Have a causally consistent new year

… so what? Another year, another orbit of the earth. What’s the big deal, you say?

Well! I have some New Year’s news for you. Firstly, did you know that this year we get an extra second? To deal with this I suggest counting like a computer scientist; …3, 2, 1, 0! Happy New Year!

This year will, apparently, be the International Year of Astronomy! Georgia at Earth & Sky Science has found a great way to celebrate: 365 days of Astronomy Podcasts.

If that’s not enough, why not follow your lightcone this year? I found a great site that provides an RSS feed of astronomical bodies you (yes you!) could possibly have influenced since your birth.

… what’s a lightcone, you ask?

A lightcone is the 4-D surface in space and time that a flash of light forms as it travels away from its origin. The name is actually a bit misleading. It’s less of a cone, and more of a hyper-cone; that is a cone in four dimensions. Imagine a flash of light. As it moves forward in time the light will move outwards in all directions. At any point in time the light will be confined to the area of a sphere. As time progresses, the sphere will grow in size at a constant rate. If we think of time as another dimension, and tried to draw a 4-D graph of the flash, it would be a hyper-cone.

If you are still confused, a good way to begin thinking about this is to imagine a very small circle lying flat on the ground. Now, imagine it growing and as it grows you move it upwards. Every time the circle grows one centimeter in radius, it moves one centimeter higher up. This traces out the 3-D cone you know and love. The upward direction represents time and the other directions represent a 2-D space. To generalize to a 3-D space with time, you change the idea of a growing circle to a growing sphere. Et voila: a lightcone.

… ok, so what’s so special about a lightcone, you ask?

Since a lightcone is the boundary on which a flash of light travels, and nothing can travel faster than light, the lightcone also marks the boundary of influence of a certain action. Let’s say, for example, you sneezed. Achoo. At some other time, in some other place, let’s say a book fell over. Could your sneeze have possibly caused the book to fall over? What you could do is mark two points on a graph; one representing the time and place of your sneeze and the other representing the time and place of the falling book. You could draw a lightcone originating at the sneeze point. If the other point is outside this lightcone then it is physically impossible for your sneeze to have caused the book to fall over.

You could also do the same for your birth. Draw a cone originating from earth at your birthday. Now draw points for all the stars in the sky at time: today. Any points inside your lightcone could have been influenced by your birth. The word “could” is in italics because it’s really saying: “sure, the laws of special relativity don’t disagree with you… but… there’s more to cause and effect than lightcones”. Still, it’s a fun way to learn about astronomy!

So this year be aware of your lightcone and keep track of the people and events inside it. The range of influence of your actions is probably a lot more vast than you originally thought…

Twinkle, twinkle galactic internet.

So far, we don’t have much in the way of galactic communication. Broadcasting messages throughout the galaxy would take enormous amounts of energy. This energy usage can be reduced by focusing the message on a certain solar system. But shining laser light or neutrino beams at a specific solar system has the “needle in the haystack” problem; it would only be effective if you knew someone was listening. This is why the paper I found on arXiv is so interesting. It’s called The Cepheid Galactic Internet, and the authors put forth an idea for using Cepheid variable stars to broadcast messages that can be picked up by anyone in the galaxy (or maybe further). Now, implementation of this idea is not really within human capability, and probably won’t be for millenia. For one thing, we’d have to actually get up close to a Cepheid variable star, which aren’t exactly in the neighborhood. Instead the authors suggest that this is a physically possible technique that an advanced civilization might use to try to communicate with beings across a galaxy, without knowing their exact location.

…so what the heck is a Cepheid variable star, you ask?

Well. A Cepheid is a special type of star that continually gets brighter and dimmer over a period of anywhere between one to fifty days, depending on the star. These oscillations happen at regular intervals and, amazingly, there is a correlation between the period of the Cepheid, and how intrinsically bright it is. Because of this, Cepheids are frequently used to measure distances. By looking at the Cepheid’s period of oscillation we can tell how intrinsically bright it is, and when we compare that to how bright it looks to us, we can determine how far away it is. An analogy would be putting a 60W light bulb at some distance and measuring how bright it appears to you. You know it’s 60W, so you know its intrinsic brightness. Comparing that with how bright it looks to you will tell you how far away it is. The dimmer it looks to you, the farther away from you it must be.

… so how can you encode messages in it?

I’m glad you asked, but in order to understand that, you first have to understand a little about how a Cepheid variable oscillates. Cepheids are special in that they burn their fuel at a temperature high enough to ionize Helium (He⁺) which is already present in their atmosphere a second time to become He⁺⁺. Cepheids have an atmosphere that contains Helium which has already been ionized. As they burn their fuel, Cepheids heat up the He⁺ in their atmosphere enough to give the outermost helium electron enough energy to escape. When an electron escapes from an He+ atom you are left with He⁺⁺. As it turns out, He⁺⁺ is not as transparent as He⁺ (physicists say it has a higher opacity). This means that the newly formed He⁺⁺ atmosphere does not let the light from the star — and thus, the energy — escape as quickly as it could before. All of this energy builds up and creates pressure inside the star. The star then has to expand because of this pressure. As a star expands it cools down (as dictated by basic thermodynamics). As the star cools, the He⁺⁺ atmosphere cools and becomes He⁺ again. This means the atmosphere is more transparent, which releases more energy, which lowers the pressure, which shrinks the star, and starts the whole thing over again.

