Gravity 13: Frontiers

by Shane L. Larson

I grew up in the American West, where our self-identity is inexorably melded with a deep romanticism about the Frontier. My family homesteaded near Briggsdale, Colorado, where the Rocky Mountains fade into the vast expanse of the Great Plains of North America. You can still visit the old homestead site, now on my family’s cattle ranch, and see the foundations that were laid down many generations ago. I can remember crawling around those walls as a young boy, trying to imagine the world in those long forgotten days — before cars, before computers, before rockets.  What did my old-time relatives think about every morning when they got up? What did they work on every day? Did they stare at the sky, virtually identical to the sky I stare at (except theirs was probably much darker), and wonder?

At the ruins of my family’s homestead (circa 1982), near Briggsdale, CO. Left to right: my maternal grandfather, my younger brother, my mother, my youngest brother, me, and my dad.

We portray the Frontier as a place full of adventure, discovery, and possibly undying fame. But Frontiers are in a very real sense the boundary between all the hard-won knowledge of our species, and our ignorance. This is perhaps captured no where better to my mind than in Ortelius’ 1570 Map of the World, known as Theatrum Orbis Terrarum.

Ortelius’ 1570 Map of the World, known as Theatrum Orbis Terrarum.

Made in the last decades before the dawn of the Age of Enlightenment, the map was one of the first to capture the knowledge of the true sphericity of the World. The map very clearly shows the boundaries of what was known and what was unknown in western culture. Consider: in 1520, Magellan’s expedition passed through what today is known as the Straights of Magellan, between the mainland of South America and the Isla Grande of Tierra del Feugo. Ortelius’ map captures that Frontier of exploration explicitly, showing the path around South America, but also showing complete ignorance of the nature of the Isla Grande. In fact, the entire lower part of this map shows the boundary of European knowledge of this part of the world, showing the farthest south on the globe any explorer had ever been. Even closer to Europe there are boundaries between knowing and ignorance that can be seen as well: the northern fringe of the Scandinavian Peninsula is clearly not correct, nor is the shape of the Caspian Sea.

Frontiers define those regions where explorers for the first time are discovering and documenting what has only been suspected or imagined before. Frontiers are more often than not enabled by technology. In Magellan’s day, access to the Frontier was enabled by great sailing vessels. When my family homesteaded in the plains of Colorado, their journey had been enabled by Conestoga wagons. Technology is almost always helping us push the boundaries of the Frontier outward. It is as true today as it was in the past.

Technology enables discovery. In the Age of Exploration, the development of great sailing vessels allowed European explorers to cross the oceans of the world.

Today, there are frontiers in science, both in terms of our knowledge, as well as in terms of what our technology is capable of. On both fronts, gravity is at the frontier. In the 100 years since the birth of general relativity, our understanding of the Cosmos has grown dramatically, and at each step, gravity has played a role. Einstein showed us how gravity can explain Mercury’s lagging orbit, and suggested it could bend the trajectory of light and change its color — effects that had never been measured. Since then, the frontiers have expanded well beyond those initial speculations. Modern cosmology was born less than 15 years after Einstein’s initial presentation of general relativity, and even today challenges our understanding of the Cosmos. We have explored the gravitational collapse and death of stars, and discovered the skeletons that survive the throes of death. Closer to home, we have harnessed gravity to allow us to navigate and map the world to exquisite precision. Our satellites have measured the gentle warp of the Earth’s gravity to map out the world in ways Ortelius never imagined.

For the past 100 years, gravity has been a major player at the frontiers of physics and astronomy. (L Top) Our understanding of the expansion of the Universe derives from general relativity. (L Bottom) The gravity of the Earth tells a tale of the movement of water and changing climate of our planet. (R Top) The evolution of stars, and their ultimate death, are consequences of gravity. (R Bottom) High energy astrophysical phenomena like black holes are staples of astronomy knowledge today.

Despite all these discoveries, there is still much to learn. Gravity is right on the boundary between our most exquisite triumphs and the precipice of our deep ignorance about the Cosmos. Science is about looking over that precipice and wondering what is at the bottom; we know there are still great mysteries Nature is hiding behind the facade that we call “gravity.” We have come a long way from the frontier Einstein imagined. What are the frontiers of gravity today?

Consider the interiors of black holes. A black hole has gravity so strong, not even light can escape. It’s boundary, the event horizon, forever hides the inside from the external Universe.  If you could somehow peer past the event horizon, deep down inside you would find a point of infinite density and infinitely strong gravity called the singularity.

The structure of a black hole is relatively simple to sketch out: the “surface” is the Event Horizon, and shrouded beneath it is the singularity.

Perhaps the greatest enigma, the greatest failing of general relativity, is the existence of the singularity. From a classic perspective, gravity is a purely attractive force that can grow without bound when matter is compressed into a small enough space. The limitless growth in its strength means if you squeeze hard enough, it can grow so large than no other known force can oppose it. When nothing can oppose it, everything collapses in a dramatic collapse not unlike the collapse at the end of a star’s life. But nothing can stop the collapse, and mathematically, everything falls into an infinitely small, infinitely dense point that we call “the singularity.”

Singularities — “infinities” — are perfectly fine in mathematics. They are less desirable in physics. There is a strong, prevailing belief that in the physical world, nothing can be “infinite.” Objects and phenomena can be ridiculously large or ridiculously small when compared to the scale of human experience, but never infinite.

The prevailing belief is that the singularity is an indicator that general relativity is a classical theory — it is good for large scale descriptions of the world, not for the microscopic landscape of the Cosmos. For that, we will need a new idea, an extension of general relativity into the quantum regime — “quantum gravity.” Where does the realm of quantum gravity become relevant? At distances separated by the Planck length (10^-35 meters = 0.000 000 000 000 000 000 000 000 000 000 000 01 meters).

What is quantum gravity? Fundamentally it is expected to be a theory that describes the nature of space and time itself at the Planck scale; many believe that using quantum gravity to describe the interior of a black hole will obviate the need for a singularity, but no one really knows how that will happen because we don’t have any working models that make predictions testable with observations. But there are many, many seductive and enticing ideas that are waiting for us to attain a state of understanding sophisticated enough to put them to the test.

Fritz Zwicky

There are also challenges for gravity on scales that are enormously large, spanning the size of the Cosmos. Some of these challenges are recent, some have been known for the better part of a century, but they are all unresolved. Part of the story begins in the 1930s with astronomer Fritz Zwicky.  In 1933 he was observing the Coma Cluster of galaxies, a group of about 1000 galaxies whose center lies 320 million lightyears away, in the direction of the constellation Coma Berenices. This was less than 10 years after the discovery that galaxies were in fact like the Milky Way, but enormously far away. Astronomers were still trying to learn all they could about galaxies, and studying their behaviour.

The Coma Cluster contains about 1000 galaxies (the yellow objects in this image), and is 320 million lightyears away.

Zwicky made a very reasonable assumption: the light of the galaxy is made by all the stars in a galaxy, and since most of the mass is contained in stars measuring the light is a way to get a handle on how much a galaxy masses. If you could measure the mass of all the galaxies, then you can use gravitational theory to explain their motions. But when Zwicky measured the motion of the galaxies, he found they were moving faster than expected — given the speeds they were moving, the cluster should have flown apart long ago. The only explanation is there was missing matter he could not see — more matter would simultaneously make the galaxies move faster, but also provide enough gravitational attraction to hold the cluster together.

Vera Rubin

By the 1960s, the missing matter problem had yet to be resolved. Astronomer Vera Rubin was studying the rotation of individual galaxies. Stars orbiting the center of a galaxy obey Kepler’s Laws of Orbital Motion, just like planets orbiting the Sun. Kepler’s laws say that the farther you are from the center of gravity, the slower your orbital speed should be. What Rubin found was that the outer reaches of galaxies did not slow in their rotation; in fact they rotated just as fast as stars that were closer to the center. This is known as the “galaxy rotation problem” and the plot of the rotation speed versus distance from the center of the galaxy is described as a “flat rotation curve.” Just as was the case with the Coma Cluster, the galaxy should have flown apart. The only explanation is that there is unseen mass — more matter would simultaneously make the stars move faster, but provide enough gravitational attraction to hold the galaxy together.

The “galaxy rotation problem” is that the speed a galaxy rotates with is NOT what we would expect. We expect it to rotate slowly near the edges, but observations show galaxies rotate too fast near the edges.

Rubin began her investigation with the Andromeda Galaxy, but in surveys of many more galaxies found that it was always true — all galaxies appear to have enormous amounts of unseen matter. Today, we call this dark matter.

This has enormous implications for cosmology. If the Universe is expanding, then the rate it expands, and the ultimate fate as a consequence of expansion, depends on the amount of matter in the Universe. This begs some important questions, like “is there enough matter to slow the expansion?” and “is there enough matter to cause the expansion to reverse?” Gravitational physicists classify the possible futures of the Universe in three ways:

• OPEN: There is not enough matter to slow the expansion of the Universe down at all; it expands forever.
• FLAT: There is just enough matter in the Universe that the expansion is slowing, but it will never halt, instead coasting forever.
• CLOSED: There is enough matter to eventually stop the expansion, and cause the Universe to recollapse in a backward version of the Big Bang that is often called the Big Crunch.

One way astronomers measure the expansion scenario of the Universe is looking at the spots on the Cosmic Microwave Background. The direction light travels to us from opposite sides of the spot depends on the expansion geometry of the Universe. (L) In a Closed Universe, the light is bent to make the spots appear larger. (C) In a flat Universe, the spots are seen at their true size. (R) In an open Universe, the spots appear smaller.

Each of these scenarios has particular signatures in observational data, and astronomers have found strong evidence that the Universe is indeed in the FLAT mode. That being the case, this has spawned a multi-decade quest to make a census of all the stuff in the Cosmos and characterize not only its gravitational influence, but also figure out what it all is!

