The Big Redshift Picture

Before the 1990s, the picture on the above was never seen before. If I were shown that picture without any introduction, I would not have guessed it. It looks sort of like a diagram of fine black sand splattered on snow. But there is a curious rippling.

If I was given a hint, the white should be black and the black points white, or whitish with other colors, I might have guessed this was a map of the stars around the sun, but I would be wrong. The image above shows a plot of observed galaxies versus their measured redshifts (1).

As explained in previous blog entries, redshift is the amount light is shifted to greater wavelengths (which for visible light is toward the red side of the spectrum) indicating that the space between us and the galaxy has expanded. The greater the redshift, the greater the space has expanded. It is analogous to hearing a police or ambulance siren as it moves away from us -- but not quite. In our experience, hearing sirens sounding at a lower pitch as the vehicle moves away from us, the earth around us is stationary and the vehicle is moving. Imagine instead that the ambulance is stationary and the earth is stretching and growing so fast that we see the ambulance move away from us and hear the pitch drop. Pretty bizarre, but that is what is happening with the universe -- it is expanding, stretching, all around us.

We don't notice the universe expanding in our ordinary lives for a couple of reasons. The first is that the rate of expansion is very small and difficult to measure on the human scales we are used to: meters, yards, kilometers, miles, even thousands of kilometers or miles. Secondly, gravity holds the big things around us together. So while space expands, the earth does not expand (at least due to the expansion of space), nor does Toledo Ohio, nor does earth's orbit change from the expansion of space. Now the distance between our galaxy group and distant groups of galaxies there is noticeable expansion because the tug of gravity between us and and the distant galaxy groups is so small that it does not overcome the expansion of space.

For huge distances, greater than several million light years, redshift gives us an approximation of the distance of the galaxy. It is an approximation because the two other major causes of light frequency change are the Doppler effect (the actual motion of galaxy moving towards and away from us) and gravitational redshift. These two can have a major effect on the redshift of nearby galaxies. The effect be seen in more detailed images of the Sloan Digital Sky Survey nearer to our galaxy (2).

The overall image spans approximately 6 billion light years, or about 3 billion light years away on either side of our galaxy. A light year is the distance it takes for light to travel in one year. One light year is 9,460,730,472,580.8 kilometers, or 5,878,625,373,183.61 miles. We are eight light minutes from the sun. These are staggering distances.

The number of galaxies diminish at the outer edges of the diagram. This is an problem in observation, not in the actual number of galaxies There are galaxies behind galaxies and other matter. The density of galaxies should be about as dense as in the inner areas.

While there are denser regions and "bubbles," overall, the pattern as you look at it is rather evenly distributed over the very large scale. This indicates a lower level of entropy than if it were much clumpier. Just from a natural point of view, this lack of clumpiness is puzzling. There are some ideas that I'll explore.


The images and information keep improving. The image at the top of the blog entry is an older image from around 2001 or 2002 data. The thumbnail on the left is a newer image (3). Visit http://www.sdss.org/ for more information. The Anglo-Australian Observatory also has conducted redshift surveys. They have some beautiful images and a JPEG and PDF poster. Their guidlines for using their images were stricter so I did not use them in this blog.

Sources

1. Large Sloan Digital Sky Survey map by Lauren Grodnicki of the University of Chicago, Department of Astronomy and Astrophysics. The images are based on the work of the Sloan Digital Sky Survey (http://www.sdss.org/).

2. See Wikipedea, The Fingers of God.

3. Image from Sloan Digital Sky Survey Background webpage. Copyrighted by SDSS and used under the copyright guidlines of http://www.sdss.org/.

Issues, Etc Second Coming!

Good news! Issue Etc is coming back on the air. Their website is www.issuesetc.org. I blatantly stole the banner at the start of this post from them. I hope they forgive me for breaking the eighth commandment, oh yes, they're Lutherans, it's the seventh commandment for them (inside intramural Protestant joke). They will start Internet broadcasting on June 30, 2008 from 3-5 pm Central Time (USA) at www.piratechristianradio.com. I am guessing they will archive, as they did before, mp3 files for uploading and playing on your favorite player.

I am a theologically conservative Presbyterian. Issues Etc is run from a theologically conservative Lutheran perspective (I think they are still associated with the Lutheran Church, Missouri Synod -- correct me if I am wrong). I have some theological differences with them, such as their view on the elements of Communion, and some other things. However, the vast majority of things I agree with them. But even with those things I disagree, I love to hear about it because no matter what, I study and think more deeply about what Scripture says -- and that is always a good thing.

Issues, Etc is my favorite radio/internet program, along with Renewing Your Mind and the White Horse Inn. I cannot recommend it enough to everyone. My prayers are with Todd Wilken and the crew for an even more successful Issues, Etc.

More details can be found at the Augsburg 1530 blog.

The Night Shift

From a long train of astronomers, Edwin Hubble developed the formula for how galaxies exhibited a redshift. The further away the galaxy, in general the greater the redshift. Galaxies near our galaxy, the Milky Way Galaxy, do not necessarily move away from us. Andromeda, for instance, is actually moving closer to us and is on a collision course. Don't loose sleep over it, it would take millions of years before it collided with us.

