The Discovery of Gravitational Waves

The February 2016 announcement that gravitational waves were detected caused great excitement among scientists, but most people wonder, “Why is it a big deal?” The answer has to do with the extreme difficulty of detecting tiny waves from very far away. The quest to find such waves lasted a century, and combined profound physics with instrumentation of unprecedented delicacy.

  1. General Relativity vs. Classical Mechanics

Einstein’s General Theory of Relativity (GR) was published 100 years ago. It was a completely revolutionary way of understanding both the force of gravity and the structure of the universe. GR theory made certain predictions of effects that could be observed with accurate enough instruments. Within a few years, his predictions about light bending as it passed a heavy object (like a star) were observed, and that gave credibility to the theory. However, the prediction by GR that there could be gravitational waves has proven to be far more elusive, only being detected now, a century after the theory was published.

Nowadays, physicists accept General Relativity as “true,” and the layman nods in agreement without thinking it exceptional. But it wasn’t like that long ago. To understand why GR was such a revolutionary theory, it’s necessary to understand the theory that had prevailed for several previous centuries. Isaac Newton developed what became known as Classical Mechanics (CM) near the end of the 17th century, and in the centuries that followed, it became such a “sure thing” that not the slightest whiff of doubt was entertained. By the end of the 19th century, Classical Mechanics was considered an absolute certainty. Everything in the entire universe, from stars to planets to baseballs to atoms, was believed to be governed by that very comprehensive theory.

In particular, CM held that space and time were basic components of reality that simply existed; they were not variable in any way, but were the foundation -- the coordinate system – upon which the universe was built. No one could imagine questioning the coordinate system.

Near the end of the 19th century, little cracks in that edifice were noticed, and soon it was clear that some corrections would be needed. Max Planck came up with the quantum hypothesis in 1900, and in 1905 Einstein published the Special Theory of Relativity, wherein space and time were related to each other, and indeed convertible from one to the other. Meanwhile, the force of gravity was understood as the force that pulls two masses toward each other, but that force was distinct from space and time, existing within the space-time coordinates that existed “out there.”

Einstein noticed that it’s impossible to tell the difference between an inertial acceleration and a gravitational acceleration; they are equivalent. That got him thinking anew about the very nature of gravity. In GR, gravity is the bending of space (and time) caused by the mass of an object. Of course, that bending is a terribly small effect, only detectable when an object is very massive (like a planet or star). Detecting terribly small effects is what delights experimental scientists the most, and immediately after publication of GR, conditions were sought where such effects could be detected. A solar eclipse in 1919 provided the opportunity, and sure enough, the prediction Einstein made (about light bending) was observed.

  1. Philosophical Implications

It took a while to sink in, but the philosophical implications of GR are enormous. If space and time can be distorted and converted into one another, then what is the meaning of any “center” in space? What about time? We always thought it just marched along in one direction, totally uniformly, with any variation inconceivable. Time was believed to be absolute. What could be the meaning of time bending or stretching or curving? At first these concepts were so mind boggling that a lot of people just couldn’t accept GR at all.*

In the 1920s, the equations of GR were solved for the case of a “singularity” meaning a simultaneous beginning of time and space, subsequently leading to matter, galaxies, stars, etc. Today we know that as “the Big Bang” but in those days, not even Einstein believed it possible. The notion that space and time (and hence the universe) had a beginning was very tough to swallow. Nearly all philosophers from Aristotle onward had just assumed that space and time were always there, forever.

People had long been asking “What was God doing before he created the universe?” The surprising answer from GR is that creation brought time into existence, and the word “before” has no meaning in the absence of time. That long-standing question utterly vanished. Again, the reverberations through the field of philosophy were enormous.

  1. Stellar Evolution

The newly-detected gravitational waves came from the collision of two black holes.

A black hole is a region in space that is completely cut off from everything else. The concept is a direct result of the General theory of Relativity (GR). Under Classical Mechanics, it cannot possibly happen. But we’re confident that black holes are out there. Moreover, the center of a galaxy is usually a very massive black hole.

