Everything You Need To Know About Gravitational Waves

Thursday, February 11, 2016
8:12 pm

Although it has been my most enduring, meteorology was not my first foray into the natural sciences. When I was in preschool, I was obsessed with volcanoes and astronomy, two things I still love today. I clearly remember taking a trip to the “Big Island” of Hawaii when I was in kindergarten with my family and throwing a fit when we went to Kilauea and the “hot lava” that was so vividly portrayed in the video cassettes I religiously watched at home was nowhere to be found. Although I don’t remember any of them now, my mom says that I memorized all the moons of Jupiter given in the book above. Seeing as Jupiter has 67 moons, I think she might be exaggerating a bit, but I may have memorized the four Galilean moons (she recalls me memorizing 8 or so).

I may have been a highly touted intellectual science prospect throughout preschool, but those expectations fell flat when I encountered a more strenuous workload in middle school, and you need look no further than my performance in the calculus-based introductory physics series at the University of Washington to see that I’m a hobbyist at heart, not a scientist. Thankfully, scientists came along and developed the internet, so hobbyists like myself can still entertain ourselves by blogging about things we aspire to comprehend.

So, as you can imagine, when I heard the news on Thursday that a team of absurdly smart scientists were claiming to have discovered direct evidence of gravitational waves, waves in the space-time fabric of the universe, from two black holes smashing into each other over a billion light years away, I had to enter the blogosphere and give the internet my two cents on it.

But before I did that, I had to brush up on my knowledge of Einstein’s theories of special and general relativity.

We are used to thinking of space and time as independent of each other. We imagine that there are three spatial dimensions that describe our world, and there is time, which just ‘keeps on going’ at the same rate for everybody. Time anchors us. In a crazy world with terrorism, climate change, nuclear proliferation, disease, and reality TV stars storming their way to the Republican nomination, we can all rest easy knowing one thing. At least we all abide by one common clock, right?

Wrong.

In 1905, Einstein was a 26-year-old university graduate who was working in a patent office. He enjoyed producing groundbreaking physics work in his spare time, and in 1905, he produced his theory of special relativity. This theory has two parts. First, it says that the laws of physics are identical throughout the universe for any “inertial” (non-accelerating) observer. Second, it says that the speed of light is the same for all observers. These may seem like commonsense, innocuous statements, but they have profound implications. As you will see, while some things are absolute, such as the speed light, other things are relative based on the observer, such as space and time.

Imagine that you are in a vintage race car traveling 70 miles per hour to the east, and your buddy’s jalopy is traveling at 30 mph to the west. In this case, your buddy’s car is traveling towards you at 100 mph. This is because YOUR car is not traveling away from you at all – it is traveling at a lowly 0 mph relative to you. Likewise, from your buddy’s perspective, his car is not moving at all, but your car is moving towards him at 100 mph. At first, this seems like a paradox: how can something be moving at 0 mph and 100 mph at the same time? Of course, it all makes sense when you take who’s driving the car into account. This illustrates the concept of inertial reference frame, where any arbitrary, non-accelerating object can be defined as being stationary while other objects are whizzing all around in every direction. I may think I’m stationary sitting here writing this blog, and I am from my reference frame, but try asking the man on the moon if I’m stationary. Heck, he can only see me for half of the day!

Weird things happen when you travel at speeds close to the speed of light. Say, for example, that I am flying in a spaceship at the speed of light to the east, and my buddy is flying at the speed of light to the west. It would seem, then, that from my inertial reference frame, my buddy is traveling at two times the speed of light away from me. In the graphic below, ‘c’ stands for the speed of light, while ‘2c’ stands for twice the speed of light.

However, this is not possible. Due to the theory of special relativity, since we are both non-accelerating objects, the same laws of physics apply for us, and the speed of light is the same for us. Nothing can travel faster than the speed of light. Therefore, my buddy is only traveling the speed of light away from me, not twice the speed of light. How can this be?

In the car example, the speed of my car was completely dependent on reference frame. I could’ve been going 0 mph or I could have been going 100 mph. If there was a hitchhiker standing on the side of the roadway, he would have said I was going 70 mph. And as it turns out, time, just like speed, position, and so many other things, is relative.

If I’m traveling at light speed away from my buddy and he doesn’t appear to be going anywhere, then time is going normally for me, but no time has passed for him. If time was going for him, he would be moving!