We are aware of dark matter because of its gravitational influence on the rest of the Cosmos, but we have no idea what it is. And there is a LOT of it. Current estimates suggest that the Cosmos is 27% composed of this dark matter. The stuff you and I and planets and stars are made of — atoms — only make up about 5% of the total amount of stuff in the Universe.

So what is the other 68% of the Universe? Astronomers were perplexed by this for a long time, and began to doubt that the Cosmos was put together the way we thought it was. Maybe the Cosmos wasn’t FLAT but was instead OPEN and our observations were wrong in some way.

Supernovae, for a time, shine very brightly compared to other stars in the parent galaxy.

But in the late 1990s, there was a breakthrough. Mulitple teams of astronomers were using supernovae to measure the size and expansion of the Universe. Certain supernovae (Type Ia supernovae) are standard candles — they all explode with the same brightness. This means that the brightness of the supernova gives you a way to measure distance — the dimmer the supernova, the farther away it is. But cosmology gives us another way to measure distance, using Hubble’s law — redshift is also a measure of distance. The larger redshift an object has, the farther away it is.

But in 1998, the Supernova Cosmology Project and the High-Z Supernova Search Team discovered that these two methods of measuring the distance to supernovae did not agree — distant supernovae were dimmer than expected given the redshift distance. How can that be? The only explanation seems to be that the expansion of the Universe is accelerating.  An unknown something is accelerating the expansion of the Universe, ever so slightly, on the largest scales. Today, we call that something dark energy. Dark energy, whatever it is, makes up the remaining 68% of the expected stuff in the Universe.

A simple demonstration of the energy content of the Cosmos. Atoms are colored; all the unknown things (dark matter and dark energy) are black.

At long last, astronomers and physicists have discovered all the stuff we expected to find in the Universe. But we still don’t know what it is. We call this stuff “dark matter” and “dark energy”, but we don’t know anything about their behaviour and properties beyond their gravitational influence. Maybe they are some new, exotic bit of particle physics we have never seen before. Maybe they are some new, exotic behaviour of gravity on large scales. Or maybe they are something completely new, completely unexpected, and completely unexplained. Whatever they are, dark matter and dark energy are clearly at the frontiers of our understanding of gravity and cosmology. The future lies on the other side.

What these discoveries will mean and how they will change the course of human history is not for us to know, just as it was not for Einstein to know how general relativity would change the world. Those are questions for our posterity, our future children, who will have moved on from the simple mysteries that confound us today, and will be challenging their own new frontiers.

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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.

This post concludes this long series for the GR Centennial. Thanks to everyone who read, commented, and supported this effort! We will certainly talk about gravity again at this blog… 🙂 This post was completed while in residence at the Aspen Center for Physics.

Gravity 12: Listening for the Whispers of Gravity

by Shane L. Larson

The Cosmos is alive with energetic happenings.  Planets barrel along their orbits, unstoppable by anything short of a collision with another planet.  There is a cluster orbiting the black hole at the center of the Milky Way, with stars being flung and slingshot around their orbits like they were nothing more than ping-pong balls. Massive stars, in a last desperate gasp for attention, explode and spew their guts all around the galaxy, leaving a dark, compact skeleton behind. Billions of light years away, the shredded remains of galaxies slowly coalesce to make a larger elliptical galaxy and their central black holes dance together in a deadly inspiral, spewing jets of energetic material outward to mark their titanic struggle.

Gravitational waves are created by the dynamic motion of mass, a common occurrence in the Cosmos: supermassive black holes mergering or eating stars, stars exploding, and compact interacting binaries are all likely sources.

All of these examples have one thing in common: huge masses moving in dynamic ways.  The changing gravitational structure in these systems will manifest itself as gravitational waves propagating across the Cosmos, whispering ripples in the structure of space and time.  Encoded in those waves, if we could detect them, is a previously unheard story for the reading.

The “sticky bead experiment,” worked out at the 1957 Chapel Hill conference, taught us the effect of gravitational waves on the world: they change the distance between points in spacetime. Once we knew what physical effect to look for, physicists began to ask “how do we detect it?”  It was straight-forward to compute the size of the distance change caused by gravitational waves, and it was tiny. But seemingly impossible measurements have never stopped physicists and astronomers from trying to imagine clever and imaginative ways to probe Nature’s secrets.

One of the first people to seriously consider how to measure the extremely tiny stretching effect of gravitational waves was Joseph Weber at the University of Maryland. After the Chapel Hill conference he began to think seriously about the problem of gravitational wave detection, and settled on a clever and imaginative idea: if gravitational waves change the distance between any two points in spacetime, it should stretch a physical object as they pass through it. Once the wave goes by, the inter-atomic forces that hold the object together take over, and try to snap it back into its original shape. This kind of snapback motion would set up acoustic waves — sound waves — in the object. If you could detect those tiny, faint sound waves, it would be an indicator of the passage of a gravitational wave.  Weber fashioned such an experiment from a 0.61 meter diameter, 1.5 meter long cylinder of aluminum that massed 1.5 tons. Such a device is now called a Weber Bar.

(L) Joe Weber instrumenting his bar detector with sensors in the 1960’s. (R) You can visit the bar, live and in person, at the LIGO-Hanford Observatory.

There are, of course, many influences and physical effects that can set off acoustic vibrations in a large aluminum bar. Random acoustic vibrations could be mistaken for a gravitational wave, or more likely, hide the putative effect of a passing gravitational wave. Random signals like this are called noise; filtering noise is one of the foremost problems in any experiment. The solution to this difficulty is to have more than one bar; you set them up and wait to see if both bars ring off at the same time. Since noise is random, it is unlikely to influence both bars identically at the same time, so a common signal is most likely a gravitational wave. Weber’s detection program grew to include a second bar at Argonne National Laboratory that operated in coincidence with the bar he had built in Maryland.

By the late 1960’s, Weber’s analysis of his bar data convinced him he was seeing coincident events, which he dutifully reported to the scientific community.  The ensuing debate has been roundly documented (e.g. in Harry Collin’s book “Gravity’s Shadow”), but that tale is not germane to our discussion here. The important point is this: the scientific community suddenly became cognizant of the idea that gravitational waves could be detected through clever, high precision experiments, and Joe Weber set us on that path.

(Top L) The EXPLORER bar at CERN; (Top R) the AURIGA bar in Italy; (Lower L) The NAUTILUS bar in Italy; (Lower R) The new MiniGRAIL detector at Leiden.

In the years following the construction of the Maryland experiment, many other Weber bars were built around the world. These included ALLEGRO at Louisiana State University; EXPLORER at CERN; NAUTILUS in Frascati, Italy; AURIGA at the INFN in Legnaro, Italy; and Niobe in Perth, Australia.  While most of the classic bars have gone offline, new efforts in bar detection technology have turned to spherical detectors, of which MiniGRAIL at Leiden University is the archetype. But still, no gravitational wave signal has been confirmed by any bar.

Given the steadfast absence of confirmed signals in our detectors, why are physicists so confident in the existence of gravitational waves? The answer lies in traditional, telescopic observations of the Cosmos.

The Hulse-Taylor pulsar is located just off the wing of Aquila.

In 1974, radio astronomers Joseph Taylor and Russel Hulse were observing on the 305 meter diameter Arecibo Radio Telescope in Puerto Rico. They were looking for new pulsars, and discovered one in the constellation of Aquila. Pulsing every 59 milliseconds, the pulsar rotates at a staggering 17 times per second. After studying it for some time, Hulse and Taylor noticed that the pulses varied regularly every 7.75 hours. The explanation? The pulsar was orbiting another neutron star (that was not pulsing)!  Masquerading under the scientific name PSR B1913+16, this remarkable system is more readily known by its common name: the Hulse-Taylor binary pulsar, or usually “THE Binary Pulsar.” We can track the arrival time of the pulses from the pulsar in the system, and precisely determine the size and shape of the orbit over time. After 40 years of observations, it is clear that the orbit of the binary pulsar is shrinking, by an amount of roughly 3.5 meters per year. This is exactly the amount of orbital decay astronomers expect to see if gravitational waves were carrying energy away from the system, sucking the energy out of the orbit. If all goes according to Nature’s plan, the orbit will decay to the point of collision in 300 million years (mark your calendars!).

The system has a neutron star that orbits with a pulsar — the pulsar is a neutron star that sweeps a strong radio beam toward the Earth as it rotates. As they orbit, they emit gravitational waves, causing the orbit to shrink.

We now know of many systems like the Hulse-Taylor binary pulsar, giving astronomers confidence that gravitational waves do, without question, exist. So why haven’t we seen them?  The problem with Weber bars is they are “narrow band” — they are most sensitive to gravitational waves that are close matches to the sound waves that are made in the bar (a condition physicists call “resonant” — the gravitational waves closely match the shape and vibration time of the sound waves, so they reinforce each other). Since it is  unlikely a gravitational wave source will exactly match your bar’s vibration frequency, and because many phenomena generate gravitational waves at all kinds of different frequencies, an ideal detector should be “broad band” — sensitive to a wide range of gravitational waves. One solution is to build a laser interferometer.

Michelson (T) and Morley (B) built one of the first interferometers to make precision measurements.

Interferometers have a storied history with relativity and astronomy. The earliest scientific interferometers were made in the 1880’s by Albert A. Michelson, and used by Michelson and his collaborator Edward Morley to examine the propagation of light. The results of their experiments demonstrated to the scientific community that light was not propagated by a “luminiferous aether,” and was in fact able to propagate in pure vacuum. Their conclusions also support the founding postulates of special relativity, namely that all observers measure the speed of light in vacuum to be a constant, irrespective of their state of motion.

