Monday, February 15, 2016

Gravitational Waves


On February 11, 2016, researchers at the Advanced Laser Interferometer Gravitational-Wave Observatory (LIGO) announced that they detected gravitational waves. Gravitational waves, ripples in the curvature of space-time that travel outward from their source, were predicted by Albert Einstein in 1916, one hundred years ago, as part of his theory of general relativity.

About 1.3 billion light-years away from Earth, two black holes – one of about 36 times the Sun's mass and the other about 29 solar masses – spiraled into one another and merged into a single 62 solar mass black hole. Energy equivalent to approximately three solar masses radiated away from this colossal merger in the form of gravitational waves.

This wave signal generated by the black hole merger has been traveling at the speed of light through space in all directions for 1.3 billion years. It was detected on September 14, 2015 by two LIGO detectors. The signal was exquisitely faint and heart-stoppingly brief, lasting just over 0.2 seconds. It quickly increased in frequency and amplitude over about 8 cycles from 35 to 150 Hz, where the amplitude reached its maximum. And then it was gone.

This almost imperceptible event has enormous consequences for our understanding of space-time. This is the first time that we've seen, or perhaps better, heard, the fabric of space-time rippling around us (and through us). Even more astounding is that this ripple, or moving deformation, proved Einstein right once again. Space-time means more than a static matrix that is deformed by mass and felt as gravity. It is a dynamic system that reverberates and ripples.

Except for our personal experience of gravitational attraction and our sense of time's arrow, we don't experience this complex four-dimensional matrix of space and time all around us and inside us. The direct evidence of gravitational waves was very difficult to extract from nature. Gravity is a subtle and very weak fundamental force, leading some theorists to wonder if it is acting across extra dimensions, like a mother calling to her child from the other end of the house. The current data suggests that space-time has a little physical "wiggle" to it. To visualize this, let me exaggerate greatly: imagine what our universe would look like if gravity were many factors stronger. It would be impossible because the universe would have collapsed in on itself long ago, but if it could exist and gravity was a much more powerful force in it, we might see space-time wobble around us and see our bodies wobble along within it. Light and other radiation would bend all over the place. Distance would change all the time. Time would speed up and slow down. GPS wouldn't work. The positions of stars and starlight would be ever changing. A measuring stick of any kind would be useless. Luckily for us and for the universe, gravity is the feeble force it is, but that fact makes space-time wiggles almost undetectably miniscule. To actually observe a space-time ripple rippling past is astounding. It has already inspired some among us to think up lofty ideas: Can we manipulate this space-time matrix? Can we someday manipulate gravity (which is actually an equivalent undertaking)?

What did the researchers actually see that has us all aflutter? Below is a figure of the data LIGO collected taken from the just-published scientific paper: Abbott et al. - B. P. Abbott et al. (LIGO Scientific Collaboration and Virgo Collaboration). "Observation of Gravitational Waves from a Binary Black Hole Merger". Phys. Rev. Lett. 116: 061102 (image courtesy of Wikipedia). You can read the article online here for free.

The gravitational waves were simultaneously received by LIGO instruments in Hanford, Washington (left) and Livingston, Louisiana (right). These detectors were brought online (in what is called engineering mode) just one year prior, in February 2015. Both signals (right and left top) are compared to a signal theoretically expected from a black hole merger (right and left graphs second down). The bottom images show how the signal frequency increased to a maximum and then stopped (green curve). Data was collected from 16 days surrounding the signal and then statistically analyzed to confirm is it was a real event.

This discovery brings home how serendipitous scientific discovery can be. The "Advanced" name of these detectors indicates that this isn't the first time around. Scientists have been trying to detect such waves for several years. The search for them has been frustrating and enormously expensive. LIGO originally operated between 2002 and 2010 and did not detect any gravitational waves. Those results had the physics community second-guessing general relativity, which predicted them. Was it incomplete or perhaps even wrong? LIGO was shut down until 2015 for an upgrade and another try. When the brief black hole merger signal swept past Earth on its journey through the cosmos, another gravitational wave detector called Virgo was offline for upgrades and the GEO600 detector was not sensitive enough to detect that signal. It was very lucky that Advanced LIGO was ready and capable at the right moment to detect what Einstein had predicted a century ago.

