What is frame dragging? How do we measure it? And how can we turn this into a method for extracting energy from rotating black holes? I discuss these questions and more in today’s Ask a Spaceman!

Support the show: http://www.patreon.com/pmsutter

All episodes: http://www.AskASpaceman.com

Watch on YouTube: http://www.youtube.com/PaulMSutter

Read a book: https://www.pmsutter.com/books

Keep those questions about space, science, astronomy, astrophysics, physics, and cosmology coming to #AskASpaceman for COMPLETE KNOWLEDGE OF TIME AND SPACE!

Big thanks to my top Patreon supporters this month: Justin G, Chris L, Alberto M, Corey D, Michael P, Naila, Sam R, Joshua, Scott M, Rob H, Scott M, Louis M, John W, Alexis, Gilbert M, Rob W, Jessica M, Jules R, Jim L, David S, Scott R, Heather, Mike S, Pete H, Steve S, Lisa R, Kevin B, Aileen G, Deb A, Michael J, Phillip L, Steven B, Mark R, Alan B, Craig B, Richard K, Joe R, David P, Justin, Tracy F, Thomas K, James C, Syamkumar M, Homer V, Mark D, Bruce A, Tim Z, Linda C, The Tired Jedi, Bob C, Stephen A, James R, Allen E, Michael S, Sheryl, David W, Chris, Michael S, Erlend A, James D, Karl W, Den K, Edward K, Scott K, Vivek D, M0PPET, Brad, Azra K, Steve R, M D Malahy, Brian O, Alonna M, Joseph B, and Anders J!

Hosted by Paul M. Sutter.

 

EPISODE TRANSCRIPT (AUTO-GENERATED)

In 1969, Roger Penrose, yes, that Penrose, the one who'd later win a Nobel Prize, worked out a way to steal energy from a black hole. It's easy. You fly a spacecraft close to a spinning black hole, drop a payload at just the right angle, and you come back with more energy than you started with. In response, the black hole has a little bit less energy and therefore a little bit less mass. But nothing escapes the event horizon, no laws are broken, and yet the universe just handed you free energy. My favorite. kind of energy. Ah yes, the land of black holes, where nothing makes sense and everything we thought we knew turns out to be not quite right. But that's okay, we're going to take our time with this episode. We're going to unpack how this process works, why it doesn't break any laws of physics, and hopefully at the end, the universe will make a little more sense. And to get started, we need to introduce a rather beefy physics concept. It's called frame dragging. It's real, it's fun, and most importantly, it's the subject of today's episode.

To get to frame dragging, we first need to change how we think of space-time. We need to level up here. The level one way most of us imagine space is basically Newton's version. An empty stage. Objects sit in it, move through it, exert forces on each other across it, etc. etc. But the space itself is a passive backdrop. A giant three-dimensional room that doesn't care about what's inside. In this picture, space has no properties by itself. It doesn't stretch. It doesn't push back. It doesn't do anything. It's just where stuff happens. It exists, and that's enough for us to get physics done. Of course, this level one picture was blown up by Einstein's general relativity, which is our level two way of imagining space, now called spacetime, but that's not really relevant right now. And in this view, space or spacetime is not a passive stage. It's a physical thing with a shape. Mass and energy bend that shape, and the bent shape is what we experience as gravity. Picture one seamless four-dimensional thing that can be stretched, curved, twisted, and spoiler alert, dragged.

Okay, it's not much of a spoiler because I've already said frame dragging, and it's kind of the title of the episode. Anyway, space-time is an object in its own right, imbued with physical existence, just like particles and forces and fields are. It's dynamic. It's alive. But still, that's only level 2 thinking. It's good enough for most work in general relativity, but it's not where we're going today. So, we need level 3. Because spacetime has shape and behavior, we can treat it as a kind of fluid. Now, this is going to be mostly analogy, but also not 100% analogy. General relativity gives us a lot of freedom in how we describe spacetime and its interactions with matter. For example, you can imagine the space around a black hole as fixed with things falling in. Eventually, the gravity gets so strong, the walls of the well around the black hole are so steep that nothing can escape. But you can also imagine it as space-time flowing towards the black hole, like water into a sinkhole. And as you approach the event horizon, space flows faster and faster until you try to get out and you finally have to push against a current that's moving faster than light.