In the decades that followed, interferometry became a recognized technique for making precise measurements that could not be obtained in any other way. By the time the first results from Weber bars were being reported, people were thinking about other ways to make precision distance measurements, and laser interferometry was a prime candidate technology. The first laser interferometer designed for gravitational wave detection was a table-top experiment built in 1971 at Hughes Aircraft by Robert Forward, who was a student of Weber’s.

(L) Bob Forward’s first gravitational wave interferometer at Hughes Aircraft. (R) Rai Weiss’ initial sketch of the components and operation of a laser interferometer like LIGO.

A year later, Rai Weiss at MIT published a report outlining in great detail the basic considerations for building what would evolve into modern day gravitational wave interferometers. Those initial musings came to fruition in the 1990s, when kilometer scale interferometers began to be constructed around the world with one intention: to observe the Cosmos in gravitational waves.

In the United States, there are two observatories that are called LIGO: one is in Hanford, Washington and the other is in Livingston, Louisiana. In Europe, a 600 meter interferometer called GEO-600 was built outside Hannover, Germany, and a 3 kilometer interferometer called VIRGO was built outside of Pisa, Italy. The Japanese built a 300 meter prototype in Tokyo called TAMA, but have now embarked on a much more ambitious instrument built underground in the Kamioka Observatory called KAGRA. These instruments are enormous endeavours, on the scale of large particle accelerators in terms of their physical size and in terms of the number of people required to bring the project to fruition. All of them can be seen from space (just fire up Google Earth or Google Maps: LIGO-Hanford from space, LIGO-Livingston from space, VIRGO from space, and GEO-600 from space).

(Top L) LIGO-Hanford; (Top R) LIGO-Livingston; (Lower L) GEO-600; (Lower-R) VIRGO.

For the first time, these observatories will show us a view of the Cosmos seen not with light, but with the whisper of gravity. The bread-and-butter source, the thing we expect to detect most often, are the merger of two neutron stars. Viewed from the right seats, such collisions generate tremendous explosions known as gamma ray bursts, but we only see a small fraction of the gamma ray bursts in the Universe because they aren’t all pointing toward us. LIGO and its fellow observatories will have no such difficulties — gravitational waves are emitted in every direction from these cataclysmic mergers.

What will we learn from these events? We hope to learn what the skeletons of exploded stars are like — what is their size and what are they made of? What is the matter at their cores like, and what do they become when they merge? Every detected neutron star merger is a clue in the story of stellar lives, which of course, is part of our story too, because we are all of us descended from the exploded ashes of ancient stars.

Where do all these stellar skeletons come from? It’s a curious thing, looking out at the sky. The thing we see the most of are stars, and over the course of a human life, they change little if at all. Night after night, the stars wheel overhead, distant points of light that no human has ever visited, and no human is likely to visit in my and your lifetimes. But over the last few centuries, through a careful application of technology smothered under an insatiable desire to know, we have figured out their story. Like shrewd protégés of Jane Marple, we have pieced together many parts of the the puzzle to discover how stars are born, how they live, and ultimately how they die. Gravitational wave astronomy investigates these final end-states of stellar life. But when we see the stars, we are seeing the snapshot of the stars alive today — where are all the stars that have gone before?

They litter the galaxy — the Milky Way is a vast graveyard of stellar remnants, the burned out stellar husks of those stars that came before. Since only the largest stars produce neutron stars and black holes, and most stars are lighter-weight, like the Sun, astronomers think most of that stellar graveyard is full of white dwarf stars — tens of millions of them.

LIGO can’t see white dwarf stars because they are too big — they never shrink to small enough orbits to make gravitational waves that LIGO can detect. If we want to study this part of the stellar life story, we have to build something new.

In the next decade, NASA and ESA hope to fly laser interferometers in space. The LISA gravitational wave observatory will consist of three free flying spacecraft 5 million kilometers apart, using lasers to measure the distance between the three spacecraft. The first step toward flying LISA is a mission called LISA-Pathfinder that will launch in October 2015.

LISA will listen in on the gentle gravitational whispers of tens of millions of white dwarf stars — so many whispers that the galaxy will actually sound like racous party. Like any rowdy party, there will be loud contributors that can always be heard above the noise, perhaps as many as 20,000 that shout out above the cacophony.  These systems are called “ultra-compact binaries”, and orbit each other on orbits so small they would fit between the Earth and the Moon. We think of LISA’s view of the Cosmos as being complementary to LIGO’s — with observations from both observatories, we will be able to construct our first complete picture of the “decomposition phase” of stellar evolution.

But perhaps the most interesting thing LISA will detect are the supermassive black holes at the centers of galaxies. Some of the most fantastic pictures we have taken of the Cosmos show galaxies in collision. Occurring over billions of years, the graceful and delicate spirals are shredded, giving birth to a new, transformed galaxy. How often does this happen? Do all galaxies experience this at some point in their lives, or is it rare? How does it change the kinds of galaxies we see? Does it change the shapes of galaxies irrevocably, or do they return to their whirling spirals of arms?  And perhaps most interesting, what happens to the black holes that once lurked in their cores?

Examples of colliding galaxies. (T) NGC 4676 [the Mice], and (B) NGC 6621

If astronomers are correct, those black holes will sink to the core of the new galaxy that forms, and eventually merge together. When they do, they will emit a wailing burst of gravitational waves that will be visible to LISA all the way to the edge of the Observable Universe. Encoded in that cry will be the birth announcement of a new, bigger black hole, as well as the threads of the story that led to its birth — where they were born, when they were born, and what the Cosmos was like at that time.

These stories and more are contained in the faint whispers of gravity that even now are washing across the shores of Earth. As you are reading this, astronomers and physicists are tuning up our technology to listen closely to those faint messages, and when we finally hear them, they will transform the way we think about the Cosmos.

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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 10: Signatures of the Big Bang

by Shane L. Larson

Science has two interlocking pieces that always work together. One part is “describing the world to predict the future and explain the past.” This is the part that many of us remember from science class, involving pen and paper and mathematics and the Laws of Nature. Another part is “observing the world and seeing what Nature is up to.” This is also a part that many of us remember from science class, involving doing experiments and recording numbers and making graphs. These two pieces are called theory and experiment respectively, and they constantly validate and reinforce each other in a never-ending cycle of upgrading and refining our knowledge of the Cosmos.

All science is a combination of theory and experiment. In Cosmology, theory is an application of general relativity embodied in the Friedmann Equations (left); experiment is captured in astronomy (right).

Cosmology has seldom had both theory and experiment walking hand in hand. Instead one or the other has been out in front — sometimes way out in front — waiting for the other to catch up. This was certainly the case when general relativity was announced to the world — as a description of the machinery of the Cosmos, it was perfectly capable of making predictions that were so far beyond our ability to observe and verify that we didn’t recognize the truth for what it was. This famously happened early on, in 1917 when Einstein published one of the earliest papers about relativistic cosmology entitled “Cosmological Considerations in the General Theory of Relativity.”

As city dwellers, it is often easy to forget that the sky is full of stars. This fact leads to the most natural assumptions about the Universe based on experience: the Universe is full of stars.

At that time, we were profoundly ignorant about the nature of the Universe. The prevailing view was that the Cosmos was full of stars, and that the Universe was static. It’s the most natural assumption in the world based on your experiences when you step out the door every night — the sky is full of stars and they change little, if at all, night to night.

Einstein considered a Universe simply filled with stars, and asked what general relativity predicted. He found it only predicted one thing: the Universe must collapse.  Preconceptions are a powerful force in science, and Einstein believed strongly in the static Universe, so much so that he supposed maybe he had not gotten general relativity completely correct. So he introduced a mathematical addition to general relativity that pushed back against the collapse, called the Cosmological Constant.

Before 1924, the nature of galaxies was unknown. They were grouped with the “nebulae” — wispy, cloud like structures that could be seen through the telescope. These included Messier 31, the Andromeda Nebula (L) and Messier 51, the Whirlpool Nebula (R). The Whirlpool was the first nebulae that spiral structure was detected in, by Lord Rosse in 1845.

But science is always on the move. Telescopes in that day and age were getting larger. In 1917 the 100-inch Hooker telescope first saw starlight on its mirror, as it embarked on a long and storied history of astronomical discovery. Telescopes gave us the capability to probe deeper into the Cosmos, and we had started to discover vast diaphanous complexes of light that showed no stellar qualities. These were called nebulae, Latin for “cloud.”  A few of the nebulae, the “spiral nebulae,” perplexed astronomers — some thought they were simply odd nebulae (vast complexes of gas and dust), and others thought they were island Universes (other galaxies, like the Milky Way).

The 100-inch Hooker Telescope on Mount Wilson, used to discover the expansion of the Cosmos.

The discovery of the distances to the spiral nebulae, using Leavitt’s Cepheid variable method, was a watershed moment in the history of cosmology. It put on the table two  important facts: first, the Universe was vast — enormously vast — with distances far beyond the boundaries of our own galaxy.  Second, the major constituent especially on large scales, was not stars, but galaxies (which are agglomerations of stars). These two simple facts suddenly and irrevocably changed the way we thought about the Universe. In the first years after the discovery of the nature of galaxies, Friedmann and Lemaître used general relativity to imagine a Universe filled with galaxies, and discovered the idea that the Universe was expanding. This notion, discovered on paper, was bourne out in 1929 when Humason and Hubble, once again using the 100-inch telescope on Mount Wilson, found all the galaxies in the Universe were receding from one another.

At that time, Lemaître made a great leap of imagination — it was a thought that was well outside the comfort zone of astronomers of the day, though today we may view his leap as completely obvious. From the mindset of the future, it is difficult to imagine just how hard it was to think different. Lemaître supposed that if the Universe was expanding, then in the past it would have been smaller, and hotter. The idea was met with incredulity and derision, sparking enormous debate for decades to come. But science is the blend of ideas on paper with observations of the Universe. If Lemaître’s ideas were right OR wrong, the evidence could be found by looking into the Cosmos.

