Tuesday, March 16, 2010
Olbers Paradox and Where is the Edge of the Universe.
The edge of the Universe. Beyond is heartbreak and despair.
For any observer A, the edge of the Universe is a sphere outside of which information sent from any point N to A and A to N can never be received because the rate of expansion of space between A and N exceeds the speed of light. And this does happen.
Olbers Paradox says that if the Universe is infinite and is inhabited by an infinite number of stars, the sky should be infinitely bright, since every conceivable spot in the sky should be occupied by a star. Since ocular evidence suggests this is not the case we have to ask why.
One answer is the expansion of space itself, as shown by Edwin Hubble's study of distant galaxies, in which Hubble found the farther away a galaxy is from us, the faster it is moving away from us. In the 1920s, Hubble used the 100-inch Mount Wilson telescope near Los Angeles to become the first human to document the expansion of space itself. He discovered that all the matter in the Universe is riding along in expanding space like raisins in a rising loaf of bread.
The deep space field photographs from the Hubble Space Telescope, named for Edwin Hubble, show us galaxies which are so far away and moving so fast away from us that their light is visible to us only in the infra-red.
Edwin Hubble and his pipe discovered the Universe.
It is posited that due to the Hubble expansion (ie. the farther away the galaxy, the faster the galaxy is moving away from us), some unknown number of galaxies very far away from us are now riding the expansion of space at a speed faster than the speed of light, which means the photons leaving these galaxies now will never reach us. Bizarrely, we can see many of these galaxies today and take very sharp photos of them. 
One way to think of how the expansion of space changes the light reaching us from these distant galaxies is to take a thick elastic and draw on it a long chain of regular, curvy sine waves with a ball point pen. Make the waveforms nice and steep and tightly packed together.
Now stretch the elastic. When you stretch it, you are forcing every molecule of the elastic to be farther apart from every other molecule than it was before. When you do this, your ink-drawn wave forms change quite a bit. From the perspective of the ink and the wave forms you drew with the ink, the surface of the elastic is their Universe. When you stretch the elastic, you are stretching the only Universe these ink lines know. Like a God, you are making their Universe bigger.
As you stretch the elastic, each trough and crest you drew moves farther apart. Waves are defined as peaks and troughs. The distance from one peak to the next makes one wave length.
Here is a sine wave from an oscilloscope, representing a light wave, then stretched with Photoshop. It's analogous to what happens as light travels and space stretches "beneath" it: the wavelength gets longer and as a result, the light gets "redder."
Visible light packs tens of millions of individual waves into a millimeter. For radio waves, the distance between one peak and the next can be as long your outstretched arms.
The only thing that light "knows" is that when its wavelength gets longer it gets "redder." Instead of x-rays it becomes ultraviolet, instead of ultraviolet it becomes visible light, instead of visible light it becomes microwaves, instead of microwaves it becomes radio waves. This is all light knows.
The stretching of an elastic containing your ink drawing of sine waves is analogous to the effect of the Hubble expansion of space on the light that tries to cross it. As space itself is stretched out, the light waves are stretched as well. This is what Edwin Hubble discovered in the 1920s by looking night after night at the farthest away objects anyone on Earth had ever seen.
The stars of the globular cluster Omega Centauri, completely ignoring the expansion of space.
Light is Information
We call light "information" because the fastest possible way to communicate information is by light. This is because nothing moves faster than light. Not sound, not planes, not boats. If you want to send a message to someone fast, you have to use light. And if light is not fast enough to get your message through when it needs to get through, you're out of luck.
It's one thing to have to wait three months for a letter from London to Boston to arrive by ship. But what if even as the ship takes sail, the Atlantic Ocean itself keeps stretching out faster than the ship can sail? Light travels much faster than any ship. What happens if you use light to send your message? And what happens if the thing that light travels through stretches faster than light can travel through it? What happens if your message, sent by light, is not just a bit late, but can never reach its intended destination because space is expanding faster than light can travel? This is the weird reality Edwin Hubble confronted looking through the 100 inch telescope at Mount Wilson, California in the 1920s. In doing so, Hubble completely and forever changed how intelligent humans think of the Universe.
A rising loaf of bread is one way to think about the ongoing expansion of the Universe. You start out with a wet, heavy lump of dough the size of a softball. When you let the yeast rise and heat it, this lump of dough quadruples in size. When you take the bread out of the oven and cut it open you can see why: it is full of tens of thousands of air bubbles. As each of these bubbles grew they pushed each little bit of dough farther away from their nearest neighbor pieces of dough. Your lump of solid dough is now chock full of "non-dough." We call this bread.
