Dark Flow, Gravity and Love

By Rob Bryanton

The above video is tied to a previous blog entry from last January of the same name, Dark Flow.

Last time, in Placebos and Biocentrism, we returned to the idea that so much of what we talk about with this project is tied to visualizing our reality from “outside” of spacetime, a perspective that many of the great minds of the last hundred years have also tried to get us to embrace. Here’s a quote I just came across from Max Planck that I think is particularly powerful:

As a man who has devoted his whole life to the most clear headed science, to the study of matter, I can tell you as a result of my research about atoms this much: There is no matter as such. All matter originates and exists only by virtue of a force which brings the particle of an atom to vibration and holds this most minute solar system of the atom together. We must assume behind this force the existence of a conscious and intelligent mind. This mind is the matrix of all matter.

Image-Golden ratio line

Image via Wikipedia

It’s so easy to look at some of the phrases from this quote and imagine them on some new age site, where mainstream scientists would then smugly dismiss these ideas as hogwash from crackpots. Like me, folks like Dan Winter and Nassim Haramein also sometimes get painted with the crackpot brush, but they are both serious about the ideas they are exploring, and they are not far away from the ideas that Max Planck promoted above, or that I have been pursuing with my project.

On July 1st of this year, I published a well-received blog entry called Love and Gravity. It looked at some new age ideas about wellness and spirituality, and related them to some mainstream science ideas about extra dimensions, timelessness, and the fact that physicists tell us that gravity is the only force which exerts itself across the extra dimensions.

Last week Dan Winter forwarded me a link to a new web page of his which yet again seems to tie into the same viewpoint that I’m promoting: Dan is calling this new page “Gravity is Love“. As usual, this page is a sprawling collection of graphics, animations, and articles, most of which are found on a number of Dan’s other pages, but there’s important new information here as well. Here’s a few paragraphs excerpted from the page which will give you the flavor of what Dan is saying about this concept:

Love really IS the nature of gravity!
First we discovered Golden Ratio identifies the change in pressure over time- of the TOUCH that says I LOVE YOU: goldenmean.info/touch
Then we discovered (with Korotkov’s help) … that the moment of peak perception- bliss – enlightenment- was defined by Golden Ratio in brainwaves :goldenmean.info/clinicalintro
Then medicine discovered: the healthy heart is a fractal heart. ( References/ pictures:goldenmean.info/holarchy, and also: goldenmean.info/heartmathmistake
Then – I pioneered the proof that Golden Ratio perfects fractality because being perfect wave interference it is therefore perfect compression. It is my view that all centripetal forces- like gravity, life, consciousness, and black holes, are CAUSED by Golden Ratio in waves of charge.
Nassim Haramein says that although he sees Golden Ratio emerge from his black hole equations repeatedly – he sees it as an effect of black holes/ gravity – not the cause… Clearly – from the logic of waves – I say the black hole / gravity is the effect of golden ratio and not the other way around!
– although some might say that this is a chicken and egg difference – may be just semantics… at least we agree on the profound importance of Golden RATIO…/ fractality…
AND love :

perfect embedding IS perfect fusion IS perfect compression… ah the romance.

Dan Winter is a fascinating fellow, I hope you can spend some time following the links in the above quote. Next time we’re going to look at another somewhat related approach to imagining the extra-dimensional patterns that link us all together, in an entry called Biosemiotics: Monkeys, Metallica, and Music.

Enjoy the journey!

Rob Bryanton

Carnival of Space #168

Welcome to the Carnival of  Space #168 and WeirdSciences. If you are visiting the carnival of space for the first time and you have no idea what a carnival of space is, you can try to go to Universe Today page.  Now it’s time to start the carnival of space:-

  • Discovery images of Neptune Trojan 2008 LC18Congratulations to Scott Sheppard and Chad Trujillo for identifying the first known L5 Trojan asteroid of Neptune! This story is not just interesting because it is a first-of-its-kind discovery, but because of the tricky way that the astronomers went about searching for it, and because of the collateral benefits that their search will have for the New Horizons mission.

Emily Lakdawalla at Planetary Blog has explained about the discovery of  Trojan Asteroid[and yeah, Trojan Asteroid itself too] with animation showing how this excelling discovery was made.

What? You can’t believe..? Dr. Ian O’Neill of Discovery Space has a stunning article delving much into the topic with high resolution images of moon obtained from LRO.

  • Interesting fact of the day: examining the fossil record suggests that mass extinctions on Earth occur approximately once every 26 million years (Myr). One possible explanation for this is a companion dwarf  star to the Sun on a 26 Myr orbit.