This is very likely to be just the beginning. LIGO hasn't yet reached its design sensitivity, which will increase the likelihood of detections by a factor of 27. A new improved Advanced Virgo will also contribute to gravitational wave detection. In addition, a third LIGO detector might be built in India, which will also improve source position reconstruction. These are exciting times!

Gravitational Waves are Predicted By General Relativity

Einstein revolutionized our understanding of gravity by describing it as a geometric property of space and time. According to this theory, space and time are treated as a unified four-dimensional geometric construction that can stretch and bend. Energy and momentum are what do the stretching and bending, and how they do that is described by a set of field equations. This means that radiation and objects with mass can bend space-time. Planets and stars, for example, stretch the space-time around them into a kind of four-dimensional depression or well, in which other objects may spiral inward toward them, or circle around them in stable orbits. This is a model that transcends Newton's laws of universal attraction. Starlight, for example, travels in a straight line through space-time, but that straight line bends as the space-time it is traversing through bends (a phenomenon called gravitational lensing, which has been observed many times). Perhaps an even less intuitive consequence of general relativity is that time itself is treated as a dimension. It is no longer an independent timer ticking along into the future. It slows down where space-time stretches out, relative to an observer. It speeds up from the observer's point of view when he is the one in stretched out space-time, such as inside a gravity well.

Once we think of space-time as a kind of stretchy fabric, it isn't too hard to visualize how a disturbance in that fabric might spread outward in all directions just like how a wave ripples outward from a leaf when it lands on a pond. A four-dimensional gravitational wave has similarities to a mechanical wave in two dimensions. It is even more closely analogous to an electromagnetic wave. Both waves propagate energy at the speed of light, and like electromagnetic waves, it is accurate to describe a gravitational wave as gravitational radiation. Newton's gravitational effects were described as instantaneous. Einstein's gravitational effects are limited to light speed. If the Sun somehow blinked out of existence, it would take about eight minutes for Earth to drop into darkness and fly off from its orbit, freed from the Sun's gravity well.

When a massive object moves around in space-time, the curvature in space-time it creates moves around with it. If that object changes momentum (if it accelerates in other words), those changes in the curvature of space-time can propagate outward at the speed of light as gravitational waves. An observer can in theory detect these distortions in space-time. The observed distances between stars, for example, can increase and decrease rhythmically as the waves pass by, as if the stars are held in an invisible spider web that has been tapped. The frequency of that observed reverberation is the frequency of the gravitational wave.

To visualize the effect of a passing gravitational wave imagine a perfectly flat perfectly spaced ring of objects resting motionless in space. Imagine this ring lies flat on your computer screen. Now a gravitational wave travels from inside your computer through the ring outward toward you. The animation below shows what the effect would look like (greatly exaggerated).

The objects don't move forward along with the propagation. They remain at rest as the space-time around them is distorted in an oscillating manner. This would be analogous to the up and down bobbing motion of a boat as waves propagate past it through the water.

Both the spider web and boat analogies break down, however, when we think about the forces involved in space-time reverberation. Flies caught in a spider web experience a changing unbalanced force as the web vibrates. The boat experiences unbalanced forces as it bobs up and down on the water. Those forces do work on the objects. Stars in space-time, however, move because the space-time ITSELF moves. There is no unbalanced force involved and no work is done on them, an important distinction to think about, especially when you mull over all the ways you are going to harness that wonderful energy. With this distinction noted, gravitational waves are like other waves in that they have an amplitude, frequency, wavelength and velocity.

Sources of Gravitational Waves

Gravitational waves are radiated by changes in momentum. A mass that accelerates can create such radiation – as long as its motion is not perfectly spherically symmetric. An expanding and contracting sphere or a spinning cylindrically symmetric object (a spinning disk or a spinning sphere) WILL NOT generate gravitational radiation. When we think about our previous gravitational wave analogies, this might seem strange. If we place a ball that is mechanized to rhythmically expand/contract on a pond, it will surely generate ripples.

