light, which is why, during an eclipse, stars that are viewed just around the edge of the sun will appear to be in different positions than they actually are. Continuing along this line of thinking, if objects are able to collapse space-time around themselves, as those objects move, they should generate residual waves throughout space-time, not unlike the ripples which are produced from swirling your finger around in water. These waves are called “gravitational waves”.

Can you generate gravitational waves by flailing your arms about? The answer is: yes [8]. However, the waves you generate are infinitesimal and, in effect, have no measurable effect on space-time around you, no matter how hard you flap about, but don’t let that stop you from trying.

Figure 2 

As mentioned above, the problem was that nobody knew how to measure such a thing at the time and for a great many years thereafter.

Expanding Vision
Enter the Laser Interferometer Gravitational-Wave Observatory, or LIGO. Without getting into specifics, it was built with the intention of detecting the aforementioned gravitational waves, but only those waves that were of sufficient strength and frequency [9]. The Earth’s movement, for example, cannot generate gravitational waves strong enough for scientists to measure directly with LIGO. Indeed, a much stronger wave was required to come crashing towards us to have any chance of our detecting it. Luckily for us, and Einstein, it just so happens there is an astronomical phenomenon which can be detected by terrestrial interferometers such as employed by LIGO.

Imagine two black holes swirling about each other “in a galaxy far, far away”. These black holes are so massive that light cannot escape their gravitational pull (hence, they are “black” holes). As they circle each other, they are being drawn closer and closer together, until finally they collide in a massive shudder. The impact produces large ripples in the fabric of space time – or gravitational waves – which are large enough to propagate extremely long distances, billions of light years away. In fact, such a collision did occur approximately 1.4 billion years ago and those residual gravitational waves, amid much celebration, were confirmed to have been detected at LIGO and announced on February 11, 2016.

Like Galileo and Copernicus before him, Einstein’s theories relied upon mathematics to make predictions which, as technology developed, were eventually observed. And, also like his predecessors, the journey from theory to observation was cluttered with obstacles: some political, some technological and some scientific.

The gravitational waves that were detected by LIGO were only a fraction of their original strength 14 billion years ago.

Effectively, we are now able to “see” black holes billions of light years away by detecting their gravitational waves similar to our ability to “see” galaxies billions of light years away by detecting the electromagnetic waves they emit. In other words, we have expanded our ability to “see” the universe by building a set of “eyes” that are capable of detecting gravitational waves.

Figure 3

LIGO was the first step in expanding our vision beyond the electromagnetic spectrum, allowing us to peek into the gravitational wave spectrum for the first time. The journey to arrive here was long and arduous, an epic saga which finds its roots several millennia before. If history tells us anything, it is that, being human, we will struggle to produce new scientific knowledge, but
eventually it will be produced. We have an insatiable curiosity – an itch which must be scratched – which will continue to compel us further.

Will we eventually “see” gravitational waves outside of our current, narrow range and perhaps allow us to delve further into the nature of the universe? Will we be able to detect the gravitational waves generated by the early universe? If I were a betting man, I’d say yes. Perhaps the more important question is, will we come to better understand who we are and our place in the universe? Or will that knowledge, as Plato has asserted [10], be forever transcendent and unavailable to humans?

1. Baretti, Giuseppe (1757). The Italian Library. Containing An Account of the Lives and Works of the Most Valuable Authors of Italy. With a Preface, Exhibiting The Changes of the Tuscan Language, from the barbarous Ages to the present Time. London: Printed for A. Millar, in the Strand. p. 52. “Text preceded by: “This is the celebrated Galileo, who was in the inquistion for six years, and put to the torture, for saying, that the earth moved.””

2. Galileo affair

3. first telescope

4. Chronicles 16:30

5. BH book on rhetoric

6. Scientific Revolution

7. Brian Greene reference

8. ASU article 


10. plato gorgias