Tag Archives: Einstein

Looking Back 108 Years…

by Shane L. Larson

Today would have been Carl Sagan’s 82th birthday. It is an auspicious year, because after a 108 year drought, the Chicago Cubs have won a World Series title. The Cubs win reminded me of Sagan because his son, Nick, had told a story once of introducing his dad to computer baseball based on statistics, whereby you could pit famous teams in history against one another. Sagan apparently said to Nick, “Never show me this again; I like it too much.”

Today, Carl Sagan would have been 82 years old.

Today, Carl Sagan would have been 82 years old.

It is an instantly recognizable feeling to those of us who do science — a nearly uncontrollable urge to ask, “What if…” and then construct an experiment to answer that question. When faced with the prospect of being able to pit two great teams from baseball history against each other, the little science muse in the back of your mind begins to ask, who would win? What if I changed up the pitchers? Does the batting order matter? What if they played at home instead of away?

This incessant wondering is the genesis of all the knowledge that our species has accumulated and labeled “science.”  And so, to commemorate Sagan’s birthday, and the Cubs win this season, I’d like to look back at what we knew of the world the last time the Cubs won the World Series, 108 years ago, a time well within the possible span of a human life.  The year is 1908…

The title page of Einstein's PhD Thesis.

The title page of Einstein’s PhD Thesis.

In 1908, a young physicist named Albert Einstein, 3 years out from his college degree and after a multi-year stint working as a clerk in the Swiss Patent Office, got his first job as a professor, at the University of Bern. This era was a time in the history of physics where scientists were trying to understand the fundamental structure of matter. Einstein’s PhD thesis was titled, “A New Determination of Molecular Dimensions.” Despite the fact that he could not find a job as a faculty member in the years after he graduated, Einstein worked dutifully at the Patent Office, and did physics “in his spare time.” During 1905, he wrote a handful of transformative papers that would change physics forever. Like his PhD work, some of those were about the invisible structure of matter on the tiniest scales. One explained an interaction between light and matter known as the “photoelectric effect,” which would be the work for which he would win the Nobel Prize in 1921. Physicists had for sometime known that some materials, when you shone a light on them, generated electric current. Einstein was the first person to be able to explain the effect by treating light as if it were little baseballs (Go, Cubs! Go!) that were colliding with electrons and knocking them off of the material. Today we use that technology for devices like infrared remote controls to turn your TV on and off!  By the time Einstein became a professor, he was thinking about new and different things that had caught his attention, sorting out some new ideas about gravity that would, after an additional seven years of work become known as General Relativity.

(Top) Marie Curie in her laboratory. (Bottom) Curie's business card from the Sorbonne. [Image: Musee Curie]

(Top) Marie Curie in her laboratory. (Bottom) Curie’s business card from the Sorbonne. [Image: Musee Curie]

Other physicists were hard at work exploring other aspects of the properties of matter. In 1908, already having earned her first Nobel Prize (in 1903), Marie Curie became the first female professor ever at the Sorbonne in Paris. Her 1903 Nobel Prize in physics was for her work in the characterization of radioactive materials. She and her collaborators were not only trying to understand the nature of radiation and the properties of radioactive materials, but were discovering many of them for the first time. Today, we look at a periodic table of the elements and there are no gaps, but in 1908 there were. Curie and her colleagues discovered radium and polonium. They also discovered that some previously known elements, like thorium, were radioactive and we hadn’t known it. Before this pioneering work, the world knew nothing of radioactivity. At this time, the dangers of radiation were unknown. Curie for years exposed herself to radiation from samples in her laboratory; today, many of her notebooks are still too radioactive to be handled safely without protective equipment. In 1934, Curie died of aplastic anemia, a blood disease brought on by radiation exposure whereby your body cannot make mature blood cells.

We think a great deal of Curie’s exposure to radiation came not just from carrying radioactive samples around in her pockets (something that today we know is a bad idea), but also exposure from a new technology that she was a proponent of: medical x-rays. During World War I she developed, built, and fielded mobile x-ray units to be used by medical professionals in field hospitals. These units became known as petites Curies (“Little Curies”).

Orville Wright (R) and Lt. Thomas Selfridge (L) in the Wright Flyer, just before take off at Fort Myer. [Image: Wright Brothers Aeroplane Co]

Orville Wright (R) and Lt. Thomas Selfridge (L) in the Wright Flyer, just before take off at Fort Myer. [Image: Wright Brothers Aeroplane Co]

There were other technological advances being introduced to the world in 1908.  That year, the world was still becoming acquainted with the notion of flying machines. The Wright Brothers had successfully demonstrated a powered flying machine at Kitty Hawk in 1903, but in May of 1908, for the first time ever, a passenger was carried aloft when Charlie Furnas flew with Wilbur Wright over the Kill Devil Hills in North Carolina. Just as with Curie, the Wrights were in unexplored territory, learning about the art and science of flying for the first time. Dangers and unexpected events abounded — the Wright Flyer experienced a crash late in 1908 after a propellor broke during a demonstration for the military at Fort Myer. Orville Wright was seriously injured, but his passenger, Lieutenant Thomas Selfridge, sustained a serious skull injury and died 3 hours after the crash: the first person to perish in the crash of a self-powered aircraft.

(L) The 60-inch Telescope at Mount Wilson. (R) A young Harlow Shapley. [Images: Mt. Wilson Observatory]

(L) The 60-inch Telescope at Mount Wilson. (R) A young Harlow Shapley. [Images: Mt. Wilson Observatory]

On the opposite coast of the United States, also in 1908, the largest telescope in the world was completed on Mount Wilson, outside of Los Angeles: the 60-inch Reflector, built by George Ellery Hale. The 60-inch was built in an era when astronomers had discovered that building bigger and bigger telescopes enabled them to see deeper into the Cosmos in an effort to understand the size and shape of the Universe and our place within it. One of the biggest discoveries made with the 60-inch was still ten years away — astronomer Harlow Shapley would use the great machine to measure the distances to globular clusters near the Milky Way and discover that the Sun did not lie at the center of the galaxy(see Shapley’s paper here); today we know the Sun orbits the Milky Way some 25,000 light yeas away from the center.

