Tuesday, December 12, 2006

Hubble Radius Misconseptions

The Hubble Radius is one of those things about the standard cosmology that's commonly missunderstood. The distance keeps growing. So pages like the following are incorrect.

The Universe Adventure - Hubble Distance
(If that doesn't work, try this.)

The Hubble Radius
You might read that the Hubble Radius is what we can see, like it's another way of saying the visible universe. But that's not right. The Hubble Radius is the distance at which the expansion of the universe adds up to the speed of light. An important part of the standard cosmology is: the farther galaxies are away from us the faster they move away from us. It's not acurite but it's pretty consistant on average. A galaxy twice as far moves away twice as fast. So if you go really far, far enough, galaxies must move away at the speed of light. That distance is the Hubble Radius. It surounds us like a bubble. Anything outside of it moves away even faster than the speed of light. To be clear, cosmologists don't like to say "move" since that implies those things are actually moving through their space. And nothing can go faster than light. It's really the space between us is expanding. So instead, they say "recede". So at some point, galaxies must reciede away from us at the speed of light.

The Expanding Radius
The interesting part about the Hubble Radius is that the light beyond that distance can't get closer to us. The space between us is expanding too fast for the light to get any closer. You might think it reasonable to conclude that we can't see anything beyond that hoizon. And this is where the trouble starts. If the radius stayed the same size, that would be true. But it's expanding with the universe. It use to be a lot smaller back when the universe expanded faster. The size of the radius is closely tied the the age of the universe. The radius now is about 14 billion light years. That's close to the age of the universe. And when the universe was younger, the radius was smaller.

Seeing Beyond the Radius
We can see galaxies that are outside the the Hubble Radius and have always been outside. Few galaxies cross from inside to outside the radius (or vice-versa). Any galaxy with a redshift Z of 2 or more is outside the radius and has been outside since the light we see left that galaxy.

Tuesday, December 05, 2006

The Life of a Well Traveled Photon

The farthest object ever discovered is nearly 13 billion light years away. That's not the distance it is now and it's not the distance it was then. It's just the time it took the light to reach us. Astrophysicists call that the Light Travel Time distance. That distance isn't very informative and it's hard to explain why. Truth is they give us the Light Travel Time to avoid any obvious confusion. It's kind of an editorial policy. For example, if I told you that the object is actually 29 billion light years away right now, you might think that's impossible since it would have to go faster than twice the speed of light to get that far away. After all, the universe is only 13.7 billion years old.

Understanding such astronomical distances is an important part of understanding the expansion of the universe and the standard cosmology (Big Bang or Lambda-CDM). Most people, while learning about the expansion, bump into a couple popular analogies used to explain the theory. One involves a balloon and the other, raisin bread. Both models have their flaws. For me, it helps to add a third. I like to imagine one of those photons traveling all that way.

I can't keep myself from making a point about "Faster-Than-Light". Special Relativity and General Relativity are 2 different things. Special Relativity says the speed of light is the limit. But General Relativity says sufficiently distant objects have sufficiently different frames of reference. [Wikipedia] They do not contradict each other. They work together. So don't let Special Relativity keep you from accepting that distant objects can recede from us faster than light.

Let's go over what we know. Really, all we know is the redshift of the object. It's somewhere between 6.6 and 7.1. So let's just say 7. The redshift tells us how much the light has stretched since it started its journey. [wikipedia] From that, we know how much the space between us has expanded. It's now 8 times bigger than when the photon began its journey. (1 + redshift = 8) From the standard cosmology and the theory of General Relativity, we can figure out more. You can even do your own calculations with Ned Wright's Cosmology Calculator. Dr. Wright takes a lot into account that I am no good at. So I use a simpler model. That's cheating, I know, but it's not so bad. The biggest difference is that our photon starts out 12 billion years ago instead of 13. The rest is very much the same. The object is now 29 billion light years away. We see it as it was when it was 3.6 billion light years away. That's 1/8 the distance and fits the redshift. The object has been and still is receding away from us at just over twice the speed of light.

It's reasonable to assume the source object is a galaxy but we can't see it so well. It's very faint, which means the light we see contains few photons. Still enough reach the telescope's spectrometer to make a nice spectrum. Some of those photons started their trip on the ultraviolet or black light side of the visible spectrum, a nice deep purple with a wavelength of 400 nanometers. But by the time those photons reach us, their wavelength has stretched by 8 times to 3200 nanometers (1/20 the width of a human hair) pushing them through the visible spectrum and far into the infrared. Compared to sound, that's 3 octaves. That's like going from middle C to the deepest note on a piano. Visible light doesn't even cover one octave.

Our photon began it's journey by leaving the source object at the speed of light. But, because of the expansion of the universe, the source object is receding away from us at over twice the speed of light. So even though the photon is heading right toward us, it's still moving away faster than the speed of light. On its first birthday, that photon has traveled a light year, which is about 6 trillion miles. Yet it is slightly more than a light year away from the source. That's because the space behind it has expanded by about 200 miles. It's a tiny addition but it's something. Here, I'm assuming the expansion is applied evenly everywhere. But astrophysicists don't think that's the case so close to a galaxy. So forget what I just said.

Three billion years is when our photon gets the farthest away from us. It reaches 5 billion light years away. That's a billion and a half farther than when it started. Plus, it's showing its age. It started off a nice deep purple. But by this time, it's gone through the visible spectrum and well into the infrared.

Three billion years is also when things start to change for our photon. Although it's farther than it has ever been, it's just as far from the source object. That object is now 10 billion light years away from us. Even though 3 billion years have passed, expansion has added to the distance. Plus, by this time, the expansion of the universe has slowed considerably. It expands 1/3 as fast as when the photon began its journey. In fact, it has slowed enough that the space between us and the photon expands at just the speed of light. That means our photon won't get any farther away. For the rest of the trip, it just gets closer.

After an additional 5 billion years, it has reclaimed all the distance it lost and then some. It may be getting a little long in the tooth (and the wavelength) but the expansion isn't enough to keep it from moving toward us at nearly the speed of light. It travels the remaining 3.4 billion light years in 4 billion years. You can see all that in this Space-Time diagram.

This is called a Space-Time diagram but I think it should be called a Distance-Time diagram. Although the photon is shown as a curved line, the photon does not turn. It started off heading straight toward us and kept that heading even when it was getting farther away. The part I should explain is the Hubble Radius Cone. The Hubble Radius is the distance at which the expansion adds up to the speed of light. It surrounds us like a bubble at about 13.7 billion light years away. But when the universe was younger, the bubble was smaller. So in this diagram, it ends up looking like a cone. The bigger the bubble, the slower the expansion. Notice that the cone crosses our photon's path just when it began getting closer.

So now you know that some of the light we see may have taken a strange path and gotten farther away from us before heading toward us.

Monday, December 04, 2006

Iraq War Adds 40% to Deficit

As of November 2006, $350 billion has been spent on the 3.5 year long Iraq war. That’s $100 billion a year. That means the Iraq war has added 40% to the deficit over the same period of time (May 03 through October 06) from $840 billion to $1190 billion. That $350 billion accounts for 73% of the budget approved by congress for the “war on terror”. The rest is for Afghanistan, domestic and some other war related stuff. This does not include a $127 billion request that has not yet gone through congress. All these numbers come from the Congressional Budget Office. The deficit numbers come the Historical Budget Data PDF link right on the home page. I estimate the 2006 deficit to be $250 billion.

http://cbo.gov/budget/historical.pdf (PDF)