When a star forms from dust and gas somewhere out in space, it accumulates a certain total mass that is pulled together by gravity into one place, and only then does the star start “burning,” turning hydrogen into helium. This goes on for a long time (typically billions of years) until all the hydrogen fuel is burned up.  The sun is a very typical star, of average size and mass, with a life cycle of perhaps 10 billion years. How long it takes a star to burn up depends upon how much mass accumulated in the first place. Very massive stars burn up much faster than average – some last only 100 million years. Objects of very low mass may never compress tightly enough to start burning in the first place. (Some theories say that Jupiter is such an object.)

It is not exceptional for a star to have a mass 10 or 20 times the mass of the sun. Such stars will burn out in a shorter time than the sun’s duration.

Under normal “burning” conditions, the energy released as hydrogen turns into helium creates a pressure that pushes outward on the star, at the same time as gravity is constantly trying to pull everything inward. With this balance, a star like our sun has a diameter of about 1.4 x 106 kilometers (864,000 miles). It will stay that way for several billion years.

However, when the fuel is all burned up and the hydrogen has been converted to helium, then the outward pressure diminishes and gravity takes over. The star shrinks to a very small size. There are several possible outcomes. These outcomes each depend on how much mass was there in the first place, when star formation started. The most spectacular finale is a supernova, an explosion that sends fragments hurtling far into space. The most recent supernova took place in 1987 in a neighboring galaxy. Another final outcome is for the remnant of the star to become a brown dwarf, basically a “cinder” left over from past burning sitting out in space. For a star with greater mass, gravity can pull everything so tightly that even the individual protons and electrons are squeezed together, producing a star made entirely of neutrons.

  1. Black Holes

The gravitational compression is extreme and the density enormous. A neutron star with mass comparable to the sun might be only 10 kilometers across. That will cause quite a lot of curvature of space-time in its vicinity. If the mass is higher still, gravity can compress even more, and the distortion of space-time becomes so great that not even photons of light can escape from the object. With no photons visible, the disappearing object is termed a black hole. If another nearby mass comes within a radius known as the event horizon, it is swept into the black hole and becomes part of it, making the total mass larger. We think that is the pathway by which a massive black hole forms at the center of a galaxy.

It is possible for two independent black holes to get near each other, in which case they’ll start to orbit around a central point. Each will strongly distort the space-time in its vicinity. As they whirl around and pull closer together, those overlapping regions of space time will produce wrinkles, or waves of gravitational force. When the two black holes finally combine and collapse, the surrounding space-time will be very wavy indeed.

Recently a pair of black holes, having 29 solar masses and 36 solar masses, collided in this way and produced one larger black hole having 62 solar masses. That means the energy equivalent of 3 suns was released and had to go somewhere. It was released in the form of gravitational waves propagating away across the universe. Those waves originated 1.3 billion years ago in a distant galaxy, and have been spreading out across the universe ever since.

  1. Detecting Waves

Can such waves be detected far away (on earth)? When Einstein first predicted the possibility of gravitational waves, he never actually expected them to be detectable, because the distortion of space is only about 1 part in 1021.  If you prefer words, that’s a thousandth of a billionth of a billionth. Our best analytic instruments can detect a few parts per billion of some chemical, so you can imagine the huge difference.

For another half century, people wondered how to do it. Then in the 1970s, an idea was proposed by Rainer Weiss of MIT that used lasers in a unique way to make so delicate an observation. It took many decades (an entire career length!) to come to fruition. The device is named the Laser Interferometer Gravitational Wave Observatory (LIGO). Construction began in the 1990s, and with several upgrades over the years, LIGO has morphed into advanced LIGO. The total cost is over $600 million.

  1. Interference

To understand how it works, some words about interference are necessary. Throw a stone into a placid lake and you’ll see ripples spread out circularly. Throw a second stone in and the waves from each will interfere with each other, producing a more complex pattern. A third stone makes the pattern harder to recognize. For a real, non-placid lake, there are so many waves going every which way that no pattern is visible.