The nature of the Milky Way was still, at that time, a matter of intense debate among astronomers. Some thought the Milky Way was the entire Universe. Others argued that some of the fuzzy nebulae that could be seen with telescopes were in fact “island universes” — distant galaxies not unlike the Milky Way itself.  The problem was there was no good way to measure distances. But 1908 saw a breakthrough that would give astronomers the ability to measure vast distances across the Cosmos when astronomer Henrietta Swan Leavitt published her observation that there was a pattern in how some stars changed their brightness. These were the first Cepheid variables, and by 1912 Leavitt had shown how to measure the distance to them by simply observing how bright they appeared in a telescope. A decade and a half later, in 1924, Edwin Hubble would use Leavitt’s discovery to measure the distance to the Andromeda Nebula (M31), clearly demonstrating that the Universe was far larger than astronomers had ever imagined and that the Milky Way was not, in fact, the only galaxy in the Cosmos. By the end of the 1920’s, Hubble and Milton Humason would use Leavitt’s discovery to demonstrate the expansion of the Universe, the first hint of what is today known as Big Bang Cosmology.

(L) Leavitt at her desk in the Harvard College Observatory. (R) The Magellanic Clouds, which Leavitt's initial work was based on, framed between telescopes at the Parnal Observatory in Chile. [Images: Wikimedia Commons]

(L) Leavitt at her desk in the Harvard College Observatory. (R) The Magellanic Clouds, which Leavitt’s initial work was based on, framed between telescopes at the Parnal Observatory in Chile. [Images: Wikimedia Commons]

Today, it is 108 years later. When I reflect on these items of historical note, I am struck by two things. First, it is almost stupefying how quickly our understanding of the workings of the world has evolved. It really wasn’t that long ago — barely more than the common span of a human life — that we didn’t know how to fly and we didn’t know that the Cosmos was ginormous beyond imagining. The pace of discovery continues to this day, dizzying and almost impossible to keep up with. The second thing that is amazing to me is how quickly we disperse and integrate new discoveries into the collective memory of our society. Flying is no longer a novelty; it is almost as common and going out and getting in a car. Large reflecting telescopes capable of making scientific measurements are in the hands of ordinary citizens like you and me, gathering starlight every night in backyards around the world. Most people know that the Milky Way is not the only galaxy in the Cosmos, and that radioactive materials should not be carried around in your pocket.

It is a testament to our ability to collect and disperse knowledge to all the far flung corners of our planet and civilization. In a world faced by daunting challenges, in a society in a tumultuous struggle to rise above its own darker tendencies, it is a great encouragement to me that the fruits of our knowledge and intellect are so readily shared and accessible. When the challenges facing the world seem to me too daunting to overcome, I often retreat to listen to Carl’s sonorous and poetic view of our history and destiny (perhaps most remarkably captured in his musings on the Pale Blue Dot). He was well aware of the problems we faced, but always seems to me to promote a never ending optimism that we have the power to save ourselves– through the gentle and courageous application of intellect tempered with compassion.  It seems today to be a good message.

Happy Birthday, Carl.

And Go Cubs, Go.

cubswinwrigley

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Gravity 9: The Evolving Universe

by Shane L. Larson

Of all the fundamental forces in Nature, gravity is the weakest. What do we mean by that? Let’s forego our usual thought experiments, and do something real to demonstrate this idea.

pizzaFirst, go eat a piece of pizza (or any other food you enjoy). This is the process by which you accumulate the eenrgy needed to make your body go. Without pizza, you wouldn’t be able to do anything.  Second, go stand in the middle of the room (where you won’t hurt yourself) and jump straight up in the air, as high as you can.

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

Energy from pizza, gives me the power to defy the gravitational pull of the entire planet.

What happened? Since I’m pretty sure most of you reading this aren’t superheroes and can’t fly, you probably ascended up in the air a bit, and then came back down to the floor. It’s an everyday sort of thing, completely ordinary. But this is science, and there are remarkable and deep truths hiding in the simplest of circumstances. So consider this:

Using some simple chemical energy, which your body gleaned by breaking down some food you ate, you were able to (momentarily) overcome the gravitational pull of the ENTIRE EARTH.

This is what we mean when we say gravity is weak. But despite this fact, it is fundamentally the most important force of Nature if we want to think about the Cosmos as a whole. It has no competitor on the largest scales imaginable, meaning that even with its weak ability, gravity is able to change the Cosmos over the long, inexorable flow of time. It made sense that general relativity could and should be used to consider the past, present and future of the Universe itself.

The night sky over the Pando Forest in central Utah. Pando is an 80,000 year old aspen grove -- it has seen almost 30 million nights like this one, but very little has changed. The constellations change over thousands of years, but the sky is still full of stars, and the Milky Way still arches over the sky, giving the impression that the Universe is unchanging. [Image: Shane L. Larson]

The night sky over the Pando Forest in central Utah. Pando is an 80,000 year old aspen grove — it has seen almost 30 million nights like this one, but very little has changed. The constellations change over thousands of years, but the sky is still full of stars, and the Milky Way still arches over the sky, giving the impression that the Universe is unchanging. [Image: Shane L. Larson]

In 1915, when Einstein first presented general relativity to the Prussian Academy of Sciences, there was precious little we knew about the Universe, though perhaps we didn’t realize it at the time. The only objects outside the solar system that we knew a lot about were stars, and many scientists (including Einstein) supposed the Universe was comprised entirely of stars. Einstein himself made one of the first attempts to use general relativity to describe the Universe. He considered the case where the Universe was uniformly filled by stars, and found a result that disturbed him — no matter what he tried, general relativity predicted the Universe would collapse. To counteract this, Einstein modified general relativity through the introduction of a “Cosmological Constant” that made the Universe slightly repulsive. The result was precisely what Einstein hoped to find, what he and most scientists thought the Universe was: static, unchanging in time. But great changes were afoot, being driven by our ability to see the Universe better than ever before.

Henrietta Swan Leavitt, in her office at the Harvard College Observatory. She made one of the most important discoveries in the history of astronomy: how to measure distances to a common type of star, known as a Cepheid variable.

Henrietta Swan Leavitt, in her office at the Harvard College Observatory. She made one of the most important discoveries in the history of astronomy: how to measure distances to a common type of star, known as a Cepheid variable.

In 1915, the largest telescope of the day was the 60-inch reflector on Mount Wilson, though it would be eclipsed two years later by the 100-inch Hooker Telescope, also on Mount Wilson. Enormous telescopes such as these were enabling us to probe the size of the Cosmos for the first time. The key to making those measurements was discovered by a pioneering astronomer at the Harvard College Observatory, Henrietta Swan Leavitt.

Delta Cephei is a naked eye star, in the lower corner of the constellation of Cepheus ("The King").

Delta Cephei is a naked eye star, in the lower corner of the constellation of Cepheus.

