Tag Archives: GPS

Gravity 5: Putting Einstein in the Navigator’s Seat

by Shane L. Larson

When Einstein put general relativity forward in 1915, the world had barely entered into the electrical era. Automobiles were not unheard of, but were not common. The great Russian rocket pioneer, Konstantin Tsiolkovsky, had published the first analysis of rocket flight through space in 1903, but the first successful liquid fueled rocket would not be flown until 1926 by American rocket engineer, Robert H. Goddard, reaching an altitude of just 41 feet. Earth gravity, though weak by the standards of general relativity, was a formidable foe. Of what possible use was general relativity?

The great rocket pioneers  Konstantin Tsiolkovsky (L) and Robert H. Goddard (R). They were actively trying to design machines to escape Earth's weak gravity at a time when Einstein was developing general relativity to understand gravity in more extreme situations.

The great rocket pioneers Konstantin Tsiolkovsky (L) and Robert H. Goddard (R). They were actively trying to design machines to escape Earth’s weak gravity at a time when Einstein was developing general relativity to understand gravity in more extreme situations.

At the time general relativity was first described, it was very much in the form of what is today called “fundamental research.” It described Nature on the deepest levels. It extended the boundaries of human knowledge. It challenged our conceptions about how the Cosmos was put together. But for all practical purposes, it had little impact on the average person. It did not contribute to the Technological Revolution, electrifying the world and changing the face of industrial manufacturing. It did not provide a reliable way to make crossing the Atlantic faster or safer. It did not transform the way steel was made or assembly lines were automated. It did not make the lives of the common worker easier, nor scintillate the conversations around family dinner tables.

Chicago in 1915, when general relativity was first presented. South State Street (L) and Water Street (R). Horses were still common, electricity was just coming to cities, and buildings were short by today's standards. General relativity was "fundamental research" and, at the time, had little direct bearing on everyday life.

Chicago in 1915, when general relativity was first presented. South State Street (L) and Water Street (R). Horses were still common, electricity was just coming to cities, and buildings were short by today’s standards. General relativity was “fundamental research” and, at the time, had little direct bearing on everyday life.

In fact, the implications and predictions of general relatively were not fully understood in those early years. It has taken a full century to come to grips with what it is telling us about the structure of the Universe. Over time, it has slowly become a prominent tool to understand astrophysics and cosmology, but those applications are still the purview of exploratory, fundamental science.  It is only now, after a century of tinkering and deep thinking that the full potential of general relativity is being realized. Today, it impacts the lives of every one of us through the magic devices we carry in our pockets that tag our photos with the locations they were taken and help us navigate to business meetings and ice cream shops. Virtually every phone and handheld electronic device in use today uses global positioning system technology (GPS), which cannot work without a full and deep understanding of general relativity.

How do you navigate around the world? When I was a youngster, I would go to camp in the Rocky Mountains every summer. Those long ago days were filled with all manner of woodland adventures, ranging from ropes courses, to archery, to cliff jumping into swimming holes. My favorite activity, however, was hiking and navigating. We tromped all over the forests and mountainsides of Colorado, and every now and then stopped to pinpoint our location on a paper map of the forest. It was an activity that agreed well with me, instilling a lifelong love of maps.  So how did it work?

Traditional navigation using a compass and map. (L) The direction to multiple known landmarks is measured with a compass. (R) Those directions are transferred to a map, passing through the landmark. The place where the sightlines cross is your location.

Traditional navigation using a compass and map. (L) The direction to multiple known landmarks is measured with a compass. (R) Those directions are transferred to a map, passing through the landmark. The place where the sightlines cross is your location.

The basic notion of navigation on paper is to recognize some landmarks around you — perhaps two distinct mountain peaks in the distance.  Let’s call them “Mount Einstein” and “Mount Newton.”  Using your compass, you determine the direction from your location to each of the mountain peaks. Perhaps Mount Einstein is due northwest, and Mount Newton is north-northwest (a hiking compass is finely graded into 360 degrees, so you could have more precise numerical values for direction; the procedure is the same one I describe here with cardinal directions).