What are the candidates for causing the redshift? The first candidate Hubble commented on was the Doppler shift. When an object emitting waves (such as sound waves or light waves) moves toward us, the frequency shortens. You can hear this whenever you hear an ambulance move towards you. The siren is higher pitched. When the object moves away, the waves are longer. The ambulance siren drops its pitch. The same thing happens with light. As a light emitting object moves toward us, the wave lengths are "compressed" as in the following illustration. The light shifts towards the blue spectrum. As the object moves away from us, the light waves are elongated, shifting the light towards the red or longer wavelengths.



The next two ways light can be redshifted is explained by Einstein's General Relativity theory. Gravitational fields will also shift the wavelength of light towards longer wavelengths.



The third way that light can be shifted towards longer wavelengths is when space/time itself expands. This is illustrated in the following schematic. At the right, time/space is in a smaller volume, but it is expanding to the left. As space expands, light traveling through it has its wavelength elongated. From careful observations, the redshifts show the particular signature of space/time expanding as the main component of the redshift for galaxies far away. Doppler and gravity will do some of the shifting, but far and away the major factor in the redshift is the expansion of space/time. Doppler effect will actually have as its part just as many distant galaxies moving towards us as away -- but the expansion of space overwhelms any blue Doppler shifts for distant galaxies.



Space expanding. This is a difficult concept to grasp -- at least for me. What is it expanding into? Not empty space. It isn't like there is an empty region would could travel to and watch the universe expand into it, because anywhere we could with space ships, etc., is only in space/time -- and it's getting bigger.

Seeing Red

When our family lived in France for a little less than a year, we visited many cathedrals in France and elsewhere in Europe. I remember walking around one time, looking at the pattern of light on the floor from the stained glass windows, when I saw a little rainbow on the stone floor. Curious, I put myself in front of the rainbow, casting my shadow on it an caught the light in my eyes. I saw the light came through a clear piece of glass.

As a kid, I had read that Issac Newton discovered making rainbows from prisms. But I was walking through cathedrals older than Newton -- and here I saw an example of the work of skilled artisans that clearly understood that sunlight going through shaped glass would make the colors of the rainbow. Now I realize that much of what I saw in sainted glass could be the reconstructions of modern glass workers. But nevertheless, those who worked with glass many centuries ago, even before Newton must have noticed the colors of the rainbow from sunlight going through clear glass. I wondered if I misunderstood, but that people had known for a long time that glass could make colors from sunlight, but that Newton was the first to state that white light was composed of the colors of the rainbow and that glass prisms refracted out the colors. As I read various web sources (2), it does seem that people understood understood that glass can make colors -- but the modern understanding based on refracting the light into colors started with Newton.

If you take light from the sun and direct it tough a prism onto a dark screen, you see the colors like this(3):



However, if you carefully construct a very thin and straight slit and have the sunlight go through the slit into a dark screen and observed the results, you will see (4):




What you see is the continuous spectrum of light with thin black lines in it.

The recorded first observation of this was made by William Wollaston in 1802 (5). Wollaston was a chemist who became wealthy from developing a method of refining platinum from ore. Wollaston did not perform any detailed analysis of the black lines.


However, it was Joseph von Fraunhofer, who independently in 1814, rediscovered the the dark lines on the spectrum from the sun (6). He created the first working spectroscope and was able to catalog 574 lines in the spectrum of the sun. This pattern of lines, Fraunhofer Lines, for the sun are named so in his honor. Later the German physicist Gustav Robert Kirchhoff and German chemist Robert Bunsen determined in the late 1850s to early 1860s that the lines were caused by chemical elements.

Kirchhoff developed the three laws of spectrography (7):

1. A hot solid object produces light with a continuous spectrum.

2. A hot tenuous gas produces light with spectral lines at discrete wavelengths (i.e. specific colors) which depend on the energy levels of the atoms in the gas.

3. A hot solid object surrounded by a cool tenuous gas (i.e. cooler than the hot object) produces light with an almost continuous spectrum which has gaps at discrete wavelengths depending on the energy levels of the atoms in the gas. (quoted from Wikipedia)

The lines seen in the spectrum of the sun are a composite of many elements, notably hydrogen and helium. Each element has a spectral "fingerprint". Experiments were conducted, isolating each element, heating it, and looking at the spectrographic results. Those that were heated as a gas or burned would have a spectrum that is primarily black with bright thin lines:



If, on the other hand, a bright light is shown through the element as a cloud of gas, you see a continuous spectrum with dark, thin lines though it:



I could go into the mechanisms of why these lines occur, but instead I want to explore something else. These spectral lines, measured in an earth laboratory, establish the "baseline" of the spectral images. These spectroscopic images where made with samples that were not moving. When we look at objects that move, something interesting happens.

In 1842, an Austrian mathematician and physicist named Christian Andreas Doppler (8) predicted that both sound and light would change frequencies when it moves toward us (higher frequencies) or away from us (lower frequencies). French physicist Armand-Hippolyte-Louis Fizeau (9) described the observed changing of the spectral lines of elements observed in some stars and attributed it to the Doppler Effect.


The amateur London astronomer, William Huggins (10), was the first to observationally calculate the speed of a star relative to earth. Huggins lived in a period where amateurs, especially amateurs with some means, could contribute just as much as professional scientists.

