A blog about physics from a well caffeinated grad student.
Found some really neat pictures of Hurricane Ike, courtesy of the NASA website. They were taken from the International Space Station on September 10th, 2008. The pictures really show the neat structure and you can even see the shadows that the clouds create over the earth. Amazing.
Picture of Hurricane Ike taken from the International Space Station.
With all the ruckus going on about Black Holes at the LHC, and my attempts to explain it all to my friends, I’ve realized that many people probably have little idea of what a black hole is… or worse, have misconceptions about them. I’d like to take a shot at explaining a bit about black holes.
You already know what happens when you clump bits of matter together. The combined gravitational pull of the matter will hold it together. The more matter you put on this thing, the bigger the gravitational force will be, and the more tightly it will hold itself together. You might have read my post about how space and time are curved. If you factor in this idea of matter curving spacetime then eventually you get a limit for the amount of mass you can pack into a certain volume. This volume is defined as a sphere of a certain radius called the Schwarzschild Radius. The size of this radius depends on the amount of mass in question.
So what is this so called Schwarzschild limit? Well, if you cram all of the mass involved inside a sphere with a radius equal to the Schwarzschild radius, then all this stuff you have crammed in must travel towards the center. I feel like I have to stress the word must here, because I don’t mean it in the same way that things must fall towards the center of the earth. Sure, things must fall towards the center of the earth, but eventually the thing will hit the ground, and the ground will stop it from moving any further. On the other hand, if something is falling inside this Schwarzschild radius, the object must move towards the center, and must keep moving! It can’t stop moving towards the center of the “sphere” in the same way that everything must travel slower than the speed of light. This means that if something is inside the Schwarzschild radius, regardless of what the thing is, regardless of how fast it’s going, regardless of what acceleration it has, it will always move and keep moving towards the center. In other words, all the stuff your cramming together is doomed to end up at a single point: the center of the sphere. So if you get a large amount of stuff, like a giant star, and this star begins to stop producing enough energy to counteract the pull of its own gravity, then the stuff might compress too much (within the Schwarzschild radius) and will be forced to compress to a single point. This is a Black Hole.
The term Black Hole has two different meanings. It can mean the single point where all of the mass has been compressed. This is also called the singularity (it’s a mathematical term). Black Hole can also mean “the sphere who’s radius is the Schwarzschild radius”. This is what people are talking about when they say things like “size of the Black Hole”. The size here means the Schwarzschild radius. It’s not the same idea as the “size” of the earth. When it comes to measuring the earth, we measure things like the radius that contains the earth’s matter. In a Black Hole, all of its mass is at a single point. So, to follow that same meaning of size we would have to say that the size of a Black Hole is zero. In other words, a Black Hole has infinite density.
So what would it be like to get up close to a Black Hole? Firstly, I should say that it is not the scary, cosmic vacuum cleaner as it is portrayed in some sci-fi. Planets, stars, and all things could happily orbit a Black Hole much like they orbit anything else. For example, if our sun suddenly became a Black Hole (which it can’t, it’s not massive enough), all of the planets, including the earth, would keep their same orbital trajectories, like nothing happened. Secondly, anything that falls into the Schwarzschild radius of a Black Hole (including light!!!) is subject to the same fate as the stuff it is made of, namely, it would be forced to fall towards the center, with no hope of escape (unless you consider Hawking Radiation an escape…). Lastly, theories that Black Holes are gateways to other universes can safely be ignored as speculation.
How would we observe a Black Hole if even light is doomed to fall into it? Well, we can infer the existence of a Black Hole (as we do with many things in astrophysics) by looking at effects of its gravitational influence. We can look for orbital trajectories of stars orbiting Supermassive Black Holes at the center of galaxies and see if they look like orbital trajectories things around a Black Hole might have. Recently there has been an effort to measure the mass of a certain Black Hole by looking at variations in temperature around galactic centers. There are tons of neat facts about Black Holes, so for more, visit your local Wikipedia page.
So, you’ve heard about the expansion of the universe. If you haven’t, well…surprise! The universe is expanding. But what does this mean? Well, in a previous post, I explained a bit about how space and time are not rigid, they can be bent. You might like to think of the universe as being made of rubber (I do…sort of). So what physicists really mean when they say the universe is expanding is that the rubbery spacetime in which we live, is being stretched.
