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.

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.

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]

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").

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]

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]

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!

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. :-)

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.

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.

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?

—————————————

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?

1280px-Black_hole_consuming_star

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).

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.

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 nuclear fusion, keeping the star from collapsing.

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.

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 fusion stops (pop the balloon), there is nothing in the star pushing outward against gravity, so the star can collapse.

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.

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]

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]

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.

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).

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.

—————————————

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 my colleague, Christian Ott, who pointed out that my original explanation of core-collapse was seriously flawed, following very old (and wrong!) 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.

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.

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 tested the Equivalence Principle on the Moon.]

(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.

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?

speedLimitBecause 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 escapse 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.

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.

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.

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.

—————————————

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

Gravity 5: Putting Einstein in the Navigator’s Seat

by Shane L. Larson

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Third generation GPS satellite (GPS IIIa).

Third generation GPS satellite (GPS IIIa).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

—————————————

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

Gravity 04: Testing the New Gravity

by Shane L. Larson

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

—————————————

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

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

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 thing you are looking at. 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 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.

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 your gigantic room are repulsive.

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!

(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.

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!

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.

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

efes

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.

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]

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.

—————————————

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 2: The Road to General Relativity

by Shane L. Larson

Science is, to some extent, a skill set that can be learned. Like playing piano or solving Rubik’s cubes or cooking Belgian cuisine. Using scientific thinking and applying it to the world is in large part a matter of practice and relentless dedication to getting better. But like all artforms, there is a small element of je ne sais quoi to it as well — a hidden reservoir of intuition and stupendous insight that is unleashed only sometimes.

einsteinAppleApple once had an ad campaign built around the mantra, “Think Different” (grammarians, hold your tongues, and your “ly”s and follow the mantra!). There were images of famous thinkers through the ages who approached the world differently than the rest of us. One of those was Albert Einstein.

Among a community of bright and creative people, it gives me pause to consider those people that we all think of as being remarkable. Albert Einstein is arguably the most famous scientist in history of the world, commanding the respect not just of the general populous, who have grown up immersed in his legend, but also the respect of the scientific community. Why is that? My colleague Rai Weiss, now an emeritus professor at MIT, recently noted that it wasn’t just that Einstein was smart, it was that he exhibited tremendous intuition. His great ability was to look at the same world the rest of us look at every day, and think different.

When Einstein began his quest to refine our understanding of gravity, he knew he was going to have to “think different” — this was, after all, what had led to special relativity in the first place! One of the earliest musings on the road to general relativity was a simple question: how do you know if gravity is pulling on you?

Everything I need to start developing some new ideas about gravity!

Everything I need to start developing some new ideas about gravity!

It’s a seemingly simple question, but it led to an interesting thought experiment. Imagine you and I are each in a small, windowless room with nothing but an apple and our smartphones (so we can text each other the results of the experiment I am about to describe).

Each of us drops our apple, and we see that it accelerates downward — it falls!  The apple starts from rest (at our hands) and speeds up as it falls toward the floor of our small room.  We excitedly text the result to each other and tweet pictures of apples on floors. Should we conclude from these experiments that we are both conducting experiments under the influence of a gravitational field?

[Top] You and I conduct identical experiments (dropping apples) in enclosed spaces and get identical results. [BOTTOM] The reality of what is outside our little rooms may be completely different! A falling apple is equally well explained by the gravity of a planet, or by an accelerating rocket!

[Top] You and I conduct identical experiments (dropping apples) in enclosed spaces and get identical results. [BOTTOM] The reality of what is outside our little rooms may be completely different! A falling apple is equally well explained by the gravity of a planet, or by an accelerating rocket!

Einstein realized the answer to that question should be “No!” There are multiple ways to explain what we saw.  One way is to assume our little rooms are sitting on the surface of planet Earth, where the planet’s gravity pulled the apple down. But another, equally valid way to explain this experiment is to assume the little rooms are really the space capsules of rocket ships, accelerating through empty space (the apple is pressed down to the floor — “falls” — the same way you are pressed back in your seat when a jetliner takes off).  What Einstein realized is that there is no way, based on our experimental results, to tell the difference between these two cases. As far as experiment is concerned, there is no fundamental difference — that is to say, no observational difference — between them. Einstein knew that the laws of physics had to capture this somehow.

[TOP] You and I both find ourselves weightless, floating without feeling forces acting on us. [BOTTOM] The reality external to our rooms could be that we are floating in space, or that we are in a freely falling elevator plummeting to our doom.

[TOP] You and I both find ourselves weightless, floating without feeling forces acting on us. [BOTTOM] The reality external to our rooms could be that we are floating in space, or that we are in a freely falling elevator plummeting to our doom.