William Huggins (11) had entered Cambridge University, but dropped out to help in the family drapery business. While he never finished a degree, he always had an interest in astronomy and optics. His wife, Margaret who was very gifted and sharp, and he would collaborate in their astronomical work. William was fascinated with the work of Kirchhoff and Bunsen with their spectroscope. William purchased a high quality refracting telescope and built an observatory attached to his house. He made his own spectroscope and started observing stars and various nebulae.

There are a couple of discoveries by Huggins I will note. The first is that in 1868 Huggins published his work showing that the star Sirius was moving away from earth at over 20 miles per second. This was a practical use of Dopper's work in showing that the spectral lines in Sirius were shifted towards the red side of the spectrum, as illustrated to the left (12). There are stars moving towards us, the the shift in the absorption lines would be shifted towards the blue.

The other discovery I'll note is that Huggins discovered that most nebulae, such as the Great Nebula of Orion, or Ring Nebula, showed emission line spectrum with the dark background and bright thin lines, indicating these were gaseous objects. Huggins discovered that the spiral nebulae, such as Andromeda, were absorption line spectra, the same kind of spectra that stars had. I have not read Huggins' thoughts on the matter, but this would have been a clue these were huge star clusters and thus galaxies.

There was considerable progress in spectroscopic technique into the twentieth century. Vesto Slipher (13) was an astronomer at Lowell Observatory in Flagstaff, Arizona. He would eventually become the director of the observatory who later hired and supervised Clyde Tombaugh, the discoverer of the erstwhile planet Pluto.

Vesto used spectroscopy in much of his work. Vestro was the first to publish the spectral redshifts of the absorption lines in the spiral nebulae. Thus Vesto Slipher is the one who should be credited with the discovery of the redshifts of the galaxies. Several astronomers, including Vestro, were understanding the significance of this by 1917.

And now we come back to Edwin Hubble. Hubble had discovered a way to measure the distance of many galaxies based on the luminosity of certain types of variable stars, now known as Cepheid Variables. Working with the foundation laid by others, and with observations from Vesto Slipher, Hubble, working with Milton Humason, discovered a distance relationship to redshift. The greater the distance, the greater the redshift. Hubble and Humason plotted the data from 46 galaxies and estimated a constant of constant of 500 kilometers per second per Mega Parsec (perhaps I'll explain the units in another post -- best yet, google them). Because of problems in estimating distances, which still trouble astronomers today, this is much higher than the currently accepted value.

Edwin Hubble first explained this growing redshift over distance as the result of the Doppler effect of objects moving ever faster away from us with distance. As strange as that sounds, Hubble's first explanation was wrong. Something even stranger is happening...



Sources:
1. Image of Sainte Chapelle

2. Newton and the Color Spectrum

3. Continuous spectrum image.

4. Solar Spectrum with Fraunhofer Lines. From the Historical Introduction to Spectroscopy,

5. Image and information on Wollaston from William Hyde Wollaston, Wikipedia.

6. Image and information on Fraunhofer from Joseph von Fraunhofer, Wikipedia.

7. Image and information on Kirchhoff from Gustav Kirchhoff, Wikipedia.

8. Image and information on Christian Doppler from Christian Doppler, Wikipedia.

9. Image and information on Hippolyte Fizeau taken from Hippolyte Fizeau, Wikipedia.

10. Image of William Huggins from William Huggins, Wikipedia.

11. Information on William Huggins discoveries from Engines of our Ingenuity, William Huggins, by John H. Lienhard of the University of Houston.

12. Image of spectral red shift was taken from Redshift, Wikipedea.

13. Image of Vesto Slipher from the University of Warwick. Information from Vesto Slipher, Wikipedia.

Andromeda -- What is it?

Okay, this is a shameless Daddy bragging kind of story. Our oldest daughter (and only child at the time) learned words quickly. I am an amateur astronomer at heart. Our daughter was only two, but I taught her how to distinguish between nebulae and spiral galaxies. We were visiting Mt. Palomar Observatory north of San Diego. In the museum on the observatory grounds pictures of deep sky objects were displayed on the walls. Hmmm, I thought. I walked towards one where there were other people looking at it. I pointed to the picture and asked my 2-year-old, "What is it?"

"A nebuwa" she correctly answered.

I pointed to another picture and asked again, "What is it?"

"A gawaxy" she correctly answered again.

Yeah, I know. That is one of the ways a parent can brag in front of others. Shameless.


Prior to 1925, the question of what the spiral objects actually were, like Andromeda above, was quite a debate. The Hooker 100-inch telescope on Mt. Wilson above Los Angeles, was finished and started operating in 1918. Ten years earlier the 60-inch telescope was completed. Both these telescopes marked the beginning of the modern period of telescopes. The were designed to reflect light to a variety of instruments that were too big to place inside the telescope -- including a spectrometer, a way of spreading out the colors of the stars. Directly looking at Andromeda in the largest of telescopes of the time could not reveal where the spiral haze had stars in it or not. Pictures of Andromeda were not sharp enough to reveal the point-like stars.


Harlow Shapley, pictured above, was an astronomer at Mt. Wilson. He thought that Andromeda was a spiral of heated gas inside the Milky Way. He publicly debated the issue in a famous debate with Heber Durst (pictured on the left), director of the Allegheny Observatory in Allegheny, Pennsylvania, which was incorporated into Pittsburgh in 1907. Durst believed that Andromeda was a galaxy, much like the Milky Way. It was going to take the combined efforts of various astronomers to decide the issue.