Similarly, the electromagnetic spectrum contains countless millions of simultaneous waves all at once. However, we have the ability to tune a detector very finely so as to pick up exactly one wave out of many, and thus we can watch individual TV stations, hold phone conversations with people far away, etc. That is so commonplace that nobody even notices the interference constantly taking place.

Surfers are always looking for the “best” wave, meaning an interference pattern between several water waves that produces one big maximum. Even with a boogie board at the beach, you hope to catch a maximum, but hardly anybody thinks about wave interference.

Rather than produce maximums, if two waves are precisely out of phase they will exactly cancel each other, producing a zero sum. Then, any deviation whatsoever from that perfect state of zero sum constitutes a signal, which provides information. That is the way a laser interferometer operates.

  1. Laser Interferometers

A beam of laser light is projected into the center, where a semi-transparent mirror acts as a beam splitter, sending half the energy in direction X and half in direction Y. Each beam travels down its arm and hits a mirror, is reflected right back, returns to the central beam-splitter and recombines. The combined beam that emerges from the instrument is the interference pattern of those two waves.

If the distances in each arm are adjusted with perfect precision, one laser beam will return just a tiny bit later than the other, and will be exactly out of phase with the first. The two will then exactly cancel, adding up to zero (producing zero output voltage). That is the “at rest” condition. The required precision is stunning: for a typical light wave, 1/2 a wavelength is under a micron to begin with, so exact cancellation requires the distances to be controlled to the size of a few atoms. Before the invention of the laser, there was no hope for such precision.

Using the extremely pure (single-frequency) laser light, the arms of the interferometer can be extremely long – far bigger than a laboratory instrument. In the LIGO, each arm is 4 kilometers long, and the beam bounces back and forth 280 times, greatly lengthening the distance light travels, and enhancing the sensitivity to the slightest motion of a mirror. This all has to be done in vacuum, and it’s not easy to maintain a vacuum chamber 4 km long.

  1. Getting it Right

The arrival of a gravitational wave causes space-time to distort a little, first one way and then the other, as the wave passes by. That causes a tiny wiggle of a mirror, changing the phase slightly and generating a signal. The sensitivity has indeed reached one part in 1021. A mirror motion of 10-18 meters is detectable.

The slightest motion of a mirror changes the distance and generates a recognizable signal. However, any vibration at all (a passing truck? A seismic blip?) will cause a mirror to move, creating a false signal. Such events would totally confuse the observations. Getting rid of “false positives” is 99% of the ball game in this business.

Because of that problem, two identical systems were built: one in Louisiana and one in Washington State, 3000 Km (over 1800 miles) apart. If a gravitational wave should come along (traveling at the speed of light), the difference in arrival times from Louisiana to Washington should be about 10 milliseconds. Therefore, any signals at either site that don’t have that relationship can be discarded as noise. Each interferometer has both an X-direction arm and a Y-direction arm, so the detected signals can be used to discern where the wave came from.

The measurements reported in mid-February were made in September 2015, only a few days after the advanced LIGO went into service. Contrary to many news reports, the event didn’t make a “sound” in the ordinary sense; sound was merely a feature of the data presentation.

Scientists are optimistic that this new measurement capability will become a valuable alternate way of observing astrophysical events, supplementing the knowledge gained by optical telescopes, gamma-ray detectors, etc. “What to expect?” is a wide open question.

Summarizing: detecting that gravitational waves really do exist shows that space-time deforms and bends, which confirms Einstein’s theory of General Relativity.

* There was one side benefit of that reluctance to accept the new physics: Some ridiculed Einstein’s work as “Jewish physics.” When nuclear fission was discovered in 1938, the possibility of building an atom bomb occurred to Americans, and Roosevelt funded the Manhattan Project. Over in Nazi Germany, the equivalent proposal was not pursued with the same intensity, because the Nazis were contemptuous of Einstein’s theory.