Black Holes 4: Singularities, Tunnels, and Other Spacetime Weirdness

by Shane L. Larson

I think one of the great things about the modern world is the propensity of information. Information is free and easy to come by, and it possible to learn about anything you want. More-or-less, the total knowledge of our civilization has been written down in books and documents, and disbursed to libraries, websites, and other mediums of communication. It is not always easy to discern what is authentic and what is not, as is clearly the case when one looks at the wild, apocalyptic wastelands of modern social media. But none-the-less, it is easy to indulge your desire to simply learn. We consume books and podcasts and documentaries, sacrificing time we could spend on woodworking or yardwork or binging TV shows in favor of trying to recapture how we felt in 2nd and 3rd grade, before school became about exams and homework and was just about how awesome all the far flung corners of the world and Nature could be. 

I think deep down all of us are lifelong learners; I’ve met many of you at public lectures or here at the blog. Some of you are quiet, and sit in the back with contemplative furrows on your brow; others of you are more exuberant and can barely contain your questions. Either way, you all show up, because you remember how cool it was when you were first learning. But I’ve noticed something interesting in my years talking to all of you: as a rough rule of thumb, I can usually triple the attendance of any talk if it is about sharks, volcanoes, dinosaurs, or black holes. Vast numbers of you succumb to your curious inner child if I talk about the right things. 

People’s minds, young or old, can be captured if we talk about science in ways that stimulate their interest and imaginations. [Image: Bill Watterson]

What is it about these topics that inspires deep interest in people? I think, at the heart, they are very real examples of the Universe’s ability to put you in mortal danger with implacable indifference. Never mind that it is unlikely you will encounter any of these dangers in your life. Pondering being faced with a highly improbably danger in the Universe allows us to ask ourselves, “what would I do?” in much the same way we watch super-hero films and imagine ourselves in the fray. 

Black holes are notable in this list because not only do they have the mystique of danger about them, but they are suffused with a long list of exotic, mind-bending phenomena that add to their mysterious nature.  

Let’s talk about some of the exotic things you have hard about black holes, and I often get asked about.

“Is everything is going to get sucked into black holes?” 

This is probably the most common question I get about black holes! The simple answer is “no” — black holes are not little Hoovers running around the Cosmos sucking stuff up. I’ve thought a lot about where this idea comes from, and I think it is a mis-extrapolation of the inescapability of a black hole. When you are far from a black hole, its gravity is exactly the same as the gravity produced by ordinary objects of the same mass. If you are orbiting far away from a billion-solar mass black hole, the gravity you feel is exactly the same as if you are orbiting around a dwarf galaxy that has a billion sun-like stars in it!  If we could magically replace the Sun with a one solar mass black hole, the Earth would continue along in its orbit as if nothing had happened because the gravitational influence is exactly the same! 

Far from the black hole, you cannot tell if you are orbiting a black hole or a star of the same mass — their gravity is identical unless you get close. [Image: S. Larson]

If you are silly (or unfortunate) and fall into a black hole, you are never going to get out. The gravity of a black hole is so strong that it can trap anything inside it; that is true. But it is not infinitely strong and able to influence everything outside it. 

“What does it mean to get spaghettified?” 

When you get close to a black hole, the gravity can become more intense than anywhere else in the Cosmos. Imagine you are jumping in feet first. The gravity is strongest close to the black hole, so your feet are pulled on more strongly than your head, which is farther away. The result of this dichotomy of gravitational strength is the black hole tries to pull you apart, much as you stretch a rubber band by pulling on opposite ends. Physicists call this difference in force a tidal force, and the process of pulling you apart is called tidal disruption. Stephen Hawking, in his famous book “A Brief History of Time” called this effect “spaghettification.”  

Some ways of falling into a black hole will feel less painful than others. [Image: S. Larson]

Somewhat paradoxically, the spaghettification effect is strongest near the event horizon of small black holes, and weaker near the event horizon of larger black holes. The spaghettification effect is also stronger when your head is farther away from your feet (so tall people will suffer more than us short people). The two rules of thumb for surviving spaghettification when you are jumping into black holes are this: 

1. Jump into the biggest black hole you can find; million solar mass black holes are much more fun to jump into than solar mass black holes.
2. Belly flopping into black holes is safer than jumping in feet first.

“Do black holes really bend time?” 

The movie Interstellar has revived broad interest in black holes and inspired wide-ranging conversations about what black holes are really like. One of the most common conversations we have is about time, which usually begins with “what was the deal with the guy who got old when he didn’t visit the black hole?” This plot device could just be accepted at face value, like we do with so much science fiction, but in this case it is rooted in the physics of the real world. General relativity predicts that the closer you are to a source of gravity, the slower your clock ticks compared to someone very far from the source of gravity. Here I use the word “clock” in the physics sense: anything that keeps regular time, whether it is a digital watch, a wind-up pocket-watch from your grandparents’ day, an hour-glass, or the steady beat of your heart.  