Emma at We Are All in The Gutter Blog, is seeking out the connections between mass exinction and so called Nemesis, a dwarf star based on a newly published research paper.

  • Steve Nerlich at Cheap Astronomy investigates the likelihood of Robonaut 2  refusing to open the pod bay door after it’s deployed on the ISS.
  • This is the light speed limit, which makes us too shy whenever we plan for a interstellar human mission. We can’t ignore the laws of special relativity, but we can still change the speed of  light.

Chris Dann of WeirdWarp Blog is elucidating whether it is plausible?

  • Wayne Hall at Kentucky Space is telling that the second Kentucky Space-built plug-and-play micro-G research rack will be turned up on ISS  Monday.
  • Jupiter’s moon IO is quite fascinating if you are talking about the possibility of exotic life. Jason Perry of Gish Bar Times, is exposing IO’s true colors based on datas obtained from Galileo. A well researched article!
  • Our universe is very mysterious. Astronomers are constantly looking into the past. No matter where you look out into space you are seeing things as they were minutes, hours or millions of years ago. Even at 186,000 miles per second, it takes eight minutes for light to reach us from the Sun. It takes four and a half years for light to reach us from the next nearest star, and millions or billions of years to reach us from other galaxies. So astronomers spend a great deal of time looking into the past.

Mike Somonsen of  Simostronomy Blog is focusing over future surveys to solve the mystery of universe. Really, an excellent article..!!

Alen VerseFeld of The Urban Astronomer blog has a entry featuring stunning discoveries made by LRO missions.

A ceiling full of sky, a beautiful historical  ceiling with an astronomical theme by Ian Musgrave and Peta O’Donohue of Astroblogger blog.

Daniel Sims of  Space Tweep Society Blog has a article providing more information about that contest. If you are interested in contest, please participate in it.

  • Bruce Irving of FlyingSinger blog is talking about Apollo 13 mission.
  • If, at first glance, the preceding account appears fanciful, it is because our thinking has not caught up with the engineering advances of the last few years. . .All the engines are either being developed or are programmed to be developed in the next few years. No new or exotic fuels are required. Indeed, our calculations reflect the sober degree of conservatism that should characterize a preliminary study. We believe that the feasibility has been shown. There remains now the intriguing task of doing the job.

David S.F. Portree of  BeyondApollo has a excellent article about Rosen and Schwenk’s moon mission.

Below are the two articles from Stuart Atkinson

Pradeep Mohandas of Parallel Spirals blog has a article  First anniversary of the Chandrayaan-I – LRO Bistatic Experiment today ,explaining more about that.

See the article by Paul Sutherland of SKYMANIA blog.

Enjoy!!

‘Survivor’ Black Holes May Be Mid-Sized:NASA News

New evidence from NASA’s Chandra X-ray Observatory and ESA’s XMM-Newton strengthens the case that two mid-sized black holes exist close to the center of a nearby starburst galaxy. These “survivor” black holes avoided falling into the center of the galaxy and could be examples of the seeds required for the growth of supermassive black holes in galaxies, including the one in the Milky Way.

For several decades, scientists have had strong evidence for two distinct classes of black hole: the stellar-mass variety with masses about ten times that of the Sun, and the supermassive ones, located at the center of galaxies, that range from hundreds of thousands to billions of solar masses.

But a mystery has remained: what about black holes that are in between? Evidence for these objects has remained controversial, and until now there were no strong claims of more than one such black hole in a single galaxy. Recently, a team of researchers has found signatures in X-ray data of two mid-sized black holes in the starburst galaxy M82 located 12 million light years from Earth.

“This is the first time that good evidence for two mid-sized black holes has been found in one galaxy,” said Hua Feng of the Tsinghua University in China, who led two papers describing the results. “Their location near the center of the galaxy might provide clues about the origin of the Universe’s largest black holes — supermassive black holes found in the centers of most galaxies.” 

Composite image of the nearby starburst galaxy M82

Composite image of the nearby starburst galaxy M82. Image credit: X-ray: NASA/ CXC/Tsinghua Univ./H. Feng et al.

One possible mechanism for the formation of supermassive black holes involves a chain reaction of collisions of stars in compact star clusters that results in the buildup of extremely massive stars, which then collapse to form intermediate-mass black holes. The star clusters then sink to the center of the galaxy, where the intermediate-mass black holes merge to form a supermassive black hole.