There are many lines of evidence that confirm the basic idea of the Big Bang, but there are three major pillars of support. The first, is the expansion itself. The Universe is not like a sports car, starting and stopping on a whim, braking and accelerating at random. Its evolution is driven by the Laws of Nature, in a smooth and predictable fashion. If we see expansion today, that expansion started in the past. The rate and trends in the expansion are a function of the amount of matter in the Universe, and the initial conditions of the expansion. These quantities can be determined from astronomical observations, and are consistent with the Big Bang picture.

A popular T-shirt meme about atoms, a clever science pun!

The second and third pillars of evidence for the Big Bang have to do with what happens to the Universe as it expands and cools, and the consequences for matter.  Everything you and I see around us here on Earth — rocks, trees, candy bars, platypuses — is made of atoms. Atoms are a composite structure. The center is a compact heavy core called the nucleus comprised of protons and neutrons. It is surrounded by a cloud of electrons, equal in number to the protons in the nucleus.

The fact that the atom holds together is a manifestation of the forces at work. The electrons are held to the atom by virtue of attractive electrical force between them and the nucleus. If you bang two atoms together hard enough, they break apart into free nuclei and free electrons.

The nuclei, built of protons and neutrons, are held together by a very strong force that acts over short distances called the nuclear force. The nuclear force is tremendously strong, but if you bang to nuclei together hard enough, they too can be broken up into free protons and free neutrons.

In the distant past, shortly after the Big Bang, the Universe was very compact: everything in it was closer together, and extraordinarily hot. As the Universe gets smaller, it’s a bit like being squished together in the mosh pit at a concert — you can’t really move anywhere without crashing into something else. The enormous temperatures mean that everything was moving extremely fast — the hotter the temperatures, the faster the motion, the harder the crashes. If you go far enough back in time, the Universe gets so hot you can’t have atoms. If you go even farther back, it gets hotter and the Universe can’t even have atomic nuclei.

The basic constituents made during Big Bang nucleosynthesis. Protons (red) and neutrons (green) bind to form the simplest atomic nuclei.

The second pillar can be understood by going back to a time in the first minute after the Big Bang. Up to this point, the Cosmos was a primordial soup of free electrons, free neutrons, and free protons, all swirling around in a maelstrom of churning energy. The Universe had started its inexorable expansion, and was cooling as a result.  By the time the Cosmos was 10 seconds old, it had cooled from its hot beginnings down to a temperature of about 2 billion degrees Celsius. At this temperature, protons and neutrons begin to stick together to form the first atomic nuclei. This process of formation is called primordial nucleosynthesis — it makes hydrogen, deuterium, helium, and small amounts of lithium and beryllium.

Big Bang theory predicts how much of each of these was synthesized in the first 15-20 minutes, a delicate balance astronomers call the primordial abundances. What astronomers can see agrees with the predictions of Big Bang nucleosynthesis.

But perhaps the most important observational signature of the Big Bang has to do with light. After the formation of the atomic nuclei, the Cosmos was still too hot to form proper atoms. Every time a nucleus tried to bind with an electron, a collision would knock the electron free. So, for the next 400,000 years, the Universe remained a seething fluid of atomic nuclei, free electrons, and energy.

When light is packed in so tightly with charged particles, like the electrons and atomic nuclei, it is not free to travel about of its own free will. It travels only a short distance before it encounters an electron, and it scatters.  Light simply can’t go very far.

(L) Before recombination, light cannot travel very far because it encounters free electrons, which interact with it causing it to scatter. (R) After the electrons bind to nuclei to make atoms, the light decouples from matter, and is free to stream through the Universe unimpeded by scattering interactions.

But, after 400,000 years, the Universe cools to a balmy 3000 degrees Celsius, cool enough that each time an electron bumps into a nucleus, it binds together to form an atom. This process is called recombination. From the point of view of the light, all of the charged particles suddenly disappear (atoms are neutral, having no overall electric charge) and the Universe becomes transparent. The light can travel anywhere it wants without being impeded by the matter; astronomers call this decoupling.  The Cosmos is full of freely streaming light.

A map of the Cosmic Microwave Background across the whole sky. First detected by Penzias and Wilson in 1965, this light is the signature of ever cooling Universe after the Big Bang. The band of stronger microwave light along the center of the map is the signature of the Milky Way Galaxy.

For the next 13 billion years, the Universe continued to expand to the present day. All the while the streaming light — the signature from the birth of atoms — surfed right along.  Spacetime is stretching as the Cosmos expands, and the light from that early, hot, dense state had to give up energy to fight against the expansion, shifting to longer and longer wavelengths as time progressed. By the time light reaches the Earth today, it should appear as microwave light.  And indeed, it is. In every direction we look on the sky, we see a uniform background of microwave light called the Cosmic Microwave Background. This is the third, observational pillar, the evidence, that tells us our thinking about the Big Bang is on the right track.

This is the basic picture of the Big Bang that was developed since the late 1920’s — decades of careful comparison of observations with theoretical calculations. The refinements and developments — of both theory and experiment — continue to this day.

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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 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.

First, 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.

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]

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.

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.

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.

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!

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.

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 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.

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.

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.

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 8: Black Holes in the Cosmos

by Shane L. Larson

When I give talks about black holes, I usually lead with a question for the crowd: “You’ve all heard about black holes. What do you know about them?”  The responses are varied, but can be succinctly summarized as this: black holes mess things up!

This little chat captures the essential truth about black holes: if you fall inside, you are without question doomed.  That notion is a bit horrifying, and one of the reasons why these enigmatic objects are so fascinating to us — there exist objects in the Cosmos that have the ability to utterly destroy anything. No amount of human ingenuity or heroics by Bruce Willis can ever spare your fate if you fall down the throat of a black hole.

People’s intuitions are all (more or less) based on solid science, and can help us understand how astronomers find and study black holes. One of the classic thought experiments is often posited to me as a question: what would happen to Earth if you replaced the Sun with a black hole (of equal mass)?  The answer is simple: absolutely nothing!

Oh sure, 8 minutes after the transformation it would get dark on Earth because there would be no more sunlight, and eventually Earth would turn into a snowball and all life as we know it would die. But in terms of the orbit nothing would change! The Earth would continue to happily speed along its appointed path, obeying Kepler’s laws of orbital motion, with nary a concern that it is orbiting a black hole instead of a friendly star. Far from a black hole, the gravity is not extreme at all.

That doesn’t sound very interesting, but as is often the case in the Cosmos, the most innocuous of ideas are often hiding a deeper, more profound notion, if you open your mind to it. This is the case here.

A binary star is a pair of stars that orbit one another, just like a planet orbits our Sun. They are often roughly the same mass, so they both move around a common center that astronomers call the “center of mass.” The stars more or less continue with their lives as if they lived alone, but if they are close enough together their interactions can have profound consequences for their evolution.

We know that a large fraction of stars in the galaxy are actually binary stars — two stars mutually orbiting one another the way planets orbit the Sun. So what would happen if we replaced one star in a binary with a black hole? This is eminently reasonable because we think black holes are one of the possible skeletons of dead stars.

In terms of the binary orbit, if the star and it’s black hole companion are far apart, nothing would change! The star that remains a star would continue to happily speed along its appointed path, obeying Kepler’s laws of orbital motion, with nary a concern that it is orbiting a black hole instead of the friendly star that was once its gravitational partner in the Cosmos.

Even though the orbit of the companion star is not dramatically affected by the presence of a black hole, there is an important consequence for astronomers: if they are watching this star system they will see the single star apparently orbiting … nothing! The star will continue to trace out its orbital path, appearing in our telescopes to wobble back and forth for no discernible reason.  This is something we have looked for, and it is something we have found!

Cygnus, the Swan, is a constellation in the northern sky. Three bright stars (Deneb in Cygnus, Vega in Lyra, and Altair in Aquila) make up “The Summer Triangle.” The black hole system, Cygnus X-1, lies near the center of the Triangle, in the neck of Cygnus.

In the northern sky, the Milky Way can be seen high in the sky on clear summer evenings. Prominent along the faint, diaphanous band is the constellation of Cygnus, the Swan, flying south along the great river of the galaxy. In the neck of Cygnus, near the naked eye star Eta Cygni, astronomers have found a bright blue-supergiant known as V1357 Cygni (also known as HD 226868 — there are a lot of stars, so astronomer names for them are not always the most pleasing for idle conversation!). It is bright enough to see in a telescope from your backyard, but there is little else you or I can discern. But in 1964, astronomers flew an x-ray detector on a rocket to the edge of space, and discovered this star is one of the strongest sources of x-rays in the sky. We now call it Cygnus X-1.  Since then, astronomers have watched this star closely, and note that ever so slightly it is wobbling back and forth once every 5.6 days, suggesting its unseen companion is about 14.8 times the mass of our Sun; the orbit between the two is about half the size of Mercury’s orbit.

An artist’s impression of Cygnus X-1. The strong stellar wind blowing off the supergiant is captured by the black hole and pulled down to form an accretion disk. [ESA/Hubble image]

But what about the x-rays? Ordinary binary stars don’t spew off as many x-rays as Cygnus X-1. What gives? This is another clue pointing toward the companion being a black hole. The blue supergiant blows off a strong stellar wind, much like the solar wind from our own Sun, but stronger. That material is captured by the gravitational pull of the companion and pulled down onto a turbulent maelstrom of material called an accretion disk. The accretion disk swirls just above the black hole, and is subject to intense gravity. Heuristically, the picture is this: the intense gravity makes the gas move very fast. When gas moves fast, it gets hot. When gas gets hot, it emits light. The faster it moves, the hotter it gets, and the more energetic the light. X-rays are very energetic, so the gas must be moving very fast. Why? The extreme gravity of a black hole.