Consider two people, one close to the black hole and one farther from the black hole. Every clock ticks slower when you are close to the black hole — this could mean an actual clock that tells time, but it can also mean a regular biological clock, like your heartbeat. [Image: S. Larson]

The bending of time is definitely one of those counter-intuitive predictions of general relativity, but if space and time are one entity (“spacetime”), then bending space very strongly must necessarily also bend time. It doesn’t take much to bend time by a measurable amount — the bending of time is the central physical effect behind the Global Positioning System, which you use everyday on your phone to navigate to the nearest ice cream shop (or coffee shop — whatever). The difference between the bending of time around the Earth and the bending of time around black holes is the strong gravity near the black hole makes the effect much more pronounced. 

“Are black holes are infinitely dense? What does that mean?” 

Anything labeled infinity is, generally, an anathema to scientists. “Infinity” is a perfectly good concept in mathematics, but with respect to the natural world, it seems that the Cosmos is only filled by things that are finite and measurable. That is not to say there aren’t enormous, gigantic, mind-bogglingly huuuuuuge numbers, but they are all tiny compared to “infinity.” In the natural sciences, we have often encountered “infinity” in the mathematical ways we describe Nature, but we’ve found most of them were simply artifacts of our early poor understanding of how the world works, particularly on the microscopic scales of fundamental particles. Gravity is the last frontier in this regard, and there are many persistent “infinities” we encounter, and they often manifest themselves in the study of black holes. 

An example of your common experience with density. This cube of tungsten and this clown nose are about the same size, but the tungsten is significantly heavier. Why? because more stuff is packed into roughly the same amount of space. [Image: S. Larson]

To think carefully about this, let us be precise about what we mean. “Density” is a common concept in physics and chemistry. It is how much stuff (mass) is squeezed into a given amount of space (volume). Dense objects feel heavy in your hand, while less dense objects feel lighter.  As a matter of practical everyday experience, you most often encounter the notion of density when thinking about things floating or sinking in water (objects more dense than water, like rocks, sink; objects less dense than water, like styrofoam, float). 

So let us define the “density of a black hole” the way we define the density of any other object in the Universe: the mass of the black hole, divided by the volume of the black hole. Those of you who are practicing gravitational physicists will recognize that we should be careful when computing the “volume”, but for practical purposes here let us use the ordinary formula for the volume of a sphere where the radius of the sphere is the radius of the event horizon of the black hole. This is practical and intuitive, and will illustrate our point effectively.  

The first picture of the black hole at the heart of M87, formed by light being bent around the inner most regions of space outside the event horizon. This black hole has a diameter larger than the diameter of our solar system! [Image: Event Horizon Telescope Collaboration]

Imagine two black holes: one that is the mass of the Sun, and one that is one billion times the mass of the Sun (a bit smaller than the black hole in M87 that was the subject of the Event Horizon Telescope picture). The solar mass black hole only has a radius of about 3 kilometers, and a density of about 18 quadrillion times more the density of water (1.8 x 10¹⁹ kg/m³, for those calculating themselves). By comparison, a 1 billion solar mass black hole has a radius just under 3 billion kilometers (about the radius of Uranus’ orbit); it would have density of only 2% the density of water (numerical value: 18 kg/m³; slightly less than the density of styrofoam). If you could somehow drop it in a gigantic cosmic bathtub, its density suggests it should float. 

If black holes were solid objects and could interact with the world like ordinary “things,” a calculation of their density suggests some are less dense than water and could float in a cosmic wading pool. [Image: S. Larson]

It can’t float, of course — the event horizon is not a hard surface that water can act on and thus provide buoyancy in a ginormous cosmic pond. Water would flow right through the event horizon and disappear, so all the water in the cosmic pond would essentially flow into the black hole like some kind of drain.  But that’s not the point in the floating analogy. As a general rule, we think we understand the physics of things that have densities less than the density of water, so the idea that the density of a black hole is the same as materials that do float is a strange and discomfiting result. And it should be! Just remember your discomfiture is related to the odd nature of black holes — density defined in the classical way really doesn’t apply to black holes the way we’ve done it here, because as we’ve noted before, they are mostly empty space! This odd result has little to do with their overall size, and more with what lies at their heart… the singularity. 

“The Singularity” 

The real mystery of black holes lies at their heart, in the center of the space defined by the boundary of the event horizon. All the gravity of the black hole is concentrated there. All the matter that collapses to form the black hole is still being drawn together even after it falls through the area we call the event horizon. Gravity keeps pulling it inward, inexorably inward, squeezing it smaller and smaller with a force so great no known force in Nature can stop it. Everything that fell inward to create the black hole gets squeezed down smaller and smaller, becoming more and more dense. Eventually it gets squeezed into a space that is vanishingly small, or so general relativity predicts. This point of zero size with everything squeezed into it is infinitely dense, and is called the singularity. The laws of physics as we understand them break down before you ever really reach the singularity, at a distance away from it called the Planck length, about 10^-35 meters (0.00000000000000000000000000000000001 meters). This is the length where we expect the physics is governed by quantum gravity, a description of gravity, space, and time on the tiniest scales. We have searched for such a mathematical description of Nature for many years, but so far have been unsuccessful. 

