Friday, April 30, 2010

Understanding the Hubble Expansion of the Universe with Schlitz Light and Then Running Out of Ketchup


This is one of the most bizarre photos taken with the Hubble Space Telescope. It is a tiny section of a tiny section of the outermost halo of the Andromeda Galaxy, our nearest large galactic neighbor, 2.5 million light years from us. The stars are all in the Andromeda Galaxy's outermost reaches. Behind them are several galaxies, each one far more distant than the other. All are orders of magnitude farther from Andromeda than it is from us. Space is big.

The best way I've found to get a mental picture of the ongoing expansion of the Universe is with the following analogy. [1]

You decide to visit your friend who lives three miles up the road. You walk at three miles per hour so you get there in about an hour and both enjoy a cold, frosty Schlitz Light.

But as you start walking, a weird force begins stretching the distance between your house and your buddy's house at the rate of one inch per hour. So by the time you reach your buddy's house in an hour, his house is an inch farther from your house than when you started walking. No problem. What's an inch among friends and a cool, frosty Schlitz Light? But what if your buddy lives 3,000 miles away? Well, you start walking at 3 mph and it takes you (without sleep) 1,000 hours to get there. During that time, this weird force has made your buddy's house 1,000 inches (83 feet) farther from your house from when you started walking. But so what? Now he's got a bigger yard for you to both enjoy a cool, frosty can of Schlitz Light.

So if you keep doing the math, with your friend's house farther and farther away, you can still always get there, even if this weird force keeps making your buddy's house an inch farther from you every hour you walk. Yes, if your buddy lives 3 million miles away, his house will be 83,000 feet farther away than it was when you started, but so what? You can still make it. It just takes a bit more time and lets him go to the store and get another 12 pack of Schlitz Light, just in case.

Add a twist. Assume this weird expansive force that adds an inch between you and your friend's house each hour is not constant. It actually speeds up a tiny bit each hour. So, after 10 hours, it starts to add 1.001 inch to your distance each hour. And after 20 hours, it adds 1.002 inches to your distance. And after 1,000 hours, it adds 1.01 inches to your distance. This is still no problem if your buddy's house is only 3 miles away.

But it becomes a big problem if your buddy's house is 3 billion light years away. Not only does his house get a bit farther from yours each hour, but the rate at which it gets farther also increases every hour that you walk. If your buddy's house is far enough away from you, and since you can't faster than 3 miles per hour, at a certain distant X, the rate at which your buddy's house gets farther from you every hour will exceed your walking speed. You will never get there. No Schlitz Light for you.

This is exactly what happens to photons emitted by stars in galaxies billions of light years from Earth due to the Hubble expansion of space. Like us, photons can only move so fast. We can walk at about 3 mph. Photons travel at 186,000 miles per second. We and photons have a fixed, upper limit of how fast we can travel. As it turns out, for galaxies billions of light years from us, the expansion of space itself between us and them extends the distance between us and them faster than 186,000 miles per second. Once this threshold is reached, photons from these galaxies can and will never reach us. They are still "out there" but we will never ever have an inkling that they are.

Another way to think of the Hubble expansion is imagine your teenage son gets in the family car to go to the store to get hot dog rolls. Just as he is pulling out of the driveway you realize you're also out of ketchup. So as he starts to drive down the road you run after the car trying to get him to stop. Assuming he doesn't peel out, initially you can run fast enough to catch up with the car and flag him down. But if he's cranking up death metal in the car with the windows rolled up he can't hear you and keeps driving, pushing the accelerator pedal of the car down further. As each second goes by, he keeps going faster but you are already running as fast as you can. If he doesn't hear you or see you and stop, as every second goes by the distance between you and the car increases, even as you are running as fast as you can. After a number of seconds, he has pulled so far away from you that he disappears down the road. But in the case of space, the accelerator pedal has no bottom, and the speedometer has no top. After awhile, your son and your car are going faster than the speed of light. Even if you grabbed your cell phone and called him in the car to pick up ketchup he would not get the call because the radio waves from your phone would be moving too slow to catch up with him. So you order chinese instead.

Light Bubbles Are a Bitch

The movie "Lord of the Rings" has a scene where the message to attack is sent by glymphs or whatever using a sequence of bonfires on mountain tops. As each glymph sees the fire on the adjacent mountaintop, they set alight their bonfire and the message is quickly sent over hundreds of miles. Even though each bonfire lighter can only see the fires just above and below them, the message chain works. They are able to communicate 'over the horizon.'

In the same way, I've pondered if there's a way for distant galaxies to help us "leap frog" past the light bubble that surrounds us like these bonfires on the mountaintops. Is there a way for these galaxies to tell us what's over our horizon?

The "light bubble" is short hand for saying that because light travels at the speed of light, if the Universe is 14 billion years old, then we cannot see any object that is more than 14 billion light years from us. This doesn't mean there are no objects farther out from us than 14 billion light years, there are, it's just that we can't see them yet because the Universe is not yet old enough for their light to reach us.