So black holes can do crazy stuff to gas that streams down close to them. But what will the extreme gravity do to a solid object that gets too close? Imagine you (unwisely) decide to jump into a black hole; not being much of a diver, you jump in feet first. As expected, far from the black hole you don’t notice anything; the gravitational field looks perfectly normal, like any Newtonian gravitational field. Space and time are only distorted and stretched by noticeable amounts when you get close.

Tidal forces are a difference in the strength of gravity across your body. In the extreme gravity near a black hole, the side closest to the black hole is pulled on more strongly than the far side. As you get closer and closer to the black hole the effect is to stretch you out (“spaghettify” you) until you are pulled apart (“tidally disrupted”).

As you get closer, the strength of gravity increases — general relativity tells us the curvature, the warpage of spacetime is increasing. As you approach, the black hole pulls more strongly on your feet than your head. As you get closer and closer, this difference in force (what your physicist friends call a “tidal force”) can become quite strong! The net result — it stretches you out — provided you can withstand the strain, you’ll stay together, but get longer, like a rubber band.

Stephen Hawking has dubbed this effect “spaghettification” — the turning of you into a long piece of spaghetti. It is more extreme if your head is farther from your feet — short people have a better survival probability than tall people!  If you really want to survive the dive into a black hole, your best choice is to belly flop or cannonball — both greatly reduce the distance between the side of you close to the black hole, and the side of you farther from the black hole.

Astronomers observe tidal disruption flares. Here is an artists conception (top) and telescope observations (bottom) of a star being tidally disrupted by a 100 million solar mass black hole in galaxy RXJ1242 in 2004. [NASA]

Imagine now it wasn’t you diving into a black hole, but a star.  The exact same effects occur. Imagine a star falling toward a black hole. As it closes the distance, the strength of gravity grows inexorably stronger. The side of the star closest to the black hole feels the tug of the black hole more strongly than the far side. Despite the fact that it’s own self-gravity is strong enough to keep it together, as the influence of the black hole grows, it begins to overcome the self-identity of the star, and distorts it into a oblong caricature of its former self.  If the star strays too close, the black hole’s gravity will overcome the star’s gravity, and tear it apart. The star will be tidally disrupted.

When this happens, the guts of the star are violently exposed in an energetic event called a tidal disruption flare. Generally, the remains of the star, now a seething, turbulent cloud of gaseous debris, collapses down toward the black hole, forming an accretion disk that heats up and, for a time, becomes very bright. Slowly, the gas falls down the throat of the black hole, vanishing forever, and all evidence of the star is erased.

Two decades of observations have shown the orbits around the 4 million solar mass black hole at the center of the Milky Way. [NCSA/UCLA/Keck]

So what are these black holes that eat stars? They are the great monsters of the Cosmos. Lurking at the centers of spiral galaxies, like Charybdis in the Straits of Messina, these “supermassive black holes” have grown on a steady diet of stars and gas to enormous sizes. Our own Milky Way harbors a massive black hole that is 4 million times heavier than the Sun; even though it is millions of times more massive, the horizon is only about 17 solar radii across. But the consequences of its existence are profound. For the last two decades or so, astronomers have been watching a small cluster of stars in the center of the galaxy. We’ve been watching them long enough now, that they have traced out significant pieces of their orbits, and in some cases completed an entire orbit, allowing us to measure the mass of the black hole.

Despite being 4 million times more massive than our Sun, the black hole at the center of the Milky Way has an event horizon diameter only 17x larger than the Sun’s diameter!

Astronomers have looked for and found supermassive black holes in many other galaxies. In the course of those observations, we have discovered a tantalizing and interesting connection between galaxies and the massive black holes they host. Galaxies often have a part of them astronomers call “the bulge.” In the Milky Way, and other spiral type galaxies, the bulge is the large spherical bubble of stars that sits over the center of the galaxy. Some galaxies, like elliptical galaxies, are “all bulge.”  Astronomers have discovered an interesting relationship: the bigger a bulge, the bigger the black hole that lies at the center of it.

The black hole in the center of M87 powers an enormous, energetic jet of material spewing out from the galactic core. (L) I was one of the first amateurs image this jet in 2001. (R) HST image of the jet, for comparison. 🙂

An example of galaxies that are “all bulge” are ellipticals, like M87 in Virgo. M87 has a 2 BILLION solar mass black hole in its core that has launched an enormous jet that shoots out of the galaxy, extending nearly 5000 light years out from the core. No one knows exactly how black holes launch jets, but the best observations and models lead astronomers to believe that a spinning black hole can twist up magnetic fields into galactic sized magnetic tornadoes. Hot gas is very easy to convince to follow strong magnetic fields, and as it plummets toward the black hole, some of it is redirected up the jets.

But even among galaxies, some black holes are larger than others. In the northern sky, just below the Big Dipper is a smattering of faint stars known as Coma Berenices — “Bernice’s Hair.”  The stars of Coma Berenices are in our own Milky Way galaxy, but behind them, across 320 million lightyears of the void, lies the Coma Cluster of galaxies. A group of about 1000 galaxies, the center of the cluster is ruled by two super-giant elliptical galaxies known as NGC 4874 and NGC 4889 (both of which can be seen with backyard telescopes; NGC 4889 is easier than NGC 4874!). Both show strong evidence for massive central black holes, including enormous jets emanating from the centers. But astronomers have attempted to mass the black hole in NGC 4889 and found the black hole could be as massive as 37 billion solar masses. If true, the event horizon would be 24 times larger than Neptune’s orbit. That size boggles the mind — a void of nothing, almost 25 times larger than the solar system; anything that goes in is lost. Forever.

Coma Berenices is a pretty splatter of stars beneath the Big Dipper (which is part of Ursa Major). The Coma Cluster of galaxies, and NGC 4889, lies 320 million lightyears behind the stars of Coma Berenices.

The idea that black holes and galaxy bulges are related is a new one in astronomy, only having been proposed in 1999.  A diligent padawan of the Cosmos would ask the obvious question: if a galaxy has no bulge, does it then have no super-massive black hole? The answer may be “yes.” A classic example of this is the Triangulum Galaxy (M33), right here in our own Local Group. A beautiful, classic spiral galaxy, M33 is only marginally tipped to our line of sight and can be easily seen and studied with a backyard telescope. Curiously, M33 has no bulge; so far, no massive black hole has been found.

M33, the Great Galaxy in Triangulum. There is almost no bulge surrounding the bright core seen here; astronomers have yet to find any evidence of a supermassive black hole there.

And so the search continues. The number of galaxies for which we know the bulge-black hole relation works is still small — we have seen enough to understand the implications and possibility, but we still haven’t seen so many that we are confident stating, without equivocation, that “all bulgy galaxies have black holes.” Time and diligent observations of new galaxies will help resolve this question.

The fact that you and I can have conversations like this about black holes, dealing with what astronomers see and not (too much) about what we speculate is a mark of how far astronomy has come. When general relativity was first penned, black holes started as a curious, if somewhat suspect mathematical solution to the equations of gravity. Repeated, careful observations of the Cosmos have, however, led astronomers to the inescapable conclusion that black holes do in fact exist. They are part of our understanding of the machinery of the Universe. Now, the questions are different than what they were a century ago. Instead of asking “do they exist?” and “are they real?” we instead noodle our brains on the questions of “how many are there?” and “how big are they?” and “what are they doing to the Cosmos around them?”

And a lot of us still wonder, “what would happen if I jump in one?”

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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 7: Recipe for Destruction (Making Black Holes)

by Shane L. Larson

Black holes emit no light, by definition. For many years, the only hope astronomers had of detecting these enigmatic objects was to look for how they interact with other astrophysical objects, like stars and gas. Astronomers have been around the block a few times — they’ve studied a lot of stars, and seen a lot of gas in the Cosmos. What should they be looking for that would clue them in when the stuff they can see has drifted near a black hole? What do black holes do to things that fall under the influence of their gravity?

If you’ve ever heard about or read about black holes, you’ve learned that their gravity can be strong — extremely strong. This leads to a somewhat deceptive notion that black holes are like little Hoovers, running all over the Universe sucking things up.  The reality is that a black hole’s gravity is strong and can have a profound effect on the Cosmos around it, but only up close.

To get a handle on this, it is useful to go back to the way we first started thinking about gravity — in terms of a field. In the field picture, the strength of gravity — what you feel — is given by the density of field lines in your vicinity; gravity is stronger when you are surrounded by more field lines. There are two ways to increase the strength of the gravitational field.

The easiest way to make gravity stronger is to have more mass. Mass is the source of gravity; when we were drawing gravitational fields, the number of field lines we drew depended on the mass of the object.  The Sun is much more massive than the Earth, so we draw many more field lines to represent its gravitational field.

Two observers (Stick Picard, top; Stick Spock, bottom) are the same distance from objects. For the person near the smaller object, they feel weaker gravity (evidenced by fewer field lines around them).

Another way to increase the strength of gravity is to make an object more compact. You can see this by considering two stars of equal mass, but one smaller than the other. How do their gravitational fields compare? Far from either star, the gravitational fields look identical. There is no way to distinguish between the two based on simple experiments, like measuring orbits. But suppose you were down near the surface of each star. Here we notice something interesting. Both stars have the same number of field lines, because they have the same mass. But down near the surface of the smaller, more compact star the lines are much closer together. This was the signature of gravity being stronger.

