Tag Archives: Spaghettified

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)

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