The simplest (and least accurate) answer is that when a point mass doesn't move, gravitational waves are not produced. In gravitational theories, massive objects are treated as point masses and most of the time it seems that nature treats them as point masses as well. When a perfectly spherical object expands and contracts rhythmically, its point mass doesn't move. When a symmetrical disk or sphere rotates, its point mass doesn't move. Even a super-massive rapidly spinning black hole will not generate gravitational waves. If, however, we have a rapidly rotating neutron star that has just a tiny 2-centimetre bump on one side, it is going to generate gravitational waves, and they will probably be substantial thanks to both the ultra-dense degenerate mass involved and a neutron star's enormous spin rate. It generates gravitational waves  simply because its center of mass moves. A perfectly symmetrical supernova explosion would generate no gravitational waves but if the explosion is asymmetric even just a bit, and this is much more realistic, gravitational waves will be produced.

I should note here that even though a rapidly spinning black hole or symmetrical neutron star doesn't generate gravitational waves, it does stir up space-time. This phenomenon is a type of frame-dragging  called the Lense-Thirring effect. Even Earth satellites experience this effect: their rotation plane precesses slightly over time in the same direction as Earth's rotation, a phenomenon that has to be corrected for periodically. Interestingly I think, this effect is also proof that in reality, objects such as Earth do NOT act simply like point masses, another case that proves Newtonian gravity wrong. In general relativity, space-time must be taken into account when we describe an objects motion. The precession of a satellite could never be understood using Newtonian gravity. The angular momenta of objects must also be considered.

To be consistent with general relativity, we should now revisit our rhythmically expanding/contracting mass scenario. The Newtonian explanation is that it is a point mass that doesn't move so no gravitational waves are generated (think of the bastardization of theory I just committed). I order to understand this in general relativity, we need to take into account Birkhoff's theorem. This will introduce some technical terms, which you do not need to understand. I mention this theorem because I think it will offer a way to understand the concept. So, in technical terms, if we apply vacuum field equations (this is  the math that describes general relativity), the spherically symmetric solution (the one we want) must be static and asymptotically flat (this is a fancy way of saying that over very large distances the universe is basically even and flat; it turns into the un-curvy and un-stretchy space-time that we use for special relativity). This, in turn, means that we can describe our object by using something called the Schwarzschild metric. You may have heard of a Schwarzschild black hole before. We can think of such an object as being mathematically naked (if you know the no-hair theorem this is an extreme case I am attempting to describe here). The only thing that distinguishes one Schwarzschild black hole from another one is its mass. In a nutshell, if that black hole were to rhythmically contract and expand the only thing to change would be the location of its surface (the event horizon in this case). Yet, changing the surface has no effect on its mass. So, when we think of any object behaving according to the same Schwarzschild metric, we in effect reduce our general relativity answer to the Newtonian answer which is: the point mass doesn’t move so no gravitational waves are produced.

If we want to get even more technical (and accurate), we can say that if the quadrupole moment of a system's stress-energy tensor changes, then it will generate gravitational waves and in this case the quadrupole moment doesn't change. For keeners, look up these terms and see for yourself and give yourself and well-deserved pat on the back for it!

The best producers of gravitational waves are expected to be very massive rapidly rotating binary pairs, such as closely orbiting (inspiraling) neutron star pairs or black hole pairs. It might at first blush seem strange that two stars or two black holes orbiting each other should generate gravitational waves. After all, they orbit a single common center of mass that doesn't move (or we can assume it doesn't for our argument). The quadrupole moment of their orbit, however, which is described by general relativity, does change and that is why they generate gravitational waves.

Gravitational radiation carries off energy, so the two black holes monitored by LIGO were locked in a spiral of inevitable doom. As they began to orbit each other, they began to emit gravitational waves. While the waves carried off energy, the orbital radius shrank and they moved ever closer together. Even though their orbital spin rate increased, conserving angular momentum, the waves carried off energy that robbed them of angular momentum. As the orbit decayed and the spin rate increased, gravitational radiation became more intense. That is why the wave data shows a rapid increase in gravitational wave amplitude. When the black holes were forced to merge into a single more massive rapidly spinning black hole, the wave signal abruptly stopped. The new black hole did not possess a quadrupole moment.

This last paragraph might lead to some very good questions you might have. Let's think about gravitational radiation carrying off energy. Where does the energy go? I mentioned earlier that because space-time ITSELF does the vibrating that energy can't be harnessed to do work. The best answer I can offer, after some more research, is that the waves don't ever dissipate. They dissipate as their energy spreads outward in the expanding universe, as they do so, that energy never interacts with matter.