The first stepping stone was the work Henrietta Leavitt in 1912, reported in the previous blog entry. She painstakingly found a brightness relationship in certain kinds of variable stars. The longer the period the star changed its brightness, the brighter the star was altogether. The brightness, or luminosity, had a mathematical precision to it that could be graphed. The stars she determined the luminosity pattern were located in the Smaller Magellanic Cloud. The problem was nobody knew how far away the Smaller Magellanic Cloud was and thus could not calibrate the actual brightness of the star. These variable stars, later called Cepheid Variables, were located all over in the Milky Way, but none were close enough to determine by the "parallax" method of using the earth's orbit to measure the star's change in the background of the sky. There seemed to be an impasse.


Ejnar Hertzsprung (pictured on the right), an astronomer at the Potsdam Observatory in Denmark, built upon the work of Henrietta Leavitt. Hertzsprung assumed that the Smaller Magellanic Cloud was far away, and thus for practical purposes the variable stars in the Cloud could be considered to be at the same distance. Hertzsprung had also been studying the "proper motions" of stars (motion at right angles to our line of sight) in the formations called open groups. Through a statistical method he estimated the distance of closer Cepheid Variables and established a working absolute brightness. Unknown to him, he was off by a factor of four in the the luminosity because the light of the stars was diminished by the dust clouds in the plane of the Milky Way.

Once Ejnar Hertzsprung established his standard values for the Cepheid Variable stars, he examined the brightness of the Smaller Magellanic Cloud. His estimate was off, making it much closer than the current accepted distance, but he had the first estimate of the distance of an extragalactic object.




Harlow Shapley was interested in the Sagittarius region of the Milky Way. Sagittarius, as you can see, fills quite a bit of the sky. You can see a bulge, which can be imagined to be the center of the Milky Way galaxy. Shapley noted that there were a lot of globular clusters around this section of the Milky Way -- but outside of it, more so than any other region in the sky. Globular clusters are circular balls of thousands of stars. Shapley correctly surmised that the globular clusters orbited the center of the galaxy. Shapely also noted that the globular clusters contain many variable stars. Using the work of Henrietta Swan Leavitt and Ejnar Hertzsprung, Shapley came up with a distance to the globular clusters. Interestingly, Shapely used the incorrect calibration of the Cepheid Variables of Hertzsprung (who was off by a factor of at least 4 times), and incorrectly assumed the variables of the globular clusters were the same type as in the Small Magellanic Clouds (they are not, the are what are currently known as Population II Cepheid Variable, brighter than the Population I Cepheid Variables of the Magellanic Cloud. By luck, with the errors canceling each other out, he arrived at the correct distance of the globular clusters.

By the way, a fascinating movie of variable stars in a globular cluster taken during the course of one night is found here.

Edwin Hubble arrived at Mt. Wilson in 1919, just when the 100-inch telescope came on-line. Hubble made photographs of Andromeda in 1922–1923 and in 1925 published the results. He had discovered Cepheid Variable stars in Andromeda, and using the work of Leavitt, Hertzsprung, and Shapley, Hubble concluded that Andromeda was a spiral galaxy that was roughly 900,000 light years away from us. Because Hertzsprung's estimate was off for the luminosity of the Population I Cepheids, Hubble's distance estimate was half of what it currently known today. Nevertheless, it was a remarkable achievement.

As big as the universe was thought to be before Hubble's discovery, the universe was found to be staggeringly bigger than previously thought. Photographic plates where showing all sorts of spiral "nebulae" -- which were actually galaxies.

Edwin Hubble was to later make a discovery that made Albert Einstein admit to a huge mistake he made in General Relativity.

Cosmic Odometers and Speedometers

The universe is BIG. At the start of the twentieth century there was some debate as to how big the bigness was. Did the universe consist of one galaxy, the Milky Way that we can see stretching across the sky in the dark countryside. Or where many of the nebulae seen in ever more powerful telescopes island universes, much like the Milky Way, as Immanuel Kant suggested. What was needed were some ways to measure the distance, good cosmic yardsticks, or odometers. These odometers would be added to the speedometers astronomers were developing.


There is quite a cast of characters that moved the science of determining the distance of stars and the other deep sky objects. Let me first introduce you to Edward Charles Pickering. He was the director of the Harvard College Observatory from 1877 to 1919. The Harvard College Observatory, during the mid 1800s, the observatory had the world's largest telescope. It had made stunning photographs of the moon. In 1850, the observatory made the first photograph of a star (Vega). Now stars don't look impressive -- blobs of light, but the observatory made important scientific advances in stellar photography. Light coming from stars contains all sorts of interesting information. When you put the light of a star through a prism and break out the colors, you don't get simply the colors of the rainbow, you see black thin lines running through it:




This image from Sky and Telescope Magazine is a photograph of several stars where the light is put through either a prism or defraction grating, which spreads the colors of the light. In the rainbow colors, if you look closely, there are thin black lines. These lines are caused by cooler gas around the stars the the light passes through. The gases absorb certain specific colors based on what kind of atoms they are. In this way, astronomers are able to determine what elements the stars have in them. These spectrum images with the lines in them will also act as a speedometer, telling how fast the star is moving towards us or away from us. Also, by recording the light on the photographic plate, you record how bright the light is as the telescope sees it. This is called the apparent brightness or apparent magnitude of a star.

