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The End of Cosmology?

An accelerating universe wipes out traces of its own origins

 
LONELY PLANET: As space empties out because of the quickening cosmic expansion, the galaxy that Earth inhabits will come to be surrounded by a total void.

Graphic - Key Concepts

  • A decade ago astronomers made the revolutionary discovery that the expansion of the universe is speeding up. They are still working out is implications.
  • The quickening expansion will eventually pull galaxies apart faster than light, causing them to drop out of view. This process eliminates reference points for measuring expansion and dilutes the distinctive products of the big bang to nothingness. In short, it erases all the signs that a big bang ever occurred.
  • To our distant descendants, the universe will look like a small puddle of stars in and endless, changeless void.
  • What knowledge has the universe already erased?

One hundred years ago a Scientific American article about the history and large-scale structure of the universe would have been almost completely wrong. In 1908 scientists thought our galaxy constituted the entire universe. They considered it an “island universe,” an isolated cluster of stars surrounded by an infinite void. We now know that our galaxy is one of more than 400 billion galaxies in the observable universe. In 1908 the scientific consensus was that the universe was static and eternal. The beginning of the universe in a fiery big bang was not even remotely suspected. The synthesis of elements in the first few moments of the big bang and inside the cores of stars was not understood. The expansion of space and its possible curvature in response to matter was not dreamed of. Recognition of the fact that all of space is bathed in radiation, providing a ghostly image of the cool afterglow of creation, would have to await the development of modern technologies designed not to explore eternity but to allow humans to phone home.

It is hard to think of an area of intellectual inquiry that has changed more in the past century than cosmology, and the shift has transformed how we view the world. But must science in the future always reflect more empirical knowledge than existed in the past? Our recent work suggests that on cosmic timescales, the answer is no. We may be living in the only epoch in the history of the universe when scientists can achieve an accurate understanding of the true nature of the universe.

A dramatic discovery almost a decade ago motivated our study. Two different groups of astronomers traced the expansion of the universe over the past five billion years and found that it appears to be speeding up. The source of this cosmic antigravity is thought to be some new form of “dark energy” associated with empty space. Some theorists, including one of us (Krauss), had actually anticipated this new result based on indirect measurements, but in physics it is direct observations that count. The acceleration of the universe implies that empty space contains almost three times as much energy as all the cosmic structures we observe today: galaxies, clusters and superclusters of galaxies. Ironically, Albert Einstein first postulated such a form of energy to keep the universe static. He called it the cosmological constant [see “Cosmological Antigravity,” by Lawrence M. Krauss; Scientific American, January 1999].

Dark energy will have an enormous impact on the future of the universe. With cosmologist Glenn Starkman of Case Western Reserve University, Krauss explored the implications for the fate of life in a universe with a cosmological constant. The prognosis: not good. Such a universe becomes a very inhospitable place. The cosmological constant produces a fixed “event horizon,” an imaginary surface beyond which no matter or radiation can reach us. The universe comes to resemble an inside-out black hole, with matter and radiation trapped outside the horizon rather than inside it. This finding means that the observable universe contains only a finite amount of information, so information processing (and life) cannot endure forever [see “The Fate of Life in the Universe,” by Lawrence M. Krauss and Glenn D. Starkman; Scientific American, November 1999].

Long before this information limit becomes a problem, all the expanding matter in the universe will be driven outside the event horizon. This process has been studied by Abraham Loeb and Kentaro Nagamine, both then at Harvard University, who found that our so-called Local Group of galaxies (the Milky Way, Andromeda and a host of orbiting dwarf galaxies) will collapse into a single enormous supercluster of stars. All the other galaxies will disappear into the oblivion beyond the event horizon. This process takes about 100 billion years, which may seem long but is fairly short compared to the wilderness of eternity.

Collapsing Pillars
What will astronomers of the far future, living in this supercluster, conclude about the history of the universe? To think about this question, recall the pillars on which our current understanding of the big bang is based.

The first is Einstein’s general theory of relativity. For nearly 300 years Newton’s theory of universal gravitation served as the basis for almost all of astronomy. Newton’s theory does an excellent job of predicting the motions of objects on scales from the terrestrial to the galactic, but it is completely incapable of dealing with infinitely large collections of matter. General relativity overcomes this limitation. Shortly after Einstein published the theory in 1916, Dutch physicist Willem de Sitter solved the equations of general relativity for a simplified universe incorporating Einstein’s cosmological constant. De Sitter’s work appeared to reproduce the prevailing view of the universe at the time: an island galaxy embedded in a largely empty, static void.

