E2science

When I was in Antarctica last month I heard that the famed author and filmmaker, Michael Crichton, had come out in the press saying global warming was a myth.

That sounded quite odd to me, as I was at the geographic center of global warming studies. To most Antarcticans, global warming is a theory invented by people in the real world. Down on the ice, everyone knows it's getting hotter every year. Gallager's and the coffee house buzz with talk about icebergs the size of Hawaii and the nearly complete disintegration of the Larsen Ice shelf. I'd just come in from the dry valleys where the weather was so warm I spent most of my time outdoors in shirtsleeves and spent the night on top of my sleeping bag because the temperature inside my tent often hovered around 50F degrees. In a matter of a month the atmosphere had gone from the dry polar blast I'd come to know and love, to something akin to Boston in late April.

It was warm as the fringes of hell at McMurdo by the end of November. The continent around us was coming apart and we had the photos and chunks of floating ice the size of Mount Everest to prove it.

So when I heard that Michael Crichton himself had decided to publicly announce that global warming didn't exist I figured the man had finally succumbed to the Hollywood life. One too many spoons up the nose, one too many actress wannabee's lips below the belt--makes a man feel he's immortal and consequently irrefutable. In Silicon Valley we call this "believing your own bullshit". It's a trait akin to observing the world through the eyes of a bratty ten-year old.

Most of the glaciologists I know have taken a stand on global warming, and until now that stand was that we definitely knew nothing about it. The history of the earth, as far back as we can figure, is dominated by a cycle of warming and ice ages, the most recent of which lasted about 60,000 years and ended some 11,000 years ago when the wooly mammoths went the way of the Bering Strait land bridge.

Historically speaking, over the past 750,000 years the earth has gone into an ice age roughly every 100,000 years. Between the ice ages is a period of warming during which the ice caps melt at the poles and the ocean rises. If all the ice in Antarctica and Greenland was to melt, the oceans would rise 215 feet above its current levels, and there is evidence that it has been that way in the past.

During the ice ages, the oceans recede as the water is locked up in polar ice. Since the end of the last ice age, the oceans have risen some 300 feet above the ice age minimum.

There have always been variations in global temperature. The period between 1400A.D. to about 1860A.D. has been termed the "Little Ice Age" when average global temps were between 0.5C and 1.0C lower than they are now. That followed a much warmer period between 1000A.D and 1350A.D. when the Vikings colonized Greenland. Remember--they named it Greenland because it was green.

These are minor variations in the more significant swings that mark the advance of glaciers as far south as New York alternating with the submersion of the state of Florida. And one would be mockingly senseless if the question "why?" didn't pop into mind. Why indeed?

There could be lots of reasons. The global warming/ice age cycle seems to follow the sunspot cycle to some degree. There are also second and third order orbital perturbations between the earth and the sun that also correlate significantly. And of course, there have been periods of atmospheric disturbance during significant volcanic events.

The mechanism for the triggering of the ice ages may also be known. The so-called Greenland Conveyer describes the flows that occur because of the differences in density between fresh water and salty water. This flow is responsible for the gulf stream, which is a major mover of heat from the equator to the northern polar regions, and there is a similar mechanism in the south. It's hypothesized that an injection of fresh water from melting polar ice can disturb this stream, and when the heat distribution between the equator and the poles is interrupted, it gets much colder at the poles and the ice begins to advance.

What triggers the melting poles in the first place is clearly an increase in temperature--but what causes the temperature to increase? For that answer, we go to more hypothesis.

As a species we can't do anything about the orbital dynamics of the earth and the sun. We can look for answers there--about how the ellipse of the earth's orbit may move a focus imperceptibly closer to the sun in intervals of roughly 100,000 years. We can theorize how the sun itself, pulled by the gravitational forces of the solar system can warp slightly. And we can wonder if the fusion-driven convection and radiation inside the sun doesn't somehow oscillate to create periods of greater and lesser output.

Physicists worry about these things, and all we can do is wait for an answer from them.

The thing we may be able to influence is the air content parameter. It seems that during the brief periods of global warming that precede the ice ages, the content of carbon dioxide in the air increases. Increased CO₂ is felt to cause a greenhouse effect, reflecting thermal energy from the earth's surface back downward toward the earth instead of allowing it to escape into space, forming a sort of "blanket" that further warms the earth.

Granted, the "greenhouse effect" is just a theory, along with all the other theories explaining the increase in the earth's surface temperature. There are those who believe the CO₂ parameter is the primary driver of the warming cycle, even though the historic mechanism for introduction of CO₂ into the atmosphere is not understood. Possibly because it's one that humans may directly influence it gets a lot of attention. There is no doubt in my mind that it's why CO₂ emission is the political issue, rather than changes in the earth's orbit.

Two years ago, when I spoke with the glaciologists and atmospheric scientists in Antarctica, not one of them would go on record as saying there was a human-influenced cause to the warming effect we were all observing. Let's be clear about that--no matter how much denial we would like to toss into the equation, things are getting warmer, at least as measured by scientists in Antarctica. But the why of it was still unknown back in 2002. Nobody wanted to take up the cause of reducing human carbon emission. Why? Because back then, everyone understood that human contribution to the total carbon content of the atmosphere was a small fraction--anywhere from less than 1% to 10%, depending on to whom you were speaking.

I remember sitting with NOAA Glaciologist Ted Scambos in Gallager's Pub and asking him what was causing the warm up. It was 2002 and he'd just seen most of the Larsen Ice shelf fracture and disappear in a way no one believed could happen.