How do physicists think about the singularity? It is an infinity, and infinities are anathemas to physicists. More often than not we are trying to understand what is happening far away from the singularity when thinking about the Cosmos. This is, more or less, what astronomers do because they are observing the Cosmos outside the event horizon, which is far from the singularity. Easy peasy — you don’t even have to waste one brain cell on the singularity if you don’t want to! Sometimes physicists pretend they are okay with the singularity being infinitely dense, and use the classical laws of physics (general relativity in particular) to understand the influence of the singularity around it. Gravitational physicists often do this, in particular because they are trying to understand how the world behaves under the influence of strong gravity. All the tales and imaginings you have heard about the inside of black holes are figured out by scientists thinking about the singularity this way. The last prominent group that thinks about the singularity are the quantum gravity squad. There are many ideas about what a complete description of quantum gravity will look like — all of them are clever, and elegant, and exotic. But we don’t yet have a way of experimentally testing any of them. Someday we will be able to test them. The day we understand quantum gravity, it will tell us something about the true nature of the singularity. 

“Are Black Holes Spacetime Tunnels?”

The last and most famous example of spacetime weirdness and black holes is the astonishing idea that for some kinds of black holes, if you jump in, they may in fact be tunnels. For the movie nerds out there, this is the central plot device in many science fiction stories. For perfectly spherical black holes, there are no tunnels — if you jump in a black hole, the singularity lies in your future; you will be crushed ruthlessly and mercilessly.  But for black holes that happen to have electric charge on them (expected to be few) or are spinning (most black holes found in Nature are expected to be spinning) there are trajectories inside the event horizon that do not end at the singularity. They end… somewhere.   

Scientists struggle to visualize black holes just as much as ordinary people, so we have developed a special map called a Penrose diagram. As you go up the diagram from bottom to top, time increases from the past to the future. As you go left or right on the map, you change where you are in space. Here the white areas are the ordinary Universe, and the yellow areas are inside a black hole. The one on the left is a Schwarzschild black hole that has no tunnel; if you are inside, the singularity lies to your future and there is no ordinary Universe you can get to. The one on the right is a charged black hole, which might have a tunnel. If you are inside, you can avoid the singularities on the left and right, and possibly emerge at the top of the diagram. [Image: S. Larson]

In these kinds of black holes, if you avoid the singularity you come out of something that looks mathematically similar to a horizon. The difference is you come out of this horizon, emerging from the inside to the outside. Such things are variously called “wormholes” or more commonly “white holes.” They are, in essence, the other end of the black hole, like it is some kind of giant culvert or tunnel that connects one place to another. 

Tunnels to where? you quite astutely ask. The truth is we don’t know, but there are several possibilities. One possibility is the tunnel emerges somewhere else in our observable Universe. As an astronomer this is a very intriguing possibility, because it suggests there may be something that could be observed with telescopes. Sadly, to date, we have not seen anything exotic and unexplained that might be a white hole.  

Another possibility is that it may emerge somewhere in our Universe, but outside the observable part of the Universe. This idea is a bit harder to wrap your brain around, because it hinges on understanding that the Universe can be larger than what we can observe and could, in principle, go on forever. The “Observable Universe” are just those parts of the Universe that are close enough for us to observe in a telescope because light has had time to reach us in the time since the Universe was born. An easy way to think about this is to think about your home state where you live. Most of us can walk only a few miles per hour — let’s say 3 miles per hour. That means in one day, you could only walk 3 miles per hour x 24 hours = 72 miles. If you started walking right now, by this time tomorrow you could be anywhere in the state within 72 miles. Does that mean the rest of the state isn’t there? Of course not — it just means the parts of the state you could get to at the fastest pace you could walk (the “Observable State”) is only 72 miles away in any direction. 

If I start at Northwestern University and walk for 24 hours at 3 miles per hour (average walking speed of a human) I can reach anywhere inside the red circle. I can get no farther, but that doesn’t mean there aren’t more places outside the circle! The Universe is the same, only the time is not 1 day, but the age of the Universe, and the speed is not walking speed, but the speed of light. Inside the circle is what we call the Observable Universe, but it is not the Entire Universe. [Image: S. Larson, Map by Google]

A third exotic possibility is that the white hole may emerge not in our Universe, but in some other Universe. A Universe that is not our own, but is somehow parallel to our own. It is an interesting possibility to ponder and imagine because it opens up all kinds of possibilities. Are the laws of physics the same there, or is the other Universe some weird place that doesn’t have stars and planets and galaxies? Do all of our black holes emerge as white holes in the other Universe? Where do black holes from the other Universe go? Do they emerge in our Universe, or do all white holes in all the other Universes emerge in only one of the other Universes? Some things we can imagine within the realm of science and do calculations and simulations about, but others are mere speculation that we have yet to ponder and consider seriously. It makes your head spin, but these are the things that great speculative science fiction about black holes are made of.  

The last possibility is that tunnels through black holes simply do not exist at all, that Nature somehow closes them off, or we have not fully understood the mysteries of black hole insides completely yet. There is much we still have to learn.