In this picture, clusters that were not massive enough or close enough to the center of the galaxy to fall in would survive, as would any black holes they contain.

“We can’t say whether this process actually occurred in M82, but we do know that both of these possible mid-sized black holes are located in or near star clusters,” said Phil Kaaret from the University of Iowa, who co-authored both papers. “Also, M82 is the nearest place to us where the conditions are similar to those in the early Universe, with lots of stars forming.”

The evidence for these two “survivor” black holes comes from how their X-ray emission varies over time and analysis of their X-ray brightness and spectra, i.e., the distribution of X-rays with energy.

Chandra and XMM-Newton data show that the X-ray emission for one of these objects changes in a distinctive manner similar to stellar-mass black holes found in the Milky Way. Using this information and theoretical models, the team estimated this black hole’s mass is between 12,000 and 43,000 times the mass of the Sun. This mass is large enough for the black hole to generate copious X-rays by pulling gas directly from its surroundings, rather than from a binary companion, like with stellar-mass black holes.

The black hole is located at a projected distance of 290 light years from the center of M82. The authors estimate that, at this close distance, if the black hole was born at the same time as the galaxy and its mass was more than about 30,000 solar masses it would have been pulled into the center of the galaxy. That is, it may have just escaped falling into the supermassive black hole that is presumably located in the center of M82.

The second object, located 600 light years in projection away from the center of M82, was observed by both Chandra and XMM-Newton. During X-ray outbursts, periodic and random variations normally present in the X-ray emission disappear, a strong indication that a disk of hot gas dominates the X-ray emission. A detailed fit of the X-ray data indicates that the disk extends all the way to the innermost stable orbit around the black hole. Similar behavior has been seen from stellar-mass black holes in our Galaxy, but this is the first likely detection in a candidate intermediate-mass black hole.

The radius of the innermost stable orbit depends only on the mass and spin of the black hole. The best model for the X-ray emission implies a rapidly spinning black hole with mass in the range 200 to 800 times the mass of the Sun. The mass agrees with theoretical estimates for a black hole created in a star cluster by runaway collisions of stars.

“This result is one of the strongest pieces of evidence to date for the existence of an intermediate-mass black hole,” said Feng. “This looks just like well-studied examples of stellar-mass black holes, except for being more than 20 times as massive.”

Kerr Black Holes

The Schwarzschild reference frame is static outside the Black Hole, so even though space is curved, and time is slowed down close to the Black Hole, it is much like the absolute space of Newton. But we will need a generalized reference frame in the case of rotating Black Holes. Roy Kerr generalized the Schwarzschild geometry to include rotating stars, and especially rotating Black Holes. Most stars are rotating, so it is natural to expect newly formed Black Holes to process significant rotation too.

Features of a Kerr Black Hole

Image

The Kerr black hole consists of a rotating mass at the center, surrounded by two event horizons. The outer event horizon marks the boundary within which an observer cannot resist being dragged around the black hole with space-time. The inner event horizon marks the boundary from within which an observer cannot escape. The volume between the event horizons is known as the ergosphere.

What is a Kerr black hole?

The usual idealised “static” black hole is stationary, unaccelerated, at an arbitarily-large distance from the observer, is perfectly spherical, and has a point-singularity at its centre.

When one of these idealised black holes rotates, it gets an extra property. It’s no longer spherically symmetrical , the receding and approaching edges have different pulling strengths and spectral shifts, and the central singularity is no longer supposed to be a dimensionless point.

Image

The equatorial bulge in the event horizon can be deduced in several ways

  • … as a sort of centrifugal forces effect. Since it’s possible to model the (distantly-observed) hole as having all its mass existing as an infinitely-thin film at the event horizon itself (i.e. where the mass is “seen” to be), you’d expect this virtual film to have a conventional-looking equatorial bulge, through centrifugal forces.
  • … as a sort of mass-dilation effect. Viewed from the background frame, the “moving film” of matter ought to appear mass-dilated, and therefore ought to have a greater gravitational effect, producing an increase in the extent of the event horizon. Since the background universe sees the bh equator to be moving faster than the region near the bh poles, the equator should appear more mass-dilated, and should have a horizon that extends further.
  • … as a shift effect. This tidy ellipsoidal shape isn’t necessarily what people actually see – it’s an idealised shape that’s designed to illustrate an aspect of the hole’s deduced geometry independent of the observer’s viewing angle. In fact, the receding and approaching sides of the hole (viewed from the equator) might appear to have different radii, because it’s easier for light to reach the observer from the approaching (blueshifted) side than the receding (redshifted) side (these shifts are superimposed on top of the normal Schwarzchild redshift).
    If we calculate these motion shifts using either the SR shift assumptions f’/f = (flat spacetime propagation shift) × root[1 – v²/c²] or the plain fixed-emitter shift law f’/f = (c-v)/c, and then treat them as “gravitational”, then by multiplying the two opposing shifts together and rooting the result, we can get the same averaged dilation factor of f’/f=root(1 – v²/c²) in each case, and by applying the averaged value, we recreate the same sort of equatorially-dilated shape that we got in the other two arguments.