Leavitt was studying a class of stars known as Cepheid variables. Named for the archetype, delta Cephei, these stars are “radial pulsators” — they grow and shrink over time in a regular pattern over the course of many days. The observational consequence, if you are watching, is the brightness and the temperature the star changes. What Leavitt discovered was a regular pattern between the time it took a Cepheid star to change its appearance (its “period”), and its true brightness (its “luminosity”).

The brightness of Cepheid variables goes up and down over the course of many days. The curve here is for Delta Cephei, which changes brightness every 5.4 days. (TOP) The observed change in brightness is a direct result of the stars size pulsating in time.

The brightness of Cepheid variables goes up and down over the course of many days. The curve here is for Delta Cephei, which changes brightness every 5.4 days. (TOP) The observed change in brightness is a direct result of the stars size pulsating in time.

How does that help you measure distances? Let’s imagine a simple example here on Earth. Suppose you have a 100 Watt lightbulb and a 10 Watt lightbulb side by side.  The 100 Watt bulb looks brighter — way brighter. This is the intrinsic brightness of the bulb — it is clearly putting out more energy than its smaller, 10 Watt companion, which you can easily discern because they are right next to each other.  This intrinsic brightness at a known fixed distance is what astronomers call absolute luminosity or absolute magnitude.

Is there any way to make the 100 Watt bulb look dimmer? Yes! You can move it farther away — the farther you move it, the dimmer it appears. In fact, you could move it so far away that the 10 Watt bulb you leave behind looks brighter! By a similar token, you can make it look even brighter by moving it closer! How bright something looks when you look at it is what astronomers call apparent luminosity or apparent magnitude.

Disentangling distance and brightness is one of the most difficult problems in astronomy. Observing how bright an object is depends on two things: its intrinsic brightness, and its distance. (TOP) A bright light and a dim light are side by side at a fixed distance; one is obviously brighter than the other. (BOTTOM) If the brighter light is farther away, it can look dimmer than the closer light!

Disentangling distance and brightness is one of the most difficult problems in astronomy. Observing how bright an object is depends on two things: its intrinsic brightness, and its distance. (TOP) A bright light and a dim light are side by side at a fixed distance; one is obviously brighter than the other. (BOTTOM) If the brighter light is farther away, it can look dimmer than the closer light!

By comparing apparent brightness (how bright something looks in a telescope) to absolute brightness (how bright something would look from a fixed distance away) you can measure distance. The biggest problem in astronomy is we don’t know what the absolute brightness of objects are.

What Leavitt discovered was if you measure how long it takes a Cepheid to change its brightness, then you know its absolute brightness. Comparing that to what you see in the telescope then let’s you calculate the distance to the star! This discovery was a watershed, arguably the most important discovery in modern astronomy: Leavitt showed us how to use telescopes and clocks to lay a ruler down on the Universe. Leavitt died of cancer at the age of 53, in 1921.

Harlow Shapley.

Harlow Shapley.

Despite her untimely death, astronomers rapidly understood the power of her discovery, and began to use it to probe the size of the Cosmos. Already by 1920 Harlow Shapley had used the Mount Wilson 60-inch telescope to measure Cepheids in the globular clusters in the Milky Way. What he discovered was that the globular clusters were not centered on the Earth, as had long been assumed, but rather at some point more than 20,000 lightyears away. Shapley argued quite reasonably that the globular clusters are probably orbiting the center of the galaxy. This was the first indication that the Copernican principle extended far beyond the Solar System.

In 1924, Edwin Hubble, who Shapley had hired at Mount Wilson Observatory, made a stunning announcement — he had measured Cepheid variables in the Andromeda Nebula, and it was far away. At 2.5 million lightyears away, the Andromeda Nebula was the farthest object astronomers had ever measured the distance to. In fact, it wasn’t a nebula at all — it was a galaxy. Here, for the first time, some of the long held, cherished beliefs about Cosmology that were prevalent when Einstein introduced general relativity began to unravel. (Historical Note: Hubble’s original distance to the Andromeda Galaxy was only 1.5 million lightyears. Why? Because there are two different kinds of Cepheids, both of which can be used to measure distances, but calibrated differently! Astronomers didn’t know that at the time, so Hubble was mixing and matching unknowingly. Eventually we learned more about the Cosmos and arrived at the current known distance — science is always on the move.)

The Hubble Ultra Deep Field (UDF), showing what is unseen but can be found if you stare at an empty part of the sky for long enough.

The Hubble Ultra Deep Field (UDF), showing what can be found if you stare at an “empty” part of the sky for long enough. Virtually every object in this image is a distant galaxy.

The Universe was not full of stars…. it was full of galaxies, and those galaxies were further away than we had ever imagined. This was a dramatic discovery that shook astronomers deeply. But it was only the beginning. A scant five years later, Milton Humason and Hubble, using the 100-inch telescope at Mount Wilson, made another astonishing discovery: every galaxy they looked at was receeding away from the Milky Way, in every direction. Furthermore, the farther away the galaxy was, the faster it was receding from us.  This result is now known as “Hubble’s Law.” Humason and Hubble had stumbled on one of the great secrets Nature — the Universe was not static, as a casual comparison of the night sky from one year to the next may suggest.  But what was going on? Why were all the galaxies flying away from us, in every direction we looked? This would seem to contradict the Copernican principle that we weren’t the center of everything!

(L) Alexander Friedmann. (R) Georges Lemaître.

(L) Alexander Friedmann. (R) Georges Lemaître.

As it turns out, the answer was already in hand. It had been discovered several years before Humason and Hubble by two scientists who had sought to use general relativity to describe the Cosmos: Alexander Friedmann, a Russian physicist, and Georges Lemaître, a Belgian priest. Friedmann had used general relativity to describe a Universe that was homogeneous (the same everywhere) and isotropic (looks the same in every direction). The “Friedmann Equations,” as they are now known, describe the evolution of such a Universe as a function of time. Lemaître derived the same result in 1927, two years after Friedmann’s death. In the mid 1930’s, American physicist H. P. Robertson and UK physicist A. G. Walker showed that the only solution in general relativity describing a homogeneous and isotropic Universe as that of Friedmann and Lemaître. This is now called the FLRW (“Friedmann-Lemaître-Robertson-Walker”) Cosmology.

What the FLRW cosmology tells us is that the galaxies aren’t really flying apart from one another — if the Universe is homogeneous and isotropic, then spacetime itself is changing, stretching and deforming. The reason the galaxies are receding from one another is the spacetime between them is expanding — the Universe is getting larger, expanding all the time.

Imagine the galaxies floating in spacetime, unmoving with respect to one anther (they are stapled down to their location in spacetime). General relativity predicts that the galaxies don't move, but that spacetime itself expands, it stretches, so the distance you measure between galaxies increases.