Which of course is the point. Black holes, on any given day, seem completely unfathomable, especially in the context of the weird implications about what they do to the world around them. But is precisely that mystery that draws our attention time and again. Partly because we like that feeling of being completely baffled by Nature, but also because some deep part of us knows that these inscrutable mysteries hide deep and precious secrets, secrets that lie at the core of how Nature and the Cosmos work. 

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This post is the fourth in a series about black holes.

Black Holes 01: Imaging the Shadow of Darkness

Black Holes 02: What are black holes made of?

Black Holes 03: Making black holes from ordinary stuff

Black Holes 04: Singularities, Tunnels, and Other Spacetime Weirdness (this post)

My Brain is Melting — GW150914 (Part 2)

by Shane L. Larson

It has been just more than a week since we told the world about our great discovery. It was a cold winter morning in Washington DC, the temperature hovering just below freezing. In a room at the National Press Club, the world press had gathered, and at the behest of NSF Director, Frances Córdova, LIGO Executive Director, Dave Reitze, took to the podium.

“Ladies and gentlemen. We have detected gravitational waves. We did it!” Mic drop. (Well, he should have; in the movie dramatization, he will. You can watch the moment here on YouTube, or the full press conference.)

Dave Reitze makes the announcement to the world that LIGO had detected gravitational waves. “We did it!”

So began a ninety minute press conference delivering the news of the first gravitational wave detection to the world. In the days that followed, social media and press outlets exploded in a veritable tidal wave of excitement and awestruck wonder. On twitter, the hashtags #gravitationalwaves, #LIGO, and #EinsteinWasRight have accumulated more than 70 million tweets in just one week.

Everyone has the same sense that we scientists have — this is a doorway, now open, to a Universe we have only imagined. Beyond the threshold are certainly things we have predicted and speculated about, but also many wonders yet to be found or understood.

We have done our best to explain what we are doing with LIGO, and how it works. We have made a Herculean effort to describe the astrophysical significance of the discovery. We have tried mightily to explain what Einstein’s ideas about spacetime and gravity are all about.

But this is hard stuff to think about, it is hard stuff to understand, and it is hard stuff to explain. It is well outside our normal everyday experience, so it is easy to feel like your brain is melting.

You shouldn’t worry that these things are hard to understand. It took physicists 41 years to even decide gravitational waves were real, and then another 59 years to build an experiment capable of detecting them. There is no doubt these are hard, brain melting matters. But the beauty of the discovery of gravitational waves is that this can be understood!

A large number of my colleagues in LIGO (and myself) have spent the last week collecting and responding to questions emailed to us, asked in public forums, and delivered on social media (if you have more questions, ask in the comments below, or please email question@ligo.org). All of them are thoughtful, genuine, and demonstrate a pleasing curiosity and wonder about the nature and workings of the Cosmos. I am constantly amazed by the questions people ask.

Here are a few of the more common brain-melters we have been asked, and some meager attempt to answer them. The questions are marked in red, to make them easy to find. Some responses are more complicated than others, and you may or may not want to read them all. They are here to help stem the meltdown, if you find your brain is still reeling. 🙂

What does this mean for ordinary folks?  Far and away, this is the most common question I’ve been asked, particularly from the press. What does this mean for the world? How will this help my golf game?

LIGO’s discovery is what we call “fundamental physics.” It is a discovery that tells us something about how the Universe works and why it behaves the way it does. Figuring out how to use knowledge like that to make your life better or turning it into a gadget that’s useful in your kitchen or garage takes time — we’ve only just now made the first detection of gravitational waves, and are trying to wrap our brains around it.  Scientists and engineers will have to think a long time, maybe decades, before they can make this knowledge “useful for everyday life.”  That’s always how it works with scientific discoveries. How it will impact our everyday lives is not for us to know — that is for the future.

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

That is not to say that there isn’t some amazing future application. We only have to look at the history of general relativity itself to know the truth of this. Einstein worked out general relativity between 1905 and 1915. This was an age before cars and electricity were mainstays in everyday life. Yet Einstein had the where-with-all to understand that gravity could be thought of as the warpage of spacetime, and that one consequence of that warpage is clocks tick at different speeds depending on how strong the gravity is.

Did you know that little, obscure fact of general relativity is used by you and most other people every, single day? It is an essential part of how the GPS in your phone works. It took nearly a hundred years for the “fundamental physics” we call general relativity to be turned into an essential piece of technology that now gets millions of us from place to place in the world every day. Without GPS and general relativity, you’d still be navigating using paper maps. Einstein had to rely on his neighbor to tell him where to find a pub; you have a smartphone.

Is it really that important? I think this is one of the most important discoveries in astronomy in the last 100 years. It is as important as discovering that there are other galaxies beyond the Milky Way, it is as important as discovering the expansion of the Universe, it is as important as discovering the Cosmic Microwave Background.

The reason I think this is just about everything you’ve ever heard about the Universe, or seen a picture of, has been discovered using LIGHT. Telescopes are just instruments that do what your eyes do (collect light), though telescopes collect much more light than your eye or collect light that your eye cannot see (like infrared or ultraviolet light).