"We don't know," is what he said.

Ted's credentials are solid. Google him and see for yourself. He's the one the networks calls every time something happens to the ice in Antarctica or at the north pole. He's the one other scientists listen to. Professor at University of Colorado, Boulder. Works at the National Snow and Ice Data Center. He's been interviewed by every major news organization in the United States, and some overseas. Recognized as the voice of what is happening with melting ice and he said, "I don't know," when I asked him what was warming up the world.

"But it's warming up," I said.

"Undeniably. But it could be normal."

Dr. Ted Scambos at NSIDC confirmed that the disintegration events listed on the map were unusual given our current understanding of the mechanics of ice shelves. Very large icebergs calving off other Antarctic ice shelves (e.g., Ross) were not included because they are considered to be part of the normal calving process.
- www.climatehotmap.org -


The Larsen A ice shelf suddenly collapsed in 1995. The Wilkins Ice Shelf is shrinking. In 2002, the 3400-square kilometer Larsen B shelf — at least 12,000 years old and up to 70 stories thick — disintegrated into the Weddell Sea in the space of a few months (satellites images of the collapse are available at http://nsidc.org/iceshelves/larsenb2002/animation.html).
. . .
The calving of monster icebergs is now common. Ted Scambos, an expert from the University of Colorado's National Snow and Ice Centre, found that after Larsen B's collapse, nearby glaciers began entering the sea up to eight times faster than previously.
- www.worldpress.org -

I rooted around and found these quotes from Ted. In the latter reference, there are positions like these reflected:

Weather scientist Charles Keeling, who began measuring atmospheric CO₂ at Mauna Loa in 1958, told the Guardian that "it is possible that this is merely a reflection of natural events like previous peaks in the rate, but it is also possible that it is the beginning of a natural process unprecedented in the record ...

Which in of itself doesn't seem like an alarmist opinion. After all, according to Ted, nobody can say for certain a CO₂-driven greenhouse effect is the cause for concern. But then this is added from Keeling's excerpted speech:

{The rise} could be a weakening of the Earth's carbon sinks, associated with world warming, as part of a climate change feedback mechanism. It is cause for concern.

In fact the rest of that website and many others you find are imbued with news magazine style, "The Day After Tomorrow" evoking imagery that things are changing faster than anyone could have anticipated. Carbon levels must be reduced now. Most advocate the Kyoto accord which seeks to limit world-wide production of greenhouse gasses.

And yet, according to Ted in 2002, there was absolutely no scientific evidence linking production of CO₂ to either global warming or the subsequent ice age. We know CO₂ levels do increase in times of cyclic global warming, as they appear to be now. But we are not sure if that is the cause, or a side effect of some other trigger process.

In fact, I scanned through numerous websites and could not find one in which Ted was quoted as saying anything he was observing had to do with increased levels of CO₂ in the atmosphere. Ted is very careful about what he says in public, generally. When talking about the giant iceberg called B15 that calved from the Ross Ice Shelf in 2002:

“I don’t think the calving (breaking off) of this iceberg is any indication of global warming,” says Ted Scambos, a scientist with the National Snow and Ice Data Center at the University of Colorado in Boulder.
- USA Today, May 12, 2002 -

Things are warming up in Antarctica. They're probably warming up all over the world. There are lots of theories. No one knows for sure why the earth warms periodically, but it does. When it does we note, from taking samples of air trapped in ice cores, that the amount of CO₂ in the atmosphere increases. A classic rise during a warming cycle would be to see CO₂ levels go to 240 parts per million.

But no one can say if this is what causes the warming, or if it's a consequence of the warming. Up until now, all the additional CO₂ has come from natural sources, the largest of which is the ocean itself, out gassing through biological processes. Other contributors are volcanic activity and land-based biological processes. And of course, man-made pollutants contribute as well. But how much? And would it even matter.

According to Ted in 2002, nobody really knew. What we did know was that ice shelves the size of Texas were disintegrating leaving tiny icebergs in their place, and allowing the glaciers that fed them to now drain directly into the sea.

What the hell is happening -- please be like Ted and don't answer if you don't know.

This is what Michael Crichton was trying to get across in his speech to a Caltech audience in January of 2004. He said,

My topic today sounds humorous but unfortunately I am serious. I am going to argue that extraterrestrials lie behind global warming. Or to speak more precisely, I will argue that a belief in extraterrestrials has paved the way, in a progression of steps, to a belief in global warming.

To Crichton, the world of scientists was brimming with qualified researchers who were willing to provide answers in absence of data or any other logical evidence. Start with the so-called Drake equation for guessing at the number of inhabited planets in the known universe. Number of planets with intelligent life that can communicate to us is equal to

"N*fp*ne*fl*fi*fc*fL"
"Where N is the number of stars in the Milky Way galaxy; fp is the fraction with planets; ne is the number of planets per star capable of supporting life; fl is the fraction of planets where life evolves; fi is the fraction where intelligent life evolves; and fc is the fraction that communicates; and fL is the fraction of the planet's life during which the communicating civilizations live. "

There is not one parameter in that equation which can be known for certain. Therefore the number of worlds upon which there could be a culture that could communicate with us by the Drake equation could be as Carl Sagan said, "Billions and Billions," or zero. There is no reason why any number is more valid than any other using that logic.