Cosmologists soon realized that the stasis was a misinterpretation. In fact, the de Sitter universe is eternally expanding. As Belgian physicist Georges Lemaître later made clear, Einstein’s equations predict that an infinite, homogeneous, static universe is impossible. The universe has to expand or contract. From this realization, the big bang theory, as it would later be called, was born.

The next pillar came in the 1920s, when astronomers detected the expansion of the universe. The first person to provide observational evidence for expansion was American astronomer Vesto Slipher, who used the spectra of stars to measure the velocities of nearby galaxies. Waves of light from a star moving toward Earth are compressed, shortening the wavelength and making the light bluer. Light waves from an object moving away from us are stretched, making the wavelength longer and the light redder. By measuring the lengthening or compression of the light waves from distant galaxies, Slipher was able to determine whether they were moving toward us or away from us and at what speed. (At the time, astronomers were not even sure whether the fuzzy patches of light that we call “galaxies” were actually independent bodies of stars or simply gas clouds inside our own galaxy.) Slipher found that almost all these galaxies were moving away from us. We seemed to be sitting at the center of a runaway expansion.

The person who is generally credited for discovering the expansion of the universe is not Slipher but American astronomer Edwin Hubble. (When was the last time you read about the Slipher Space Telescope?) Hubble determined not just the velocities of nearby galaxies but also their distances. His measurements led to two conclusions that justify his fame. First, Hubble showed that galaxies were so far away that they really were independent collections of stars, just like our own galaxy. Second, he discovered a simple relation between the distance to galaxies and their velocities. The velocity was directly proportional to its distance from us: a galaxy twice as far away as another was moving twice as fast. This relation between distance and velocity is exactly what happens when the universe is expanding. Hubble’s measurements have since been refined, most recently by the observations of distant supernovae, which led to the discovery of dark energy.

The third pillar is the faint glow of the cosmic microwave background, discovered serendipitously in 1965 by Bell Labs physicists Arno Penzias and Robert Wilson as they tracked down sources of radio interference. This radiation was quickly recognized to be a relic left over from the early stages of the expansion of the universe. It indicates that the universe began hot and dense and has since cooled and thinned out.

The final observational pillar of the big bang is that the hot, dense early universe was a perfect location for nuclear fusion. When the temperature of the universe was one billion to 10 billion kelvins, lighter nuclei could fuse into heavier nuclei, a process known as big bang nucleosynthesis. This process can occur for only a few minutes as the universe expands and cools, so fusion was limited to the lightest elements. Most of the helium in the universe was produced then, as was deuterium, or heavy hydrogen. The measured abundances of helium and deuterium match the predictions of big bang nucleosynthesis, providing further evidence for the theory as well as an accurate estimate of the abundance of protons and neutrons in the universe.

Dark Skies
What will the scientists of the future see as they peer into the skies 100 billion years from now? Without telescopes, they will see pretty much what we see today: the stars of our galaxy. The largest and brightest stars will have burned up their nuclear fuel, but plenty of smaller stars will still light up the night sky. The big difference will occur when these future scientists build telescopes capable of detecting galaxies outside our own. They won’t see any! The nearby galaxies will have merged with the Milky Way to form one large galaxy, and essentially all the other galaxies will be long gone, having escaped beyond the event horizon.

The disappearance of distant galaxies is not immediate but gradual. The redshift of these galaxies becomes infinitely large as they approach the horizon. Krauss and Starkman calculated that this redshift will exceed 5,000 for all galaxies by 100 billion years, rising to an unfathomable 1053 by 10 trillion years—at which time even the highest-energy cosmic rays will have redshifted so much that their wavelength will be larger than the horizon size. These objects will then be truly and completely invisible to us.

As a result, Hubble’s crucial discovery of the expanding universe will become irreproducible. All the expanding matter in the universe will have visually disappeared beyond the horizon, and everything remaining will be part of a gravitationally bound cluster of stars. For these future astronomers, the observable universe will closely resemble the “island universe” of 1908: a single enormous collection of stars, static and eternal, surrounded by empty space.