Imagine the galaxies floating in spacetime, unmoving with respect to one anther (they are stapled down to their location in spacetime). General relativity predicts that the galaxies don’t move, but that spacetime itself expands, it stretches, so the distance you measure between galaxies increases.

Lemaître was the first person to think differently about this problem. He had the presence of mind to ask, “We see the Universe is expanding, but what if I run time backward? What did the Universe look like in the past?” In 1931, he argued that the expansion seen in every direction suggested that the Universe had expanded from some initial point, which he called the “primeval atom.” If today we see everything expanding away, and you look backward in time, it must have all been much more compressed and compact, a state which would have made it hot, and dense. Lemaître didn’t know what might have initially caused the expansion of this primeval atom into the Cosmos we see today, but he did not see that as a reason to suppose the idea was invalid.

Lemaître with Einstein in California, 1933.

Lemaître with Einstein in California, 1933.

Change in science is hard, especially when data is new and our ideas are undergoing a dramatic evolution from past modicums of thought. Einstein is widely known to have critically panned both Friedmann’s and Lemaître’s work before the discovery of the expansion, still believing in the notion of a static Universe. Once the scientific community had come to understand and accept the expansion data, it required another great leap of faith to contemplate Lemaître’s notion of a hot dense initial state. Einstein again was skeptical, as was Arthur Stanley Eddington. For more than a decade, the arguments about the idea raged, and in 1949 during a BBC radio broadcast, astronomer Fred Hoyle coined the term by which Lemaître’s “primeval atom” idea would forever be known as: the Big Bang.

All ideas in science stand on equal ground — they are valid for consideration until they are proven wrong by observations. If the Universe did indeed begin in a Big Bang, then the obvious question to ask is what signatures of that dramatic event would be observable today? As it turns out, there are many observational consequences of the Big Bang, and they all have been observed and measured by astronomers, lending confidence to Lemaître’s initial insight.  This will be the topic of our next chat.

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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.

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.

Gravity 04: Testing the New Gravity

by Shane L. Larson

In the world of artistic painting, connoisseurs have a word: pentimento. It is the revelation of something the artist hid from us.  There are many reasons why changes to a composition may come to light. Sometimes it is because as paint ages, it becomes more translucent, revealing a previous facial expression or position of a hand. Sometimes, close and careful study reveals that a slight alteration was made to disguise a mistake or a shift in ideas about the composition. And still sometimes technology can be used to see through the painting to what lies beneath — the artist’s original sketch or painting that was altered in the final production

nakedCookieJarThe word pentimento is an Italian word, meaning “repentance.” Its use in the context of art is an implication that the artist has been caught red-handed, changing their mind about a particular composition! The idea of repentance and being caught red-handed carries a certain amount of emotional baggage in our culture; I suspect it is ingrained in us at an early age, when our parents catch us doing something we’d rather them not know — like stealing cookies from the cookie jar, or seeing what we look like if we cut our eyelashes off, or getting caught reading Scientific American under the covers with a flashlight (I just made all of those things up — my parents never caught me doing any of those!).

But science is different. Part of the game is about being wrong and getting caught. There is no shame in changing your mind, no repentance for previous incorrect speculations about the nature of the Cosmos. You make up cool ideas, that you present to the world not as art, but as proposed mathematical explanations for how the Cosmos works. Any crazy idea is fair game, with one requirement: you have to also suggest a way for us to do an experiment to test if your crazy idea is right! If it’s right, we go think of new experiments; if it is wrong, then we look at your crazy idea and figure out which crazy bits of it aren’t quite right. We make some changes, turning it into a new crazy idea, and then go conduct another test.

Science is always these two parts — the first part, describing the world, is called “theory”; the second part, testing your ideas, is called “experiment.”

The leading header of the paper where Einstein introduced general relativity, his writeup of the presentation he made to the Prussian Academy of Sciences in November, 1915.

The leading header of the paper where Einstein introduced general relativity, his writeup of the presentation he made to the Prussian Academy of Sciences in November, 1915.

Albert Einstein introduced General Relativity to the world in a presentation to the Prussian Academy of Sciences in November of 1915; his written summary of that presentation may be read (in German) online: Die Feldgleichungen der Gravitation (“The field equations of gravitation”).  If you look at that paper, you will see it looks a lot like your introductory physics textbook looked — lots of mathematical symbols and equations. What does it all mean?  This is the “theory” side of gravity, where we imagine the Laws of Nature that describe gravity — in this case, the idea that gravity can be explained as the curvature of spacetime.

General relativity was a tremendous step forward in our understanding of gravity — it was consistent with special relativity and extended our understanding into physical regimes that Newtonian gravity could not address. But at the same time, especially early on, very little was actually known about GR. It was mathematically difficult to work with (in the lingo of physics, it is “non-linear”), and in 1915 there were no known astrophysical systems that absolutely required general relativity to describe them. Einstein knew it was fine to write down new and possibly crazy ideas about the Universe, but the real task was to decide if there were ways to test those ideas. Were there some observations that could be made and compared against the predictions of general relativity? Observations that confirmed the predictions of general relativity would demonstrate its viability as a description of gravity. There have been many tests of general relativity discovered over the course of the past 100 years, but Einstein himself set the stage for testing his ideas by proposing three immediate tests that scientists could put their efforts into.

The first test was one that Einstein used to convince himself that general relativity was going in the right direction. In 1859 Urbain Le Verrier had noticed something odd about Mercury’s orbit.  Like all planets, Mercury has an elliptical orbit — it is a slightly squashed circle, closer to the Sun on one end than on the other. The point where the orbit comes closest to the sun is called perihelion, and it lies in a particular direction. Over time, the direction to perihelion changes — the orbit of Mercury pivots slowly, in a dance that astronomers call precession.

The point of closest approach to the Sun is called perihelion, and occurs in a certain direction (green dashed lines). Over time, an orbit pivots slowly -- it precesses -- changing the direction to perihelion.

The point of closest approach to the Sun is called perihelion, and occurs in a certain direction (green dashed lines). Over time, an orbit pivots slowly — it precesses — changing the direction to perihelion.

Some precession is expected, because the Sun is not a perfect sphere (it is actually a bit squashed, fatter at the equator because it is spinning), but Le Verrier had looked at 150 years of observations of Mercury’s orbit and discovered the perihelion was shifting by an anomalously large amount — 43 arcseconds every century! That is to say, the angle of Mercury’s orbit was pivoting by an extra angle over the course of 100 years, equivalent to 43 arcseconds. How big is 43 arcseconds? Take a quarter and put it 382 feet away (a bit longer than a standard US football field) — 43 arcseconds is the angle between pointing from one side of the quarter to the other side of the quarter. It is a VERY small angle! But astronomers had detected this small change in Mercury’s behaviour through diligent and careful observations of the Cosmos.