Now, you go to your paper map, and locate the two mountain features you are looking at. When you find Mount Einstein, you draw a line on your map that goes through Mount Einstein, pointing due northwest. If you are standing anywhere along that line, you will see Mount Einstein due northwest.  Now you do the same thing with Mount Newton, drawing a line that points due north-northwest. If you are standing anywhere along this line, then you will see Mount Newton due north-northwest.  If you extend your two lines as far as you can, you will see they cross at one place and one place only. This is the only place a person can stand and see these two landmarks in the directions indicated — it happens to be exactly where you are standing!

In the modern era, many of us navigate using GPS technology, built directly into our smartphones.

In the modern era, many of us navigate using GPS technology, built directly into our smartphones.

This navigational process is called triangulation and it is the most basic form of locating your position. But when was the last time you navigated around the city with a paper map and a compass? This is the future, and if you are in downtown Chicago and want to get from the ice cream shop to the Adler Planetarium, you whip out your smartphone and ask your favorite Maps program to give you some navigational instruction!

How does your phone know where you are? Your phone has a microchip inside it that uses a network of satellites to locate your position on Earth by figuring out where you are with respect to each satellite. In essence, it is kind of like the triangulation method we just discussed.

Third generation GPS satellite (GPS IIIa).

Third generation GPS satellite (GPS IIIa).

The Global Positioning System satellite network is a constellation of 32 satellites orbiting at an altitude of approximately 20,200 km (12,600 mi, almost 50x higher than the International Space Station). Each of the satellites carries on board an accurate atomic clock that is synchronized to all the other satellites. They sit in orbit, and transmit the current time on their clock.  Those signals spread outward from the satellites, and can be detected on the ground by a GPS receiver, like the one in your smartphone.

Each satellite transmits the same signal at the same time. If you are the same distance from two satellites, you get the same signal from both satellites at the same time.  But suppose you are closer to one satellite — then the time you get from one satellite is ahead of the other! The time you receive from each satellite tells you the distance to the satellite (for aficionados: distance is the speed of light multiplied by the time difference between the received satellite time and your clock, if you ignore relativity!) . The exact position of the satellites in their orbits is known, just like the position of Mount Einstein and Mount Newton were known in the map example above. You can triangulate your position from the satellites by simply drawing a big circle around each satellite as big as the separation you figured out from the timing — you are standing where those big circles cross. GPS allows you to exactly pinpoint your location on the surface of the Earth!

GPS satellites broadcast their own time signals which your phone receives on the ground. Above, the "310" time signal from the red satellite is reaching you at the same time as the "309" signal from the blue satellite. This tells your phone is is closer to the red satellite than the blue satellite. The position of the satellites is known, so your phone uses this information to compute the distance to each of the satellites, and triangulates its position.

GPS satellites broadcast their own time signals which your phone receives on the ground. Above, the “310” time signal from the red satellite is reaching you at the same time as the “309” signal from the blue satellite. This tells your phone it is closer to the red satellite than the blue satellite. The position of the satellites is known, so your phone uses this information to compute the distance to each of the satellites, and triangulates its position.

So what does this have to do with general relativity? One of the predictions of general relativity is that massive objects (like the Earth) warp space and time. The warpage of time means that clocks down here on the surface of the Earth (deep down in the gravitational well), tick slower than clocks carried on satellites high above the Earth.

General relativity tells us time moves more slowly deep down in the gravitational well. If you are going to navigate using clock signals from satellites (GPS) you have to account for this!

General relativity tells us time moves more slowly deep down in the gravitational well. If you are going to navigate using clock signals from satellites (GPS) you have to account for this!

Being appropriately skeptical, you should immediately ask “Okay, how much slower?” and once you hear the answer ask “Does that make a difference?” The military commanders in charge of developing GPS in the 1970s famously asked exactly these questions, uncertain that we had to go to all the effort to think about general relativity for navigation by satellite.

The GPS time correction calculation is well understood, and only takes a couple of pages to work out.

The GPS time correction calculation is well understood, and only takes a couple of pages to work out.