Imagine two stars with exactly the same mass, but one is larger in size (top) than the other (bottom). Observers far from either star (Stick Spock, both panels) feel the same gravity if they are the same distance away. For close-in observers (Stick Geordi, both panels) the gravity is stronger. But for the compact star (bottom) the observer can get closer, and when they do, they feel even stronger gravitational forces. The gravity is much stronger near a compact object.

The field picture of gravity is associated with the idea of forces (it is a “force field”), which is the foundation of Newton’s approach to gravity. But one of the requirements of general relativity when it was developed was that it correctly describe situations where we would normally use Newtonian gravity, as well as any situation that required relativistic thinking. We’ve seen in these examples that gravity gets stronger if an object is more massive, or if it is more compact. In the language of general relativity, we would say “there is stronger curvature” in both these cases. Remember our mantra: “mass tells spacetime how to curve.” Spacetime is told to curve more where the masses are bigger, or when the mass is very compact.

So what does this tell us about black holes? It says that to make an object whose gravity is so strong that the escape speed is the speed of light, I can do one of two things: I can dramatically increase the mass, or I can make the object more compact.  This is the first clue we have to where black holes might come from — they have to be either very massive, or extremely small. We actually encounter both in the Cosmos, as we shall see, but for the moment let’s focus on the small ones. So how do you make things extremely small?

Wrap a balloon in aluminum foil. The foil is like the stuff of the star; the balloon is an outward force, keeping the star from collapsing.

Let’s do an experiment to think about this. Go find a balloon and some aluminum foil. Blow the balloon up (it doesn’t have to be huge) and wrap it in aluminum foil.  This is a mental model of a star at any given moment in its life. Gravity is always trying to pull everything toward the center. But the star is not collapsing — why not?  Deep in the cores of stars, the temperature and pressure is so high that nuclear fusion occurs — through a series of interactions with all the nuclei that are packed together, hydrogen is “burned” into helium. This process releases energy — it’s nuclear fusion power! In your balloon and foil model, the foil is stuff in the star — all the churning roiling gas and plasma that make up the body of a star. What is keeping it from collapsing? In this case it is the balloon, pushing the foil outward — the balloon is acting like the fusion energy bursting out from the core, supporting the star and keeping gravity from collapsing it.

Gravity (turquoise arrows) is constantly trying to pull the star inward on itself. The pressure from the nuclear fusion generating energy in the core presses outward (yellow arrows) preventing the star from collapsing.

As a star ages, the fusion process in its core evolves, slowly burning the core fuels into heavier and heavier elements, until a large core of iron builds up. There are no effective nuclear reactions that can sustain the burning of iron into heavier elements.  The iron is effectively ash (that’s what astronomers call it!) and it settles down into the core.  The iron is not burning, so there is no fusion energy pushing outward against gravity’s desire to collapse the core — what’s stopping it?

In addition to the iron nuclei, the core is also full of the other constituents that make up atoms, electrons.  Electrons are a particular kind of particle we encounter in the Cosmos called a fermion. Fermion’s are okay to hang out together, provided they all think they are different from one another (in the language of the physicists — the fermions all have to have different “quantum numbers”); this is a well known physical effect known as the Pauli Exclusion Principle. If you do pack fermions together they dislike it immensely. They start to think they are all looking the same, and they press back; this is called “degeneracy pressure”, and it is what keeps gravity from being able to crush the iron core of the star.

When gravity overcomes the electron degeneracy pressure in the iron core (pop the balloon), there is nothing pushing outward against gravity, so the core can collapse.

High above, the star continues to burn, raining more and more iron ash down on the core. The mass of the core grows, and the gravity grows with it. When enough iron amasses in the core, the gravity will grow so strong not even the degeneracy pressure of the electrons can oppose it. When that happens, gravity suddenly finds that there is nothing preventing it from pulling everything down, and the iron core collapses.  In your model, this is equivalent to popping your balloon — you’re left with a lot of material that is not being supported at all, so it collapses.  Collapse the foil shell in your hands — you are playing the role of gravity, crushing the material of the star down into a smaller and smaller space.

When the collapse occurs, the iron nuclei are the victims. The compression of the iron core squeezes down on the iron nuclei, disintegrating them into their constituent protons and neutrons. The extreme pressure forces protons and electrons to combine to become more neutrons (a process creatively called “neutronization”). In less than a quarter of a second, the collapse squeezes the core down to the size of a small city and converts more than a solar mass worth of atoms into neutrons. We call this skeleton a neutron star.

Gravity wants to compress all the matter, to pull down as close together as it can get. The explosion helps gravity move toward its goal by applying astronomical pressures from the outside, squeezing and squeezing the matter down. What stops it?

You hands act like gravity to crush the foil into a small remnant of its former self. There is a minimum crushing size, because the foil presses back against your efforts.

Let’s go back to your model. The balloon has been popped — that’s gravity overcoming the supporting pressure of the electrons. The foil has collapsed — that is gravity pulling as hard as it can to get all the material down into the center. Now squeeze that lump of foil as hard as you can; make the smallest, most compact ball of foil you can. Odds are there is some minimum size you can make that ball of foil. What is keeping you from squeezing the foil smaller? The foil itself is getting in the way! It is pushing back against the force that is trying to crush it — you — and you are not strong enough to overcome it!

This is the case with the neutron star. When neutrons are so closely packed together, their interactions are dominated by the strong nuclear force, which is enormously repulsive at very short distances. As more and more neutrons are packed into a smaller and smaller space, they become intensely aware of one another and the pressure from the strong nuclear force grows until it is strong enough to oppose gravity once again.  The collapse stops, suddenly.

The iron core is heavy (more than a solar mass) and moving fast (between 10-20% the speed of light) — it is not easy to stop so suddenly. When the center of the core stops, the outer layers of the core are unaware of what lies ahead. In the astrophysical equivalent of a chain-reaction traffic pile-up, the layers crash down on one another; the outer layers rebound outward.  This rebounding crashes into the innermost layers of the star above the core, setting up a shock wave that propagates outward through the star.  The wave begins to tear the star apart from the inside.

The Western Veil Nebula (NGC 6960), just off the wing of the constellation Cygnus. Visible in amateur telescopes, it is one of the most exquisite supernova remnants in the sky. [Wikimedia Commons]

Energized by an enormous flux of neutrinos produced by the newly birthed neutron star, the shock is driven upward through the star, until it emerges through the surface, destroying the star in a titanic explosion known as a supernova.  It is an explosion that would make Jerry Bruckheimer proud — the energy released is enormous, for a time making the exploding star brighter than all the other stars in the galaxy combined. The material of the star is blown outward to become a supernova remnant, a vast web of ejected gas and atoms thrown out into the Universe. We see many, many supernova remnants in the galaxy — every one of them is unique, they are all exquisite and beautiful in ways that only the Cosmos can create.

Left behind, slowly settling down into a well-behaved stellar skeleton, is the neutron star.  At the surface of the neutron star, the gravity is enormous — about 200 billion time stronger than the gravity at the surface of the Earth. The escape speed is 64 percent the speed of light. If you fell just 1 millimeter, you would be travelling at 61,000 meters per second (136,400 miles per hour!) when you hit the surface!

Lego Neil deGrasse Tyson and Lego Me visit the surface of a neutron star. [click to enlarge]

But this is still not the extreme gravity of a black hole. If a star is massive enough, the crushing force of the collapsing star and the ensuing explosion is so strong it cannot be stopped even by the protestations of the neutrons. In fact, the infalling matter crushes the matter so strongly that gravity becomes triumphant — it crushes and crushes without bound. The strength of gravity — the warp of space and time — soars. At some point the escape speed at the surface of the crushing matter reaches the speed of light — the point of no return has been reached, but the matter keeps falling right past the event horizon, continuing to fall inward under the inexorable pull of gravity. All the matter is crushed into the smallest volume you can imagine, into the singularity, at the center of the empty space we call the black hole. No force known to physics today is strong enough to overcome this event.

Different effects in astrophysical systems fight against gravity’s inexorable pull. If the gravity gets strong enough, nothing can prevent the collapse to a black hole.

The process just described is known as core-collapse and is just one way that astronomers think black holes might be made. Similar explosive events that lead to collapse include the collision of two neutron stars, the parasitic destruction of a small star by a compact companion that grows its mass large enough to collapse, and possibly even the collision of smaller black holes to make larger black holes.

So how compressed do you have to be to become a black hole? The answer for a perfect ball of matter is called “the Schwarzschild radius.” If you squeeze an object down to a ball that fits inside the Schwarzschild radius (that is, it fits inside the event horizon) then no known force can stop gravity from collapsing that object into a black hole. For the Sun, the Schwarzschild radius is about 3 kilometers — if you shrink the Sun down into a ball just 6 kilometers in diameter, the size of a small city, it will be a black hole. For the Earth, the Schwarzschild radius is about 1 centimeter — if you shrink the Earth down to the size of a marble, it will be a black hole.

What it would take to make the Sun or the Earth into a black hole. The Sun as a black hole would cover your town, but you could carry the Earth in your pocket (though this is NOT recommended).

Given a notion of how black holes form, astronomers can start probing the Universe, peering into places that should give birth to black holes. The same physical effects that we used to understand their formation can be used to understand how they interact with the Cosmos around them, giving astronomers clues about how to detect them. Next time, we’ll use this information to find out how black holes influence the Universe around them, and use that information to go black hole hunting in the Cosmos.

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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.

[9 March 2015] This is revised version of the original post. I owe many thanks to a colleague who pointed out that my original explanation of core-collapse followed very old ideas about how stars die. In this revision, I have endeavoured to present a correct but still clear picture of what is going on. Any inaccuracies that still persist are my own.