43 arcseconds is about the apparent visual size of a US quarter when viewed from a distance of 382 feet (116.4 meters), slightly farther than the length of a regulation NFL football field.

43 arcseconds is about the apparent visual size of a US quarter when viewed from a distance of 382 feet (116.4 meters), slightly farther than the length of a regulation NFL football field.

When he was developing his new way of thinking about gravity, Einstein realized that the anomalous precession might be described by general relativity. He calculated that general relativity predicts an extra 43 arcseconds in perihelion precession for Mercury, the exact amount observed by astronomers. This not only resolved a 50 year old mystery in astronomy, but firmly convinced Einstein he was on the right track.

The second test is arguably one of the most famous tests in the history of gravity, and its success catapulted Einstein into the public eye, making him a world-wide celebrity. One of the central features of general relativity is that everything experiences gravity — everything “falls.” This is certainly true for things like rocks and slurpees, but Einstein also realized it should apply to light. Light, like all freely moving objects, wants to travel in a straight line, and generally it does so. This is one of the features that makes it such a useful messenger in astronomy: if you receive some light on Earth, and look back along the direction the light came from, you should be looking at the object that generated the light!

[A] When viewed alone in the sky, two stars (yellow and red) have a well defined separation, defined by the direction you have to point to look directly at them. [B] They appear separated, and that amount can be measured. [C] During a total solar eclipse, light from the yellow star passes near the Sun and is bent. Looking back along the line of sight, the yellow star appears to be closer to the red star than it was when the Sun was not in the way. [D] The deflection of starlight is the amount the position of the yellow star appears to move on the sky.

[A] When viewed alone in the sky, two stars (yellow and red) have a well defined separation, defined by the direction you have to point to look directly at them. [B] They appear separated, and that amount can be measured. [C] During a total solar eclipse, light from the yellow star passes near the Sun and is bent. Looking back along the line of sight, the yellow star appears to be closer to the red star than it was when the Sun was not in the way. [D] The deflection of starlight is the amount the position of the yellow star appears to move on the sky.

If on its long journey through the Cosmos a little bit of starlight (called a “photon”) passes near an object with strong gravity, the gravity will bend the path the light travels on. This is exactly what would happen to any massive object. If an asteroid is flying through deep space, it will travel in a straight line. If it strays too close to an object with strong gravity, like Jupiter or the Sun, the gravity deflects that asteroid and it ends up travelling in a different direction.

One of Eddington's images recorded during the 1919 Eclipse. The small horizontal hash lines mark the stars that would be measured.

One of Eddington’s images recorded during the 1919 Eclipse. The small horizontal hash lines mark the stars that would be measured.

So how can you measure the bending of light predicted by general relativity? The trick with light is if you want to see the deflection, it has to pass through a strong gravitational field. Einstein suggested you could look for the deflection of starlight during a total solar eclipse. The gravity of the Sun is strong enough to bend the path of light by a measurable amount; during an eclipse when the Moon blocks most of the light from the Sun, the stars near the edge of the Sun’s disk should be visible.

The first realization of this test was organized in the United Kingdom by the Astronomer Royal, Frank Watson Dyson, and Arthur Stanley Eddington. Eddington led an expedition to the island of Príncipe, off the west coast of Africa, to observe the total solar eclipse on 29 May 1919. Eddington imaged several stars around the eclipse, and confirmed general relativity’s predictions. These measurements are difficult to make, and their accuracy has often been debated, but the experiment has been repeated during many eclipses since then, continuing to confirm the predictions of general relativity.

The leading header of the paper summarizing Eddington's measurements to confirm the deflection of starlight.

The leading header of the paper summarizing Eddington’s measurements to confirm the deflection of starlight.

The last proposed experiment is called the gravitational redshift. Think about tossing a rock up in the air. What happens? When the rock leaves your hand, it has some initial amount of energy that physicists call “kinetic energy” — energy associated with motion. As it climbs, it slows down. It looses kinetic energy, expending it to fight upward against gravity. Einstein argued based on the Equivalence Principle that a photon must also expend energy to climb upward against a gravitational field.

Photons travelling upward in a gravitational field lose energy, becoming redder. Photons travelling down gain energy, becoming bluer.

Photons travelling upward in a gravitational field lose energy, becoming redder. Photons travelling down gain energy, becoming bluer.

But photons — all photons — propagate at the speed of light! The notion of “kinetic energy” as it applies to objects like rocks is hard to extend to photons. But the Equivalence Principle demands that a photon climbing up through a gravitational field must give up energy. How? It can change its color. Photon energy is directly related to its color — blue light is more energetic than green light which is more energetic than red light.  A photon can give up energy as it climbs upward against gravity by changing its color, shifting from bluer light toward redder light.

Measuring the change in color of light is easy to do, but notoriously difficult to attribute to general relativity because all kinds of things change the color of light! But in 1959, Robert Pound and Glen Rebka successfully measured the gravitational redshift at the Jefferson Laboratory at Harvard.

Pound and Rebka’s triumphant measurement concluded a more than 40 year effort to complete the three classical tests proposed by Einstein in 1915. Since those early days, many other tests of general relativity have been suggested, and measured. To date, no experiment has uncovered any chinks or holes in the theory. If there had been, then general relativity would have been relegated to the trash bin of Cool Ideas that Failed, and we would have moved onward to look for a new understanding of gravity. Instead we find ourselves in that happy frame of mind where we use general relativity to describe the Cosmos with swagger and aplomb. There may yet be another revolution in our understanding of gravity, but if there is, I am confident that it will have to successfully include both general relativity and Newtonian gravity as parts of its core infrastructure.

In the end, there is a bit of pentimento in the game of science, but it is not on our part — it is Nature’s. General relativity is the latest in a series of tools that we have developed and used to peer closely at Nature. Slowly — ever so slowly — we are seeing through the paint Nature has clothed herself in. The secrets of the Cosmos are becoming slowly transparent, revealing the clockwork wonder of the Universe that hides beneath.

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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.