The time difference between a clock on the ground and a clock in a GPS satellite due to general relativity warping time is about 1 nanosecond for every two seconds that passes.  What’s a nanosecond? It is one billionth of a second. What kind of error does a nanosecond make? GPS navigation is based on how long it takes radio signals (a form of light) to get from a GPS satellite to you. Light travels about 12 inches in a nanosecond (watch the indefatigable Admiral Grace Hopper explain what a nanosecond is), so for every nanosecond your timing is off, your navigation is off by about 1 foot.  The accumulated error is about 1000 nanoseconds every 30 minutes, amounting to a difference of 1000 feet. This is a substantial difference when you are trying to accurately navigate!

Every satellite in the GPS constellation is constantly in motion, orbiting the Earth once every 12 hours.

Every satellite in the GPS constellation is constantly in motion, orbiting the Earth once every 12 hours.

This is not the only correction that has to be accounted for. The GPS satellites are also moving along their orbits, so there is a speed difference between you and then. One of Einstein’s early discoveries was special relativity which said that moving clocks run slower than clocks that are standing still. So while the warpage of spacetime is making your clock on the ground tick slower than the satellite’s, the satellite’s motion makes its clock tick slower than yours!  These two effects compete against one another, and both must be accounted for. Special relativity means the satellite clock ticks about 0.1 nanoseconds (1 ten-billionth of a second) slower for every second that passes compared to your clock on the ground. On a 30 minute walk then, this produces an error in location of almost 200 feet.

einsteinPocketBoth special and general relativity were discovered in an era where they had little application to everyday life. None-the-less, as the years have worn on clever and industrious scientists and engineers have discovered that they both have important and profound applications. Both special and general relativity have grown into important tools in modern science and technology, with applications in the most unexpected places in our lives. Usually, it is hidden from me and you under the slick veil of marketing and glossy industrial design, but they are there none-the-less.  Just remember this the next time you’re out walking around, using your phone to navigate: there is a whole lot of Einstein in your pocket.

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This post is part of an ongoing series written for the General Relativity Centennial, celebrating 100 years of gravity (1915-2015).  You can find the first post in the series, with links to the successive posts in this series here: http://wp.me/p19G0g-ru.

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Days of Pi and Wonder

by Shane L. Larson

My watch on Pi-day, 2012. The time makes the 4th through 8th digits of Pi: 3.14 15926!

My watch on Pi-day, 2012. The time makes the 4th through 8th digits of Pi: 3.14 15926!

Each year when Pi Day (March 14, or 3-14) rolls around, geeks around the world rejoice. Everyone seems to get their geek on, and that makes me walk around with a grin on my face.  People do all kinds of things, like make pies shaped like the Greek letter Pi, or making square pies because they are punny (“pie are square,” which is a pun for Pi*r2, the area of a circle). Or they take pictures of their watches at exactly a moment to write out the digits of Pi.

What is all this Pi business? Fundamentally, it is the number you get by dividing the distance around the outside of a circle by its diameter.  Not just any circle — every circle. It is one of the great wonders of the fabric of the Cosmos that it works for every circle. It’s the kind of thing that keeps me up late at night!

Pi is a natural number that appears from Nature. It is the ratio of the circumference around a circle to the diameter.  It is the same for EVERY circle!

Pi is a number that appears from Nature. It is the ratio of the circumference around a circle to the diameter. It is the same for EVERY circle!

Pi is an irrational number, meaning it cannot be written as a fraction. It has an infinite number of digits that go on and on and on and on.  The first 200 digits are: 

3.14159265358979323846264338327950288419716939937
5105820974944592307816406286208998628034825342117
0679821480865132823066470938446095505822317253594
0812848111745028410270193852110555964462294895493
038196...

You can see a million digits here, and here. There are even more digits (in case you want to memorize them in an effort to attract a date 🙂 ).

Wikipedia lists a LOT of things that happened on Pi Day in history, but I want to focus on a warm spring day in 1879, in the city of Ulm on the banks of the River Danube. On that day Hermann and Pauline Einstein welcomed their son, Albert, into the world.