Of course, none of these “film” arguments work for a rotating point, which immediately tells us that the distribution of matter within a rotating black hole is important, and that the usual method of treating the actual extent of a body within the horizon as irrelevant (allowing the use of a point-singularity) no longer works when the hole is rotating (a rotating hole can’t be said to contain a point-singularity).
In the case of a rotating hole, the simplest state that we can claim is equivalent to the rotating film of matter for a distant observer is a ring-singularity.

Notes

  • The idea of being able to treat a non-rotating black hole as either a point-singularity or a hollow infinitely-thin film is a consequence of the result that the actual mass-distribution is a “null” property for a black hole, as long as it is spherically symmetrical. If the mass fits into a Schwarzchild sphere, the usual static model of a black hole allows the hole’s mass to be point-sized, golfball-sized, or of any size up to the size of the event horizon.
    It’s usual to treat all the matter as being compacted to a dimensionless point, but sometimes it’s useful to go to the other extreme and treat the matter as being at its “observed” position – as an infinitely-thin film at the event horizon (see Thorne’s membrane paradigm).
  • The idea of being able to treat all shifts as being propagation effects is something that probably ought to be part of GR – in the context of black holes, the time-dilation effect comes out as a curved-space propagation effect due the enhanced gravitation due to kinetic energy. However, there’s a slight “political” problem here, in that GR is supposed to reduce to SR, and SR is usually interpreted as having Lorentz shifts which are supposed to be non-gravitational (because allowing the possibility of gravitational effects upsets the usual SR derivations). A GR-centred physicist might not have a problem with this approach of treating all shift effects as being equivalent, a SR-centred one probably would.
  • The “bulginess” of a Kerr black hole is illustrated on p.293 of the Thorne book (fig 7.9). Thorne says that the effect of the spin on the horizon shape was discovered Larry Smarr in 1973.

Overview of Kerr Spacetime

Kerr spacetime is the unique explicitly defined model of the gravitational field of a rotating star. The spacetime is fully revealed only when the star collapses, leaving a black hole — otherwise the bulk of the star blocks exploration. The qualitative character of Kerr spacetime depends on its mass and its rate of rotation, the most interesting case being when the rotation is slow. (If the rotation stops completely, Kerr spacetime reduces to Schwarzschild spacetime.)

The existence of black holes in our universe is generally accepted — by now it would be hard for astronomers to run the universe without them. Everyone knows that no light can escape from a black hole, but convincing evidence for their existence is provided their effect on their visible neighbors, as when an observable star behaves like one of a binary pair but no companion is visible.

Suppose that, travelling our spacecraft, we approach an isolated, slowly rotating black hole. It can then be observed as a black disk against the stars of the background sky. Explorers familiar with the Schwarzschild black holes will refuse to cross its boundary horizon. First of all, return trips through a horizon are never possible, and in the Schwarzschild case, there is a more immediate objection: after the passage, any material object will, in a fraction of a second, be devoured by a singularity in spacetime.

If we dare to penetrate the horizon of this Kerr black hole we will find … another horizon. Behind this, the singularity in spacetime now appears, not as a central focus, but as a ring — a circle of infinite gravitational forces. Fortunately, this ring singularity is not quite as dangerous as the Schwarzschild one — it is possible to avoid it and enter a new region of spacetime, by passing through either of two “throats” bounded by the ring (see The Big Picture).

Image

In the new region, escape from the ring singularity is easy because the gravitational effect of the black hole is reversed — it now repels rather than attracts. As distance increases, this negative gravity weakens, just as on the positive side, until its effect becomes negligible.

A quick departure may be prudent, but will prevent discovery of something strange: the ring singularity is the outer equator of a spatial solid torus that is, quite simply, a time machine. Travelling within it, one can reach arbitrarily far back into the past of any entity inside the double horizons. In principle you can arrange a bridge game, with all four players being you yourself, at different ages. But there is no way to meet Julius Caesar or your (predeparture) childhood self since these lie on the other side of two impassable horizons.