Our own experience demonstrates that even when we have data, the correct cosmological model is not so obvious. For example, from the 1940s to the mid-1960s, with the edifice of observational cosmology resting only on Hubble’s discovery of the expanding universe, some astrophysicists resurrected the idea of an eternal universe: the steady-state universe, in which matter is created as the universe expands, so that the universe as a whole does not really change with time. This idea proved to be an intellectual dead end, but it does demonstrate the kind of mistaken notion that can develop in the absence of adequate observational data.

Where else might astronomers of the future search for evidence of the big bang? Would the cosmic microwave background allow them to probe the dynamics of the universe? Alas, no. As the universe expands, the wavelengths of the background radiation stretch and the radiation becomes more diffuse. When the universe is 100 billion years old, the peak wavelengths of the microwave radiation will be on the scale of meters, corresponding to radio waves instead of microwaves. The intensity of the radiation will be diluted by a factor of one trillion and might never be seen.

Even further into the future, the cosmic background will become truly unobservable. The space between stars in our galaxy is filled with an ionized gas of electrons. Low-frequency radio waves cannot penetrate such a gas; they are absorbed or reflected. A similar effect is the reason that AM radio stations can be picked up far from their cities of origin at night; the radio waves reflect off the ionosphere and back down to the ground. The interstellar medium can be thought of as one big ionosphere filling the galaxy. Any radio waves with frequencies below about one kilohertz (a wavelength of greater than 300 kilometers) cannot penetrate into our galaxy. Radio astronomy below one kilohertz is forever impossible inside our galaxy. When the universe is about 25 times its present age, the microwave background will be stretched beyond this wavelength and become undetectable to the residents of the galaxy. Even before then, the subtle patterns in this background radiation, which have provided so much useful information to today’s cosmologists, will become too muted to study.

Burning Up
Would observations of the abundances of chemical elements lead cosmologists of the distant future to a knowledge of the big bang? Once again, the answer is likely to be no. The problem is that our ability to probe big bang nucleosynthesis hinges on the fact that the abundances of deuterium and helium have not evolved very much since they were produced 14 billion years ago. Helium produced in the early universe, for example, makes up about 24 percent of the total matter. Although stars produce helium in the course of their fusion reactions, they have increased this abundance by no more than a few percent. Astronomers Fred Adams and Gregory Laughlin of the University of Michigan at Ann Arbor have suggested that this fraction could increase to as much as 60 percent after many generations of stars. An observer in the distant future would find the primordial helium swamped by the helium produced in later generations of stars.

Currently the cleanest probe of big bang nucleosynthesis is the abundance of deuterium. Our best measurements of the primordial deuterium abundance come from observations of hydrogen clouds backlit by quasars, extremely distant and bright beacons thought to be powered by black holes. In the far future of the universe, however, both these hydrogen clouds and quasars will have passed beyond the event horizon and will be forever lost to view. Only galactic deuterium might be observable. But stars destroy deuterium, and little will survive. Even if astronomers of the future observe deuterium, they might not ascribe it to the big bang. Nuclear reactions involving high-energy cosmic rays, which have been studied today as a possible source of at least some of the observed deuterium, might seem more plausible.

Although the observational abundance of light elements will not provide any direct evidence for a fiery big bang, it will nonetheless make one aspect of future cosmology different from the illusory cosmology of a century ago. Astronomers and physicists who develop an understanding of nuclear physics will correctly conclude that stars burn nuclear fuel. If they then conclude (incorrectly) that all the helium they observe was produced in earlier generations of stars, they will be able to place an upper limit on the age of the universe. These scientists will thus correctly infer that their galactic universe is not eternal but has a finite age. Yet the origin of the matter they observe will remain shrouded in mystery.

What about the idea with which we began this article, namely that Einstein’s theory of relativity predicts an expanding universe and therefore a big bang? The denizens of the far future of the universe should be able to discover the theory of general relativity from precision measurements of gravity in their own solar system. Using this theory to infer a big bang, however, rests on observations about the large-scale structure of the universe. Einstein’s theory predicts an expanding universe only if the universe is homogeneous. The universe that our descendants survey will be anything but homogeneous. It will consist of an island of stars embedded in a vast emptiness. It will, in fact, resemble de Sitter’s island universe. The ultimate future of the observable universe is to collapse into a black hole, precisely what will in fact occur to our galaxy in the distant future.