Albert Einstein is one of the most easily recognized figures in our culture, so much so that he is recognized in imaginary fantasies, like this one of Albert being a master of the electric guitar in my band ("MC Squared and the Relatives"). In reality, his colleague Robert Oppenheimer noted that Einstein was "almost wholly without sophistication and wholly without worldliness ... There was always with him a wonderful purity at once childlike and profoundly stubborn."

Albert Einstein is one of the most easily recognized figures in our culture, so much so that he is recognized in imaginary fantasies, like this one of Albert being a master of the electric guitar in my band (“MC Squared and the Relatives”). In reality, his colleague Robert Oppenheimer noted that Einstein was “almost wholly without sophistication and wholly without worldliness … There was always with him a wonderful purity at once childlike and profoundly stubborn.”

There is perhaps no figure in the world, historical or otherwise, more recognizable than Albert Einstein. His Facebook page has 8.7 million likes (!), even though he died in 1955 (Einstein passed from this Cosmos on April 18, 1955, almost exactly 34 years before the birth of Facebook’s founder, Mark Zuckerberg).  He is widely regarded as one of the towering geniuses of the human race, and was named the Person of the Century in the 20th Century for the impact his scientific findings had on our modern lives. While most of us know about Big Al, do you know how his work filters into your every day life?  Let me tell you a few stories of how it does.

Einstein in 1905 in his famous "patent clerk" jacket. I always imagined it to be green!

Einstein in 1905 in his famous “patent clerk” jacket. I always imagined it to be green!

Let’s go back to 1905. Einstein had finished his doctorate at the University of Zurich, but unable to find an academic position had taken up work as a patent clerk in Bern. Now in those days, there was no evening reality television, no new episodes of Cosmos, so Einstein continued to work on physics “in his spare time.” This is the sort of thing scientists do when we’re between jobs, with the hope that by still being productive we will become attractive candidates for an academic position in the future. As it turns out, Einstein was very productive in 1905. The Latin phrase “annus mirabilis” (“year of wonders”) has in modern science become synonymous with Einstein’s published works in 1905. There were four seminal papers: (1) a paper explaining the molecular origin of Brownian motion; (2) a paper explaining the photoelectric effect by revitalizing the photon theory of light; (3) a paper describing special relativity, and proposing the ultimate speed limit in the Universe; (4) a paper describing the equivalence of mass and energy, captured by the famous formula E = mc2.  These four papers laid the foundations for our understanding of much of what we call “modern physics,” fundamentally altering the way we think about energy, space, and time.  What are these concepts, and what do they have to do with your life?

Brownian motion was named after botanist Robert Brown, who in the early 1800s was using a microscope to observe pollen grains suspended in water. Inexplicably, the grains appeared to move around at random, with no discernible cause. Brown tried in vain to discover the cause of the motion, but could not explain it. He then dutifully did what scientists do, he reported his observations to his peers and the phenomena passed into the scientific memory. Nearly a hundred years later, Einstein showed that the observed motion could be explained by the constant buffeting of the large grains by the motion of the much smaller particles of water that it was suspended in, what we today call molecules. There are many applications for the use of Brownian motion once you understand it. For instance, in modern pharmaceutical manufacturing, medicines delivered through pills are created from a suspension of the active drugs with inactive ingredients that comprise the entire pill; this controls the delivery of the drug on ingestion. Brownian motion is used to control the suspension in the mixing stages, to insure the proper distribution of the active drug throughout the pill.

Mixing pharmaceutical molecules is like mixing marbles. The active ingredients (white marbles) need to be mixed evenly with the inactive ingredients (green marbles). Brownian motion can be exploited for this mixing.

Mixing pharmaceutical molecules is like mixing marbles. The active ingredients (white marbles) need to be mixed evenly with the inactive ingredients (green marbles). Brownian motion can be exploited for this mixing.

The nature of light has always been a matter of intense scrutiny for physicists. In the early 1700’s, Newton famously championed the “particle theory” of light, but these ideas fell into disfavor when a particle approach could not explain effects like diffraction and interference; this gave way to the “wave theory” of light. In 1900, Max Planck proposed his “quantum hypothesis” to explain how objects like red-hot pokers and lightbulb filaments emit energy — in discrete packets called “quanta.” Einstein adopted the quantum hypothesis, and revitalized the particle  idea to explain how some materials eject electrons when you shine light on them: electric particles (electrons) are ejected when illuminated with light (photons) — the “photoelectric effect.”  The number of applications of this effect in modern technology are numerous, including solar cells, the imaging sensors in the digital camera in your smartphone, and remote controls.