This rough description is reasonably accurate within its limits, but its apparent completeness is deceptive. Kerr spacetime is vaster — and more symmetrical. Outside the horizons, it turns out that the model described above lacks a distant past, and, on the negative gravity side, a distant future. Harder to imagine are the deficiencies of the spacetime region between the two horizons. This region definitely does not resemble the Newtonian 3-spacebetween two bounding spheres, furnished with a clock to tell time. In it, space and time are turbulently mixed. Pebbles dropped experimentally there can simply vanish in finite time — and new objects can magically appear.


Kerr-Newman Black Hole

A rotating charged black hole. An exact, unique, and complete solution to the Einstein field equations in the exterior of such a black hole was found by Newman et al. (1965), although its connection to black holes was not realized until later (Shapiro and Teukolsky 1983, p. 338).

Rotating (Kerr) Black Holes, Charged and Uncharged
Most stars spin on an axis. In 1963, Roy Kerr reasoned that when rotating stars shrink, they would continue to rotate. Kip Thorne calculated that most black holes would rotate at a speed 99.8% of their mass. Unlike the static black holes, rotating black holes are oblate and spheroidal. The lines of constant distance here are ellipses, and lines of constant angle are hyperbolas.

Image

Unlike static black holes, rotating black holes have two photon spheres. In a sense, this results in a more stable orbit of photons. The collapsing star “drags” the space around it into rotating with it, kind of like a whirlpool drags the water around it into rotating. As in the diagram above, there would be two different distances for photons. The outer sphere would be composed of photons orbiting in the opposite direction as the black hole. Photons in this sphere travel slower than the photons in the inner sphere. In a sense, since they are orbiting in the opposite direction, they have to deal with more resistance, hence they are “slowed down”. Similarly, photons in the inner ring travel faster since they are not going against the flow. It is because the photon sphere in agreement with the rotation can travel “faster” that it is on the inside. The closer one gets to the event horizon, the faster one has to travel to avoid falling into the singularity – hence the “slower” moving photons travel on the outer sphere to lessen the gravitational hold the black hole has.

The rotating black hole has an axis of rotation. This, however, is not spherically symmetric. The structure depends on the angle at which one approaches the black hole. If one approaches from the equator, then one would see the cross-section as in the diagram above, with two photon spheres. However, if one approached at angles to the equator, then one would only see a single photon sphere.

The position of the photon spheres also depend on the speed at which the black hole rotates. The faster the black hole rotates, the further apart the two photon spheres would be. For that matter, a black hole with a speed equal to its mass would have the greatest possible distance between the two photon spheres. This is because of greater difference in the speed between the photon spheres. As the speed of rotation increases, the outer sphere of photons would slow down as it meets greater resistance, even as the inner sphere would travel “faster” as it is pushed along by the centripetal forces.

Next, we move on to look at the ergosphere. The ergosphere is unique to the rotating black hole. Unlike the event horizon, the ergosphere is a region, and not a mathematical distance. It is a solid ellipsoid (or a 3-dimensional ellipse). The ergosphere billows out from the black hole above the outer event horizon of a charged black hole (a.k.a. Kerr-Newman), and above the event horizon of an uncharged black hole (a.k.a. Kerr). This distance is known as the static limit of a rotating black hole. At this distance, it is no longer possible to stay still even if one travels at the speed of light. One would inevitably be drawn towards the singularity. The faster the rotation, the further out it billows. When the ergosphere’s radius is half the Schwarzschild radius along the axis of rotation, it experiences the greatest distance it can billow out. At this point, even light rays are dragged along in the direction of rotation. Strangely enough, it is postulated that one can enter and leave as one likes since technically, you have not hit the event horizon yet.

For a rotating black hole, the outer event horizon switches time and space as we know it. The inner event horizon, in turn, returns it to the way we know it. Singularity then becomes a place rather than a time, and can technically be avoided. When angular velocity increases, both the outer and the inner event horizon move closer together.

In the diagram, you would have noticed that the singularity here is drawn as a ring, and not a point, as it was for the static black hole. In the case of a rotating black hole, the gravity around the ringed singularity is repulsive. In other words, it actually pushes one away, allowing you to actually leave the black hole. The only way to approach the ring singularity would be to come in from the equatorial plane. Other trajectories would be repelled with greater strength, proportional to the closer the angle is to the axis of rotation.