Some people may confuse the idea of an expanding universe with the idea that all of the galaxies are moving away from each other. This is not a great way of thinking about it. What’s better is to think of this rubber sheet and draw some dots on it that represent galaxies. Now, if you start stretching the rubber sheet it will look like the dots are all moving away from each other, but actually, with respect to the rubber, they aren’t moving at all (very zen).
You may have heard that some galaxies appear to move away from us at speeds greater than the speed of light. Being the knowledgeable person that you are, you worry about Einstein’s special relativity being violated, since nothing can travel faster than the speed of light. Actually, there is no problem. Since expansion does not equal motion, the apparent speeds of these galaxies are not due to movement, but to the expansion of spacetime, so Special Relativity is not violated.
This may tie your brain in a knot at first, but I’ll say it anyway; there is no center of the universe. Remember that the universe is like a piece of rubber. If we were riding on one of those dots drawn on the surface while the rubber was being stretched, what would we see. Well, we would actually look around and see all of the dots moving away from us. This is because since the universe is being stretched the same amount in all directions, the distances between all dots are increasing at the same rate. It doesn’t matter which dot (galaxy) we choose to ride on, it will still look like all of the other dots (galaxies) are moving away from us. So since what we see doesn’t depend on from where we are looking, there can’t be any center.
Now consider this: if the very space in which we exist is expanding, then why aren’t the atoms in our body expanding away from each other? Why aren’t we just falling apart? Well, on very small distance scales, this effect is tiny… very tiny. The atoms in our body hold on to each other by electromagnetic forces. On larger scales (like a galaxy), gravity is the dominant force holding things together. That’s why galaxies don’t disintegrate because of spacetime expansion, gravity holds the stars together.
Imagine you are now floating in space. There is no gravity, no air, and nothing there except, perhaps, a screen in front of you. You shine a flashlight onto this screen. You can probably guess what will happen: the light will follow a straight path to the screen and you can now make shadow puppets. Now a slightly different but surprisingly similar case. You are in a glass elevator, and again, you have the shadow puppet screen in front of you and your trusty flashlight in hand. Suddenly, the elevator drops and you feel yourself become weightless just like you were in space. You don’t panic, no, you decide to make some more shadow puppets. Shining your flashlight you notice no difference in the shadow puppets. The light (from your perspective) travels in a straight line to the screen.
Here’s the kicker. The light takes some time after leaving the flashlight to reach the screen. A very short time, yes, but some time none the less. Let me remind you that the elevator is falling, so some time after the light has left the flashlight, the screen has moved downwards a slight amount. But you don’t see the light fly upwards because you are falling down, no, to you it travels to the screen like it should. Someone on the ground, however, will see you falling and making shadow puppets, but this peeping tom will see you and the light falling towards the earth.
If you have ever thrown a ball into the air, then you know that it follows a curved path as it falls. The light beam must do the same thing by our earlier logic. But light always takes the path of shortest distance (aka geodesic). But now you say, “Wait. The shortest distance between two points is a straight line! The falling light must not be taking the path of shortest distance!” No. Actually it seems, the shortest distance between two points is not a “straight line”. How, you ask? Because space and time are curved by the earth.
So what does space “look like”? Are we living on some kind of five dimensional sphere? Maybe and maybe not. There is no requirement, physically, for a “fifth dimension” to have space and time curve into. People always like to give the image of a bowling ball on a bed sheet and relate that to the earth curving space and time but you need to be careful with this image. This bed sheet is actually only a two dimensional space (excluding time), when really we live in a three dimensional space, but it’s impossible to imagine a three dimensional space curving. Here’s a nice picture of what I’m talking about.
This bed sheet analogy also leaves out the image of time curving. What does that look like? I have no idea. I don’t know what time “looks like” in that sense. One result of the curvature of time, though, is that someone on a high mountain (a really high mountain) looking down on you will see you travel more slowly and they will see you travel more quickly (or do whatever it is you are doing, more quickly). This effect actually makes a difference for GPS satellites, who’s internal clocks travel more quickly than ours do. (The engineers take this into account, of course, because GPS works well.)
So what is gravity? It’s just a result of the curvature of space. Baseballs, cats, and that bit of coffee you spilled earlier this morning, all fall towards the earth because they all must follow paths of shortest distance, which happen to be what we call: down. We must constantly fall towards the earth because we must move through time. As we move through time, we must take the shortest paths. So it’s not that gravity is pulling us down, it’s the earth that is pushing up on us, preventing us from traveling on the paths of shortest distance. That is what we feel as gravity.
Neat things to read…