Your TV remote emits infrared light (which you eye cannot see). When the sensor on your TV is hit by the light, the photoelectric effect generates an electrical signal that activates the control circuit in the TV.  The image on the right was taken by pulling the infrared filter off of an ordinary digital camera (most digital cameras can see infrared, but that light is blocked so your pictures don't look weird).

Your TV remote emits infrared light (which your eye cannot see). When the sensor on your TV is hit by the light, the photoelectric effect generates an electrical signal that activates the control circuit in the TV. The image on the right was taken by pulling the infrared filter off of an ordinary digital camera (most digital cameras can see infrared, but that light is blocked so your pictures don’t look weird).

Special relativity is one of the most profound and important discoveries about Nature that humans have ever made, and its veracity has been borne out, literally, by billions of experiments since its inception in 1905. Einstein’s insight that there is an Ultimate Speed Limit in the Universe (the speed of light) has profound consequences for how we think about motion and dynamics at high speeds, and challenges our old-fashioned notions about the distinguishability of space from time. Most of us have heard all kinds of special relativity stories about how it changes the nature of measurements of distances and times, and the resulting perception of paradoxes — length contraction, time dilation, old and young twins. It blows your mind and is vaguely unsettling because it seems far from our everyday lives, and as a result our everyday intuition built around watching baseballs, Volkswagens and chipmunks doesn’t seem to apply.

Calvin's father doesn't quite understand relativity. [From Calivn & Hobbes, by Bill Watterson]

Calvin’s father doesn’t quite understand relativity. [From Calivn & Hobbes, by Bill Watterson]

But special relativity explains why we see cosmic ray muons from space when they should have decayed before they hit ground; it is demonstrated by every one of the 115 billion protons the LHC bashed together at a time; and we have discovered that if our engineering is up to it, we can use special relativity to travel to the stars.  Mass-energy equivalence (E = mc2) is usually mixed into our thinking about relativity, and most prominently impacts the world through its application ot nuclear weapons and nuclear energy.  Deep in the heart of the Sun, the nuclear fusion of hydrogen into helium converts some of the mass of hydrogen into energy, which you and I eventually feel as the warm dapple of sunlight during a lazy afternoon picnic.

The Disintegration of the Persistence of Memory, by Salvador Dali. We have a vague and unsettled feeling, especially when confronted by relativity, that we do not understand the fabric of space and time.

The Disintegration of the Persistence of Memory, by Salvador Dali. We have a vague and unsettled feeling, especially when confronted by relativity, that we do not understand the fabric of space and time.

Perhaps the most important way that special relativity changed our lives is that it made us realize that all the laws of physics had to obey special relativity, which led Einstein to think about gravity. It took about 10 years, but he was the first person to understand how gravity and special relativity worked together, and the result was called “general relativity.” Today, general relativity has transformed the world because the Global Positioning System (GPS) would be impossible without it. General relativity (and special relativity) tells us that if you have two clocks that are moving differently, and experiencing gravity differently, then you will think they are ticking at different speeds when you compare them.  What does that have to do with GPS?  

Fundamentally, GPS works by broadcasting a clock signal from satellites. On the ground, your smartphone receives those signals and triangulates your position from the clock signals.  Suppose there are two GPS satellites, one is 100 km away from you, and the other is 200 km away from you. At the same moment, they broadcast their current time, say 2:00pm.  The 2pm clock signal from the satellite closest to you arrives first; the 2pm signal from the distant satellite arrives later. By comparing the arrival times of those two signals, you know exactly where you stand between the two satellites.  Where does relativity fit into this picture?  If you don’t include relativity, the clock signals from the satellites, compared to clocks on the ground (in your smartphone) are different by 38 microseconds — 38 millionths of a second!  That is so tiny!  Does it matter?  Sure it does, because the radio signal from the satellite is a kind of light, which travels 11.4 kilometers (7 miles!) in 38 microseconds!  If you didn’t have a little bit of relativity working inside your phone, your GPS would not be useful for navigation!  11.4 km is a HUGE distance when you’re trying to find a Dairy Queen, the Lego store, a hospital, or your kids’ baseball game.