It's two completely different visual pictures, but a single unified mathematical structure underneath it. This happens all the time in physics, by the way, when we have equivalent descriptions and models of the same phenomenon. And this is just especially fun with general relativity. Now, of course, when I say let's treat space-time like a fluid, I don't mean a real fluid made of molecules. I mean a substance with its own local geometry that responds to what mass and energy are doing inside of it. When something moves through spacetime, it interacts with the geometry, like motion through water. You push the water, the water pushes back on you. It's a two-way dialogue. When you move through spacetime, spacetime pushes back on you. It's a two-way dialogue. And when something spins, it doesn't just churn the air or the water around it. It churns the geometry of spacetime itself. And churning fluids have a very curious property. Think of stirring honey. with the spoon. The honey right next to the spoon moves fastest.

A little further out, the honey rotates a little more slowly. Farther still, it barely moves at all. The spoon has set up a slow decaying swirl in the fluid around it just by rotating. General relativity says the spinning mass does exactly the same thing to spacetime. The spacetime itself picks up a slow rotation that is strongest near the object and fades with distance. This is frame dragging. Mass drags spacetime and spinning mass drags it in a rotational pattern. In this level 3 view, where spacetime is a fluid participant, not a stage, it has a local flow. It responds to what mass is doing and it goes on to do its own thing. And the thing that we care about it is that spinning things generate swirls. There's genuinely a sense in which spacetime is carried along By what's inside it. Of course, this is only a model to help guide us through the math. So let's not get carried away with ourselves. Space-time is not made of anything the same way that the ocean is made of something. It's not molecules with pressure and velocity and viscosity.

It doesn't have a temperature. It doesn't slosh. And if you set up a swirl, there's no friction to slow it down over time. In space-time, as long as the source is spinning... The swirl persists, and then as soon as you shut it off, it turns off. This is a geometric effect, not a mechanical one, but it is a real effect. Space-time is real. It's a thing, even though it's only made of itself. But that thing is responding to the motion of what's inside it, and that response persists. Which means, even with those caveats, our level 3 thinking is going to help us understand how we can pull energy out of black holes. Or was there a level four thinking? Sure, it's Patreon. Patreon.com slash PM Sutter. It's how you can keep supporting this show at a much higher level. I appreciate all of your contributions. Frame-dragging was worked out in 1918. Yes, just barely after Einstein published General Relativity itself. By two dudes, Josef Lenz and Hans Thuring. And so it's often called the Lenz-Thuring effect, which is yet another useless fact that will never come up in a trivia game.

And also none of your friends or dinner party guests will be impressed that you know it. But now it's stuck in your brain, isn't it? Anyway, Lenz and Thuring calculated that a rotating spherical mass, which is not exactly realistic, but it's the simplest possible setup to explore this effect, twists spacetime around it. Which is pretty crazy. When we think of stirring honey, we're physically pushing the stuff around with a spoon. But with spacetime, You can have a perfectly smooth, featureless ball just twirling around, and it's almost like spacetime has a certain stickiness to it that responds to that rotation. And they calculated that the strength of this twist, this rotation, drops off roughly as the cube of the distance, which is much, much faster than space. how gravity itself drops off, which is the square of the distance. So the further out you get from an object, gravity itself is getting weaker and weaker. And this frame dragging effect is getting even weaker, even faster. And frame dragging isn't exactly a strong effect.

Anyway, it's already a tiny effect. And the further you get from the spinning object, it becomes essentially nothing. To give you a sense of what we're talking about here, for Earth, the space-time around Earth our planet is being twisted at a rate of about 40 milliarcseconds per year. A milliarcsecond is a thousandth of an arcsecond, and an arcsecond is one 3600th of a degree. So Earth is dragging space-time around it at a rate of roughly 0.00001 degrees per year. To put it another way, if you were to compare the space-time around a spinning Earth versus a perfectly stationary Earth, after one year, the spacetimes would be different. They'd be rotated by less than the width of a human hair viewed from 10 kilometers away. So, like, not much. Anyway, that's the dragging part of frame dragging. It's tiny, but it's real. But what about the frame part? Why do we call it frame dragging anyway? Sometimes in physics, we just have useless jargon words that don't mean anything. I'm looking at you, virtual particles.