Gravity 1: Seeing the Invisible

by Shane L. Larson

General Relativity is only the latest refinement of our ever growing understanding of gravity. Most of us become aware of gravity at a very young age. It is a playmate when we throw balls, an accomplice when we knock our unwanted food off the table, and our Nemesis as we learn to stand up and walk. All things being equal, gravity is a source of much mayhem when we are children, but hidden in the chaos we learn a few things, and we learn them deeply. When we drop things, they fall. When we jump in the air, we always come back down. It is such a pervasive part of our lives, that we seldom give it a second thought. Once you start school, you learn that gravity is a thing, and that thing keeps you on the floor, makes rain fall from the sky, and makes planets go around the Sun.  Gravity is something you learn about in science class. But why is it a part of science class, when you learned about it as a toddler?

(TOP) Most of us develop an intimate relationship with gravity at a very young age. (BOTTOM) Whether we know it or not, gravity impacts all aspects of our every day life in subtle ways.

(TOP) Most of us develop an intimate relationship with gravity at a very young age. (BOTTOM) Whether we know it or not, gravity impacts all aspects of our every day life in subtle ways.

The job of a scientist (and a toddler) is to look at the world around us, take note of those “obvious” things that we don’t even give a second thought to, and ask “why is the world that way?” The answers to that question enable us to harness Nature by predicting the future. If I understand gravity, I can figure out how strong a building needs to be without tipping over (like the Leaning Tower of Pisa), I can figure out how much pressure a water tower will provide for a city, or I can figure out how big to make an airplane wing so it can fly.  There is other physics to be sure in all of these, but gravity is at the heart of it all, just as we learned as children.

The authors of our fundamental thinking about gravity. (L) Isaac Newton, who developed the Universal Law of Gravitation and (R) Albert Einstein, who developed General Relativity.

The authors of our fundamental thinking about gravity. (L) Isaac Newton, who developed the Universal Law of Gravitation and (R) Albert Einstein, who developed General Relativity.

So how do we think about gravity? After all, it is not like an orange or a Lego brick — it’s not something tangible that you can pick up. In fact, if anything, it is totally invisible! The discovery of the invisible and how to talk about it is still one of the greatest feats of the human imagination. The first person to do this for gravity, was Isaac Newton. Fundamentally, Newton put us on the path to describing gravity using mathematics, the language of science. He first wrote down the Universal Law of Gravitation in his 1687  book, the Principia, along with all the math you needed to work with the Universal Law (read: calculus). Einstein refined and extended our understanding of gravity by writing down general relativity using a new mathematical approach: curvature and tensor calculus.

gravityEquations

But learning how gravity works in the Cosmos from mathematics can take years of practice and patient study. Fortunately, we can develop some intuition about how gravity works by learning to draw some simple pictures.

Physicists describe the long range effect of gravity using the concept of a “force field,” or simply a “field.” As is often the case with spoken language, scientists adopt common words to mean very specific things that don’t always jive with what the rest of us think the word means. What do you think of when I say “field?” If you’re a country kid like me, you may imagine a vast expanse of rolling hillsides in eastern Oregon, stalks of wheat heavy with ripening grain rippling as the wind blows across the “field.” Others of you may imagine a late July afternoon, the hot sun shining down on the bleachers in Wrigley Field as the Cubs once again try to chalk up a win in the run to the pennant. Neither of these examples is what a scientist means by “field,” but they both have an important element to the scientific definition — big, open spaces.

Some other kinds of fields.

Some other kinds of fields.

An important part of understanding gravity is recognizing that no matter where you are in space, if there is a source of gravity somewhere (say a planet, or a star), then you feel the tug of that gravity. Gravity fills all of space. That simple fact leads to the concept of a “field” in physics. We are going to draw pictures of fields, but there is a robust and well understood mathematical treatment of fields that will give you the same intuition (and more) as our simple pictorial model.

So how do we draw a picture of the “gravitational field?” The rules are:

  • Draw arrows to represent the “gravitational force.” Those arrows fill all of space, and point toward the source of gravity (the direction that gravity is trying to pull you); they are usually called “lines of force.”
  • Big, massive objects have more gravity than small objects, so they have more arrows pointing toward them — they exert more gravitational force on their surroundings.
  • The gravity any object experiences is understood by how closely packed the field lines are in the vicinity. Lots of field lines near you equates with stronger gravity in your vicinity.

Demonstration of the drawing of gravitational "fields." [TOP] The field lines (lines of force) point toward the mass creating the gravity. The number of field lines depends on the mass of the object; more mass, more field lines. [BOTTOM] What you feel in terms of gravitational forces depends on how many field lines are around you. The gravitational force felt far away from the source of gravity is weaker, evidenced in our picture view by fewer field lines.

Demonstration of the drawing of gravitational “fields.” [TOP] The field lines (lines of force) point toward the mass creating the gravity. The number of field lines depends on the mass of the object; more mass, more field lines. [BOTTOM] What you feel in terms of gravitational forces depends on how many field lines are around you. The gravitational force felt far away from the source of gravity is weaker, evidenced in our picture view by fewer field lines.

So how do we use this pictorial approach to gravity in practice? Let’s imagine a trip to one of the most picturesque destinations in our solar system: Jupiter. Spacecraft from Earth have visited Jupiter nine times so far.  They have returned stunning pictures and made astonishing discoveries about Jupiter and it’s ragtag group of moons.

The planet itself is enormous, comprised mostly of gas surrounding a small rocky core. Deep beneath the clouds the pressure and temperature soar, making Jupiter glow in the infrared, cloaked in the light of its own inner heat.

On the top of the clouds, an enormous cyclonic storm has roiled and churned for at least the last 400 years, sometimes growing to three times the size of the Earth. We call it “The Great Red Spot.”

Among Jupiter’s entourage of moons is a wild and unpredictable world with volcanoes that spew molten sulfur 500 kilometers into space. This is the most volcanically active world we know, called Io.

In 1992, Comet Shoemaker-Levy 9 strayed too close to Jupiter and was torn apart into 22 fragments. In 1994, as we watched from the relative safety of Earth, each of those 22 chunks of rock and ice pummeled into Jupiter one after another.  Any one of them could have leveled our cuvilization; they burned and scarred the clouds of Jupiter, but over time even those marks faded into memory and Jupiter kept on about its business as if nothing had happened.

Wonders of the Jupiter system, all ultimately connected to Jupiter's strong gravity. (L to R) Jupiter glows in the infrared; the 400+ year old storm known as the Great Red Spot; the volcanic moon Io; the scars left by the impact of Comet Shoemaker-Levy 9, crushed by Jupiter's gravity.

Wonders of the Jupiter system, all ultimately connected to Jupiter’s strong gravity. (L to R) Jupiter glows in the infrared; the 400+ year old storm known as the Great Red Spot; the volcanic moon Io; the scars left by the impact of Comet Shoemaker-Levy 9, crushed by Jupiter’s gravity.