Electromagnetic radiation, in contrast loses, energy that is absorbed by matter when it interacts with it as it travels along. Eventually photons are lost altogether as electrons in matter absorb them. Still, the universe is awash in low-energy microwave photons released after the Big Bang. Like gravitational waves that are never completely dissipated, these photons have never interacted with anything on their long journey through expanding space.

The question about gravitational wave energy leads to an interesting thought experiment: What would happen if Earth were very close to a black hole merger and the gravitational waves that washed through it were very large and energetic? I have seen all kinds of arguments online for the potential destructive power of such waves, but can they disrupt matter? Earth will seem to compress and stretch and that would seem to lead to some catastrophic earthquakes etc. But the atoms, themselves in the space-time, stretch and compress. Where is the opportunity for friction?

You might be wondering if gravitational wave energy loss is eventually going to doom Earth to a similar fate as the black holes. After all, the Earth and the Sun orbit one another around a common center of mass just as the two black holes did, 1.3 billion years ago. The same physics is at play here too. Earth's orbit shrinks at a rate of 1.1 x 10-20 meters per second (by about 1/300 of the the diameter of a hydrogen atom) due to gravitational radiation. At this rate, it would take about 1013 times longer than the current age of the universe for Earth to spiral into the Sun. As well, the Sun is constantly losing mass in the form of solar radiation, an effect that increases Earth's orbit as the Sun's gravitational pull decreases. This effect more than compensates for the inward effect of gravitational radiation, an effect too small to worry about in any case, so we are good from a gravitational radiation standpoint.  

Detection of Gravitational Waves

How do you detect and measure a desperately minute ripple in space-time as it briefly whispers past you at the speed of light?

Researchers, being practical by nature, didn't start from nothing. This discovery was preceded by promising indirect evidence for gravitational waves. For example, in 1974 Joseph Taylor Jr. and Russell Hulse detected a pulsar orbiting aneutron star by using radio astronomy. Later careful observation showed that their orbit was decreasing and that rate closely matched the energy theoretically expected to be lost from the system through gravitational radiation. This earned the pair a Nobel Prize in 1993.

The LIGO experiment, a billion dollar ($US) undertaking by the U.S. National Science Foundation that employs over 1000 scientists, was based upon a very good foundation of such indirect evidence. Direct evidence would seal the deal. Scientists needed to observe gravitational waves. They needed proof. The problem is that there are not that many energetic binaries in the cosmos to study and they are all very far away from Earth, making monitoring them challenging. Any gravitational waves coming from them would be exceedingly tiny and hard to detect by the time they reached Earth. Gravitational waves, just like electromagnetic waves, lose amplitude and increase in wavelength as they traverse space-time. Like electromagnetic radiation, gravitational radiation follows the inverse-square law. If the black hole merger took place twice as far away, about 2.6 billion light years, for example, the waves detected at LIGO would be four times weaker. The detector couldn't have picked them up. The waves lose energy but not to space. The space the waves must cover is ever expanding, so what happens is a kind of energy dilution. Even with the best technology, looking for gravitational waves from a distant binary system is like searching for a microscopic needle in a haystack. That is one reason why it is so exciting to see experimental proof of a phenomenon that even Einstein himself thought would never be possible.

Each Advanced LIGO detector senses distortions in space that take place when a gravitational wave passes through it. Laser light bounces back and forth off mirrors set upacross two 4-kilometre-long legs. Reminiscent of the experimental set-up to measure the speed of light, this creates a very precise atomic clock that measure how long it takes the laser light to make the journey back and forth. When a gravitational wave passes across the detector, the distance between the mirrors (the laser light path) increases and decreases (reverberates) very slightly. This changes the time it takes the laser light to cross by an infinitesimal but measurable amount, which means that the sensitivity of the sensors and timers, and their alignment, are some of the greatest challenges ever presented in physics research.