Of course, many of us want the Drake equation to have a non-zero result. But what we want to believe and what is science are two different things. The Drake equation is not science.

In 1975 many scientists went on the record with a theory they called "Nuclear Winter". That there would occur the artificial creation of an ice age due to all the pollutants thrown into the atmosphere by the atomic explosions and subsequent fires of an all-out nuclear cataclysm.

Carl Sagan put the weight of his public persona behind the theory. He and his coworkers theorized a world-wide drop in temperature of 35-degrees centigrade after a 5,000 megaton nuclear exchange. Yet, the worlds greatest volcanic eruptions with forces approximating that changed the world temperature by only 0.5 to 1.0 degree centigrade, and during the ice ages, world temperatures dropped only 10 degrees.

Crichton goes on to point out that at a conference in Washington attended by Paul Ehrlich, Carl Sagan's co-spokesman, Ehrlich was reminded that after Hiroshima and Nagasaki experts claimed nothing would grow in those cities for 75 years. But in fact, the inhabitants were growing melons the very next year. His response, to quote Crichton:

Ehrlich answered by saying "I think they are extremely robust. Scientists may have made statements like that, although I cannot imagine what their basis would have been, even with the state of science at that time, but scientists are always making absurd statements, individually, in various places. What we are doing here, however, is presenting a consensus of a very large group of scientists…"

And there, my friends, is the issue Michael Crichton rails against. "Consensus science" There is simply no such thing. Science is not the act of a group of smart guys coming together and agreeing on what reality is. Reality is reality. Science is science. You can agree all you want on whether you "believe" the earth was created in 6000BC by the hand of God in seven days, if you can't prove it irrefutably with untainted evidence, in a way someone on the other side of the earth who does not share your language or beliefs can also prove to himself, it simply isn't science.

Crichton says: "Whenever you hear the consensus of scientists agrees on something or other, reach for your wallet, because you're being had."

And he goes on to give examples of where "consensus science" has cost lives. Prior to the 21st century, the greatest killer of women giving birth was fever. In 1795, Gordon of Aberdeen suggested there was an infectious process at work. The consensus was that it wasn't. Nothing was done to investigate the possibility of unsanitary conditions killing women in childbirth. In 1843 Oliver Wendell Holmes provided evidence that puerperal fever was contagious and because the consensus was that it wasn't, his work was ignored. In 1849, Semmelweiss demonstrated that sanitary techniques virtually eliminated puerperal fever in hospitals under his management but because he was a Jew he was dismissed. In fact nothing happened for 125 years despite the ongoing deaths of thousands of women, because the consensus of scientists was that there was no infectious agent at work.

He goes on. In the 1920s thousands of people, mostly poor, were dying of a disease called "pellagra". The consensus was there was an infectious agent at work and that an antibiotic had to be found. A physician named Joseph Goldberger discovered the disease was due to malnutrition, and couldn't convince anyone until he injected himself with the blood of an individual with the disease and failed to contract it. And why would 20th century scientists ignore him? Because to cure the disease social reform would be necessary in the deep south.

Because nobody wanted to address that problem, the "science" was that pellagra was caused by a "germ". But no amount of unwillingness to accept the problem could make it true.

In 1921 Alfred Wegner proposed the theory of continental drift. Crichton says, "Any schoolchild could see that Africa and South America 'fit together', but it was denied by the greatest minds in geology until 1961 when it began to seem the sea floor was spreading. The result of consensus: it took fifty years to acknowledge what any schoolchild sees."

History proves time and time again that consensus science is bad science at best, and mostly not science at all. But the perennial problem is as it always has been: who wants to be the one to stand up and shout the king has no clothes?

Who wanted to stand up and say nuclear winter was a farce--stand up to some of the popular scientists of the 70's and 80's and say-- "Nuclear war will not cause an ice age." Why not? Because the public thinks in sound bites, and that would make one seem like an advocate of nuclear war. What people would hear is, "Professor XYZ believes we should bomb innocent women and children with nuclear weapons--they're not all that precise, you know?" when actually all that was being said was that Carl Sagan hadn't done his homework.

Ditto with lots of other sacred cows.

In 1993 the EPA announced that second-hand smoke was responsible for 3,000 deaths per year. The American Cancer Society blamed second-hand smoke on as many as 53,000 deaths per year.

But one year later, in 1994, they assigned a risk-factor to second hand smoke of 1.19. (A risk factor of 3.0 is necessary for the EPA to initiate an investigation or for the New England Journal of Medicine to accept a paper on the topic.) Back to Crichton:

Furthermore, since there was no statistical association at the 95% confidence limits, the EPA lowered the limit to 90%. They then classified second hand smoke as a Group A Carcinogen. This was openly fraudulent science..."

But now the problem--who wants to come out and call them on it? Smoking causes cancer. Second-hand smoke is a major nuisance for non-smokers. Who wants to tell the EPA they're full of it, and wind up looking like they're supporting R.J. Reynolds pushing cigarettes to kids--all in the name of science?

Nobody.

One last thing from Crichton's speech before I return to the subject of global warming and that is of the idea that science must protect itself. He gives the example of a Danish statistician named Bjorn Lomborg who wrote a book called "The Skeptical Environmentalist". Crichton never states what the content of the book is, but the example is given in context of science becoming overwhelmed by what I will term, a righteous cause--in this case, the environment, and the idea that some environmentalists may practice "consensus science" in the name of advancing one idea or another.