GPS triangulates your location by comparing the received time from multiple satellites.

GPS triangulates your location by comparing the received time from multiple satellites.

Of course, Einstein’s work did not end with the annus mirabilis. In fact, he had a long and influential career after that, as most scientists do.  Let’s end with a story about a little paper he wrote in 1917. That year, Einstein explained the idea of stimulated emission –– light can cause an atom to emit an identical particle of light, and the two photons can travel along together exactly in synch. Okay, that sounds cool, but so what? You may shrug your shoulders, but what this leads to is the LASER. In fact, “laser” is an acronym built from Einstein’s idea — “Light Amplification by Stimulated Emission of Radiation.”  Einstein was the person who predicted the possibility of building a LASER, though it took until the 1950s for us to develop enough technology that one could actually be built. Today our world is literally filled with lasers — CD and Blu-Ray players, laser pointers, lasers for cutting industrial materials, lasers used to resculpt the lens of your eyes, and a whole host of medical applications.

Einstein is just one example of one scientist who changed our lives with his passion for uncovering Nature’s secrets. There are many examples of other scientists who have had similar influence on us, in ways that you and I don’t often think about nor quite possibly even know. But it is all there in our every day lives, from our trucks and carburetors, to our antibiotics and heart stents, to our smartphones and MP3 players, to our aerobees and yoga tights. It all comes from clever insights, accidental observations, random musings, and delight in something as simple as a round shape called a circle. Enjoy your Pi Day, and enjoy your pie!

Gravity does the talking

by Shane L. Larson

Obi-wan Kenobi, in perhaps one of the most famous utterances in cinematic history, claimed that the Force “is an energy field, created by all living things. It surrounds us, it penetrates us, it binds the galaxy together.” This propagated rapidly through popular culture when it was realized that Obi-wan must have been talking about duct tape, which after all has a light side, a dark side, and also binds our world together.

The famous utterance of Ben Kenobi's description of the Force (from "Star Wars").

The famous utterance of Ben Kenobi’s description of the Force (from “Star Wars”).

But an astute citizen of the Cosmos may grow curious at Kenobi’s observation, and ask “what does bind the galaxy together?” As it turns out there is a force that penetrates the fabric of the Universe, in a way it is the fabric of the Universe. We call it gravity.

Many of us have heard the idea that there are four fundamental forces in Nature: gravity, the electromagnetic force, the weak nuclear force, and the color force (the “strong nuclear force” is a faint bit of the color force that “leaks” out of atomic nuclei to be detectable by our experiments). Why is gravity The Force? Why not the others?

The four fundamental forces of Nature emerged after the Big Bang, as the Universe cooled and expanded.

The four fundamental forces of Nature emerged after the Big Bang, as the Universe cooled and expanded.

In order to fill the Cosmos, a force must be a long range force — the Cosmos is a BIG place!  The weak nuclear force and the color force are short range — they act very strongly over very tiny distances, in atomic nuclei and in the nuclear particles that comprise nuclei. The electromagnetic force is a long range force, but it acts in the presence of electrically charged particles, which come in two flavors — positive (+) and negative (-). It is easy to make separate positive and negative charges and to locally generate strong electromagnetic forces (lightning is a prime example from Nature), but by and large the Cosmos is electrically neutral — opposite charges are attracted to each other, and they quickly neutralize and cancel each other out, leaving no free charge behind.  Gravity is also a long range force, but it has only one kind of “charge,” which we call “mass.” There is no negative mass, so gravity cannot be shielded or canceled, and it acts over vast distances.

Gravity is the only game in town when it comes to forces acting on cosmic scales, despite being so incredibly weak.  I can see the skepticism on your face!  I said gravity binds the Cosmos together, and in the same breath said it was incredibly weak!  Whatever do I mean?