"Non-dough" is what makes bread different from dough. Non-dough is something: it is air. As an analogy, we can call all of the matter in the universe the dough and we can call "space" the non-dough. And apparently, according to astronomers, as every second goes by, the collective lump of dough and non-dough we call the Universe is getting bigger. It's not because some sinister, unseen force is adding more dough. It's because some sinister, unseen force keeps adding more non-dough.
Normal Motion is Not Like the Expansion of Space
It's important not to confuse the expansion of space with the simple motion of stuff. Consider a Universe of a table and a few marbles. If you take two marbles on the table and push them away from each other, you have not increased the size of the table, even though there is now more "space" between the marbles. If you do this, you can tell you have not added space because as the marbles get farther way from each other, they get closer to the edge of the table.
Imagine that the marbles never move. Even the tiniest mote of dust on their surface remains perfectly still and undisturbed. But still, as you stand there, the marbles are suddenly much farther way from each other. If this happens, it's safe to assume your table just got bigger. Not from the edges out, but like the rising bread dough, from everywhere within, all at once.
A good way to tell if you are seeing space expand rather than just seeing stuff moving around you is if all the stuff you can see is moving away from you, and if you jump to another position, you see the exact same thing.
If you have a table covered with marbles and the table itself grows in all directions, every marble moves farther away from all the others. No matter which marble you are on, it always looks like your marble is stationary and all of the other marbles are moving away from you. No marbles are moving toward you or even sideways. They all look like they are all trying to move as far away from you in the straightest line possible. And no matter which marble you choose sit on, you see the same thing.
You are sitting on a tiny bit of dough. Very close next to you is another tiny bit of dough. Way over on the other side of the dough lump are other bits of dough. Let's analogize the yeast as "space makers" or "bubble makers" and assume that each yeast molecule makes one bubble of air in the bread every minute. If there are 10 yeast molecules between you and a nearby bit of dough, there are 10 air bubbles created each minute. So in one minute you become "ten bubbles" farther away from that bit of dough that used to be right next to you. But between you and the bit of dough on the other side of the dough lump there are a million yeast molecules, each making its own bubble.
Velocity is distance divided by time. So in one minute, the bit of dough on the other side of the lump of dough from you will have moved away from you by a distance of a million bubbles, while the bit of dough right next to you will have moved away from you by a distance of only 10 bubbles. From your perspective, the bit of dough closest to you is moving away from you at a velocity of 10 bubbles per minute while the dough on the other side of the lump is moving at a velocity of a million bubbles per minute. As we look farther and farther out across the lump of dough, the velocities become mind bogglingly enormous. How can anything move that fast? Wouldn't it tear itself apart? Wouldn't it fly right out of the dough?
No. From that bit of dough's own perspective, in its own little neighborhood far from us, its nearest neighbor bits of dough are moving away from it at the very poky and respectable velocity of 10 bubbles per minute. But to them, we are moving away at a frightening rate of speed. They are wonderingwhy we are not flying apart, being pulverized or popping right out of the loaf of bread.
This is one of the most important aspects of the Hubble expansion. To people on those extremely distant galaxies which to us appear to be hurtling away from us at a large fraction of the speed of light, they are thinking the same thing about us. To us, they are moving away at a frightening speed and we are stationary. To them, they are stationary and we are moving away from themat a frightening speed. Who is right?
Can the apparent velocity of these distant galaxies moving away from us exceed the speed of light itself? Yes. The speed of light is approx. 186,000 miles per second. According to Albert Einstein's Theory of Special Relativity, no object with mass can move at the speed of light and nothing can move faster than the speed of light. Light can move at light speed because it is a massless quantity (quantum) of pure energy: a photon. The only reason a photon can move at light speed is because it has no mass: it is pure energy. If a photon had even the slightest mass, it could not move exactly at light speed, and it would not be a photon, but something else. According to Albert Einstein, the speed of light is inviolate: it cannot be broken. So does this mean that the velocity of distant galaxies hurtling away from us hits a "wall" at a speed of 186,000 miles per second and can go no faster? Does the speed of light set a bar on the rate that space can expand?
No. The speed of light does not apply to the expansion of space itself, because space is not matter or energy. It is nothing. Apparently, "nothing" can move as fast as it wants to and we get to go along for the ride.
Nothing from Nothing = Something?