Lomborg was widely disparaged. Scientific American published their review of his book under the title, "Science Defends Itself Against the Skeptical Environmentalist."

And therein lies the inherent evil in the willingness to believe anything because its easy or convenient or because a group of people have convinced themselves without data. Science does not have to be defended. The speed of light needs no defense. F=MA needs no defense. The distance between the earth and the sun needs to be defended no more than the curvature of the earth or the temperature of a swimming pool.

Science simply is. It is to be argued violently and it is to be proven, but at the end of it, nature either is or isn't, and no amount of coming to consensus or postulating belief will change the speed with which a mass falls through the gravitational field of the earth. Any person, regardless of race, age, or religious affiliation, will fall from the International Space Station at the same speed.

The idea of defending science against skepticism, against creationism, against anthropomorphism --is simply preposterous according to Crichton. If the earth was created in one swell foop by the hand of God on October 12, 6200BC as has been postulated by some well-meaning folks in the heartland, then we will all come to that conclusion after analyzing the geological evidence whether or not we're Evangelical Christian or Buddhist or Zoroastrian or atheists. It won't matter where we are located in the entire universe. If it's true, we will find it--every last one of us. It will not require a leap of faith. It will require no faith at all. It will simply be proven the way the speed of light can be measured by anyone with a laser pointer and a bunch of lenses.

So what Crichton said, when he attacked the theory of global warming, was not that it didn't exist, but that the rationale behind the current world-wide effort to reduce carbon emissions was based on something that was not science--but rather--consensus. And we see where that got us through history.

That the earth is warming cannot be denied. It's science. Take a thermometer, go outside for a couple decades, take measurements come back and say what you've found. The Larsen ice shelf has disappeared. More ice is melting in Antarctica at a prodigious rate than we have ever measured before and it's happening not because it's getting colder, but because it's getting warmer. The level of the oceans has risen as a result, and we know it will keep rising if this trend continues. And let's not ignore the north. There are open lanes of water at the north pole in the summer, and that's also something that hasn't been seen in the decades since we've been able to monitor it.

The why of it is still under debate because nobody actually knows. And attacking CO₂ emissions because it's the "consensus" may lead us to a future of false security while we refuse to fund efforts to find the true cause or causes -- which may be entirely natural and beyond our ability to control.

Crichton indicts the computer models being used to predict the warming trends. Consider them "future weather patterns". The accuracy of the models is improving, there is no doubt. But how certain are any of us of the accuracy of the weather reports we hear on the nightly news? The modelers who are forecasting catastrophic global warming are trying to predict the outcome of what may be a fundamentally chaotic process--a hundred or more years into the future.

And we take the weather report for tomorrow with many grains of salt.

What is clear, however, is that on this issue, science and policy have become inextricably mixed to the point where it will be difficult, if not impossible, to separate them out. It is possible for an outside observer to ask serious questions about the conduct of investigations into global warming, such as whether we are taking appropriate steps to improve the quality of our observational data records, whether we are systematically obtaining the information that will clarify existing uncertainties, whether we have any organized disinterested mechanism to direct research in this contentious area.

The answer to all these questions is no. We don't.
-- Michael Crichton --

Now, on to 2004.

A few weeks ago I had dinner with Ted Scambos at Lulu’s in San Francisco. Ted was in town to present a couple papers at the American Geophysical Union conference, but the subject on his mind was the breakup of ice shelves and a research proposal he was making for the next International Polar Year.

Ted showed me a lot of data, some of which I understood, and some I didn't. The key points I remember are these:

• Ice core analysis has brought us atmospheric data from as far back as 400,000 years.
• The highest concentration of CO₂ in those samples is 240parts per million
• There are new, deeper ice core samples that date back to 800,000 years
• Ted is expecting the max CO₂ in those samples not to exceed 240ppm
• The largest sources of CO₂ in the atmosphere is the ocean itself, and then biological and geological processes on land
• The current level of CO₂ in the atmosphere is 375ppm
• The difference between the ambient CO₂ and 375 is man-made, mostly from electric power generation plants - this is a huge percentage compared to that reported at www.clearlight.com
• None of our computer models comprehends CO₂ levels like that
• The environment is changing faster than our existing models predict
• Ted believes he has data to prove this excess CO₂ is to blame - that would be the first true scientific evidence linking man-made CO₂ emission and global warming. this IPY project would be a step in the direction of proving that, scientifically
• Nobody knows what's going to happen

Me: "Is there any possibility the models are screwed up?"

Ted: "They don't have the range to account for 375. But we're already seeing some of the effects they predicted, a lot sooner than the models predict."

Me: "So, what's the problem?"

Ted: "The problem with this stuff is that nobody will listen. And by the time they do, it will be too late."

Me: "But two years ago..."

Ted: "I didn't know then what I know now. And this IPY project will help. We believe we know the mechanism for the ice shelf disintegration. We saw it on the IceSat photos, and I think we can predict it."

Ted is not going to say something he can't prove. He's not going to crash through the doors of the Senate demanding the U.S. sign the Kyoto accord. He knows the dividing line between science and policy. For what it's worth, in the three years I've known him, although he can be a fiery character, I've never heard Ted adopt a position on his science that came from a basis of emotion or consensus opinion. His work is based on technical fact alone, and all of his conclusions stand on those data. Consequently, you're not going to find him stumping for political candidates, allowing his name to be used in presentation of data intending to frighten the public into action.