I tried as hard as I could to break the apple in two!

I tried as hard as I could to break the apple in two!

I mean that gravity is weak compared to the other forces of Nature, a fact you can easily demonstrate in your kitchen. Pick up an apple.  What is holding an apple together?  It is mostly intermolecular forces between the molecules that make the apple up, and those forces are electromagnetic in nature.  Now,using your bare hands, try to break the apple half.  Not so easy, is it?

Using the chemical energy from some Dr. Pepper, I can overcome the gravitational pull of the entire planet.

Using the chemical energy from some Dr. Pepper, I can overcome the gravitational pull of the entire planet.

Now, stand up and jump up in the air. How high did you get? Even if it was just a couple of inches consider this fact: you were able to momentarily over come gravity.  Using a little bit of chemical energy, gleaned from that rabbit food you ate at lunch (perhaps an apple you ate), you were able to overcome the gravitational pull of the ENTIRE EARTH!  Gravity is weak (and you are strong).

While these kinds of deep machinations are fascinating questions into the deep nature of Nature, you might still be scratching your head wondering what good is this knowledge? The first widely understood law of Gravity was Newtonian gravity, described by Isaac Newton in 1687.  It was used almost immediately to begin describing the motion of heavenly bodies, but by and large the world went about its business more or less oblivious to this stunning achievement of the human intellect.  The practical application of Newtonian gravity, using it for something that humans build or use, was not for almost 270 years: in 1957, the Soviet Union launched Sputnik, requiring a detailed understanding of orbital dynamics, which is derived from Newtonian gravity.  By a similar token, Albert Einstein wrote down the modern description of gravity, general relativity, in 1915. There were immediate applications of general relativity to astrophysics (a trend that has only grown since), but practical applications to human affairs did not seriously arise until the late Twentieth Century.  Let me tell you some stories about how gravity, general relativity, is changing our world.

GRACE.  Our society is engaged in much teeth-gnashing about the nature of the Earth’s changing climate, but most scientists are doing what scientists do best — they put their heads down, they collect data, then they figure out what the data is telling them.  Of particular importance to climate studies is the hydrological cycle on Earth.  Gram for gram, water is a bigger player in thermodynamics than any other substance on Earth. It is extremely effective at cooling and heating, which is why you use it to cool off in the summer and warm up in the winter!  The movement of water on Earth, in the oceans, the clouds, the rivers, and the atmosphere has enormous impacts on climate worldwide.  But the hydrosphere is HUGE! We can’t possibly hope to monitor water levels and water flow in lakes and rivers and oceans worldwide by placing individual sensors.  So how are we to learn about the water on Earth and how it moves and changes?  The answer is we use gravity.

(L) Satellite geodesey monitors the orbit of a satellite to understand the underlying source of gravity. (R) The GRACE geodesey system uses two satellites keeping track of each other using a microwave link.

(L) Satellite geodesey monitors the orbit of a satellite to understand the underlying source of gravity. (R) The GRACE geodesey system uses two satellites keeping track of each other using a microwave link.

Satellite geodesey can make precision measurements of the Earth’s gravitational field. As a satellite flies over the Earth, the changing mass below the satellite changes the strength of gravity, which alters the satellite’s trajectory in its orbit.  We monitor the orbit to know how the gravity (and the mass creating the gravity) is changing!  In 2002, NASA launched a mission called GRACE (Gravity Recovery and Climate Experiment), consisting of two satellites flying about 220 km apart, monitoring each others’ orbit using a microwave signal.  For over 5 years, GRACE monitored the Earth’s gravitational field and was able to see how it changes as water and ice move around our planet.  Just one example is shown below, illustrating how the gravity in the Amazon basin goes up and down with the coming and going of the rainy season.  Similar results illustrate the changing ice around the planet, particularly in the Arctic and Antarctic.

GRACE geodesey is sensitive enough to detect the change in gravity over the Amazon basin as the rainy season comes and goes.

GRACE geodesey is sensitive enough to detect the change in gravity over the Amazon basin as the rainy season comes and goes.