Every second, for reasons nobody understands, the Universe is creating a tiny little bit more "nothing" between everything, everywhere. And this nothing makes stuff move slightly farther apart. For a photon this is like running a 100 yard dash but for every yard it covers, the judges suddenly decide to make it a 101 yard dash. No matter how fast our photon runs, it can never cross the finish line. And if it doesn't reach us, not only do we not see it, but we have no evidence it ever actually existed in the first place, like a letter written but never sent, or better yet, a letter you thought of writing but never wrote, or even better, a letter you never even thought of writing. Light is information but only if it reaches a destination.
This helps us deal with Olbers Paradox. Why is a Universe filled with infinite stars and infinite stuff not infinitely bright to our eyes? One answer is that when the galaxies become so far away from us that their apparent velocity due to the expansion of the spaces exceeds the speed of light, their light stops reaching us. They galaxies are all still out there, still burning bright, but we do not see them because the expansion of the space between us and them has outstripped the speed of light.
One reason we can see so many galaxies, some as far as 10 billion light years away from us, is due to a crazy coincidence: the Universe is only about 14 billion years old. From a photon's perspective, we live in a very young Universe. If we lived in a very old Universe, say 500 billion years old, we would see very little in the sky. Except for a few nearby galaxies locked into a gravitational embrace with us, the sky would be utterly black. In 500 billion years, all the distant galaxies we see in the Hubble field today would have long ago left our view forever, their velocity away from us long ago exceeding the speed of light. All the stuff we see today would still be out there but we could not ever see it, and people across the way could never see us.
While the Universe has no problem creating more space between stuff, it long ago stopped creating more stuff. Since we're made of stuff and will always be made of stuff, this is a real problem.
If you look at the Hubble Deep Field photos you see a lot of galaxies. But despite how many galaxies you see, they are clearly separated by a lot of non-stuff. There's a lot of non-stuff in the Hubble Deep Field, which makes the stuff stand out. They tie the room together.
We now know that with every second that passes, the amount of non-stuff in between these galaxies increases, but the amount of stuff does not. Eventually, as all this new non-stuff pushes all the stuff farther away from each other, you end up with a lower density of stuff.
It's still the same amount of stuff you started with, but it's now intermingled with and spread out amongst a lot more non-stuff. The spaces between each aggregation of stuff get bigger but the amount of stuff stays the same. We call this the Universe getting "bigger." Or, WTF?
But it's not getting bigger in the sense that a loaf of bread expands to fill the cooking dish you put it in. If you put a lump of dough in a dish it can only expand to the walls of the dish. It can go up, but it can only go so far on the sides or the bottom. But in the Universe, there is no cooking dish and there are no sides or bottom. Every bit of the loaf of bread is as "close to the middle" as any other because there is no middle, because a middle requires edges. The middle is that point equidistant from the edges. No edges, no middle.
In the Universe, everywhere is the middle because there are no edges. No matter where you look in the Hubble Deep Space field photos, no matter which galaxy you pick out, the picture from a Hubble Deep Space field photo from their galaxy, looking out to us, would look just like it looks to us. Our Milky Way would be a tiny, irregular smudge of light barely visible to their best telescopes, the light they see from it is when it was first formed billions of years ago, and Hubble's law would tell them that the Milky Way is hurtling away from them at a large fraction of the speed of light, and in the future will increase its velocity from them past the speed of light, rendering us completely and forever invisible to them.
The conundrum of thinking in light speed is that every second we are being sent tiny messages, like messages in a bottle, from places vastly distant from us, and from times deep in the past. The messages and the bottle are photons, streaking to us at the speed of light from the moment they were hurled out of these galaxies in all directions. It's like having a quintillion newspapers delivered to your door, every second, from all over the Universe. And every second, if you have the time, you can look at all the photons just delivered to your front step and read the "news of the Universe."
But like in the time of the American colonies, when it took 4 months for a letter to arrive by ship from England, the farther away from us the news comes from, the longer it takes for us to receive it. When Samuel Adams received a package of correspondence from Benjamin Franklin, representing the colonies in England, he was reading the past, since everything Franklin wrote and described had, by Adams' calendar, already occurred 4 months ago. Adams had no way to find out from Franklin what was happening "now," since Franklin wouldn't get the question for 4 months and his reply would not reach Adams for another 4 months. While Adams and Franklin's "nows" were identical, in the sense that each could say what they were doing and thinking on March 15, from the perspective of instantaneously comparing their "nows" they were made helpless by physical distance and separation.