Each of these wonders, each of these  strange and wonderful things we have discovered at Jupiter, are a consequence of Jupiter’s enormous gravity.

Let’s draw the picture of Jupiter’s gravitational field. The number of field lines is related to the mass of the planet. Suppose we drew 10 lines to represent the gravity of the Earth. Jupiter is 318 times more massive than Earth, so we should draw 3180 lines to represent the gravitational field of Jupiter!  That’s too many to easily see, so let’s just think about Jupiter’s own gravity, and decide it can be represented by 8 lines.

The gravitational field fills all of space, so no matter where you are, you feel the tug of Jupiter pulling on you, from wherever you are, directly toward Jupiter. Far from the planet, the lines are more widely spaced, so gravity is weaker than it is down close to the planet where the lines are closer together.

Rodin's "The Thinker" is probably engaged in a gedanken experiment.

Rodin’s “The Thinker” is probably engaged in a gedanken experiment.

Now, let’s conduct a gedanken experiment — a thought experiment — together. This is a time honored method in theoretical physics to try and understand how the world works. The basic idea is this:

(0) Suppose you have some aspect of Nature you are trying to understand; in this case, the “field description” of gravity.

(1) Imagine a situation to which the law of physics should apply. This could be a situation that could legitimately be addressed in the laboratory with an experiment, given enough time and money, or it could be a physical situation that we can’t recreate but might encounter in Nature. This second case is the one we would like to consider, as it involves the gravitational field of an entire planet.

(2) Apply the law of physics to your situation, and examine all the possible outcomes that would result if you could actually do the experiment for real.

(3) Lastly, you examine the consequences of your gedanken experiment by asking legitimate questions and answering them. Do the predicted outcomes make sense? Do any of the outcomes violate the laws of physics? Are there observational consequences that we might be able to see that would confirm our gedanken experiment?

For our thought experiment, let’s imagine we had the ability to simply squeeze Jupiter and make it smaller. We don’t want to take any mass away, or add any mass to it, we simply want to squeeze it into a smaller, denser ball of stuff, and ask what happens to the gravitational field.

If we follow our rules for drawing fields: (1) The number of field lines won’t change, because the mass of Jupiter doesn’t change. (2) The field lines fill all of space. When we squeeze Jupiter smaller, the field lines in the picture already fill space far away from Jupiter, so we just need to extend down toward the new, smaller Jupiter.

jupiterFields

(L) Jupiter’s gravitational field is stronger near the surface, and weaker far away. (R) If I shrink Jupiter without changing its mass, the field stays the same far away, but it gets stronger at the surface!

Now we examine the consequences of our experiment. Far away from Jupiter, nothing has changed. The same number and spacing of field lines are present with the big or the small Jupiter. If you’re an astronaut, drifting aimlessly in orbit around Jupiter, nothing noticeable happens.  But in close, things are a bit different. In the case of the big Jupiter, if we hovered over the clouds we felt some pretty strong gravity. If we compare that to the case of hovering over the clouds of the new small Jupiter, we feel even stronger gravity! How do we know this? Because near the new small Jupiter, the field lines are closer together.

So what do we conclude from this? The “surface gravity” of an astronomical body depends on the compactness (or, more properly, the density) of the planet/star/thing in question. Far away from the astronomical body, the gravitational field depends only on the total mass of the object.

Can we observe these effects for real, somewhere in the Cosmos? Yes!

White dwarfs are the size of the Earth, but the mass of the Sun. The result is a huge gravity at the surface!

White dwarfs are the size of the Earth, but the mass of the Sun. The result is a huge gravity at the surface!

When a star like the Sun reaches the end of its life, it does not explode. Instead, it shrinks to a husk of its former self, a shriveled skeleton known as a white dwarf.  White dwarfs are about the size of Earth, but have the same mass as the Sun. We observe atoms moving in their atmospheres, just over the surface and find that the surface gravity is a staggering 10,000 times greater than the surface gravity of the Sun. By a similar token, many white dwarfs orbit companion stars, and some have been observed to have planets (perhaps long ago, and we just didn’t realize it), all of which are far from the white dwarf but careen happily along their orbits as if they were orbiting an ordinary, Sun-like star.

These observations agree handily with our gedanken experiment.  We used our pictorial model to deduce that if you squeeze an object smaller without changing its mass, the surface gravity changes, but the gravity far away does not!

The Cosmos, and our brains, have not let us down. We’ll put these ideas to the test again, as we delve into the development of General Relativity and encounter even stranger and denser objects — black holes.

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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

Gravity 0: Discovering Gravity

by Shane L. Larson

You and I live in the future. We are connected to each other in ways that would have stunned people who lived only a century ago. I had the good fortune growing up to know my great-grandmother, who lived to be 98 years old. My Grandma Dora was born in 1895, at a time before electricity and telephones and automobiles were commonplace. The mode of transportation when she was born was the horse and buggy, though steam had been harnessed and train lines were beginning to gird the world. The Wright Flyer would not make its first epic flight at Kitty Hawk until 1903, when Grandma Dora was 8 years old. But she lived to see humans sail the void of space, space shuttles ply the skies, and humans walk on the Moon. In just about 100 years, the span of a single human life, she saw the world change.

(L) My great-grandmother Dora [center] with her sisters Mary [left] and Arta [right] in the early 1900s. (R) Around this same time, the Wright Brothers made their historic flight at Kitty Hawk, in 1903.

(L) My great-grandmother Dora [center] with her sisters Mary [left] and Arta [right] in the early 1900s. (R) Around this same time, the Wright Brothers made their historic flight at Kitty Hawk, in 1903.

When she was just a girl, there was a young man living halfway around the world, in Bern, Switzerland. The Industrial Revolution was in full swing, and creative minds the world over were trying to imagine how to use technology and machines to change our lives, and how to patent those ideas and make money. Some of those attempts to capitalize on the rapidly evolving world wound their way through the Bern Patent Office (the Swiss Federal Institute of Intellectual Property) to the desk of Albert Einstein. For the young Einstein, a trained technical professional, the job at the patent office was just that — a job. He very much wanted to be a professor and work on science, so in the evenings he committed himself to physics the way some of us work day jobs but in the evenings work on writing novels (or blog posts about science). In 1905, those evening endeavours paid off when Einstein published four seminal papers that transformed his life, physics, and the world forever.

(L) Einstein when he was working at the Patent Office in Bern. (R) Einstein's living room, still preserved, in the first floor apartment where he worked on special relativity during his years at the Patent Office.