Alone in the Void
Is there no way at all for our descendants to perceive an expanding universe? One telltale effect of acceleration would indeed remain within our observational horizon, at least according to our current understanding of general relativity. Just as the event horizon of a black hole emits radiation, so, too, does our cosmological event horizon. Yet the temperature associated with this radiation is unmeasurably small, about 10–30 kelvin. Even if astronomers were able to detect it, they would probably attribute it to some other, far larger local source of noise.

Ambitious future observers might also send out probes that escape the supergalaxy and could serve as reference points for detecting a possible cosmic expansion. Whether it would occur to them to do so seems unlikely, but in any event it would take billions of years at the very least for the probe to reach the point where the expansion noticeably affected its velocity, and the probe would need the energy output comparable to that of a star to communicate back to its builders from such a great distance. That the science-funding agencies of the future would support such a shot-in-the-dark is unlikely, at least if our own experience is any guide.

Thus, observers of the future are likely to predict that the universe ultimately ends with a localized big crunch, rather than the eternal expansion that the cosmological constant produces. Instead of a whimper, their limited universe will end with a bang.

We are led inexorably to a very strange conclusion. The window during which intelligent observers can deduce the true nature of our expanding universe might be very short indeed. Some civilizations might hold on to deep historical archives, and this very article might appear in one—if it can survive billions of years of wars, supernovae, black holes and countless other perils. Whether they will believe it is another question. Civilizations that lack such archives might be doomed to remain forever ignorant of the big bang.

Why is the present universe so special? Many researchers have tried to argue that the existence of life provides a selection effect that might explain the coincidences associated with the present time [see “The Anthropic Principle,” by George Gale; Scientific American, December 1981]. We take different lessons from our work.

First, this would quite likely not be the first time that information about the universe would be lost because of an accelerating expansion. If a period of inflation occurred in the very early universe, then the rapid expansion during this era drove away almost all details of the preexisting matter and energy out of what is now our observable universe. Indeed, one of the original motivations for inflationary models was to rid the universe of pesky cosmological objects such as magnetic monopoles that may once have existed in profusion.

More important, although we are certainly fortunate to live at a time when the observational pillars of the big bang are all detectable, we can easily envisage that other fundamental aspects of the universe are unobservable today. What have we already lost? Rather than being self-satisfied, we should feel humble. Perhaps someday we will find that our current careful and apparently complete understanding of the universe is seriously wanting.

PR

Fastest Way Up Hills: Zigzag

 
Trails used by humans exhibit zigzags, or switchbacks, when they traverse steep hillsides, such as this one in Mallorca, Spain

A straight line may be the shortest distance between two points, but on a steep slope, zigzagging is the fastest way to go, a new study confirms.

On flat terrain, a straight line is typically still the best way to get from point A to point B. But climbing up a steep hill is a whole different ballgame; the mechanics and energy costs of
walking up a hill alter the way we negotiate the landscape.

"You would expect a similar process on any landscape, but when you have changes in elevation it makes things more complicated," said study author Marcos Llobera of the University of Washington. "There is a point, or critical slope, where it becomes metabolically too costly to go straight ahead, so people move at an angle, cutting into the slope. Eventually they need to go back toward the direction they were originally headed and this creates zigzags. The steeper the slope, the more important it is that you tackle it at the right angle."

Llobera and co-author T.J. Sluckin of the University of Southampton in the U.K. developed a simple mathematical model showing that a zigzagging course is in fact the
most efficient way to go up or down a steep slope.

Most people don't need a model to tell them that though, they do it without even thinking.

"I think zigzagging is something people do intuitively," Llobera said. "People recognize that zigzagging, or switchbacks, help but they don’t realize why they came about."

Pandemic Hot Spots Map a Path to Prevention

Job one in stopping future pandemics: figure out where they start

 
CLOSE QUARTERS: Researchers watching out for the next pandemic are monitoring markets in Asia where people may pick up viruses from live animals.

 
HOTSPOTS where infectious diseases are thought to be most likely to jump from wildlife to people, potentially sparking the next pandemic.
Click here to enlarge.

A new study maps out areas of the world that researchers think are most likely to breed the killer diseases of the future—and the highlighted countries are not the ones getting most of the resources for disease prevention. The analysis is part of a budding effort to identify emerging viruses in particular and prevent future pandemics from reaching their full potential.