What complicates the whole thing is that we are not at the center of the Universe. We are only at the center of our 14 billion light year bubble. The Andromeda Galaxy has the same size light bubble as us but it is centered on them, and they are 2.5 million light years from us.[2] So, technically, a species from Andromeda can see things that we can't and we can see things they can't because our bubbles are in different places. But the Andromeda galaxy is really close to us so using it as an example is not very fair.

So let's choose a galaxy way way way way far from us, like one of the most distant and faintest smudges of light in the Hubble Deep Field images. These buggers are somewhere around 10 billion light years from us, getting close to the edge of our light bubble. Now let's imagine if some folks in one of these smudges of galaxies also took their own Hubble Deep Space Field photograph of the farthest galaxies they could see. What would it look like? What would it show? This is where things get very weird.

The first problem is that unless these folks took their Deep Space Field photograph 10 billion years ago and broadcast its digital code into space, we would not be able to receive it now and look at it. But let's say they did. If some very smart, benevolent folks in one of these massively distant galaxies took their own Deep Space Field photographs 10 billion years ago, digitally encoded it in a translatable form, and blasted this code via radio waves for the nearby Universe to read, the latest picture we could get from them was the one they sent out 10 billion years ago. So we would get a nice snapshot of what things looked like from their perspective 10 billion years ago. We wouldn't be in it, of course, since our solar system and sun didn't even exist until 5 billion years after they beamed out the photo that we're just receiving, decoding and seeing today.

The next question is whether these folks in this galaxy 10 billion light years away could tell us about what is "over the horizon" from us: places and galaxies that are outside of our own 14 billion light year radius light bubble. At one level it seems possible. These folks are at the very "edge" of our light bubble and their own light bubble extends much farther than ours in certain directions. They can see in certain directions much farther than we can see. So why can't they just take a picture of this stuff we can't see and beam it out into space so we decode it and see it? Well, cuz the light bubble is a bitch. Here's the problem.

Let's assume these nice folks took very deep, sharp pictures of the farthest objects they could see every hour and broadcast them out into space, and we could read these data feeds, decode them and turn them into photos. Unfortunately, the latest series of photos they sent that we could see were sent out 10 billion years ago, showing the sky as they saw it 10 billion years ago. But 10 billion years ago, the entire Universe was only 4 billion years old, not the 14 billion years old it is today. So the light bubble they had then was only 4 billion light years in radius, not the 14 billion light years we have today. And 10 + 4 = 14. Every photon they could see 10 billion years ago in their 4 billion light year bubble is one that we can see today in our 14 billion light year bubble. Certainly, the resolution and detail of their photos of their local neighborhood would be far better than ours, and would show much richer close-ups of places that to us are just tiny smudges, but every single photon that hit their telescope 10 billion years ago would be a photon that hits ours. And here's the catch. Not a single photon they could record 10 billion years ago would be from a galaxy "over the horizon" from what we can see today. We today, and they 10 billion years ago, would be both taking pictures of the same horizon and seeing the same horizon.

Today, those folks, if their descendants still exist, are definitely seeing stuff that we cannot see. At this moment, they are now seeing way past our horizon. The problem is they cannot communicate to us right now what they are seeing because, if they send us a photo of what they are seeing right now, we will not get the message for 10 billion years and more. It's sort of like having a friend in California and you live in Boston. For both of you to eat lunch at the same moment, he has to eat lunch at 9 a.m. to eat lunch when you eat lunch at your noon, or you have to eat lunch at 3 p.m. for when he eats lunch at his noon. Your noons are three hours apart and there's nothing you can do about it. Now times that a few billion. It's that intractable.

So there's no way you can use a series of galactic friends as interlocking beacons to send each other messages as to what things look like over your respective horizons because the messages cannot travel faster than the light itself. Well, you can do it, but the messages will not come any sooner than the light from the objects reaches you on their own. The photos they send will be better, of course, because your buds are much more closer to these distant objects than you and can take better close-up photos. But none of the photons their photos capture will be photons that would have otherwise been too far away to reach you. They cannot send you any "over the horizon" photos. It would be kool, but it can't happen. The light bubble is a bitch that way. It doesn't allow leap-frogging or cheating.
Notes:
[1] I like to call it the "Hubble expansion" because it was discovered by astronomer Edwin Hubble at the Mount Wilson Observatory in California in the 1920s.
[2] Here's a fun fact about how much space there is compared to stuff. The Andromeda galaxy is about 2.5 million light years from the Milky Way. Both galaxies are about 100,000 light years in diameter. So it would take 25 Milky Ways to cover the distance between the two galaxies -- and there is almost literally nothing between them. So even with two large neighboring galaxies the ratio of non-stuff to stuff is still about 25:1. The Universe is mostly non-stuff.

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