(L) Einstein when he was working at the Patent Office in Bern. (R) Einstein’s living room, still preserved, in the first floor apartment where he worked on special relativity during his years at the Patent Office.

Among those papers was the original paper to describe special relativity — the laws that govern physics at high speeds, approaching the speed of light. Nestled in that paper is one of the most important discoveries in physics and the one most germane to our story here:

Nothing can travel faster than the speed of light.

This was a stunning realization, because up to that point no one had ever really imagined that we couldn’t go faster than light. The speed of light had been measured famously by Danish astronomer Ole Romer in 1676 and by French physicist Hippolyte Louis Fizeau in 1849. But there had never been a reason to believe that the speed of light was the ultimate speed limit in the Cosmos.

Newton witnessed the falling of an apple when visiting his mother's farm, inspiring him to think about gravity. It almost certain is apocryphal that it hit him on the head! But art gives the story a certain reality!

Folklore is that Newton witnessed the falling of an apple when visiting his mother’s farm, inspiring him to think about gravity. It almost certain is apocryphal that it hit him on the head, but this was the beginning of the Universal Law of Gravitation, one of the most successful descriptions of Nature ever invented.

With Einstein’s realization, we began to examine the laws of physics that had been discovered up to that point, and we found a curious fact. Some of those laws, unbeknownst to us, had the secret about light hiding in them, like a pearl in an oyster.  Most notable among these were Maxwell’s Equations for Electrodynamics. Curiously, Newtonian Gravity did not have the ultimate speed limit. The classical Universal Law of Gravitation, which Newton had penned more than 200 years earlier, was built on the idea of instantaneous communication over any distance, an impossibility if there was a maximum speed of travel. Einstein recognized this and set about to resolve the issue. He would dedicate the next 10 years of his life to the endeavour. During those years, he would finally leave his job at the patent office for the life of an academic, holding professor positions at several universities around Europe. All the while, he worked steadfastly on merging gravity and special relativity.

This was not a simple matter of “imagining something new.” Newtonian gravity worked perfectly well in the solar system, where things moved slowly and gravity was weak. Einstein knew that whatever Nature was doing with gravity, it had to look like Newtonian Universal Gravity at slow speeds and in weak gravity, but not be confined by instantaneous propagation of signals. He went through a meticulous procession of thought experiments, explored new applications of mathematics (the language of science) and developed new intuitive ways of thinking about gravity. His long hours and years of brain-bending culminated in 1915 with his presentation of the Field Equations of General Relativity, now known as the Einstein Field Equations.

In 1902, Georges Méliès (L) created the film

In 1902, Georges Méliès (L) created the film “Le Voyage Dans La Lune” where an enormous cannon (C) was used to launch a space capsule carrying explorers to the Moon (R).

I think about this age of the world often, my thoughts fueled by memories of talking with my great-grandmother. What was the world like when the young Einstein was thinking about lightspeed and gravity?  It was an age of horse and buggy travel. What was the fastest people could imagine travelling in that era? In 1903 the great French director Georges Méliès told at tale of travelling to the Moon — “Le Voyage dans la Lune” — using a new technology called “moving pictures.” In that remarkable tale, he imagined a band of intrepid explorers attaining great speeds by being launched from an enormous cannon, still far slower than the speed of light.

The horse and buggy set the speed of life in those days. This is an ambulance for the Bellevue Hospital in New York in 1895, the year my grandmother was born.

The horse and buggy set the speed of life in those days. This is an ambulance for the Bellevue Hospital in New York in 1895, the year my grandmother was born.

The speed of life was slow in those days, far slower than the speed that Einstein was contemplating.  But still Einstein was able to apply his intellect to a question that perhaps seemed outrageous or unwarranted. At the time, the derivation of general relativity was mostly a curiosity, but today, a century later, it plays a central role in astrophysics, cosmology, and as it turns out, in your everyday lives!

Applications of general relativity, and the frontiers of general relativity in modern physics and astronomy. (TL) GPS system. (TR) Planetary orbits (LL) Black holes (LC) Wormholes (LR) Singularities.

Applications of general relativity, and the frontiers of general relativity in modern physics and astronomy. (TL) GPS system. (TR) Planetary orbits (LL) Black holes (LC) Wormholes (LR) Singularities.

In 2015 we are celebrating the Centennial of General Relativity. That means all your gravitational physicist friends will be all a-pitter-patter with excitement for the next 12 months, and impossible to quiet down about gravity at dinner parties.

On the off chance that you don’t have any gravitational physics friends (gasp!), for the next 13 weeks I’ll be exploring the landscape of general relativity right here at this blog. We’ll talk about how we think about gravity, the history of testing and understanding general relativity, modern observatories that are looking at the Universe with gravity instead of light, and some of the extreme predictions of general relativity — wormholes, black holes, and singularities.

My great-grandmother, Dora Larson.

My great-grandmother, Dora Larson.

My great grandmother passed away shortly after I went to graduate school, where I made gravity and general relativity my profession. In a time shorter than the span of her life, this little corner of physics had grown from the mind of a patent clerk into one of the most important aspects of modern astrophysics, at the frontiers of scientific research. Grandma Dora and I never got the chance to sit around and talk about black holes or the equivalence principle, but I often wonder what she would have thought of all the hoopla that gravity commands in modern life and modern science? What would she have seen, through eyes that saw the world grow up from horse drawn carts to space shuttles and GPS satellites?

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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).  This is the introductory post of the series. For the first time, I’m trying short 3.5 min videos with each post to capture the essential bits of each one. Here is the YouTube Playlist with all the videos (let me know how you like them — it’s an experiment!).

Links to the successive blog posts in this series are below for reference:

Gravity 0: Discovering Gravity (28 Dec 2014)

Gravity 1: Seeing the Invisible (7 Jan 2014)

Gravity 2: The Road to General Relativity (15 Jan 2015)

Gravity 3: Curvature & the Landscape of the Cosmos (24 Jan 2015)

Gravity 4: Testing the New Gravity (7 Feb 2015)

Gravity 5: Putting Einstein in the Navigator’s Seat (12 Feb 2015)

Gravity 6: Black Holes (28 Feb 2015)

Gravity 7: Recipe for Destruction (Making Black Holes) (7 Mar 2015)

Gravity 8: Black Holes in the Cosmos (15 Mar 2015)

Gravity 9: The Evolving Universe (27 March 2015)

Gravity 10: Signatures of the Big Bang (8 April 2015)

Gravity 11: Ripples in Spacetime (24 April 2015)

Gravity 12: Listening for the Whispers of Gravity (14 May 2015)

Gravity 13: Frontiers (27 May 2015)

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!