British and U.S. researchers compiled a database of 335 infectious diseases first acknowledged as a potential threat between 1940 and 2004. Examples include the Ebola virus (1976) and HIV (1981) as well as the more recent
Nipah virus (1999), SARS (2002) and H5N1 bird flu (1997). They compared the frequency of novel outbreaks with possible contributing factors such as population density and growth, latitude, and the diversity of wildlife.

Emerging infections have become steadily more frequent over the decades, peaking in the 1980s, they report, possibly because of the AIDS pandemic. Bacteria were responsible for 54 percent of the total, especially drug-resistant varieties such as
methicillin-resistant staphylococcus aureus, or MRSA (1961). Viruses and prions (infectious proteins) contributed 25 percent, followed by protozoa at 11 percent and fungi at six percent.

The areas showing the highest frequency of distinct outbreaks all had growing population densities. The U.S. and Europe had more reported outbreaks, but these events seemed to reflect greater disease surveillance in industrialized countries, the group wrote in Nature.

"We conclude that the global effort for EID [emerging infectious disease] surveillance and investigation is poorly allocated," they wrote, "with the majority of our scientific resources focused on places from where the next important emerging pathogen is least likely to originate. We advocate reallocation of resources for 'smart surveillance' of emerging disease hot spots in lower latitudes, such as tropical Africa, Latin America and Asia."

Overall, 60.3 percent of the emerging pathogens were
zoonoses—animal pathogens that infect humans—and 71.2 percent of these came from wildlife. The fraction of outbreaks stemming from zoonoses in general and the wildlife variety in particular both rose over time. The team says these findings suggest that emerging infectious diseases  flourish where people are coming into greater contact with wild animals.

This study and others before it increasingly show "that there are patterns which can be used for the forecasting of novel pandemics," says infectious disease specialist Nathan Wolfe of the University of California, Los Angeles, who was not part of the study. "It helps to inform the kind of monitoring that'll have to be in place to take this to the next step, to really prevent the next pandemic."

In an example of "smart surveillance," Wolfe has worked in the African nation of Cameroon monitoring the exchange of retroviruses between wild primates and human hunters exposed to their blood. He has already identified several examples of viruses jumping to people, including three new foamy viruses (which are not known to cause human sickness), and two new forms of human T-lymphotropic virus (HTLV), related to HTLV-1, which is common among IV-drug users in the U.S. and is believed to cause certain cancers.

Along with Peter Daszak of the Consortium for Conservation Medicine in New York City, a co-author of the Nature report, he has begun monitoring Chinese wet markets, where live animals are sold for food. Wolfe is seeking $50 million to expand his pilot project from sites in seven African and Asian countries into what he calls a Global Viral Forecasting Initiative.

Although the hot spot map points to areas of growing density, the detailed route of a pandemic is more complex, Wolfe says. Hunters bringing valuable bushmeat or game to market take with them potential new infections. Wildlife may also begin traveling into expanding urban areas along newly cleared roads.

"If you have close proximity, things that previously would have gone extinct now have the potential to travel from person to person and become established," Wolfe says. If a pandemic is like a wildfire, then "our hunters are kindling, [and] large, dense urban population centers are the logs."

Research Explains Formation of Unique Martian Fans

 
An image of a Martian terraced fan taken by a camera on board the Mars Odyssey spacecraft.

To figure out an odd landscape feature on Mars, play in a big sandbox.

Enlist some high school students, too.

That’s what some scientists at the Utrecht University in the Netherlands did, and they believe they now know how sediment deposits spilling out of the mouth of some water channels on Mars were shaped in a series of terraces that look like terraced rice paddies.

But no similar natural formations have been seen in river deltas on Earth. Usually river sediments spill out in a smooth, sloping fan like the Mississippi delta.

Planetary geologists have been speculating about the terraced fans since they were first spotted by NASA’s Mars Global Surveyor eight years ago. About 10 stepped fans have been identified, most at the base of a steep slope emptying into a basin like an impact crater. (Most of the 200 sediment fans seen on Mars do not have the stepped structure. Another mystery is why many of the river channels seem to have no sediment deposit at all.)

Some scientists suggested the terraced fans were the result of repeated shore erosion as a lake in the basin dried up. Others thought repeated landslides might have formed the steps.