But sometimes they tell us something. In here, frame dragging is telling us something very important. Relativity is all about reference frames. It's a way of establishing this is standing still and everything else moves around it. Your kitchen is a reference frame. When you're walking through your kitchen, you use the refrigerator in the sink. They appear fixed, and so that is your frame of reference to say, I am currently moving through the kitchen. I am currently standing in front of the fridge deciding what to eat. I am currently peeling potatoes. Like that, you use the fixed reference frame around you to decide that you are in motion. If you were on a moving train, if you were to put your kitchen... or like a little kitchenette inside of a train, even though the train is in motion, if you're inside the kitchen, that is now your reference frame. You are judging your motion relative to your surroundings. But we can switch reference frames and have different judgments of motion. If there's a soda can sitting on a tray table in a train, if someone's sitting in that seat, according to their reference frame, their surroundings inside the train, the soda can is motionless.

If you're standing on the platform watching the train go by, you have a different frame of reference from which you judge motion. You're judging from the platform, not from the train itself. So you see, no, no, no, that sort of can is moving at 80 miles an hour. Both descriptions are correct. They're just from different frames of reference. And special relativity is all about how to account for the differences in reference frames, especially when things get really fast. And in relativity, some reference frames are better than others, or at least more useful, which in my book counts as better. These are called inertial frames. A frame is called inertial when things left alone move in straight lines at constant speed. There's no mysterious drift, no unexplained tugs. A spacecraft coasting through empty space with its engines off is in an inertial frame. It's just cruising, chill, relaxed. Inertial. We like inertial frames because life, by which I mean calculations, gets a lot easier and the physics gets simpler to describe inside of inertial frames.

Frame dragging means that reference frames themselves get dragged, which means around a spinning object, there's no such thing as staying still. General relativity says that the local inertial frame The frame that is just cruising, chill, no other forces, no weird accelerations. It's perfectly inertial. Everything's chill and relaxed. Around a spinning mass is not fixed. It rotates. It gets dragged. What counts as standing perfectly still in the space around Earth is itself slowly turning in the same direction that the Earth spins. And remember... inertial reference frames, references, they are our definition of motion. They are a definition of not moving at all. When I say I am not moving, I say I'm not moving relative to my kitchen. But if you put your kitchen above the Earth, not in orbit, forget about orbit, forget about rotating around the Earth like the International Space Station. If you put your kitchen above the Earth and you say this kitchen is fixed, your kitchen itself is going to move why because reference frames around a spinning object like the earth are dragged along with the rotation the very thing by which you judge motion and judge standing still not moving at all is being pulled so if we were to put you perfectly stationary not in orbit but actually stationary above the spinning Earth, after one year, you would be a tiny, tiny, tiny amount shifted to your side, following the direction of rotation of the Earth.

No rockets, no boosters, no momentum. The Earth pushes you by twisting space-time around it, and the twisting of space-time carries you with it. Which sounds ridiculous, but hey, this is general relativity. This whole frame-dragging business has been validated by experiments. At least, kind of. It's a long story and really should be the subject of another episode, but decades ago, a bunch of scientists launched the Gravity Probe B to measure this. They had to make the world's most sensitive gyroscope and put it in a drag-free orbit. By encasing a perfectly smooth metal sphere suspended inside the experiment, any little nudge from the outside world would shift the position of the metal sphere, which would let them adjust the experiment to compensate. This way, they could get a clean measurement of the orbit and pick out the frame-dragging effect. But when they hauled in all the data, they realized they made little oopsie-daisy and didn't account for little patches of extra electrostatic forces on the satellite body, so they had to spend six years figuring out a way to account for them.

The result was a measurement of the frame-dragging effect to within 19% of the theoretical prediction. Not great. Not terrible, but generally considered good enough to call it a win. Anyway, where were we? Right, okay, frame dragging is cool and all and barely makes sense, but it's so tiny we can barely even measure it, even after decades of work and the creation of the most exquisite gyroscopes ever made. It's a whisper. It's a twitch. It's a rounding error on a rounding error. So, that's boring. Let's get off the earth. It's no good trying to measure it here. Who even measures things in widths of human hairs per 10 kilometers distance anyway? Let's go somewhere else where frame dragging is a little more interesting. Let's go straight to the black hole. I mean, why not? The most concentrated concentrations of matter in the universe. And not just any black holes. Rotating black holes. But to crack the frame dragging of rotating black holes, we actually have to figure out, well, rotating black holes.