Edward Pickering was organizing a photographic study of stars. The effort required a lot of computation. In the 1880s, Pickering started hiring women to perform tedious calculations he needed. Pickering had been frustrated with his male staff and thought the women would do the job better. Apparently they did, with very low wages, 25 to 50 cents an hour. The wages were better than factory wages, but less than clerical work. For such low wages he was able to hire a number of women. The women became known as "Pickering's Harem" or as the "Harvard Computers".


Henrietta Swan Leavitt joined the Harvard College Observatory women "computer" team in 1893. Her job was to measure and catalog the star brightness of the photographic plate collection of the Observatory. Leavitt examined thousands of variable star images of the Magellanic Clouds.

The Magellanic Clouds are quite visible in the southern hemisphere. They look like torn off pieces of the Milky Way. Persian astronomers noted them in their writings in 964 AD. Europeans noticed the clouds during Ferdinand Magellan's voyage around the world in 1519–1522. They would not be called the Magellanic clouds for until much later.

In 1891, the Harvard College Observatory opened an observatory in Arequipa, Peru. The observatory had a 24-inch reflecting telescope and from 1893 to 1906 it was used to take pictures of the Small Large and Small Magellanic Clouds.



Henrietta Leavitt studied thousands of stars in the photographic plates from Arequipa, finding that many of the stars were called "cluster variables". Later, these kind of stars were later designated cepheid variable, named after the one of the stars in the constellation Cepheus (Delta Cephei -- which signifies that it is the fourth brightest star in the constellation Cepheus), which various in brightness in a 5.4 day cycle. Leavitt discovered that an individual star's luminosity or brightness was related to the period of the its variability. The longer the star variated, the brighter the star. Leavitt published the results in 1908 and refined the results in 1912. These were based on the variable stars she saw in the Small Magellanic Cloud. There was one problem. While she could determine the brightness as registered by the photographic plate in from the telescope, she did not know the actual brightness of the star. No one knew how far away the Small Magellanic Cloud (or the Larger Magellanic Cloud) was. The stars could be dim but close, or bright and far away.

One possible solution was to identify close variable stars and see if their distance could be determined by other means, such as parallax. For some close stars, you can notice that they change there position slightly in the sky compared to the far-away stars behind it. This illustration shows how the earth orbit, at 6 months apart, can make the close star be seen at different angles.



As you look in the sky six months apart, the close star looks like it moves:



It then becomes a geometry problem to solve the distance. You know the base of the triangle (150,000,000 x 2 kilometers or 93,000,000 x 2 miles). Bingo, you solve the distance for the star. Unfortunately, there are only a few stars close enough, with 1912 technology where the parallax measurements like this could be made -- and none of them were these variable stars.

The problem was how to calibrate the brightness of Henrietta Leavitt's variable stars. What was needed was a way to estimate the distance of one or several cepheid variable stars.

That would come soon...

Taking Temperatures of Black Holes

Since we're doing thought experiments, let's imagine you're on a space ship that came into the region of a black hole. This particular black hole is sitting far out away from other things, not in the middle of the remains of an exploded star, no nearby star orbiting around it being shredded by the tidal forces of the black hole, no in falling gas clouds lighting up the region around the black hole. Its just a solitary black hole roaming in a quiet region of space. The black hole is not spinning either.

As you look at the black hole, you notice some weird things about it. There seems to be a halo around it. It's actually the distorted image of the stars we see in the sky around us, distorted by the immense gravitational field of the black hole. The image on the top left is from Wikipedia, who got it in turn from Step by Step into a Black Hole by Ute Kruas. This image is taken from a simulated location you hopefully will not be in, 600 kilometers (374 miles) away from the black hole that is ten times as massive as the sun -- and stationary. To be stationary to the this black hole at this distance, you'd be squeezed by the ship's rocket engines blasting so hard that you'd feel 400,000,000 times the gravitational force on earth (well, maybe you wouldn't feel it, you'd be dead so you wouldn't feel anything).

In any case, if you orbited at a safe distance and looked at the black hole with your telescope, you'd see this kind of weird distortion in the starlight surrounding the black hole.

Your spaceship's captain has told you to take the temperature of the back hole. Hmmm, you look at the low tech thermometer for checking the temperature of chemical solutions you heat. Maybe if you tied the thermometer on a strong thread and lowered it our of the space ship down to the surface of the back hole, you could get its temperature. There's a problem. No thread, cord, rope, or tether would be strong enough for you to do that. It would break long before you got close. The thermometer would shatter also because of the tidal gravitational effects as it got closer to the hole. Further, any part that reaches the "surface" of the black hole (its not really a surface), it would be pulled in with no possibility of being retrieved.