He will tell you what he thinks if you ask him, but mostly, he'll tell you what he knows, and that's always going to be verifiable science.

I think if Michael Crichton were to meet Ted Scambos, he'd find someone from whom he could get the straight, scientific viewpoint on global warming. What we know and what's conjecture. Where the truth might be hiding in the data, and what's man's contribution to the problem.

He would also learn that Ted writes screenplays, and wrote the original screenplay for the movie "The Red Planet" before it was stolen by the guy who eventually produced that really awful version of the script. I'm positive Crichton would find a kindred spirit in Ted.

"If anyone was waiting to find out whether Antarctica would respond quickly to climate warming, I think the answer is yes," said Dr. Ted Scambos, a National Snow and Ice Data Center glaciologist and lead author of the second study. "We've seen 150 miles of coastline change drastically in just 15 years." He used data from IceSat, a NASA laser altimetry mission launched in 2003, and Landsat 7, jointly run by NASA and the U. S. Geological Survey.
. . .
Scambos and colleagues used five Landsat 7 images of the Antarctic Peninsula from before and after the Larsen B breakup. The images revealed crevasses on the surfaces of glaciers. By tracking the movement of crevasses in sequence from one image to the next, the researchers were able to calculate velocities of the glaciers.
. . .
The surfaces of glaciers dropped rapidly as the flow sped up, according to IceSat measurements. "The thinning of these glaciers was so dramatic that it was easily detected with IceSat, which can measure elevation changes to within an inch or two," said Dr. Christopher Shuman, a Goddard Space Flight Center researcher and a co-author on the Scambos paper.
. . .
The studies provide clear evidence ice shelves restrain glaciers, and indicate present climate is more closely linked to sea level rise than once thought, Scambos added.

-- U.S. Department of State, International Information Program, September 23, 2004

References:


http://www.clearlight.com/~mhieb/WVFossils/greenhouse_data.html
http://culter.colorado.edu/~saelias/glacier.html
http://www.rmpbs.org/learn/frontier/career/glaciologist.html
http://www.climatehotmap.org/fingerprints.html
http://www.worldpress.org
http://www.usatoday.com
http://usinfo.state.gov/gi/Archive/2004/Sep/23-952365.html
http://www.crichton-official.com/speeches/speeches_quote04.html
http://www.ig.utexas.edu/research/projects/agasea/
private conversations with Ted Scambos

This could be it, folks. This could be the one. This might be the one we've all been waiting for. Based on the most recent observatons as of the time of this writeup, there is a 1-in-45 chance that Asteroid 2004 MN4 will hit the Earth on Friday, April 13th, 2029. This is not a drill.

History
2004 MN4 was first observed on June 19th, 2004 by Roy Tucker, David Tholen and Fabrizio Bernardi at Kitt Peak, Arizona. The asteroid was next seen 6 months later on December 18th, and soon after that it was realized that there was a chance of impact in 2029. The risk of impact was first assessed as being approximately 1 in 233. This is a relatively high probablility of impact — in fact, it's higher than any previously observed asteroid of this size — but generally, these things turn out to be nothing in a day or so. The funny thing about this asteroid is that instead of the odds decreasing, they've increased significantly over the past few days. On December 24th, the odds were upped to 1 in 62, and on December 25th, the odds were further raised to 1 in 42, then lowered slightly to the current estimate of 1 in 45 (i.e. 2.2%) later that day.

Size and Destructive Power
It's hard to be sure of an asteroid's size, since the albedo of asteroids varies widely, but currently the best estimate of 2004 MN4's size is approximately 380 meters across, with a mass of about 7.5 x 10¹⁰ kilograms. This is down from the initial estimates, which were 440 m for the diameter and 1.2 x 10¹¹ kg for the mass. Current NASA estimates for the energy of the impact, if it does occur, are around 1.4 gigatons of TNT (1400 megatons) — for comparison, the bomb dropped on Hiroshima was about 15 kilotons. This wouldn't cause worldwide extinctions, but it would cause severe "regional devastation," as NASA puts it. But what region? Well, if it does hit, it will be on the night side of the Earth, towards the end of the day in UTC, implying that an impact would probably be somewhere in the Eastern Hemisphere.

More on the Odds
Saying that there's a 1-in-45 chance of the asteroid hitting the Earth in 24 years is somewhat misleading. Its orbit is set, and either it will hit us or it won't — we just don't know exactly what its orbit is yet. The issue is one of observation. The more the asteroid is observed, and the greater the period of time over which it is observed, the more precisely its orbit can be calculated. So right now, there's a range of orbits that 2004 MN4 may have, and 2.2% of those are orbits which will lead to an impact. What astronomers are currently trying to do is narrow down the possibilites so they can determine the path of the asteroid with greater precision. (Here is a wonderful animation from the Spaceguard Foundation in Italy explaining how the orbits of asteroids are determined from observations.)