General relativity is famously hard to solve. Einstein's field equations are actually ten equations all tangled together and related to each other, not to mention each one individually as difficult to solve as they're non-linear for all the math nerds out there. And finding an exact solution, a formula that tells you the shape of spacetime in some real physical situation, is often mathematically impossible. For most practical applications, we have to turn to numerical approximations to get work done. But there are a few notable exceptions. For nearly 50 years after Einstein published general relativity, we only had one black hole solution. It's for the non-rotating, uncharged, perfectly spherical black hole. This was worked out by Karl Schwarzschild in 1916, by the way, from a trench on the eastern front six months before he died. But this is not the story of Karl Schwarzschild. The Schwarzschild solution is beautiful and useful, but it does have one small problem. It describes a black hole that isn't spinning.

And real black holes always spin. Everything in the universe spins all the time, including stars. And when they collapse, angular momentum has nowhere to go, so it stays with the collapsing star, which means that every realistic astrophysical black hole is rotating. And not just a little bit. Black holes are some of the fastest spinning objects in the universe. So huge mass, tons of rotation. There's got to be some real frame dragging going on, but how much? But for half a century, we're stuck. Our best theory of gravity had a solution for the black holes that didn't exist and no solution for the black holes that do exist. That changed in 1963 when a New Zealand mathematician named Roy Kerr figured it out. He found the exact solution for a rotating black hole, a set of equations that tell you exactly, precisely, with no numerical fuzziness, what a rotating black hole is up to and how it changes spacetime around it. His solution is called, unsurprisingly, the Kerr solution, and it describes every black hole we've ever observed.

Not some, every single one. Rotating black holes add something spicy to their surroundings. There's more than the usual event horizon. It's still there, although bulgy around the middle and pinched at the poles, kind of like an egg laying on its side, or maybe an M&M. Dark, crunchy, ever so slightly dangerous M&M. But sitting outside the event horizon is a second surface. This surface is called the static limit. And the region between the static limit and the event horizon is called the ergosphere. The name comes from the Greek word ergon, which means work, and ergosphere. that will become important in just a hot minute here. Here's what makes the ergosphere, that region just outside the event horizon, so strange. Frame dragging inside it is so strong that no observer, no object, not even photons, can hold still relative to the distant stars. Not because gravity is dragging them into the black hole, you're outside the event horizon, you can still leave. But because inertial frames, the local definition of not moving, is being pulled around the black hole faster than the speed of light in the opposite direction.

Check this out. If you wanted to counteract the frame dragging of the Earth, all you have to do is move in the opposite direction. No big deal. Just fire your rockets just a tiny bit and you'll counteract space-time pulling you along. If you want to counteract the frame dragging of, I don't know, a neutron star, you have to work harder, but it's doable. In either case, you fire your rockets just right to balance out the frame dragging, move in the opposite direction of the local rotating spacetime, and maintain your fixed position. But a black hole? Told still relative to one of these dead stars within the ergosphere, you'd have to move backwards through the local rotating spacetime faster than light, which you can't. Which means everything in the ergosphere is required by the geometry of the universe to rotate along with the black hole. Even photons trying to push against the spin get carried forward anyway. Anything that falls into the ergosphere gets swept along like leaves in a whirlpool.

There is quite literally no such thing as stationary inside the ergosphere. Rotation is compulsory, and we can use this to our advantage. In 1969, Roger Penrose was thinking about what physics you could actually do inside the ergosphere. And you realize something remarkable. Because objects in there are forced to co-rotate with the black hole, and because that forced co-rotation carries energy, you can, in principle, extract some of that energy and take it with you. Here's all you have to do. Fly a spacecraft towards a black hole with some payload on board. Spare fuel tank, empty people, an empty pizza box, whatever's handy. Cross the static limit into the ergosphere. Once you're there, you're compelled to move and nothing you can do can counteract it. So you start rotating in the same direction as the black hole spin. So now that you're in there, you kick the payload backwards, meaning in the opposite direction of the black hole spin. In flat space, this would just mean your spacecraft speeds up a little in the forward direction.

This is Newton's third law, action and reaction. And the total energy is conserved. Nothing gained, nothing lost. But the geometry of the ergosphere... is not flat space. Inside the ergosphere, the payload you kicked backwards can actually end up with negative energy, as measured by a distant observer. This is a genuinely strange feature of the geometry, not something I'm making up, and it's only possible because the ergosphere exists. Payload then falls into the black hole, carrying its negative energy with it. By conservation of energy, your spacecraft, now lighter, and having received a kick in the forward direction, flies out of the ergosphere carrying more energy than you brought in. The extra energy came out of the black hole's rotational reserves. And so, obedient to the laws of conservation of angular momentum, the black hole spins down ever so slightly. No violation. The negative energy I mentioned, that's a bookkeeping device to keep track of where everything is. Newton's reaction-action-reaction thing occurs just the same.