Gravitational waves are different — none of us have a “gravitational wave detector” as part of our bodies. Gravitational waves are something that we predicted should exist, and we built an experiment that showed us our ideas were right.  The beginning of gravitational wave observations will change how we see the Universe in ways that we cannot yet imagine.

Dr. France Córdova, Director of the National Science Foundation.

As a scientist and a teacher, I can appreciate the importance and utility of the collection of knowledge. But LIGO’s discovery goes far beyond the mere acquisition of yet another fact to post on Wikipedia. What the scientists and engineers working on LIGO have done was often regarded as impossible to do. But as Dr. Córdova intoned at the LIGO press conference, we took a big risk. Through a judicious application of sweat, brains, and stubbornness, we endured a decades long effort to design a machine to do the impossible. We encountered countless challenges and obstacles, and diligently overcame every single one of them to arrive at this day. That should make every person sit up a little bit straighter and prouder. That should make every single person aware that whatever challenges or problems we face on our small world, we have the means to overcome them, if we have the will to commit our time and brains and resources to them.

The black hole collision LIGO observed was more than 50 times brighter than all the stars in the Universe. How can that be?  The comparison is “the gravitational energy released by the merger is about 50 times the energy released by all the stars in the Universe during the same time.”  This is an example of a “Fermi problem” which astrophysicists use all the time to figure out if our numbers are right when we are doing complex calculations.

The night sky over the Pando Forest in central Utah. Pando is an 80,000 year old aspen grove — it has seen almost 30 million nights like this one, bathed in the light of the stars of the Milky Way. [Image: Shane L. Larson]

Astrophysicists measure brightness in watts, just like you are used to expressing the brightness of a light bulb in watts — the “wattage” tells you how much energy is released in a fixed amount of time. The higher the wattage, the more energy is released in a given moment, so the brighter the star (or bulb). Astronomers call this the “luminosity.” We can estimate the luminosity of all the stars in the Universe and compare it to what LIGO measured from the black holes. [[I’m going to use some scientific notation here to write some mind-bogglingly big numbers; a number like 10⁶ means a 1 followed by 6 zeroes: 10⁶ = 1,000,000. ]]

If you express the luminosity of the black holes (3 solar masses in just about 20 milliseconds) as a “wattage,” the brightness is about 3.6 x 10⁴⁹ watts, or about 10²³ times brighter than the Sun.

The Hubble Extreme Deep Field (XDF). We can use images like this to estimate the total number of stars in the Cosmos.

Now suppose we make the assumption that all the stars in the Universe are just like the Sun. This isn’t true, of course — some are brighter, some are dimmer, but on the average this is a good starting guess. There are about 100 billion stars in a galaxy like the Milky Way, and if you look at an image like the Hubble Extreme Deep Field, there are on order 100 billion galaxies in the Universe. So there are 100 billion x 100 billion = 10²² stars in the Universe. If each one of them is the brightness of the Sun, the total brightness of stars in the Universe is 10²² times the brightness of the Sun.

But we said the black hole merger seen by LIGO was 10²³ times brighter than the Sun, so: 10²³/10²² = 10. The black hole merger was 10x brighter than all the stars in the Cosmos. With a careful calculation, we could get the 50 number you hear from LIGO, but 10 is pretty close. This is the nature of Fermi problems — they don’t give you the exact number, but they quickly get you close to the exact number so you can understand the Universe.

What do you mean “spacetime is stretching LIGO’s arms?” What is spacetime? Spacetime is the substrate, the matrix upon which everything in the Universe is built — as we like to say, spacetime is the “fabric of the Cosmos.” It is, of course, easy to say that, but difficult to wrap your brain around. We’re used to not thinking about space at all; it is the nothing between everything. But it is exactly that nothing of which we speak — if we were not here, if nothing were here, there is still space.

Imagine a gravitational wave shooting through LIGO, directly out of the screen at you. (A) When there are no waves, the arms are at their fixed lengths. (B) When the wave first hits LIGO, the spacetime in one arm stretches and in the other arm compresses. This changes how long it takes light to go from the corner to the end of the arms and back again. (C) As the wave passes by, the arms change back and forth between stretching and compressing.

How do you measure the length of something in space? Most of the time we use a ruler or a tape measure. You lay it down along the thing you are interested in, like LIGO’s arms, and you see how many it takes. Imagine that you put down kilometer markers along LIGOs arms, just like you see on the highway — one at 0km, 1km, 2km, 3km and 4km. When spacetime between the ends of LIGO changes, the entire arm stretches. You still think the arm is 4 kilometers long, because the markers are still evenly spaced (the spacing is just larger than it was before, though you may not be aware of it). We need a way to measure the stretching without relying on the kilometer markers.