The reverberation doesn't mean that the legs moved. The space-time in which they exist moved. How much did they move? A distance less than 1/1000 the diameter of a proton! At this sensitivity, noise in the data becomes an immense challenge. An airplane flying overhead, wind against the building, tiny otherwise undetectable seismic shifts in the ground, even someone clapping in the control room all create blips in the data. Such noise is carefully eliminated as much as possible, physically as well as statistically. Having two detectors states apart also means that noise affecting one detector is unlikely to affect the other one, making elimination of noise signals easier. Achieving no results during LIGO's first run was probably a very frustrating experience. When researchers decided to upgrade the detectors, I suspect it might have been a last chance. More powerful lasers were installed and the mirrors were replaced, making Advanced LIGO three times more sensitive. They were counting on those waves being out there. It was a matter of making the apparatus sensitive enough to detect them. Alternatively, proving that gravitational waves don't exist would have been just as important, because then researchers would know that general relativity has to be revisited.

In a few years LIGO will be upgraded once again to make it ten times more sensitive than its initial setup. Researchers expect to detect gravitational waves from various sources, including collisions between stars, merging galaxies and supernovae explosions. I can't help but personally wonder if there could be a highly advanced civilization somewhere communicating by using gravitational waves. This very idea is so romantically portrayed in the movie, Interstellar, one of my favourites. In that case, the advanced civilization turned out to be our own future, how delightfully optimistic!

Uses For Gravitational Waves

Telescopes that utilize electromagnetic radiation (visible light, infrared, X-ray, radio, etc.) suffer from the fact that these waves all interact with matter. They are absorbed, blocked and scattered and, most importantly, you are limited to observing objects that emit electromagnetic radiation. Neutrinos flood the universe and many objects radiate them including the Sun, and neutrinos hardly interact with matter. These are great advantages to using a neutrino telescope. However, neutrinos are extremely elusive and neutrino detection is an indirect and challenging operation. Gravitational radiation is minute but detection is fairly straightforward with sensitive equipment. Gravitational waves pass right through matter without being changed in any way so they can let you "see" things that are invisible, such as perhaps inside black holes, or into systems that are obscured by dust and material between you and them. Researchers might be able to examine the degenerate matter inside a neutron star. Perhaps we could even "see" what is going on deep inside gas giants like Jupiter. There are so many fascinating territories to explore that until now have been off-limits.

Gravitational waves also potentially offer us a peek into a time that has always been off-limits as well. Researchers expect a background of very low energy primordial gravitational waves, created by the Big Bang. Right now, cosmologists can only look back to about 380,000 years after the Big Bang, when electromagnetic radiation first became free to stream in all directions (as low-energymicrowave photons). A neutrino background is also expected to exist and it should offer a window into a younger yet universe, but these low-energy neutrinos are not yet detectable let alone map. Gravitational waves, unhindered by even the most extreme environment possible, should have originated in the very first millionths of a second when the universe expanded almost instantaneously (and very mysteriously) from the size of a proton to the size of a grapefruit. Scientists are just now detecting the most powerful gravitational waves. It is a lot to ask to see this much weaker primordial background, but I suspect someone will someday find a way to do so, and when they do they might be able to answer some pressing questions about cosmic inflation and about the conditions of those first micro-moments.

The Future

Meanwhile, researchers can look forward to using gravitational waves as information carriers. They will no doubt let us in on some secrets of the universe. The question of whether we can manipulate gravity/space-time is probably very long off, if ever. The forces one would need to safely harness in order to create something like a wormhole, for example, are unimaginable.

Applications like wormholes and gravitational communication might a long way off but this discovery already promises new leads into theoretical physics. As researchers probe gravitational waves, they might find additional clues about the mysterious force of gravity. It might possibly lead to strategies that could test whether force particles called theoretical gravitons exist. This line of reasoning is a logical extension from the other three fundamental forces, all of which are carried out by force-carrying particles. Electromagnetism can be used as an analogous theory. In this case the field of quantum electrodynamics has successfully quantized the classical electromagnetic wave. That means that the classical wave described by Maxwell's equations now emerges seamlessly from a collection of innumerable photons, all of which are quantum mechanical particles. Gravitons could be the quantum gravitational force carrier. Countless gravitons would build a gravitational wave described by general relativity, a classical theory. A breakthrough like this would round out the Standard Model of particle physics, which currently only describes particles for electromagnetism (photons), the weak force (W and Z bosons) and the strong force (gluons). The grand hope is that such a breakthrough would link general relativity to all the other theories of physics, especially quantum mechanics. The discovery of gravitational waves might be the first step toward a seamless theory of everything.