The sandbox experiment, reported in Thursday’s issue of the journal Nature, supports a third notion. The terraces form by the interaction of the sediment flow with the water’s edge, which is rising as the basin fills.

“Where that’s happening, you’re getting a little lip,” said Erin R. Kraal, the lead author of the Nature paper. Pulses of flow and sediment produced multiple terraces. “They’re just stacking one atop the other,” she said.

While a postdoctoral researcher at Utrecht, Dr. Kraal became intrigued by the terraced fans and mentioned them to her colleagues there. Utrecht has a set-up known as Eurotank, essentially a 16- by 40-foot sandbox for studying sedimentary dynamics.

High school students visiting the laboratory as part of an educational project saw the Mars pictures on the laboratory walls and were interested in helping on an experiment, which eventually turned into a short educational movie about the Martian fans.

The students dug a crater in the sandbox and shaped a water channel. Then they sent water down the channel — and the result was a terraced fan, just as on Mars.

“We didn’t expect it to be so successful the first time,” said Dr. Kraal, now a research scientist at Virginia Polytechnic Institute and State University. “We were really surprised they formed so quickly and so easily.”

Dr. Kraal and her colleagues, Maurits van Dijk, George Postma and Maarten G. Kleinhans later repeated the experiments more rigorously so they could correlate their sandbox results with the Martian terrain.

They estimate that the water necessary to form one of the Martian fans, which measure up to a dozen miles wide, would equal 10 years of Mississippi River flow. The whole structure appears to have formed in one event lasting perhaps tens of years, they said.

“It does look like she’s experimentally shown here that this type of deposit can form in a single event type of discharge,” said Rossman P. Irwin III, a geologist at the Smithsonian Institute’s Center for Earth and Planetary Studies who has also studied the terraced fans. “It offers some good experimental support for a type of feature that is basically unique to Mars and really was not well understood.”

Scientists Measure What It Takes to Push a Single Atom 

 
An illustration of the tip of an atomic force microscope, in brown, measuring the force it takes to move a cobalt atom, the yellow sphere, on a crystalline surface. 

I.B.M. scientists have measured the force needed to nudge one atom.

About one-130-millionth of an ounce of force pushes a cobalt atom across a smooth, flat piece of platinum.

Pushing the same atom along a copper surface is easier, just one-1,600-millionth of an ounce of force.

The scientists report these minuscule findings in Friday’s issue of the journal Science.

I.B.M. scientists have been pushing atoms around for some time, since Donald M. Eigler of the company’s Almaden Research Center in San Jose, Calif., spelled “IBM” using 35 xenon atoms in 1989. Since then, researchers at the company have continued to explore how they might be able to construct structures and electronic components out of individual atoms.

Knowing the precise forces required to move atoms “helps us to understand what is possible and what is not possible,” said Andreas J. Heinrich, a physicist at Almaden and an author of the new Science paper. “It’s a stepping stone for us, but it’s by no means the end goal.”

In the experiment, Dr. Heinrich and his collaborators at Almaden and the University of Regensburg in Germany used the sharp tip of an atomic force microscope to push a single atom. To measure the force, the tip was attached to a small tuning fork, the same kind that is found in a quartz wristwatch. In fact, in the first prototype, Franz J. Giessibl, a scientist at Regensburg who was a pioneer in the use of atomic force microscopes, bought an inexpensive watch and pulled out the quartz tuning fork for use in the experiment.

The tip vibrates 20,000 times a second until it comes into contact with an atom. As the tip pushes, the tuning fork bends, like a diving board, and the vibration frequency dips.

A single atom does not roll, and even a perfectly smooth surface is not perfectly smooth. Instead, the atom rests in small indentations in the lattice, in effect like an egg in an egg carton. The resistance — what becomes friction when multiplied by millions and billions of atoms — comes from the energy needed to rearrange the bonds between the cobalt atom and surface.

When the tip pushes hard enough, the atom hops, almost instantaneously to the next indentation. “It’s not smooth,” said Markus Ternes, another Almaden scientist working on the research. “It’s faster than we can detect.”

From the changes in the frequency of the tuning fork vibrations, the scientists calculated the force that the tip applied to the cobalt atom.

Copper is less sticky than platinum, because of differences between the underlying bonds, and hence allowed the greater ease is pushing the cobalt atom along.

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