And because the speed of light is equal to length divided by time, if time is relative, it turns out that length is too! If time passes more slowly for other objects flying by the observer than the observer himself in his inertial reference frame, then the length of those objects the observer sees must contract in order to satisfy the relationship between time, length, and the speed of light. For example, if I’m flying by a spaceship at 3/5ths the speed of light, for me, the spaceship is only 4/5ths as long as it is in its own reference frame, and for every second that has passed on the spaceship, 1.25 seconds have passed for me. These concepts are called length contraction and time dilation, respectively, and they are not intuitive at all. You can learn more about them here.

There are other consequences of special relativity, a major one being that events that may appear simultaneous to one observer may not appear simultaneous to another observer. Also, weird stuff happens when you are accelerating (i.e. not in an inertial reference frame). It’s all incredibly confusing and counter-intuitive.

But what all of this stuff means is that space and time are not separate entities. They are intrinsically woven together, and we call this entity space-time.That’s right: in our overly chaotic world, space and even time are relative to the observer. Thankfully, these effects only become noticeable when traveling at “relativistic” speeds… i.e., speeds approaching the speed of light. Otherwise, I imagine everyday communication would be quite difficult!

For example, let’s imagine that the aforementioned rockets can go at all speeds. The dashed line here represents the relative speed of one rocket from another (in terms of its velocity divided by the speed of light) if we just take the sum of the parts like we did with the cars. The blue line shows the relative speed if we take special relativity into account, like we did with the rockets. There isn’t much of a difference until after v/c=.1, meaning that the velocity (v) is 1/10th the speed of light. One tenth the speed of light is 66,960,000 miles per hour! So yes, relativity affects us all, but the effects are so small that it is impossible for us to notice them. Still it’s fascinating to know that any movement has an effect on time and length from your reference frame.

Whew! If you made it through that, then you’ll have no problem getting through the rest of this blog.

Obviously, 1905 was a good year for Einstein. In addition to his theory of special relativity, he published revolutionary papers on Brownian motion, the photoelectric effect, and mass-energy equivalence (E=mc2). However, his best work was yet to come.

Einstein liked his theory of special relativity, but he wasn’t content with it. Special relativity was only concerned with inertial reference frames, and Einstein wanted to make a theory that was compatible with all reference frames. In other words, he sought to include acceleration into his theory. He began his quest for a new, more generalized theory in 1907, and after eight years of blood, sweat, and tears, he published his theory of general relativity, a theory which has served as one of the pillars of modern physics ever since.

In his law of universal gravitation, Isaac Newton stated that any two objects in the universe attract each other, and that attraction is due to the intrinsic mass of the objects. He didn’t know why they attracted each other, but he just knew that they did, and that the more massive the object and the closer the object was to neighboring objects, the stronger the attraction was.

When coming up with his theory of general relativity, Einstein actually apologized to Newton in his notebook, writing “Newton, forgive me. You found the only way which, in your age, was just about possible for a man of highest thought and creative power.” In his theory, Einstein finally had an explanation for why gravity existed. In Einstein’s theory of general relativity, gravity is not simply an innate force between two objects. Instead, gravity is a consequence of the influence of mass on space-time. Mass, he proposed, curves space-time, and this curvature is felt as the “force” of gravity.

Take a look at the diagram of the Earth above. Due to its mass, it bends space-time, with the most bend occurring closest to the Earth. Now, imagine that you have a ball rolling on the space-time surface. It will roll towards the Earth, and will roll fastest when it is closest to the Earth, where the slope of space-time – and therefore, the force of gravity – is the steepest/strongest. Of course, this ball, which has mass, will also bend space-time. Technically, this bend extends throughout the entire universe, but the effect of the Earth’s mass on the curvature of space-time is negligible once you get out of our solar system, so it’s really negligible in galaxies billions of light-years away.

The fact that mass bends space-time has some important implications, with two of the most important being the theorized existence of black holes and gravitational waves. Black holes are regions where the curvature in space-time, and by association, the gravitational force, is so drastic that nothing, not even light, can escape past a certain point, known as the event horizon. In fact, all the mass of the black hole is located at the “singularity,” which has no volume, infinite density, and infinite space-time curvature. Black holes had been theorized and indirectly observed but never observed directly until September 2015. After a lengthy, arduous process of research and verification, these findings were announced to the world on Thursday, February 11, 2016.

However, the bigger story has been how we obtained direct evidence of the existence of black holes. And we did that by the first ever direct observation of gravitational waves.

Gravitational waves are undulations in space-time that propagate as waves from a given source. Although mass curves space-time, the curve stays centered on that specific mass. With gravitational waves, these curves propagate throughout the universe, far away from the center of mass from which they are originating.