Sources and More Information:

• The NASA press release on the subject: http://neo.jpl.nasa.gov/news/news146.html
• The latest Slashdot post: http://science.slashdot.org/article.pl?sid=04/12/25/2147200
• Wikipedia: http://en.wikipedia.org/wiki/2004_MN4
• JPL's Earth Impact Risk Summary: http://neo.jpl.nasa.gov/risk/2004mn4.html
  (NB: there is more than one possible date on which 2004 MN4 could hit. April 13th, 2029 is simply the most likely (by far) out of all of them. This website gives odds on all of them up through 2092.)
• A wonderful CGI script that allows you to see the effects of various impact scenarios: http://www.lpl.arizona.edu/impacteffects/
• Some kind of impromptu information center: http://2004mn4.info/
• The Near Earth Objects Dynamic Site (NEODyS) object listing: http://newton.dm.unipi.it/cgi-bin/neodys/neoibo?objects:2004MN4;main
• MSNBC ran a story on it: http://www.msnbc.msn.com/id/6751433/

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Update, December 27th, 2004: The odds have increased again. There is now a 2.7% chance that 2004 MN4 is on an impact trajectory, making the odds about 1 in 37. Also, NASA has changed their estimate of the asteroid's size slightly — they now believe it is about 390 m across, with a mass of 7.9 x 10¹⁰ kg. The estimated energy of impact has changed correspondingly as well, to 1500 megatons. I'll post more information here as I become aware of it.

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IT'S OVER: Later in the day on the 27th, previously unrecognized images of 2004 MN4 from March 15th were uncovered at the Spacewatch Observatory in Tuscon, Arizona. When this data was taken into account, the possibility of an impact in 2029 disappeared entirely (though the asteroid will still pass within the moon's orbit) and the cumulative probability of any impact at all anytime in the 21st century was lowered to .0018%, or approximately 1 in 56,000. Its estimated size has changed too — it's now believed that its diameter is about 430 m, its mass is about 1.1 x 10¹¹ kg, and the energy of impact would be 2100 megatons. (Note: While I was writing this update, the cumulative odds changed to .0041%, or about 1 in 24,000. The most probable impact is now April 13, 2053, with odds of 1 in 45,000. This is still pretty darn low, and I doubt it will get bigger.)

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WE WILL SEE IT! (and it might hit after all): Radar observations of 2004 MN4 made at Arecibo Observatory have made it possible to predict the path of the asteroid with great precision until its flyby in 2029. It turns out that it's going to make a very close approach — closer than geostationary orbit! In fact, it'll be close enough for it to be visible with the naked eye. The night of Friday, April 13, 2029, observers in the Eastern Hemisphere will be able to see 2004 MN4 moving across the sky at quite a clip, about 42 degrees per hour. (There are 180 degrees in the sky given a totally flat horizon, so this translates to 180/42 = about 4 hours for the asteroid to make it across the sky.) There's no chance that it can hit the Moon, though it will be heading in that general direction.
For more information:

• NASA's Near Earth Object Program press release: http://neo.jpl.nasa.gov/news/news149.html
• Wikipedia's article on MN4: http://en.wikipedia.org/wiki/2004_MN4
• Sky and Telescope ran an article on it: http://skyandtelescope.com/news/article_1458_1.asp
• Space.com had something as well: http://www.space.com/spacewatch/050204_2004_mn4.html

It should be noted that due to the closeness of the approach, it's very hard to predict the asteroid's orbit after the 2029 flyby. As a result, there is a chance that 2004 MN4 will hit Earth at some point after 2029. (See this Slashdot post for more information.) Current odds on that can be found at the JPL Earth Impact Risk site listed above, but these may well change after the 2029 approach. Also, the Arecibo observations have altered estimations of the size and mass of the asteroid. It's now believed that 2004 MN4's diameter is approximately 320 m and its mass is 4.6x10¹⁰ kg. This means that if it were to hit, the impact energy would be about 860 MT. But once again, the odds on it hitting the Earth at any point in the forseeable future are very low.

The no cloning theorem states that it is impossible to make an exact copy of something at the quantum level while retaining the original. More precisely, it says we can't make an exact copy of an arbitrary, unknown quantum state. This was first revealed by Wootters and Zurek in 1982. It may be possible to make copies if we relax some of the requirements (exactness, what kinds of states we can copy, or how much we know about the state), though to what degree is still an open question at the current time. The issue of quantum cloning is of interest to physicists for one reason because making copies is a basic part of doing error correction in a classical computer. Physicists want to build a quantum computer, which will also need error correction, and the extent to which copying of states is possible could be rather important. It is also interesting on a more basic level that nature seems to forbid making an exact copy of something. In quantum teleportation we are able to send an exact copy of something to a remote location but only by destroying the original.

So, why can't we make a copy of a quantum state? Well, I'll try to sketch the basics in plain English, then we can delve into the mathematical details for the experts. In quantum mechanics there are two ways you can change a quantum state,measuring the system and introducing potentials to the system that cause it to evolve according to Schrodinger's Equation. It turns out that neither of these methods allows one to make an exact copy of a system. You can't use a potential to do it, because if you examine the process closely, you find that it would violate the principle of superposition. It's not possible to do it by measurement because a measurement can generally have several different results, unless the system starts out in the desired state, which wouldn't be arbitrary. So, generally, the measurement could result in any number of other states. In essence, the measurements generally destroy quantum information about the state being measured.

Proof

We consider a system that consists of 3 subsystems. The first is the state to be copied, the second is the system to be copied to (the "blank" system"), and the third represents the copying apparatus, and anything else for that matter. Generally, the exact copying of an arbitrary unknown state can be represented schematically as

|ψ>_A*|i>_B*|η>_C → |ψ>_A*|ψ>_B*|η(ψ)>_C

where |ψ> is the state to be copied, |i> is the initial ("blank") state of the system to be copied to, and |η> is everything else. |η(ψ)> is the final state of all other parts of the system, which may depend on the state being copied. First we discuss why measurement is not useful in making a copy and discuss unitary evolution.