You push the payload out the back, you get pushed forward a little, but you get pushed forward a little more than you would expect in that energy was stolen by the black hole. So even though nothing can escape a black hole, the connection between a spinning black hole and the spacetime around it in the ergosphere means that we can extract energy. The black hole pays the price For every bit of energy we sip out of the ergosphere. Absolutely for free. All we need is a black hole in some empty pizza boxes and we're done. Now, I mean, don't get too excited. This isn't exactly an efficient process. A single Penrose event is fantastically inefficient. Real analyses show you'd extract only a percent or two per go of the energy of the object you kick of your payload. Like, you only get 1-2% of that kinetic energy back out. But hey, it's free. And for a typical solar mass black hole with typical rotation rates, if you drained it of all its available rotational energy, you would get, I mean, roughly 10,000 times all the energy the sun will emit across its entire 10 billion year main sequence lifetime.

So that's nice. But listen, we're not going to do this anytime soon. And when it comes to sci-fi speculation on the subject of the Penrose mechanism and extracting energy from black holes, my line is always, if you've managed to actually get to a black hole in the first place and construct a working energy extraction Penrose machine, then you've kind of already solved all the hard problems of energy to get there in the first place. So you don't really need the energy that the black hole is providing. But hey, you do you. And that's okay. Because nature does it for us. Shortly after Penrose made his calculations, a couple physicists named Roger Blanford and Roman Najak figured something out. The universe doesn't have a lot of pizza boxes just floating around, but it does have a lot of gas. And that gas likes to make its way into a black hole. And by the time the gas actually reaches the black hole, it's usually heated up to a quadrillion degrees and turned into a plasma. Which means that threading through the gas are complex weaves of magnetic fields.

My favorite. of all the fields. These magnetic fields plunge in and out of the ergosphere. Remember, unlike an event horizon, you're allowed to come and go as you please. Once inside the ergosphere, they can't help but move. They get all twisted up, and strong magnetic field forces push positively charged particles in one direction and negatively charged particles in the opposite direction. It's just like throwing the trash out the backside of a rocket, except one particle at a time. The threading magnetic fields extract energy from the rotating black hole and feed it back into the surrounding gas. But that energy has nowhere to go except into even stronger electric and magnetic fields which twist themselves up within and around the ergosphere, eventually channeling themselves into a blaze of radiation and particles coming out of the rotational poles of the black hole. These are the jets of quasars, powered by the rotation of supermassive black holes. These jets are enormous. They can stream relativistic particles for tens of thousands of light years, clear out of a host galaxy altogether, and push heat and radiation out into cluster environments.

One of the most famous of these are the Cygnus A radio lobes, which, well, they're pretty dang gorgeous to look at. So no, we can't realistically steal energy from a black hole, but the universe can and does. And we get to see it happen with our very own eyes. Thanks to AllyRBase on YouTube for the question that led to today's episode. Thank you to all my Patreon contributors. That's patreon.com slash pmsutter. Thank you. Please keep sending me questions. It's askaspaceman at gmail.com or the website askaspaceman.com. There's a form you can fill out there. Yes, I have a backlog of questions. No, I don't know when I'll get to your specific question, but I'm putting it on the list for the questions. somewhat random draw that happens twice a month and I really do appreciate it. Thank you for all the reviews you're dropping on your favorite podcasting platform that really helps. Once again, that's patreon.com slash pmstar. I'd like to thank my top Patreon contributors this month. They are Justin G, Chris L, Alberto M, Corey D, Michael P, Nyla, Sam R, Joshua, Scott M, Rob H, Scott M, Lewis M. John W. Alexis Gilbert M. Rob W. Jessica M. Jules R. Jim L. David S. Scott R. Heather Mike S. Pete H. Steve S. Lisa R. Kevin B. Eileen G. Dembe.

Michael J. Phil Bell. And Stephen B. That is patreon.com slash pmsutter. And I will see you next time for more Complete Knowledge of Time and Space.

Comment