Gravity 6: Black Holes

by Shane L. Larson

There are many topics that set the mind afire with wonder, wild speculation, and imaginative ramblings into the unknown and the unknowable. Particularly popular, especially among human beings less than about 12 years old, are dinosaurs, volcanoes, alien life, and black holes. “Grown-ups” will often rediscover a bit of their childhood wonder when these topics come up, and have been known to engage in deep question-and-answer marathons to try and understand what it is that we, the humans, have learned and understood about these enigmas of Nature.

There are many things in science that spark our imaginations in dramatic ways, no matter your age, like dinosaurs, volcanoes, alien life (or freaky life on Earth, like octopuses), and black holes.

While most of us lose our penchant for crazy trivia factoids as we age, there is still a lingering desire to think about dinosaurs, volcanoes, alien life, and black holes. These topics can be understood quite well on a heuristic level, and from those simple descriptions emerges a rich tapestry that serves as a playground to let our imaginations run wild.  All four topics are particularly interesting because they in a very real way represent the frontiers, the boundaries of our understanding of what is possible in the Cosmos. The dinosaurs were among the largest lifeforms ever to walk the Earth. Volcanoes are among the most violent, explosive, destructive natural phenomena on Earth, the planet vomiting its guts onto the surface for us to see. A single instance of alien life would transform our parochial view of life in the Cosmos.  But even among these grand mysteries that are so enjoyable to speculate and dream about, black holes hold a special place. Black holes are the ultimate expression of Nature’s power to utterly erase anything from existence.

What are these enigmatic black holes? Where do they come from, and what do we understand about them?

Imagine Stick Picard, Stick Geordi, and Stick Spock are throwing apples in the air. If Picard throws an apple up, it comes back down. If Geordi throws an apple up faster, it goes higher, but still comes back down. If Spock throws an apple fast enough, at escape speed, it will not come back down — it will break free of the Earth’s gravity.

Fundamentally, a black hole is an object whose gravity is so strong that not even light can escape its grasp.  What does that mean?  Imagine we go stand out in the middle of a field. You take a baseball, and throw it up in the air as fast as you can.  What happens? The ball rises, but gravity slows it down until it turns around and falls back to Earth.  If you have a friend do the same thing, but she throws her baseball even faster, it goes higher than your baseball, but still it turns around and falls back to Earth.  The faster you throw the baseball, the higher it goes. As it turns out, there is a certain speed you can throw the ball that is so fast, the ball will escape the gravity of the Earth and sail into deep space. That speed is called, appropriately enough, the escape speed.  On Earth, that speed is 11.2 km/s — if a rocket reaches that speed, it will make it into space, slipping free of the Earth’s gravity forever.

(T) The fasted “plane” ever built was the rocket powered X-15, which attained a speed of 2.02 km/s, far short of the escape speed of Earth (11.2 km/s). (B) Rockets, like the Apollo 15 Saturn V, have broken free of the Earth’s gravity. [aside: Apollo 15 famously tested the Equivalence Principle on the Moon.]

Our operational definition of a black hole is this: a black hole is an object whose escape speed is the speed of light. You may notice that this definition has nothing related to relativity in it. Black holes are a natural consequence of any description of gravity. The first ponderings about black holes were made in 1783 by the Reverend John Michell. A graduate of Cambridge University, Michell was by all accounts a genius of his day, an unsung polymath who pondered the mysteries of the Cosmos as he went about his duties as the rector of St. Michael’s Church in Leeds. He made many contributions to science, including early work that gave birth to what we today call seismology, and the idea for the torsion balance that Henry Cavendish later employed to measure the mass of the Earth and the strength of gravity. But here we are interested in Michell’s mathematical work on escape speed.

At the time Michell was thinking about escape speed, the speed of light was the fastest speed known (it had been measured to better than 1% accuracy more than 50 years earlier by James Bradley), though no one knew it was a limiting speed. Michell asked a simple and ingenious question: how strong would the gravity of a star have to be for the escape speed to be the speed of light?

No known picture of John Michell survives. But he still speaks to us from the past, through his scientific writings.

He described his result to his friend Henry Cavendish in a letter, noting that light could not escape such a star, assuming “that light is influenced by gravity in the same way as massive objects.” A prescient statement that ultimately turns out to be true, as Einstein showed when he proposed general relativity 132 years later. Michell called such an object a dark star.

Michell’s ideas were published in the Proceedings of the Royal Society, and then more or less faded into history until they were revived by the publication of general relativity. Most of us associate the idea of black holes with relativity and Einstein, not Newtonian gravity and Michell. Why?

Because special relativity adds an important constraint on Michell’s dark stars: there is an ultimate speed limit in the Universe. Nothing can escape from one, because nothing can travel faster than the speed of light. General relativity has this idea built into it, together with the idea that light responds to gravity just as matter does, completing the picture. The first true black hole solution in general relativity was written down by Karl Schwarzschild in the months after Einstein first announced the field equations to the world.

So how can we think about black holes in general relativity? An easy heuristic picture is to appeal to our notion of curvature. Imagine flat space — space with no curvature, thus no gravity. If you give an asteroid a little nudge, it begins to move, and continues to move on a straight line. It will do so forever, in accordance with Newton’s first law of motion: an object in motion stays in motion (until acted up on by an external force). Now imagine that same asteroid in an orbit a little ways down inside a gravitational well. If you give the asteroid a little nudge outward, its orbit will wobble around a bit, but still remain confined to the gravitational well. If you give it a bigger nudge, it can climb up out of the well and escape into the flat space beyond — this is escape speed.

Weak orbits, far from a source of gravity, are not deep in a gravitational well (top orbit); a small nudge will give a rock in these orbits escape speed and it will break free. Strongly bound orbits, deep in the gravitational well (bottom orbit) require much larger nudges to reach escape speed and break away.

But what happens if the asteroid orbit is in a deep gravitational well? A deep well is indicative of strong curvature — what a Newtonian gravitational astronomer would call a “strong gravitational field.” If you are going to nudge the asteroid so it can climb out of the gravitational well, it will require a BIG nudge — objects strongly bound by gravity need BIG escape speeds.

For a black hole, the gravitational well is infinitely deep. Imagine you are orbiting far from the black hole. This is just like any orbit in any gravitational well; you are somewhere down in the well, and with a big enough nudge, you will have the escape speed to break free and climb out of the well. As you go deeper and deeper in the well, you have to climb further out, so the required speed to break free is higher. But there will come a point of no return. At some point deep down in the well, the escape speed becomes the speed of light. At that point, no matter what speed you attain, you will never be able to climb out of the gravitational well. That point, is a point of no return — we call it the event horizon.

Around a black hole, there is a point, deep in the gravitational well, where the escape speed is the speed of light. This is called the event horizon, and is the point of no return. Outside the event horizon is outside the black hole — you can still escape. Inside the event horizon is inside the black hole — you are trapped forever, being pulled inexorably toward the singularity.

This is an overly simple picture of the event horizon, but is a perfectly good operational definition. General relativity predicts that time and space behave weirdly inside this surface, but for those of us on the outside, we’ll never know because that information can never be carried up the gravitational well, past the event horizon, and to the outside Universe.

The existence of the event horizon as a one way membrane, as a point of no return, means black holes are exceedingly simple — they are among the simplest objects in the Cosmos. What does that mean?

Think about an average automobile, like my prized 1990 Yugo GVX. What does it take to completely describe such an object? You have to describe every part of it — the shape and size of the part, what it is made of, where it goes on the vehicle, what it touches and is attached to. All told, there may be 10,000 parts — bumpers, windshields, lugnuts, u-joints, battery leads, spark plug cables, fuses, windshield wiper blades, turn signal indicators, and on and on and on.

Magazines devoted to cars and black holes may look the same. There may be a LOT to talk about in a car magazine. In a black hole magazine, there are only 3 things to talk about, but those 3 things have tremendous influence on the Cosmos, which is quite interesting.

What about a black hole? There are only THREE numbers you need to specify to completely characterize all the properties of a black hole. Those numbers are (1) the mass, (2) the spin, and (3) the electric charge. If you know these three numbers, then general relativity tells you everything you can know about the black holes.

What does that mean everything? The idea that you only need 3 numbers to describe a black hole is a central feature in general relativity, known as the “No Hair Theorem.” Here the word hair hearkens back to our idea of a “field” as being some invisible extension that spreads out from an object in every direction (like hair). General relativity says that if the black hole has any properties besides mass, spin, and electric charge, there should be other kinds of hair emanating from the black hole.

Now, that statement should incite the little scientist in the back of your brain to start jumping up and down. This is a prediction of general relativity. Predictions were meant to be tested — that is what science is all about. One could pose the question “are the black holes we find in Nature the same ones predicted by general relativity?” Are black holes bald (described only by mass, spin, and charge) or do they have some kind of external hair that affects the Universe around them?

For astronomers to address questions like this, they have to understand what happens to things that get too close to a black hole. How do black holes appear in and influence the Cosmos? This will be the subject 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.

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.

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.

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.

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).

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 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!

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 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.

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.

Both 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

The 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.

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.

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.

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.

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.

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 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.

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 03: Curvature & the Landscape of the Cosmos

by Shane L. Larson

Had he been alive when Queen formed in 1970, perhaps Einstein might have jammed with them.

“Is this the real life? Is this just fantasy?”  So opens the classic rock song by Queen, Bohemian Rhapsody. Trying to understand modern gravity often puts one in the frame of mind that the mental machinations we go through are somehow not connected to reality. Albert Einstein’s genius was that he persevered through those uncomfortable feelings. He willfully ignored traditional ways of thinking about the real world, and imagined new and inventive ways to describe how Nature behaves.

One of those inventive ways of thinking was to noodle about unusual situations, like the Equivalence Principle. What a happy little thought — an idle daydream to imagine an elevator on the Earth, or flying in a rocket, and asking what would happen if you did something as simple as drop an apple? Dropping an apple is an act of everyday life, but the conclusion seemed almost a fantasy. Einstein’s thought experiment had discerned that there was no way for a person to distinguish if they are in a rocket controlled elevator, or under the influence of the gravity from a planet. At face value, the conclusions would seem to be this: since I can’t tell the difference between gravity and a rocket, maybe gravity isn’t real at all.