GPS.  phoneGPSPerhaps the most ubiquitous use of gravity in your everyday life is the global positioning system. Once relegated to navigation on planes and automobiles, the advent of GPS built into smartphones has enabled an explosion of location services that allows you to find friends, local restaurants, comic book stores, and concert venues in unfamiliar cities.

Fundamentally, GPS works by triangulation.  Satellites send out timing signals that are received by your smartphone or GPS navigator. The signals are broadcast in synch with one another. This means that if you are an equal, fixed distance from two satellites, you’ll get the same time from both (this is like using headphones — the sound from the L and R side are synchronized so you hear all the right parts of the song and the same time!).  If you are closer to one satellite, then you receive a time from that satellite sooner than a distant satellite (this is like watching a track meet from the stadium — runners hear the starting gun before you do, because they are closer).  Your navigator compares your local time to the time received from the satellites, allowing the determination of distance to each satellite. Since the position of each satellite is known, your location can be computed.

GPS triangulates your location by comparing the received time from multiple satellites.

GPS triangulates your location by comparing the received time from multiple satellites.

The satellite timing signals must be modified, using general relativity.  Why?  The satellites are much higher in the Earth’s gravitational field than you are, and general relativity tells us their clocks tick at a different speed. How much different? Over the course of a day, the general relativity correction to the clock times is about 38 microseconds — 38 millionths of a second!  You may be thinking “But that is so tiny!”  Yes it is tiny, but GPS works based on how far light travels in a given time.  In 38 microseconds, light travels 11.4 kilometers (7 miles)!  When you are trying to find a sushi restaurant, or the soccer field for your kids next game, 11 kilometers is a long way off!

Gravitational waves. ein_1920Let me tell you one last story, not about the practical uses of gravity, but about our dream of using gravity to reveal the secrets of the Cosmos.  In 1918, while exploring the implications of general relativity, Einstein discovered that there exists a kind of gravitational radiation, where the gravity from an astrophysical system carries energy away and into the far reaches of the Universe.  He calculated the strength of this radiation, and very quickly decided that it would be exceedingly difficult (if not impossible) to experimentally measure.

But fast-forward the blu-ray to today, and we have technology at our disposal that Einstein could never have imagined — high precision, high power lasers; GPS positioning systems to accurately locate anything anywhere on the planet; high performance computers capable of performing billions of computations per second; a globe girdling network that passes information from one continent to another as easily as one might shout down the hallway to a colleague; and most importantly, a vast community of scientists well-trained and well-versed in wresting secrets from Nature, the best minds our planet has to offer. You add that all together, and we find ourselves in the land of Einstein’s dreams, poised to measure the faint echoes of gravity bathing the Earth from distant corners of the Cosmos.

Nearly a century of thinking on the matter of gravitational radiation has coalesced around a magnificent machine called LIGO — the Laser Interferometer Gravitational-wave Observatory.  Using lasers shining up and down 4 kilometer long beam arms, a new generation of astronomers — gravitational wave astronomers — hope to detect the dance of neutron stars and black holes spiralling toward collision, the constant drone of young pulsars spinning down into their final rest in the stellar graveyard, and maybe (if we are lucky) the cataclysmic supernova explosion of a star dying, a process that synthesizes most of the atoms that comprise what we are all made of.

The LIGO Observatory at Livingston, LA. There is a companion observatory in Hanford, WA.

The LIGO Observatory at Livingston, LA. There is a companion observatory in Hanford, WA.

Gravitational wave astronomy is a way of asking anew the questions about who we are and what our place in the Cosmos is; it is a way of once again indulging in the unique gift to our species, an insatiable sense of curiosity and wonder.  But are there practical outcomes from this remarkable feat of human imagination? Perhaps not obvious ones, because the practical outcomes were not the driving force in the creation of the experiment. But as with all great feats of science and engineering, from the Manhattan Project to Apollo to LIGO, there are always beneficial outcomes.  Already LIGO’s technology is pushing the frontiers of optics and laser technology, environmental monitoring, and computer network capabilities.  But changes you see in your living room may be 7 or 70 or 270 years away.

This has always been the case for gravity; the timescale is simply a matter of how creative our engineers and scientists get!