How would you measure the temperature? Well, here is where Astronomy 101 you took in the academy helps you out. You measure the light coming out of it to see its color. After all, that's how star's temperatures are measured. No one puts a thermometer on a star. But wait, this is a black hole. Nothing is supposed to come out of it. Light inside the black hole can't escape, it gets pulled down to the singularity inside it. But here is the odd thing about black holes, they radiate. This black hole radiates very little, but it does radiate a little. This is because of some weird properties of quantum physics. There are several ways to explain it, but each of the ways is an approximation of what happens, which means it doesn't quite happen that way. One explanation is that anywhere in space, particle pairs can temporarily appear and disappear. These events violate the conservation of matter and energy, provided you can directly observe it. But these particle pairs disappear almost as soon as the happen, so overall the conservation is preserved. However, right around the event horizon of a black hole, there is a rare occasion where the particle pair appears, where one of the particles falls into the back hole, and the other escapes. Due to the principle of the conservation of matter and energy, the universe balances the books by have the particle that falls into the black hole have negative energy while the other has positive energy, hence some energy leaks away from the back hole, diminishing the hole slightly. This is not a completely accurate description, but it is somewhat of an approximation, so says some of the literature I read (okay, Wikipedia maybe shouldn't be called literature -- but it is convenient).

As you take the temperature of this, you discover it does emit some radiation -- but very little. You calculate the temperature of this black hole at the event horizon is in the tens of nanokelvins, very close to absolute zero and colder than anything we can get in a lab on earth. Since the space around the black hole has a temperature of 2.7 kelvins (meaning there is light weakly bathing the black hole), the black hole is growing ever so slowly just from the temperature of the overall universe. If this black hole were sitting in an unbelievably cold region of space, it would slowly evaporate away -- and the operative word is slowly. For a black hole with just a tenth of the mass of the this hole, with the mass of the sun, scrunched to a point, it would take 10⁶⁷ years (1 with 67 zeros). Interestingly, the smaller the black hole, the more it radiates. Black Holes with the mass less than the moon with evaporate more quickly than what it takes in. As they get tiny, it is expected this could evaporate with a noticeable bang. A satellite just launched recently by NASA has as one of its missions to look for gamma ray bursts that would fit the profile of tiny back holes evaporating. It is even possible that CERN's new collider could produce mini black holes that would quickly disappear (see CERN's article on this here).

Black holes have an extremely high amount of entropy, the most concentrated amount for any enclosed area. In fact, just the single massive the black hole at the center of our galaxy, which 2 million times the mass the sun, has an entropy that exceeds the combined entropy all the stars, heated dust and gas, and the background radiatio in the rest of the universe (see What is the entropy of the universe? by Paul H. Frampton, Department of Physics and Astronomy, UNC-Chapel Hill, NC 27599, Stephen D. H. Hsu and David Reeb, Institute of Theoretical Science, University of Oregon, Eugene, OR 97403, Thomas W. Kephart Department of Physics and Astronomy, Vanderbilt University, Nashville, TN 37235). It is thought that our galaxy is typical of other galaxies, each one having a super massive black hole. The black holes hold the bulk of the entropy of the universe.

It is a bit of a mystery why black holes have so much entropy. The entropy can be calculated, but the physical interpretation is not known. Part of the problem is that there is no description for "quantum gravity" and a way to describe the micro states of all the matter and energy inside a back hole when gravity is considered. Dr. Paul H. Frampton and company propose one theory, based on the possibility of the most matter and energetically disorganized glob of stuff that a star or other matter could tunnel into just prior to a gravitational collapse -- which they call monsters. However, many other physicists find that explanation implausible.

So, what is the extreme future of the universe (imagining there is no God nor heaven, etc.)? Are we doomed in some sense to being all crunched up into ever bigger super massive black holes? Stay tuned, it gets more interesting.

Imagine

Imagine there's no heaven
It's easy if you try
No hell below us
Above us only sky...
(John Lennon)

I am a Christian, a theologically conservative Christian (theological conservatism is not to be confused with political conservatism -- another topic sometime) who believes that God created the heavens and the earth. As I explore the topic of entropy further, I am going to conduct a thought experiment. As we look at the universe around us, let us explore the questions: How could the universe get to its present state without the existence of God whatsoever? What could the universe be like in the extreme future if we assume no God?

This does not mean I subscribe to the theories I will discuss. But in order to explore these ideas, there is an implicit assumption that God does not exist, or at the very least he does not interact with the universe in any way that disturbs matter, energy, and the topics discussed (which for a Christian means there is no Christian-like God). There are some very interesting results of this thought experiment that I will comment on. I think it is fun to explore different "scenarios of reality" -- understanding there is one objective reality that we want to find and describe. I think there is much warrant to believe in God and that he created the universe.

Here is a bit of a road map for ideas that will be coming up.

• Further exploration of black holes and entropy -- finishing up some dangling threads.
• Edwin Hubble's big discovery.
• Running the clock backwards.
• A startling discovery in 1998, the runaway universe.
• The far distant future.
• Entropy measures of the universe.
• Exploring how this improbable universe emerged.
• Some strange consequences.
  