Visualization of LIGO interferometry. (A) When no gravitational wave is present, the laser timing is set up to make a “dark fringe” at the output [square panel on the right]. (B) At the output, the light is like waves canceling each other out. (C) When a wave stretches or compresses the arms, it changes how the light is added together at the output. [Frames from video by Caltech/LIGO]

A reliable way to measure the distance in a space that is changing and stretching, is to time a beam of light as it makes its way through the space you are trying to monitor. In LIGO, we use laser light. Imagine two photons, injected into LIGO at the corner, with a photon traveling down each of the two arms (in terms of the the optics, there is an element at the corner called a “beamsplitter” that splits a laser beam and sends part of it down each of the two arms). When there are no gravitational waves distorting LIGO, the two photons arrive back at the beam splitter and are combined to make an interference pattern, which is a brightness pattern that depends on how the photons arrive together. We set it up so the pattern is a “dark fringe” — the two photons cancel each other out (what physicists call “destructive interference”).

A simple demonstration of how sensitive interference can be to small shifts in space. These interference patterns are made with overlapping patterns of regular circles (as opposed to moving waves) and create Moiré patterns. Here the horizontal dark region in the left image is analogous to LIGO’s “dark fringe.” The difference between the left and right image is a shift of only 0.05 inches, but the pattern difference is easy to see. What was a “dark fringe” now has a sliver of white, indicating the shift happened. [Image: S. Larson]

When a gravitational wave goes through LIGO it stretches the spacetime in one arm, and compresses the spacetime in the other arm. That means the photon in the stretched arm arrives back at the beam splitter LATE (it had farther to travel) and the photon in the compressed arm arrives at the beam splitter EARLY (it had less distance to travel). The result is the brightness pattern CHANGES. The changing pattern of brightness is exactly in tandem with the passing gravitational wave, telling us about the shape of the wave as it passes by.

They said the stretching that LIGO measured was a fraction of the width of a proton. But I remember from Chemistry that atoms are always moving, so how can you make such a precise measurement? Remember that LIGO is not measuring the distance shift in single atoms — it is watching the mirror, which is comprised of many atoms, each of which is moving exactly as you remember from Chemistry.

Everyone on a boat is doing their own thing, but they are all moving together as the boat moves on the waves.

When we make our measurements, we are looking at the behaviour of many, many photons that have travelled down the arm together, hit the mirrors, and made the return journey. Sure — some of the atoms are going one way, and some are going some other way, but overall they are all moving together, going wherever gravity is pushing the center of mass of the mirror. When we read out the light, we are looking at all of those photons that hit the mirror at the same time and using that information to determine where the mirror is.

It’s a bit like having a big gravitational wave discovery party on a boat. If you are on the shore, watching all the physicists and engineers having a good time, you see they are all going every which way on the deck. But they are all on the boat, which moves them all together in response to the underlying waves of the sea.

Will this help with time travel? quantum gravity?  Einstein’s great discovery with general relativity was the idea that gravity can be described as the interaction of mass with the shape and warpage of spacetime. The unification of space and time into a single entity — spacetime — is a huge conceptual leap that is sometimes hard to come to grips with because of the way we think about space and time.

In our everyday lives we measure space with rulers and car odometers, and we measure time with wristwatches and calendars. If they are the same thing, why don’t we measure them the same way? The idea that the two are connected takes some getting used to, though as I like to remind people: when you go somewhere, you are usually comfortable saying your destination is “25 minutes” away or saying “20 miles” away!

You think about travel as travelling through space or travelling through time without even noticing! You are used to being a “spacetime traveller.”

Since gravitational waves are moving ripples, propagating warpage in spacetime, it is natural to ask: can this discovery can help us understand space and time? Can we understand “time travel” and “warp drive?”

Time itself, despite being part of general relativity, is still a great mystery to us. But what we often forget is that we are time travelers. Even as you are reading this, you are traveling through time from this moment, heading toward next Tuesday. It is not possible, so far as we know, to go backward toward last Friday, and that is a great mystery. It appears to be true based on experimental evidence, but we don’t yet understand how the laws of Nature — general relativity — tell us that. So in as much as gravitational waves will dramatically improve our understanding of how spacetime works and behaves, that deeper understanding could lead us down a path of thinking that will ultimately give us more insight into the mystery of time.

In a similar way, the LIGO detection does not address the enduring questions about the microscopic, quantum nature of gravity. The gravitational waves are a “big world” phenomenon, created by strongly gravitating astrophysical objects. But based on our experience with other quantum physics, we expect that there will be a clear (though not now obvious) connection between quantum gravity and general relativity. The more we expand our understanding of general relativity, it becomes more likely we will stumble on the deep connections that would lead to ultimately understanding quantum gravity.

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I encourage you to continue asking your favorite physicist your questions and share what you learn. Also, send questions to: question@ligo.org

Remember: no question is a dumb question. If you are wondering something, I’ll bet you a jelly donut someone else has the exact same question!

Gravity 13: Frontiers

by Shane L. Larson

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Fritz Zwicky

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

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

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

Vera Rubin

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Gravity 11: Ripples in Spacetime

by Shane L. Larson

We have travelled far in our journey to explore gravity, far from home and into the deep reaches of the Cosmos. But all that we know, all that we have learned, has been discovered from our home here, on the shores of the Cosmic Ocean. Today, let us return home.  In the words of the space poet Rhysling,

We pray for one last landing
On the globe that gave us birth
Let us rest our eyes on the fleecy skies
And the cool, green hills of Earth.