Any normal person might throw up their hands in exasperation and decide this discussion of the Equivalence Principle is nonsense and go work on something simpler (like brain neurochemistry). But Einstein was a persistent fellow, and pushed a little harder.  He asked, “Is this the real life? Is this just fantasy?” Could it really be the case that there is no way to tell if you are in a gravitational field? What can we experience — what can we observe — that convinces us that we are caught in the grip of gravity?

We understand the world through experiments; they are the medium by which we observe. All experiments — thought experiments in particular — are recipes. Experiments produce results (knowledge about the Cosmos) the same way a recipe produces a cookie. We look at that result, and we ask ourselves a few fundamental questions — they are the same for physics experiments as cookies. Why is the result this way? Can I change what went into the result? Will I get a different result if I change what I put in?

Science and baking are both built around experiments that seek to discover what small changes reveal about the world. In cookies, a relatively small change can change a chocolate cookie into an almost identical vanilla cookie (TOP). A more substantial but not completely different approach might make a peanut butter cookie (BOTTOM). But getting a chocolate chip cookie (RIGHT) takes a completely different approach. [Photo by S. Larson; I don’t know what happened to these cookies after the #science was done; sorry.]

Science is a game of tearing apart ideas and seeing what makes them tick. Changing the assumptions, the recipe of the experiment, could change the outcome. So once again, Einstein returned to our thought experiment with the elevators, and imagined something new. There is a big assumption hidden in our thought experiment — the rooms you and I were confined to were “small.”

Why should that matter? Let’s imagine that our rooms were larger — much larger — and consider each of them in turn.

First, think about your room, on a spaceship. This is a BIG spaceship, of the sort that only the Galactic Empire has the metal and economic resources to build. The entire bottom of the spaceship is covered by rockets, all of them pushing with the same force to make you go.  Now conduct the apple dropping experiment again, first at one end of the spaceship, and then at the other end, very far away.  Both apple drops show the same thing — the apple falls directly down, parallel to the walls of your spaceship.

No matter how large you make a room, if it is being propelled uniformly by rockets, apples all over the room fall straight to the floor, along paths that are everywhere parallel to one another.

Now think about my room, on the planet Earth. This is a BIG room, far larger than any room ever built as it is large enough that if my floors are flat, the curvature of the Earth falls away from under my room at both ends (though I am not aware of this — no windows, right?). If I drop my apple at either end of my huge room I make an astonishing discovery — my apple does not fall parallel to the wall! It lands farther from the wall than it started. Given the outcome of my experiment, I could imagine all sorts of plausible explanations.

Perhaps the walls of my gigantic room are repulsive.

Maybe the walls are repulsive!

That’s an interesting idea; maybe it’s true, maybe it’s not. Can I test it?

Sure!  I build a few new walls at different places in the big room and drop many apples many times. What I find is this: if a wall is closer to the center of the room, a dropped apple falls closer to straight down. At the exact center of the room, two apples fall straight down and land the same distance apart as when they were released. Two apples dropped at opposite ends of the room are closer together when they land on the floor! Physicists get grandiloquent about this and call it “tidal deviation.”

What is going on? The walls clearly aren’t repulsive — a wall in the center of the room doesn’t push apples away from it at all.  We have talked about the lines of force that show the gravitational field.  The gravitational field always points to the center of the source of gravity. What this experiment seems to show is that if my room is big enough, I can detect the shape of the gravitational field!

(TOP) When my apples are dropped, their paths are not parallel; we say there is a tidal deviation between the paths. This is a key experimental signature of gravity. (BOTTOM) We can understand the tidal deviation of the apple paths if we imagine they are following the lines of force in the gravitational field (this is how Newton would have explained it). But this is not the only way to explain gravity!

This idea of the shape of the gravitational field, and its relation to the motion of falling objects, would be a key part of Einstein’s mathematical development of general relativity: it led him to the thought that motion and geometry could be connected.

That may seem like an odd thought, but the fundamental building blocks of elementary geometry are exactly the elements of motion that we discovered in our Giant Room Apple Dropping Experiments: lines can be parallel or not parallel. Einstein recognized that was important, so he explored it. We can too! Let’s think about a flat table top.

If I have two Matchbox cars on my table, and give them a push, they travel in a straight line and never stop (in the absence of friction — every little kid’s dream!).  If I take those two cars and set them in motion  exactly parallel to one another, what happens? The two cars speed off across the table and their paths never cross, no matter how far they go. In many ways, this example is like our two apples on opposite ends of the Gigantic Rocket-Propelled Room — the apples both started falling on straight lines, parallel to each other, and they ended up hitting the floor falling on straight lines that were still parallel to each other.

On a flat surface, two lines that begin parallel stay parallel, no matter how far you extend the lines across the surface.

So this leads to the inevitable question: is there a way in geometry to make the Matchbox cars start out along parallel paths, but ultimately draw closer together? This would be analogous to the Gigantic Room the size of Earth, where apples dropped on opposite ends of the room landed closer together.  As it turns out, the answer to this question is YES.

Imagine a sphere, like a playground ball or a desk globe.  The surface of the globe is two dimensional, just like the table top — there are only two directions you can go: front-back, or left-right. Suppose I take my two cars and set them on the equator in different spots, but both are initially travelling due north — the paths are parallel! What happens? Eventually, the paths of the two cars get closer together, and if we wait long enough, they cross.

If two travellers start at the equator travelling due north, their paths are initially parallel. By the time they reach the top of the globe, their paths cross each other — the paths don’t remain parallel because of the curvature of the globe!

Now, that is no way for parallel lines to behave on a piece of flat two-dimensional paper, but it is perfectly acceptable on a two-dimensional curved surface. THIS is the watershed idea of general relativity — maybe we can describe gravity as curvature. Maybe we can replace the concept of a gravitational force with the idea of particles moving on a curved surface — on flat surfaces, motion along parallel paths stay parallel, but on curved surfaces initially parallel pathways can converge and cross.

Neat idea. But curvature of what?!

Different ways we have devised to measure space or time.

Einstein brilliantly deduced that since our concern is with the motion of things, it should be curvature of the quantities that we use to describe motion — space and time. Special relativity, which motivated our reconsideration of gravity, was wholly focused on how we measure space and time, and Einstein’s former professor, Hermann Minkowski, had discovered that individually space and time are artificial elements of a single medium — spacetime.  Spacetime is the fabric of the Cosmos, the medium on which all things move. Einstein had become well versed in this notion, and concluded:

Gravity is the curvature of spacetime.

This is the heart of general relativity. So how does it work? General relativity is summarized mathematically by 10 coupled, non-linear, partial differential equations known as the Einstein Field Equations, succinctly written as

Fortunately for us, this mathematics can be captured in a simple, two-line mantra to guide intuition:

Space tells matter how to move.

Matter tells space how to curve.

In geometric gravity — general relativity — you can imagine spacetime like a large, deformable sheet. A particle can move anywhere on that sheet, so long as it stays on the sheet.  In places where the sheet is flat (“flat space”) the particle moves in an absolutely straight line.

But what happens if a particle encounters a large depression on the sheet? The only rule is the particle has to stay in contact with the sheet. It continues to travel in the straightest line it can, but if its path dips down into the depression, the direction the particle is travelling is slightly altered, such that when it emerges on the far side, it is travelling in a new direction that is not parallel to its original course!  Space tells matter how to move, with its shape.

Far from sources of gravity (edges of the sheet) spacetime is flat, and objects travel on straight lines. Small masses warp spacetime into a gravitational well (left dimple), while larger masses make larger gravitational wells (right dimple). If a particle comes close to a gravitational well, the curvature of spacetime bends its pathway. If a particle gets trapped in a gravitational well, the curvature of spacetime forces it to travel on a closed pathway — an orbit.

How do you curve spacetime?  With matter. The large, deformable sheet of spacetime is dimpled wherever there is a large concentration of mass; the larger the mass, the larger the dimple. Matter tells space how to curve, with its mass.  The larger the dimple, the larger deflection a particle passing nearby will feel. This at last, is the long awaited connection to the way we think about Newtonian gravity — the source of gravity is always matter, as we expected.

So we have done away with the concept of a “gravitational force field” and replaced it with the idea of “motion on a curved spacetime.” An astute reader will ask a pertinent question: if general relativity is really the way gravity works, why didn’t we discover it first? Where did Newtonian gravity come from?

Both Newtonian gravity and general relativity make exactly the same predictions when gravity is weak and speeds are slow.  In fact, mathematically, general relativity looks just like Newtonian gravity at slow speeds and in weak gravity. These are precisely the conditions we encounter in the solar system, which is why Newtonian gravity was discovered first, instead of general relativity!

You may have encountered models of spacetime gravitational wells out in the world. This one, in the Milwaukee Airport, captures coins for a museum. [Photo by K. Breivik]

It’s fine, of course, to make up a new idea about gravity. But this is science — fancy theories are only as good as the tests that can be conducted to verify them.  Einstein knew this, and proposed a series of tests for general relativity, which we’ll talk about next time.

PS: I rather enjoyed using Bohemian Rhapsody to start this bit of the General Relativity story. It was written by the great Freddie Mercury for Queen’s 1975 album, “A Night at the Opera.” As we shall see in our next installment, Mercury (the planet) plays an important role in bringing the importance of General Relativity to the attention of the scientific community, just like Mercury (Freddie) helped me explain it here. 🙂

PPS: This week I couldn’t capture all of this in one 3 minute video, so I tried to do it in two.

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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.