All of the stars and galaxies around Earth put us in the position of Adams in Boston and Franklin in London, except our communications with the rest of the Universe cannot be sped up with a faster boat or the invention of the telegraph or radio or telephone. Every time Adams in Boston opened a package of letters from Franklin in London he had no idea if Franklin was still alive, since the letters were 4 months old. And he would not receive word of Franklin's demise until 4 months after the fact. Every time Adams penned a letter back to Franklin, he had no idea if he was writing to a dead man.
When we look at the Hubble Deep Space field it's like we are Ben Franklin receiving a giant brick of newspapers and dispatches at his door each morning from every corner of the world. Because of the very slow time of ship travel, the newspapers from the farthest parts of the world in the package are the oldest and the news in them is the stalest. The local newspapers are the freshest, telling Franklin what happened the night before in London, where he lives. Even though all the newspapers are written in the present tense, and their writers are describing events near them as they had just happened, for us, if we are far enough away, it is as if we are reading an old history book, like going through microfilm copies of newspapers printed in the height of the Civil War, when nobody knew if Lincoln would ever find a competent general to lead the Union Army. These distortions of time are made even more ridiculous when looking at galaxies whose light reaching us left them 5 billion years ago.
But there is no infinite regression with the visible Universe. There is a time wall which has been independently discerned by several branches of physics. We know, to a very high degree of accuracy, that everything we can see began about 15 billion years ago. There are no galaxies or stars or stuff older than this that we can see. This was discerned by Edwin Hubble through this calculations of the motions of the galaxies flying away from us at great speed, the farther away, the faster. Rolling the movie we now see backward brings everything to a tiny point about 15 billion years ago. What we see does have a beginning, and by what it's been doing ever since, we can predict what it will do next. By looking at galaxies that are 10, 9, 8, 7, 6, 5, 4, 3, 2, 1 billion light years from us we have 'snapshots' of what the Universe looked like at each of these times. It's as if we had very slow mail service and just today our copy of a Civil War era newspaper arrived in our mailbox. We get these quadrillions of these very old letters every day from the sky. They are called photons, and like a Civil War newspaper, they carry just as much information today as when they were first 'printed' and mailed out from their home galaxy to us. And as each day goes on, we get quadrillions of updates and special editions covering all the new events which have just transpired from all points of the visible Universe. We are inundated with so much paper and reading material all the time from so many places that we need vast numbers of computers just to store this stuff so we can read when we finally get done reading what came in yesterday. And it never stops.
But it will. Since it seems certain now the expansion of space itself is not stopping, and may actually be increasing in rate, and there is no new stuff being made, the number of far-flung newspapers sending us their daily bulletins will slowly but steadily decrease. Some will go out of business, as when a star dies and its light stops shining. But most will disappear because the expansion of space between us and them will exceed the speed that light can travel. It's like if when Franklin sent letters to Samuel Adams, the Atlantic Ocean was increasing in width faster than any boat could sail.
It's perfectly natural to look at the most distant galaxies in the Hubble Deep Space Field and ask, "I wonder what they're up to now?" The light we're seeing from these galaxies began its journey to us 7-8 billion years ago. The light streaking toward us from these galaxies today, if these galaxies still even exist today, will most likely never reach us. This is because in the past 7-8 billion years, our galaxy and these have been sent hurtling farther and faster away from each other with each year due to the expansion of space itself. By now the space between us and these ancient galaxies is expanding at a rate that exceeds the speed of light. A photon of light released from these galaxies toward us today will never reach us because the space between us is expanding too fast for light to catch up with. Today these galaxies have passed the light wall and our now forever outside our ability to perceive them or gain any knowledge of their present or future state. And they are saying the same about us.
But it's important to not confuse these massively distant galaxies with those nearer to us. The Andromeda Galaxy is about 2 million light years away from our Milky Way Galaxy and the two galaxies are now moving closer to each other due to the mutual attraction of their gravity. In some number of million years, our two galaxies will collide and mix together and form one truly enormous galaxy. We will be in the Andromeda Galaxy and they will be in us. The tumult caused by the billions of stars in both galaxies moving near and past each other in very complex ways will cause a massive amount of new star formation, as formerly cold and isolated clouds of interstellar dust are stirred up, combine and collapse on themselves to form millions of new stars.