Gravitational waves are sinusoidal, meaning they oscillate smoothly according to the y-coordinate of a rhythmic trace of a circle. These waves, called “sine” waves, are everywhere. Light waves, sound waves, and even water waves are sinusoidal. For example, the “A” below is a sine wave.

Music is made of a whole bunch of sine waves, and although it doesn’t look as neat, it sounds a lot better. Here is a “waveform analysis” I made of Van Halen’s “Hot For Teacher.”

Gravitational waves, by bending space and time, actually move stuff in very specific patterns. I found a handy collection of animated gifs online at Universe Today, but these were all originally retrieved from Einstein Online, a fantastic resource for laypeople who want to learn about relativity and all things Einstein. I heavily used Einstein Online when writing this blog!

Let’s imagine that we have a bunch of red dots laid out in a circular fashion. A gravitational wave, when passing perpendicular to this circle of dots (into the screen), would cause them to stretch and contract in a rhythmic fashion. Check it out!

Insane, right? And remember, it’s stretching and contracting time, too.

Now, let’s extend this to the third dimension. Instead of having one circle, we’ll stack a whole bunch of them together to make a cylinder. Also, we’ll connect the dots with some imaginary blue lines just so it is easier to see how the wave propagates through the cylinder.

Here is the view of the wave coming perpendicular to the ends of the cylinder. Trippy!

And here’s a side view. You can really see the sinusoidal nature of the wave.

There are many different types of gravitational waves. The one above is a “linearly polarized” gravity wave. There are other polarizations, such as circular and elliptical polarization, and the polarization has to do with the electromagnetic nature of the wave. Additionally, these waves occur at a vast variety of frequencies corresponding to the objects that produced the waves and how far the waves have traveled.

So, gravitational waves move temporarily distort time and space for certain regions before they continue their journey onward throughout the rest of the universe. But how the heck do we measure these things?

As we saw, the gravitational waves moving through something distort its shape. However, there are lots of waves that can move through things and distort their shapes. Seismic waves distort the shape of the ground. Water waves distort the shape of the water. Shock waves, such as the one you see emanating from the explosion above, can set off car alarms, bring down buildings, and scare the living crap out of your dog. Therefore, how did these scientists deduce that the waves they observed were of the gravitational variety?

Enter LIGO, which stands for the “Laser Interferometer Gravitational-Wave Observatory.” LIGO is primarily funded by the National Science Foundation and draws scientists from all around the world. It was originally founded in 1992 by a group of scientists from MIT and Caltech, and began operations in 2002. Between 2002 and 2010, it failed to discover any gravitational waves, and was subsequently shut down for enhancements, finally coming back online in February of 2015.

LIGO consists of two giant L-shaped observatories, one in Hanford, Washington, and one in Livingston, Louisiana, with each “arm” being 4 kilometers long. As the LIGO acronym suggests, these observatories are “Laser Interferometers,” meaning they split a laser beam and see how the two laser beams interfere with each other. The beams are calibrated so that, under normal conditions, there will be perfect “destructive interference,” which is where the light beams (which are sine waves) are perfectly opposite each other so that adding them together creates a straight line and thus a complete absence of light.

When a gravitational wave comes, space-time is distorted, and as such, the arms of the observatory lengthen and contract rhythmically, with one arm lengthening as the other contracts and vice versa. Due to this changing length, the laser beams no longer perfectly cancel each other out, and light shines through.

The change in arm length is on the small side – typical changes are on the order of 1/10,000th the width of a proton! Incredibly, the interferometers are sensitive enough to measure this change. I don’t know how they do it. To determine whether the readings were due to gravitational waves and not – say – a 9.0 Cascadia Subduction Zone earthquake, scientists are on the lookout for specific patterns that suggest the passing of a gravitational wave. Here are their exact measurements from the gravitational wave everybody is talking about.

Gravitational waves are made by extremely violent events in the universe, and these gravitational waves were theorized to have been created by the collision of two black holes, one 36 times the mass of the sun and the other 29 times as massive. They circled and approached each other at half the speed of light and eventually collided to make a single black hole 62 times as massive as the sun. Three solar masses were transformed into energy (remember E=mc2?), and 50 times as much power as the output of all stars in the universe was sent radiating into the space at the speed of light.