Black Holes

The image to the left is from the ESO (European Organisation for Astronomical Research in the Southern Hemisphere) website. Click on it and you will see the time-lapse Quick-Time video spanning from 1992 to 2002. This was done by the Max Planck Institute for Extraterrestrial Physics (MPE) using the ESO Very Large Telescope array (VLT) with adaptive optics, which results in amazing resolution. It shows several stars, in particular, one star called S2, orbiting a super massive object in the center of the Milky-Way Galaxy, our galaxy. The data strongly suggests this is a super massive black hole. As one of the principle investigators says:

When we included the latest NACO data in our analysis in May 2002, we could not believe our eyes. The star S2 , which is the one currently closest to SgrA*, had just performed a rapid swing-by near the radio source. We suddenly realised that we were actually witnessing the motion of a star in orbit around the central black hole, taking it incredibly close to that mysterious object. Thomas Ott, MPE (see ESO for details)

Black holes -- what are they? When Albert Einstein developed General Relativity in the first part of the 20th century, some rather interesting consequences followed from the theory. Light is effected by gravity. Light will not travel in a straight line, but will be "bent off course" by gravitational fields. You can actually observe this with objects as big as our sun. If you carefully observe the location of stars seen near the sun during a total solar eclipse, you will notice that the stars are not exactly in the "normal" locations in the sky. They seemed to have shifted near the sun. The shifting is due to the path of the light being pulled out of line by the gravity of the sun. It is exaggerated in this diagram:




Soon after Einstein published his General Relativity, a physicist named Karl Schwarzschild, solved General Relativity equations that showed that every mass (a quantity of matter), if squeezed tightly enough into a small sphere, there would be a point in which nothing could get away from that object, not even light. The sphere is referred to as the event horizon, the radius of the sphere is called the Schwarzschild's radius. For the sun, the radius is approximately 3 km (less than 2 miles), and the earth is 9 mm (about 1/3 of an inch, or a sphere about the size of a walnut). Nobody took this seriously until after World War 2 because it was thought the other laws of physics would prevent the formation of such objects.

How could a black hole form? Imagine from the last post a star is formed from a large cloud of tenuous gas. Let's make a simple assumption it is a non-rotating cloud of gas, although the discussion for rotating gas, after all is considered, is similar.




It forms a spherical cloud of gas, predominately of hydrogen but also substantial amounts of helium, that heats up as it contracts. When it heats up enough, and the center has enough pressure, the gas turns into a star by fusing hydrogen nuclei together into helium, which releases a lot of energy. In time, the star stops contracting because there is enough energy and pressure to counteract the force of gravity that tends to squeeze the star.



The star has an equilibrium, the gravity and the pressure from the nuclear fusion counteract each other equally.

At some point in a star's life, the hydrogen runs out. There is an energy crisis in the star, it can't produce enough energy from fusion. The temperature and pressure drop. The star is squeezed tighter. For small stars, the pressure from the nuclei of the atoms prevents further contraction. It just gets hotter for a while, then it cools, but the atomic nuclei prevent further contraction. A new equilibrium is established. For larger stars, the contraction causes enough heat and pressure for helium nuclei to fuse together to form beryllium and ultimately carbon. Again, an energy crisis can occur inside a star where it does not have enough helium to fuse into carbon and oxygen. The temperature drops, and the pressure cannot withstand the gravitation pull. The star contracts.



There are various fusion cycles a star can go through, but for large enough stars, something weird can happen. If a star big enough that ultimately squeezes the core with enough mass, which physicist Subrahmanyan Chandrasekha determined to be 1.4 solar masses or greater, that mass will overcome the pressure of atomic nuclei and squeeze into a point -- often with spectacular pyrotechnics of a supernova, a massive star explosion.

(Note: on the image above, the light outside of the back hole passing so closely would spin around more of the black hole.)

The remaining core, which becomes a point, is called a singularity. The singularity is inside a sphere where gravity is so great the no light can escape. In the theory of General Relativity, nothing can escape from the sphere, which is called the event horizon.

In considering entropy, if black holes exist as described by Einstein's General Relativity, then black holes would violate the second law of thermodynamics. Back holes would have zero entropy. Their temperatures would be absolute zero. In any enclosed region of space containing a black hole with matter outside of it with non-zero entropy, some of the matter would fall into the black hole and the entropy of the closed region would drop.

However, quantum theory has a part to play in black holes. Stephen Hawking and Jacob Bekenstein showed that black holes have the most entropy that can be squeezed into a particular volume.

Getting back to the start of this article, the center of the galaxy has a super-massive black hole. It is over 2 million times the mass of the sun. This black hole was not formed from a collapsing star. It is thought that is may have been formed by many other black holes merging together. This black hole has a massive amount of entropy.

In the next entry, I'll discuss an interesting surprise discovery in astronomy in 1998 and pick up the discussion of entropy there.

Entropy, Meet Gravity

It was a cool night in late October. I setup my orange Celestron C8 telescope on my parents-in-law's land outside of Temecula California. I had chilled the telescope for an hour to prevent the optics from fogging up. I had tilted the telescope mount platform so I could have the telescope point straight at the North Star. I found two bright stars in other parts of the sky so I could calibrate the setting circles. I aimed the telescope at one bright star, and knowing its coordinates in the sky, I could set the "right ascension" to the correct number. I verified the settings were correct on the second bright star. I had to get the settings as accurate as possible because the thing I wanted to see was faint and I would not be able to see it in my finder scope on the side of the telescope.