Imagine yourself in a soft green meadow, far from the hub-bub of everyday life. What do you hear? What do you see? The gentle rustle of the trees, and the whisper of the long grass. The tall flowers of spring rocking gently back and forth, and the dark shadows of a bird of prey soaring effortlessly against the blue sky. All these sights and sounds are the signature of something unseen — the atmosphere of the Earth, the blanket of air that protects us and supports all the life around us.

How do we know the air is there? We can’t see it. All of these observations, infer the existence of the air by recognizing its influence on other things. If we want to measure the air directly, to detect it, then we need to construct controlled experiments where we understand the physical effect of the air and how it interacts with the experiment we design to elucidate its presence. Consider a simple experiment you can do right at home.

An experiment to convince yourself air exists. (TopL) If you just dip a straw directly in water and lift it out, then (TopR) all the water runs out. (LowerL) If instead you put your finger over the straw before dipping it, then (LowerR) no water gets in the straw. Something invisible got in the way — air!

Take a drinking straw and a glass of water.  Dip the straw in the water, then place your thumb over the top of the straw, and remove it from the water.  If you take your thumb off the straw, you find that you had trapped some water in the straw.  Now do a slightly different experiment. Put your thumb over the end of the straw first, then put it in the water. If you take the straw out of the water and remove your thumb, you find that there is no water in the straw!  Why didn’t water go in the straw? There must have been something in the way, something invisible you couldn’t see. It is, of course, the air. This seems completely obvious to us now, thinking about it with 21st century brains, but two millenia ago, when we were just beginning to speculate on the nature of the world, this was a remarkable and marvelous observation of the world.

Today, astronomers find themselves in a similar brain loop with respect to gravity. One can “measure the force of gravity” through experiment. But when Einstein developed general relativity, he did away with gravitational forces in favor of motion on the curvature of spacetime. We can use this idea to describe everything we see in Newtonian gravity — objects freely falling to the ground, orbits of astrophysical bodies, and the weightlessness of astronauts in space. There have been exquisite tests of general relativity confirming its unique predictions beyond Newtonian gravity, and we rely on it every single day.

But is there a way to directly measure spacetime? Can we confirm that gravity is no more than the curvature of spacetime itself?  This is a question that has occupied the minds of gravitational physicists for a century now, and many ideas have been proposed and successfully carried out.

The most ambitious idea to directly measure spacetime curvature was first proposed by Einstein himself, and has taken a century to come to fruition. One of the motivations to develop general relativity was famously to incorporate into gravitational theory the fact that there is an ultimate speed limit in the Cosmos. If the gravitational field changes (for instance, due to the dynamical motion of large, massive objects like stars), that information must propagate to distant observers at the speed of light or less. If gravity is no more than the curvature of spacetime, then changes in the gravitational field must must be encoded in changing spacetime curvature that propagates from one place to another. We call such changes gravitational waves.

The opening pages of Einstein’s first two papers on gravitational waves in 1916 (L) and 1918 (R).

If you want to build an experiment to detect an effect in Nature, you need a way to interact with the phenomenon that you can unambiguously associate with the effect. For the first 40 years after Einstein proposed the idea of gravitational waves, physicists were vexed by the detection question because they were confused as to whether the phenomenon existed at all!  The problem, we now know, was our inexperience with thinking about spacetime.

The International Prototype Kilogram (IPK).

Scientists spend their lives quantifying the world, describing it precisely and carefully without ambiguity, as much as is possible. To this end, we use numbers, and so need a way of agreeing on what certain numbers mean. For example, we measure mass using “kilograms.” What’s a kilogram? It is the mass of a reference body, made of iridium (10%) and platinum (90%), called the “International Prototype Kilogram” (IPK). The IPK, and six sister copies, are stored at the International Bureau of Weights and Measures in Paris, France. Scientists around the world agree that the IPK is the kilogram, and can base numbers off of it. Nature doesn’t care what the IPK is; the Sun certainly has a mass, expressible in kilograms, but it doesn’t care one whit what the IPK is. The kilogram is something humans invented to quantify and express their knowledge of the Cosmos in a way other humans could understand.

Example coordinates that can be used to describe the screen or paper you are reading this on. They are all different because humans invented them, not Nature. They are not intrinsic to the surface they are describing, though they are often chosen to reflect underlying shapes of the surface.

In a similar way, when spacetime physicists describe spacetime, we have to have a way of identifying locations in spacetime, so we make up coordinates. Like the kilogram, coordinates are something we humans create to enable us to talk with each other; Nature cares nothing, Nature knows nothing about coordinates. But sometimes we get so used to think about Nature in terms of coordinates, that we begin to ascribe physical importance to them! This was the case during the early decades of thinking about gravitational waves. Physicists were confused about whether or not the coordinates were waving back and forth, or if spacetime itself was waving back and forth.  Arthur Eddington, who had led the 1919 Eclipse Expedition to measure general relativity’s prediction of the deflection of starlight, famously had convinced himself that the waves were not real, but only an artifact of the coordinates.

At the poles of the globe, all the lines of longitude come together, and there is no well defined value. There is nothing wrong with the sphere; the coordinates that humans invented are not well suited there!