1.3 billion years later, on September 14, 2015, scientists found the specific pattern they were looking for, and the fact that it occurred at both the Hanford and Livingston observatories at almost exactly the same time proved that it was not simply a local disturbance. The signal only lasted for 20 milliseconds and only moved the LIGO mirrors four thousandths of the diameter of a proton, but they had finally captured direct evidence of both black holes and gravitational waves. Although gravitational waves are not sound waves, the frequency of these waves is a frequency that our ear can detect, so by converting the gravitational waves to sound waves, we can hear the sounds of these two black holes colliding. Listen to them here.

I’m not an astrophysicist, but what from what I’ve read, the discovery of these waves is one of the most important astronomical discoveries of all-time. According to Abhay Ashtekar, a physics theorist at Penn State, “it’s really comparable only to Galileo taking up the telescope and looking at the planets. Our understanding of the heavens changed dramatically.” I think a good comparison is to the discovery of radio waves 130 years ago by Heinrich Hertz. Since then, radio waves have completely changed our way of life.

So far, the vast majority of our observations of the universe have come from electromagnetic radiation. Radio waves, infrared waves, visible light, x-rays, gamma rays… you get the idea. However, not everything in the universe emits electromagnetic radiation. Black holes don’t… that’s why they are called black holes! We would be able to see dark matter and dark energy. But that’s not what I’m most excited about.

According to the big bang theory, the very early universe was opaque to electromagnetic radiation, and we cannot see further back than 380,000 years after the big bang. However, it was not opaque to gravitational waves, meaning that if we get a clear enough view, we should actually be able to see the big bang itself. We’ll go all the way back to the very beginning of time: the “singularity,” where all of the matter in the universe was contained in an infinitely small, infinitely dense, and unimaginably hot point. Or we’ll discover that the Big Bang didn’t happen at all. However, the existence of gravitational waves adds credence to the big bang theory.

“Imagination is more important than knowledge,” Einstein once said. For knowledge is limited to all we now know and understand, while imagination embraces the entire world, and all there ever will be to know and understand.” I can only imagine what we’ll discover next!

Bibliography:

Abbott, B. P. et al. (2016). Observation of Gravitational Waves from a Binary Black Hole Merger. Physics Review Letters, 116(061102). Retrieved February 13, 2016, from http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.116.061102

Adams, K. S. (n.d.). High Energy Groove: X-Ray Binary. Retrieved February 12, 2016, from http://heasarc.nasa.gov/docs/xte/outreach/HEG/bhm/black_hole_mass.html

Albert Einstein. (n.d.). Retrieved February 11, 2016, from https://en.wikipedia.org/wiki/Albert_Einstein

Choi, C. Q. (2014, October 24). Einstein’s Gravity Waves Could Be Found with New Method. Retrieved February 12, 2016, from http://www.space.com/27510-gravitational-wave-detection-method.html

Elementary Einstein. (n.d.). Retrieved February 13, 2016, from http://www.einstein-online.info/elementary

Fowler, M. (n.d.). Special Relativity: What Time is it? Retrieved February 11, 2016, from http://galileoandeinstein.physics.virginia.edu/lectures/srelwhat.html

General Relativity. (2016, February 12). Retrieved February 12, 2016, from https://en.wikipedia.org/wiki/General_relativity

LIGO. (2016, February 13). Retrieved February 13, 2016, from https://en.wikipedia.org/wiki/LIGO

Nave, C. R. (n.d.). Time Dilation/Length Contraction. Retrieved February 11, 2016, from http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/tdil.html

Norton, J. D. (2015, January 14). Special Relativity Basics – Relativity of Simutaneity. Retrieved February 11, 2016, from http://www.pitt.edu/~jdnorton/teaching/HPS_0410/chapters/Special_relativity_rel_sim/

Polarization (Waves). (2016, February 13). Retrieved February 13, 2016, from https://en.wikipedia.org/wiki/Polarization_(waves)

Radford, T. (2016, February 11). Gravitational waves: Breakthrough discovery after a century of expectation. Retrieved February 11, 2016, from https://www.theguardian.com/science/2016/feb/11/gravitational-waves-discovery-hailed-as-breakthrough-of-the-century

Rogness, J. (n.d.). Trigonometry in Nature – Sinusoidal Waves as Sound. Retrieved February 12, 2016, from http://www.math.umn.edu/~rogness/math1155/soundwaves/

Special Relativity. (2016, February 2). Retrieved February 11, 2016, from https://en.wikipedia.org/wiki/Special_relativity

Spotlights on relativity. (2016). Retrieved February 13, 2016, from http://www.einstein-online.info/spotlights

Timeline of the Universe. (2012, December 21). Retrieved February 13, 2016, from http://map.gsfc.nasa.gov/media/060915/index.html