Measurement

If a measurement is performed on the system and it is not already in an eigenstate of that measurement operator, then the system will collapse into one of several possible states in a stochastic fashion. This destroys information about the original state and leads to a result that cannot be exactly controlled or predicted. If system starts in an eigenstate of the measurement operator, then the measurement does nothing. Either way, a measurement cannot be a useful part of a process that will lead to an exact copy of the original state.

Unitary Evolution

A copying mechanism that works via unitary evolution would copy an arbitrary state |ψ> by the process

U |ψ>_A*|i>_B*|η>_C = |ψ>_A*|ψ>_B*|η(ψ)>_C

Now suppose that |φ_n> is a complete orthonormal set on subsystem A, so

|ψ> = Σ_n a_n |φ_n>

;thus,

U |ψ>_A*|i>_B*|η>_C = Σ_n a_n U |φ_n>_A*|i>_B*|η>_C = Σ_n a_n |φ_n>_A*|φ_n>_B*|η(φ_n)>_C

But

|ψ>_A*|ψ>_B*|η(ψ)>_C = Σ_n,m a_n a_m |φ_n>_A*|φ_m>_B*|η(ψ)>_C

These two expressions are supposed to be the same, but they aren't, showing that our hypothesized copying process is not possible and not, in fact, linear, since that's the only property of the evolution we used. Put another way, the ideal copying mechanism would violate the superposition principle if it worked for more than one specific state. Of course, if it worked only for one predefined state then it wouldn't be much use, since if we know the state initially we should be able to generate it (in principle) even without copying.

We can conclude that it is not possible to clone an arbitrary unknown state exactly; however, we have not ruled out the possibility that one could perform cloning by relaxing one of the constraints. If we restricted the set of states to be copied or had some knowledge of them, we might be able to make a copy. Also, we might be able to make some degree of approximate copy, but it is unclear how close we could get to an exact copy (or, indeed, how to measure "closeness"). We could also explore mechanisms by which an exact copy is produced with some probability (less than %100). These issues are still currently being researched.

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Here * is used to denote the tensor product of two states.

Note: The derivation here is mine, so it may contain mistakes, but the result is widely known.

Sources:

• No cloning theorem Wikipedia.org
  
• Quantum Copying: Beyond the No-cloning Theorem Buzek, V. and Hillery, M., Phys. Rev. A 54, 1844 (1996)

The concept of an eigenstate is key to the mathematical formulation of quantum mechanics. Each particle in a quantum mechanical system is described by a mathematical object called a state vector or state for short. Each observable quantity, such as position, momentum, and spin, is associated with a set of states that are called its eigenstates. If a particle is in an eigenstate of an observable, it has a definite value for that quantity (i.e. there is no quantum uncertainty in that quantity). Each possible value (called an eigenvalue) for the observable quantity corresponds to at least one eigenstate

Conceptual Utility of Eigenstates

A set of eigenstates for an observable quantity forms a complete basis for the system. This means that any possible state of the particle can be written as a superposition of eigenstates for each observable. This superposition is key when a measurement of the system is made. A measurement connects the quantum system to a classical system which must obey the deteministic laws of classical mechanics. Hence, the measurement must find a definite value of the observable quantity, which only occurs when the particle is in an eigenstate of that observable. So measurements end the superposition and force the system into an eigenstate corresponding to the quantity measured.

It is possible that two different observable quantities can have the same set of eigenstates. In this case the two observables are said to commute. (Yes, I know that's weird terminology, bear with me) Physically, this means that the two quantities can have definite values at the same time, whereas two observables that do not commute obey some kind of uncertainty relation and cannot both have simultaneously definite values.

Eigenstates come in both discrete and continuous sets. The set of position eigenstates and the set of momentum eigenstates are both continuous, since there is an eigenstate corresponding to each of the possible values of these quantities. Discrete sets of eigenstates are often infinite, but can also be finite in size, particularly for observables related to angular momentum. Discrete sets of eigenstates are where many of the interesting features of quantum mechanics occur, as values of the observable quantity between the eigenvalues are simply not possible, in contrast to the continuous observables of classical mechanics.

Mathematical Formalism

In Dirac's powerful formalism of quantum mechanics, states are represented as 'kets' (|ψ>), and observable quantities correspond to mathematical operators (notated in boldface) that act upon the states. The eigenstates, |ψ>, of an arbitrary operator Q are determined by the equation:

Q|ψ> = q|ψ>

The q is the eigenvalue. Note that the operator leaves the actual state unchanged, rather than transforming it into a different state. This is the defining property of being an eigenstate.

Operators do not obey the same sort of algebra as numbers, but rather they obey the same algebra as matrices. The knowledgeable reader will notice that this implies that operators do not obey the commutative law and so for operators A and B, AB may not be the same as BA. Some operators, however, do obey AB = BA; these operators commute. It can be proven that two operators that commute must have the same set of eigenstates; this is a general theorem in linear algebra.

Energy Eigenstates and the Schrodinger Equation

The most important set of eigenstates is that associated with the Hamiltonian operator, which measures total energy. The time-independent Schrodinger equation is just the eigenstate equation for the Hamiltonian:

H|ψ> = E|ψ>

Since energy is conserved over time, we would expect a time-independent state to have a definite, constant amount of energy. So any such 'stationary state' must be an eigenstate of the Hamiltonian, whatever it might be.