What if we consider a slightly different case? Imagine you and I both suddenly found ourselves and our apples drifting weightlessly in the middle of our small rooms. We excitedly text each other that we finally made it to space and tweet messages that we are officially astronauts. Should we conclude that we are both deep in interplanetary space, far from the gravitational influence of a planet? Once again, Einstein realized the answer to that question should be “No!” There is no way to know if we are drifting inside a space capsule in deep space, or if we are merely inhabiting an elevator whose cable has snapped and we are plummeting downward toward our doom!

tweetEquivalence_smallIt is this freefall experiment that really illustrates how we have to learn to “think different” when expanding our understanding of Nature. In Newtonian gravity, we always look at problems with an exterior, omniscient eye toward the problem. A Newtonian approach to the free fall problem says “Of course you are falling under the influence of gravity! I can see the Earth pulling you down from the top of the skyscraper toward your doom at the bottom of the elevator shaft!” But Einstein asked a different question: What does the person in the elevator know? What experiments can they do to detect they are in a gravitational field? The answer is “none.”  There is no observational difference between these two situations, and the laws of physics should capture that.

The critical point here is that if you are in free fall, you feel no force! Einstein’s great insight was that the central difficulty with gravitational theory up to that point was that it was anchored in thinking about forces. This thought experiment convinced him that the right thing to think about was not force, but the motion of things.

This thought experiment came to Einstein in 1907 on a languid afternoon in the Bern patent office. Later in his life, Einstein would recall that moment and this idea with great fondness, referring to it as the happiest thought of his life.  This experiment is known as the “universality of free fall,” which physicists like to give the moniker “the Equivalence Principle.”

This is how I often imagine Einstein’s life during the years he worked in the Bern patent office! [From "The Far Side" by Gary Larson]

This is how I often imagine Einstein’s life during the years he worked in the Bern patent office! [From “The Far Side” by Gary Larson]

I have a very strong memory of my father first telling me about the universality of free-fall in about fifth or sixth grade. When you’re not used to it, the notion that falling in an elevator is the same as floating in outer space engenders a spontaneous and vehement response: “That’s crazy!” We had many long debates about this (it was following hot on the heels of my meltdown over the existence of negative numbers — maybe my dad was trying to forestall another meltdown…), and I don’t think it ever quite sank in. I, of course, feigned understanding and dutifully repeated the tale of the falling elevator to my classmates, reveling in their confusion and indignant denial of the logic of it.  I was a tween — what did you expect?

The "Leaning Tower of Niles," a half-scale replica of the tower in PIsa. Located in Niles, IL (a suburb of Chicago).

The “Leaning Tower of Niles,” a half-scale replica of the tower in PIsa. Located in Niles, IL (a suburb of Chicago).

But now, many years later and with a LOT of physics under my belt, I know that that the outcome of these thought experiments derive from a very old result that we are all familiar with — that all objects fall identically, irrespective of their mass. Galileo taught that, at least in folklore, by dropping various masses off of the Leaning Tower of Pisa. The obvious question to ask is “how is Galileo’s experiment connected to Einstein’s thought experiments?”

For the moment, imagine the various parts of your body as having different masses.  Your head masses about 5 kg (a little bit more than the 8 pounds you learned from watching Jerry Maguire), where as a good pair of running shoes may mass about 1.5 kg.  If you are standing happily in the elevator when the cable snaps, the traditional explanation is that everything begins to fall.

If objects of different mass fell at different rates, then your head would be pulled down faster than your shoes — you would feel a force between your head and your shoes. That force could be used to deduce the existence of a pulling force.  But Galileo taught us that is not the way gravity works — your head and your shoes will get pulled down at strictly the same rate in a uniform gravitational field. Every little piece of you, from your head to your toes, your kneecaps to your freckles, falls at the same rate — there are no different forces between the different parts of your body and so you feel (you observe) yourself to be weightless. This is sometimes called the Galilean Principle of Equivalence, or the Weak Equivalence Principle.

Okay — so what? Apples and freefall, elevators and rockets. What does any of this have to do with developing a deeper understanding of gravity?

What this thought experiment reveals, what the Equivalence Principle tells us, is that thinking about forces is not the best way to think about the world because we can’t always be sure of what is going on! Instead, we should think about what we can observe — how particles move — and ways to describe that. That simple intuitive leap would, in the end, change the face of gravity. Particles move through space and time, which had brilliantly been unified by Einstein’s teacher and colleague, Hermann Minkowski, into a single unified medium called “spacetime.”

What is spacetime? It is the fabric of the Cosmos —  it can be stretched and deformed. The fundamental idea of general relativity is that gravity can be described not by a force, but by the curvature of spacetime, the medium on which particles move.  That will be the subject of our next little chat.

—————————————

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