Now, what we have here is a huge pulsating signal that can be seen anywhere in the galaxy and even beyond that. All it says at the moment is: “pulse – pulse – pulse – …”. Suppose you could just control it enough so that you could get it to say something like: “pulsepulse – - pulse – pulse – pulsepulse – …”. You could use that to encode a message in a similar way you’d encode a message in Morse Code! What this comes down to is, controlling the period, just a little bit. This can be done by giving some extra energy to the star to trigger its cycle slightly too early. A nice analogy would be relating the star to a person on a swing set, swinging back and forth. As they swung back, you gave them a push a bit too soon, which slowed them down and caused them to swing forward sooner than had you left them alone. This would change their oscillation period in a similar way as changing the oscillation period of a Cepheid variable by adding extra energy a bit “too soon”. In this way, the Cepheid is like a stereo speaker. Alone it doesn’t do much for communication purposes (it might just hum a bit). If you connect the speaker to a iPod, the iPod will modulate the current in the speaker, and the speaker will amplify it. The iPod doesn’t need to use up much energy to transmit the signal; it just needs enough to control the speaker which uses its own energy (from an electrical socket, or something) to amplify the signal. So the “extra energy” is like the iPod which gets amplified by the Cepheid variable (stereo speaker).

The authors say that the best way to give this extra energy is to send a stream of neutrinos into the star, because neutrinos are the only particles small enough to travel right into the core of the star. Now, we of course have no way of producing a large enough stream of neutrinos to do this, let alone travel lightyears to a Cepheid variable and control its period with them. But hey! Who knows, maybe there’s already a civilization that has the capacity to do this. We could find out by looking at the Cepheids’ twinkling a bit more closely…

Edit: Turns out BoingBoing featured a post on this as well. Nature has an article also.

Edit #2: Bee at Backreaction posted on this paper too.

Introducing Black Holes

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.

Inflation

No, not the economic kind of inflation… I’m talking about cosmic inflation. You might have heard of it before. I’ll give you the gist of it. There are many problems with the big bang theory. When physicists talk about the big bang, they aren’t really referring to the “bang” part (strangely enough). What they actually mean is the part 10^-44 seconds after the “bang”. The big bang theory starts with some specially fine tuned initial conditions for the content and expansion of the universe and just lets it evolve from there to get our universe today. It doesn’t, however, explain what gave rise to those initial conditions. Inflation tries to do just that.

So what is inflation? Inflation is a rapid (exponential) expansion of our universe that we suspect happened just after the creation of our universe. This is, of course, unimaginably faster than the expansion rate of the universe right now. It might seem like a very strange thing for a universe to do, but if we accept the idea, we find that it solves several problems with the classical big bang model. Inflation describes how the universe could become initially so flat and homogeneous but still have small fluctuations that evolved into the galaxies we see today.

One of the strangest qualities about our universe is that it is almost perfectly flat. When I say flat, I don’t mean: like a piece of paper. I’m talking about a generalized idea of flatness. If one measures the curvature of the universe to be positive, then a triangle in this universe will have interior angles adding up to more than 180 degrees. If the curvature of the universe is negative, triangles will have angles adding up to less than 180 degrees. Our universe has a curvature of almost zero, so triangles have angles summing to almost exactly 180 degrees.

Why is a flat universe so strange? It’s because a flat universe is unstable. By that I mean that a positively curved universe will tend to collapse in on itself and a negatively curved universe will tend to expand so quickly that galaxies won’t have time to form. The best I can do at a simple explanation as to why inflation explains this apparent “coincidence” is that it has to do with how the contents of the universe (radiation, matter, dark energy), the curvature, and the expansion rate all relate to each other (the Friedman equations). An exponentially expanding universe will force itself to become more and more flat.

What could cause this inflation, you ask? Well, there are many theories of inflation that attempt to naturally account for an inflationary period, but what it mainly boils down to is the, so called, Dark Energy (aka: Cosmological Constant). That’s right, the same thing that’s confusing astrophysicists and cosmologists about the universe’s current accelerated expansion. Dark Energy, put simply, creates a repulsive gravitational force and results in an accelerated expansion of spacetime. The explanation as to why we are not “inflating” today, is that the Dark Energy today has less of a repulsive gravitational effect than it did in the early universe. Physicists are still trying to (cleanly) explain this transition.

I could keep rambling about how neat inflation is, but I think it’s best for everyone that I stop here.

A very lonely future.

I recently attended a lecture given by Lawrence Krauss which he called “Our Miserable Future”. It was a very interesting talk, giving an overview of the long term fate of Life, the Universe, and even Cosmology.

Consider this: The universe is expanding, and the farther away a galaxy is from us, the faster it will appear to travel away from us. This means that beyond a certain distance, galaxies will “appear” to travel faster than the speed of light. I should not say “appear”, really, because if a galaxy seems to travel faster than the speed of light away from us due to the expansion of the universe, then the light emitted from that galaxy will never be able to reach us. So, in fact, past a certain distance, we won’t be able to see any galaxies at all.

Now realize this: In 1998, astrophysicists discovered that the universe is not only expanding, it is an accelerated expansion. This will mean that the galaxies we see today, will eventually “speed up” and appear to travel faster than the speed of light, so we won’t be able to see them. Eventually, (well beyond the death of our sun, so don’t hold your breath) we won’t be able to see any galaxies in the universe. A very lonely thought.

What’s worse, the only way we know about universal expansion, is because we can measure other galaxies and see them traveling away from us. So well into the future, astrophysicists will have no proof that their universe is expanding.

Which kind of makes you wonder, eventually one of the amazing observations in physics won’t be observable. How many other amazing observations have we already missed by not evolving earlier after the big bang to discover them?

What’s up with this expanding universe anyway?

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.

Misconception #1: Expansion = Motion

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).

Misconception #2: Special Relativity is Violated

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.

Misconception #3: All matter is expanding away from the center of the universe.

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.