Sometimes coordinates behave badly, giving results that might seem wrong or unphysical. For instance, you can see one example of badly behaving coordinates at the top of a sphere — if you are standing on the North Pole of the Earth, what is your longitude? You can’t tell! Longitude is a badly behaving coordinate there! There is nothing wrong with the sphere, only our coordinates.

And so it was with spacetime. In the early 1930s, Einstein and a collaborator, Nathan Rosen, had discovered a gravitational wave solution that appeared unphysical and claimed this as a proof that gravitational waves did not exist. Their result was later shown to be coordinates behaving badly, and Einstein pivoted away from denying gravitational waves exist, though Rosen never did.

The argument of the reality of the waves persisted for decades; in the end, the questions were resolved by a brilliant deduction about how to measure gravitational waves. As with all things in science, the road to understanding is a slow and steady plod, ultimately culminating in a moment of  understanding. In the early 1950s, our thinking was progressing rapidly (or so we know now, with 20/20 hindsight). The watershed came in January of 1957 at Chapel Hill, North Carolina, at a now famous conference known as “The Role of Gravitation in Physics.” There were 44 attendees who had gathered to discuss and ponder the state of gravitational physics. It was barely 19 months after Einstein’s death, and the question of the existence of gravitational waves had not yet been resolved.

The community had slowly been converging on an important and central issue in experimental physics: if you want to detect something in Nature, then you have to know what the phenomenon does to the world around it. You then need to design an experiment that focuses on that effect, isolating it in some unambiguous way. At the Chapel Hill Conference, the realization of what to do was finally put forward by Felix Pirani. Pirani had settled on the notion that an observable effect of a passing gravitational wave is the undulating separation between two test masses in space (something gravitational physicists called “geodesic deviation” or “tidal deviation”). This idea hearkens back to the idea that the trajectories of particles is a way to measure the underlying shape of gravity, which was one of the original notions we had about thinking of gravity in the context of curvature.

The Sticky Bead argument was a thought experiment that convinced physicists gravitational waves were real and could carry energy. (TOP) Imagine two beads on a smooth rod. A small amount of friction keeps the beads from sliding freely. (BOTTOM) When a gravitational wave passes by, it pushes the beads apart. The friction stops the motion of the beads, heating the rod up. Measuring the heat in the rod constitutes a detection of the gravitational waves, since they were the source of the energy.

Also present at the conference was Richard Feynman, by then a professor at the California Institute of Technology. Feynman took Pirani’s notion and extended it into what we now call “the sticky bead argument.” He imagined a smooth rod with two beads on it. The beads were a little bit sticky, unable to slide along the rod without being pushed. When the motion of the beads was analyzed under the influence of gravitational waves, they moved back and forth, but their motion was arrested by the friction between the beads and the rod. Friction is a dissipative force, and causes the rod to heat up, just like your hands do if you rub them together. In the sticky bead case, what is the origin of the heat? The heat energy originated from the gravitational waves and was deposited in the system by the motion of the beads.

This idea was picked up by Herman Bondi, who expanded the idea, fleshing it out and publishing it in one of the leading scientific journals of the day. As a result, Bondi is generally credited with this argument.

(L) Richard Feynman (C) Hermann Bondi (R) Joseph Weber

Confirming that the beads move validated the idea that gravitational waves not only carry energy, but can deposit it in systems they interact with. This was the genesis of the notion that an observational programme to detect them could be mounted.  That challenge would be taken up by another person present at the Chapel Hill conference, named Joseph Weber. Weber had spent the previous academic year on sabbatical, studying gravitational waves at Princeton, and left Chapel Hill inspired to begin a serious search. Weber’s entrance to gravitational wave astronomy happened in the early 1960s with the introduction of the first gravitational wave bar detector.  This was the foundation that led to the great experimental gravitational wave experiments of today; we will start our story there in our next chat.

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I am indebted to my colleague Peter Saulson (Syracuse) who first made me aware of Pirani’s talk at the 1957 Chapel Hill Conference. That Conference is part of the folklore if our discipline, though details are often glossed over usually going directly to the Bondi Bead story. I am also indebted to Carl Sagan, who introduced me to the idea that one can detect the air with water experiments (in “The Backbone of Night,” episode 7 of Cosmos: A Personal Voyage).

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

Gravity 9: The Evolving Universe

by Shane L. Larson

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Harlow Shapley.

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

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

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

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

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

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

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

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

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

Lemaître with Einstein in California, 1933.

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

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

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

Gravity 8: Black Holes in the Cosmos

by Shane L. Larson

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Gravity 7: Recipe for Destruction (Making Black Holes)

by Shane L. Larson

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Gravity 6: Black Holes

by Shane L. Larson

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Gravity 5: Putting Einstein in the Navigator’s Seat

by Shane L. Larson

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

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

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

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

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

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

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

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

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

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

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

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

Third generation GPS satellite (GPS IIIa).

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

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

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

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

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

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

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

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

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

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

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

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

Gravity 04: Testing the New Gravity

by Shane L. Larson

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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