There are Two Edges to the Universe
The most superficial and trivial edge of the Universe is where light from stars has not yet reached us, but eventually will. It takes eight minutes for light to reach us from the Sun. We can never know what the Sun is doing "right now" because it takes eight minutes for the news to reach us. Even if we have a space probe very close to the Sun, its report of what the Sun is doing is sent at the same speed as the sunlight itself. No advance warning there. So long as galaxies stay close enough to us that the expansion of space does not make them recede from us faster than light speed, we will eventually "know" everything these galaxies did. It will just take time. If it takes 3 months for a letter from Ben Franklin to reach Samuel Adams by ship, if Adams lives at least 3 months longer than Franklin, he will receive every letter Franklin ever wrote him. All information from Franklin to Adams will be received and preserved. You just have to be patient.
The real edge of the Universe is where distant stars are just now emitting light toward us, and due to the expansion of space, this light will never reach us. Once a galaxy, in reference to Earth, attains a recession velocity from us exceeding the speed of light speed, it disappears from our view forever. Every second we are losing touch forever with entire galaxies filled with who knows how many civilizations. And there's nothing we can do to stop it.
But what about photons from this galaxy that are now halfway to Earth? The same rule applies. If the photon is close enough to us that the intervening space between it and us does not expand at a rate greater than c before it reaches us, then we will see the photon, and the galaxy. If not, not.
For any observer A, the edge of the Universe is a sphere outside of which information sent from any point N to A and A to N can never be received because the rate of expansion of space between A and N exceeds the speed of light. And this does happen.
We Can Now See Outside the Visible Universe
The faintest, smudgiest images of galaxies in the Hubble Deep Space Field were billions of light years away from us when their photons first left them to journey to us and hit the sensors of the Hubble telescope. Today, the photons leaving these galaxies today, if these galaxies still exist today, will never reach us due to the expansion of the space between us and them over these billions of years. But at least we can see them as they were, and study them, and even give them names. Astronomers 1 billion years in the future will not have this privilege. The most distant galaxies we see today will have long disappeared from view to our descendants, no matter how more advanced their telescopes are. This is because by then, the distance between Earth and these galaxies will be so large that their recession velocity will exceed the speed of light. For future astronomers, these galaxies will not exist. Not even the smallest trace, not even a single photon from them, will be able to reach us and transmit information. It's like we are able to talk to our grandparents but our great grandchildren will only know them by the photos we take of them today and the stories heard from them that we remember and pass along.
These Hubble Deep Field photos are capturing things and arrays that will never be seen again from Earth or from the Milky Way Galaxy. We are now seeing the Universe that will be outside the Universe in a few thousand millennia. What the people in the future can only wonder about, we will have seen with our eyes and our own hand-built telescopes.
Gravity is Sort of like Magnetism
The repulsive force which causes space itself to expand is only dominant at enormous distances. At closer distances, say between the Sun and Earth or the Milky Way and the Andromeda Galaxy, the attractive force of gravity is stronger and has the upper hand. One way to think of this is to compare the effects of a magnet and gravity.
If you have a nice strong magnet, you can lift small pieces of metal straight up off a table, defying the force of gravity which wants to keep the piece of metal on the table. Electromagnets at scrap metal yards do this all the time. That's how they lift up cars. But you notice that if you hold your magnet just a bit too far above the piece of metal on the table, nothing happens. The metal just sits there. Magnet loses. Gravity wins.
In an analogous way, the attractive force of gravity wins when stuff is closer together, and the repulsive force of expanding space wins when stuff is very far apart. And as stuff gets farther and farther apart, the force of expanding space gets even more of the upper hand. Without this repulsive force acting from the beginning of the Big Bang, there would be no Universe, since gravity would always have had the upper hand. When the Universe was much more compact than it is today, there was much more stuff confined in a much smaller volume of not-stuff. If gravity had the upper hand in the early Universe, all of the stuff of the Universe would have been drawn together by mutual attraction and collapsed into one big black hole. There would be no "Big" and no "Bang." Just a ginormous but increasingly small, silent sucking bortex to a singularity of lightless, spaceless oblivion. With telemarketers.
 The trick is the light we are now seeing from these galaxies left them very long ago, but the photons just now leaving them and moving toward us will never reach us. Using Hubble's constant we can even estimate at what year in the future these galaxies will stop being visible to us, which is the moment when their velocity away from us exceeds the speed of light. To make matters more complicated, it may happen that all the stars in these galaxies die off and become dark long before their recession velocity in reference to us exceeds the speed of light. What would be cool is if, by examining one tiny piece of the sky for centuries, we actually saw a galaxy "blink off" as its recession velocity exceeded the speed of light. This would be like a supernova in reverse. Instead of a dark spot in the sky blinking on, we would see a bright spot in the sky suddenly blinking off.