However, there are often a number of states with the same energy eigenvalue (referred to as degenerate), so the equation as written may not uniquely describe every state. It is, however, usually possible to describe all states using other operators that commute with the Hamiltonian. In the case of the hydrogen atom, for example, the electron states are described by eigenstates of the Hamiltonian, the total angular momentum operator, and the z-axis angular momentum operator.

Conclusion

Eigenstates are the building blocks used by physicists to build full quantum mechanical descriptions of physical systems. They are, by definition, those states that we can have definite knowledge about, making them the key we can use to unlock the quantum puzzle of small-scale matter.

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(CC)
This writeup is copyright 2004 D.G. Roberge and is released under the Creative Commons Attribution-NoDerivs-NonCommercial licence. Details can be found at http://creativecommons.org/licenses/by-nd-nc/2.0/ .

If the physical laws of a system are time reversal invariant that means essentially that if you were watching a video tape of the system then you would not be able to tell whether it was being played forward or backward. We can represent that concept more mathematically by saying that if a particular motion q(t) obeys the physical laws (e.g. is a solution to the equation of motion) then q(-t) will also obey the physical laws. You could think of this geometrically as reflecting the whole problem across the axis t = 0. If a something is invariant under time reversal it is said to have or obey time reversal symmetry, often denoted T. A system that breaks time reversal symmetry is sometimes said to have an "arrow of time".

An Example of Time Reversal Invariance

A simple example of a system with time reversal invariance is two (idealized) billiards balls colliding on a pool table. Imagine you're playing a game of 8 ball and just the 8 ball is left. You shoot the cue ball at the 8 ball and you aim it dead center, they collide, the cue ball comes to a stop and the 8 ball goes sailing off. Good, now freeze that picture in you mind, and then set it going in reverse. Notice now the 8 ball comes in, collides with the cue ball, comes to a stop, and the cue ball goes sailing off. The time reversed picture looks just as reasonable as the one for forward moving time. In fact, if you didn't know anything about the game and were just looking at the balls, you might assume someone had shot the 8 ball at the cue ball. There are many other examples one can think of that are time reversal invariant, like a mass on a spring or a (perfectly elastic) ball bouncing up and down off the ground.

An Example of Time Reversal Symmetry Breaking

Probably the simplest example I can think of for a system that seems to break time reversal invariance is a box sliding along a level floor. As the box slides, friction slows it down and it gradually comes to a stop. Good, now freeze that picture and play it in reverse. The box is just sitting there and then suddenly it starts moving and keeps speeding up. Now that clearly "just ain't natural". Put more mathematically, that's not a solution to the equation of motion. Similarly, in the example of the bouncing ball, if it's not perfectly elastic then it will bounce to a lower and lower height each time. Again, playing that backward would not look right.

The Role of Time Reversal Invariance in Physics

In the days of classical physics, before Planck, Einstein, and the rest, it was generally thought that microscopic physics was time reversal invariant, and that this was one of the fundamental properties of nature. Elastic collisions, Newtonian gravity, and classical electromagnetism are all time reversal invariant, and these were generally the types of mechanisms that they thought governed the world at the fundamental level. The subsequent development of the standard model of particle physics revealed that nature is not time reversal invariant. Indeed, experiments have been done to measure CP violation, which is equivalent to the violation of time reversal symmetry, T, in the standard model. In that theory CPT symmetry is still upheld, though there are currently experiments looking for violations of that, which would indicate physics beyond the standard model.

Macroscopic Systems and Thermodynamics

If you have been reading closely, you will notice that earlier I gave several examples of simple, everyday situations that seem to violate time reversal invariance, no particle physics necessary. As I said it was thought that microscopic physics was time invariant, but when you talk about macroscopic objects you get into statistical physics and thermodynamics. It turns out that if you talk about a large system and you look with a sort of fuzzy lens that can only really tell what the bulk is doing and not each individual piece, then you lose time reversal symmetry. That is to say that even if the individual pieces obey time reversal invariance, when you look at the whole group in this "fuzzy" way and try to work out its statistical properties, you will get rules that break time reversal symmetry.

Going back to the pool analogy, suppose you are going to break at the beginning of the game. You shoot the pool ball into the large, ordered, triangular group that the rest of the balls make up and they scatter everywhere. Now, if you ran the video tape backward you would see them all coming together, but each collision would obey Newton's laws, nothing fishy yet. On the other hand, if you were looking at this with your "fuzzy" glasses and asking the statistical question, "How likely is it that a scattered group of balls will all come together to form a large, ordered, stationary group with only one (or a few) moving?" the answer would be "Not bloody likely!"

It is these statistical sorts of laws that govern macroscopic objects like an actual rubber ball or billiards ball or a box sliding across the floor. Thermodynamics deals in these sorts of macroscopic, statistical situations and includes the second law of thermodynamics, which says that entropy (which often can be roughly thought of as disorder) in a closed system can never decrease. That law already manifestly breaks time reversal symmetry, because entropy can increase in time but never decrease indicating which direction is "forward" in time. For example, if you take a pot full of hot water and a pot full of cold and put them in contact, thermodynamics says that the hot water will cool and the cold water will warm, which increases the entropy of the system, until they reach equilibrium. You could put a thermometer in each to watch this happen. If you played a video of that in reverse, though, you'd notice it was very strange when one of the two pots started getting hotter and the other colder with no outside influence. This is sometimes called the thermodynamic arrow of time.