I now swiveled my telescope with it's 8-inch mirror by turning the dials to the right ascension of 5 hours and 31 and a half minutes (notice the units are time units, because the sky appears to move like a giant spherical clock), and the declination of 21 degrees and 59 seconds. I looked in the eyepiece and saw a field of faint stars, but not what I was looking for. There was always a margin of error whenever I set up my telescope. The Celestron C8 was with its narrow field of view (F-11 for the real camera geeks and optics wonks) could easily miss what I was looking for. The telescope's design worked well with bright planets and the moon. It took a little more effort to find faint nebulae. I slowly turned the dials to systematically pan the region of the sky back and forth. After three minutes, I found it.

The Hubble's image on the top is much sharper and better than what I saw in my telescope, but I cannot express the thrill I had whenever I located a deep sky object. I stared at the faint irregular patch for a couple of hours. The NASA image shows the remains of a star that blew up. It stretches 11 light years across. I only saw a six light year piece of it in my telescope. But think of it, it takes light 8 minutes to travel from the sun to the earth. The size of the nebula is over 7 million times the size of the distance from the sun to the earth. And this is a small thing in the Cosmos. It's about 6,500 light years away from us. Close by cosmic standards.

Entropy, as I described it in the last few posts is ... well, its perfectly boring. I suppose some chemists get excited about it. But I think entropy gets more exciting when you scale it up from test tube and Erlenmeyer flask sizes to planetary sizes, star sizes. Better yet, scale it to solar system sizes, galactic sizes and and bigger. Then throw in gravity. This is when you start blowing up stars. I like bangs. I like the 4th of July fireworks, Myth Busters when they blow up things. Stars blowing up, that's really cool.

Without considering gravity, which is what is normally done in studying small amounts of gases (room size or less), or chemical reactions in flasks, we see the dispersal of matter and energy in this manner in isolated, self-contained (referred to as closed) systems:



One of the laws of thermodynamics states (the second law):

The total entropy of any isolated thermodynamic system tends to increase over time, approaching a maximum value. (Wikipedia)

Notice the words "tends" and "isolated." Some people and groups that I am very sympathetic to, sometimes abuse the second law of thermodynamics. I will try to avoid that in this series of articles. But where I go wrong, please comment where I do go wrong. People come into my blog via Google searches on various topics I write about. I corrected an article on infinity based on comments of some British people thousands of miles away from me.

The study of thermodynamics has a formalized mathematical statistical foundation to it. The statistical part of it is especially seen in the second law of thermodynamics. Statistics entails probabilities. The second law not a universally rigid law that applies in every circumstance in every part of the universe. If we assume that the universe itself is a closed system, no inputs, no outputs to it, then we have a closed thermodynamic system. Regions inside the universe are not closed and can have temporary decreases in local entropy. Where I am headed is the total entropy of the entire universe, but I won't get there in this article.

Getting back to entropy of the previous diagram pair, we see that without gravity taken into consideration, entropy tends to disperse matter and energy in a closed thermodynamic system. Gravity changes the characteristics as seen in the following diagram:



Generally dispersed matter and energy tend to clump together in denser pockets of matter/energy leaving a more rarefied region in the rest of the system. A large volume of gas (light years across), over time, can coalesce into concentrated packed objects, the larger ones being stars, smaller ones planets and other things. This violates an intuitive notion of entropy that I presented in my first article. In systems with gravity spread over light years, the lower entropy state is dispersed gas. The volume of space that has stars and planets in the same overall region that originally had dispersed gas (or compared to a region with dispersed gas) has a higher entropy. For me, this was counter intuitive. But hang in there. It gets weirder. This is only a "medium" entropy level for the region. As I examine entropy more in the coming articles, I'm going to ultimately explore some of the implications of this if we limit ourselves to a naturalistic viewpoint. Its not going to go in a direction that most creationists take it. This is going to be stranger.

I have a limited attention span, in writing as well as reading blogs. So I am stopping this article and will continue shortly with more.

Entropy -- Take Two

In my first blog entry on entropy, I got the information a bit wrong. Entropy is the sum of all the micro-states of the individual microscopic entities in a volume. Actually, it is the natural logarithm of the sum of all the micro-states. These micro-states not only include the position of the microscopic particles, but the energy states as well.

Let's take an example of a small ice crystal.



This is a schematic of a small ice crystal. It's not an accurate schematic, because real ice forms a hexagonal molecular structure. When water freezes, there is a bond between the water molecules which keeps the molecules in a rigid order (hydrogen bonds). The water molecules have a certain amount of vibrational energy which the hydrogen bonds keep in check. As the temperature drops, the vibrational energy also drops, but it will not completely be eliminated, because the laws of quantum physics prevent all "vibrational" energy to cease.

Ice is a condition where the entropy of the system of molecules is low. It can be seen because the average micro-states of the molecules is rigid and the energy distribution is low.

If we were to heat the ice crystal, the vibrational energy of the water molecules increases:



Finally, the hydrogen bonds beak:



The ice changes to water, which has a higher entropy value:



If we keep adding heat, the water changes into steam which has yet an even greater entropy value:



Nothing earth shattering in this account of entropy. The thing to remember is that entropy deals not only with the location of pieces of matter, such as water molecules, but also the energy distributed within the system.

In some treatments of entropy a correspondence is made to information theory. I'm not going to touch on this aspect of entropy or correspondences to entropy. Rather, I am going to add gravity to the entropy and see some of the interesting things that result from that interaction. In particular I am interested in the largest scale aspects of entropy in cosmology.