In addition, there would be a third photon sphere about the ring singularity. If light is parallel to the axis of rotation, the gravity and the anti-gravity of the singularity are balanced out. Light then traces out the path of constant distance (which, in the case is an ellipsoid). Technically, this might lead the light into another universe through the singularity, and then back out again. At this point within the black hole, we may see three types of light: the light reflected from our universe behind us; the light from other universes; and the light from the singularity.

Again On The Plausibility Of Time Machine

High in the sky on a clear fall evening is the star group called Cygnus, the Swan. It is not hard to find. Look for a large pattern of stars in the shape of a cross, or a swan in flight.

A map of the constellation Cygnus is shown below. On the map, the end of the swan’s tail is marked by a bright star called Deneb. Slightly ahead of Deneb are three stars in a line. They represent the swan’s body and the tips of its wings. Finally some distance away is a fifth, fairly bright star, Albireo. It marks the position of the great bird’s head.

Now look halfway along the neck of the swan. There is a point on the map labeled Cygnus X-1. The next time you are outside on a clear, dark fall evening, locate Cygnus and gaze at the spot where Cygnus X-1 lies. Though you will not actually see anything, you will be looking at the exact point in space where scientists believe there may be a black hole.

The location of Cygnus X-1, thought to be a black hole, in Cygnus the Swan

Crushed Out of Sight

Black holes are popular subjects in films, as well as in many science fiction stories. But there is a good chance that black holes really exist in space. They are places where the pull of gravity is so strong that nothing, not even light, can escape from them. Once inside a black hole, you could never come back out the same way. However, it is possible that you could escape by a different route and arrive at a totally different part of the Universe. What is more, a journey into a black hole might transport you through time, either into the far future or the remote past.

The Crab Nebula is the remains of a massive star that blew apart at the end of its life. Though the Crab Nebula does not contain a black hole, these strange objects may be found in the supernova wreckage of some other giant stars.


How can black holes be made? One way is by the explosion of very heavy stars. A star that weighs 20 or 30 times as much as the Sun can shine brightly for only a few million years. Then it blows itself apart. During this huge explosion, known as a supernova, all the top layers of the old star are blasted away into space at high speed. However, the core, or central part, of the star may remain whole.

In a normal, middle-aged star, such as the Sun, the core is the place where light and heat are made. Here the temperature is incredibly high – many millions of degrees. The outward pressure of this light and heat prevents the inward force of gravity from squeezing the core any smaller. For most of a star’s life, these two great forces struggle against one another in an evenly matched game of tug-of-war. But in a dead star, there is no longer any light pressure to oppose gravity. As a result, the core is squeezed tighter and tighter and gets smaller and smaller.

When average-sized stars, such as the Sun, reach the end of their lives, their cores shrink down to hot balls of squashed matter. These are called white dwarfs. Then another force, caused by particles of matter becoming too crowded together, stops gravity from crushing a white dwarf to an even smaller size.

In bigger, heavier stars, the force of gravity acting on the dead star’s core is much stronger. Even after the supernova explosion has blown away much of the star’s contents, the core that remains may be heavier than the Sun. If the core is more than three times as heavy as the Sun, nothing can prevent gravity from crushing the core smaller and smaller. From an original size of more than 20,000 miles across, the core is squashed in less than a tenth of a second to a ball only 25 miles across. At this stage, a tablespoonful of its matter would weigh the same as four billion full-grown elephants. But gravity squeezes it still smaller. In a fraction of a second, more than three sun’s worth of star material becomes crammed into an incredibly tiny space. Now it may be no larger than the period at the end of this sentence.

Within a few miles of the totally crushed star, gravity is so strong that it will pull in anything that comes too close. And it will allow nothing to escape, not even a ray of light traveling at more than 186,000 miles per second. The region around the crushed star is completely black and invisible. That is why scientists call it a black hole.

The Mystery of Cygnus X-1

An artist imagines how the black hole in Cygnus X-1 might look. It lies at the center of the spinning whirlpool of matter that has been pulled off the large yellow star


If black holes are black and invisible, then how can we ever know they are there? In fact, we cannot, unless there is something nearby that can be seen and upon which the black hole has a noticeable effect. This is the case with Cygnus X-1.

From observations made by instruments in space, scientists have discovered that huge amounts of X-rays – rays that carry a great deal of energy – are coming from the direction of Cygnus X-1. They have also found that a binary star lies in the same position as the source of the X-rays. A binary star consists of two stars that are circling around each other. One of these stars is much bigger and brighter than the Sun, but it can only be seen through a large telescope because it is so far away. Astronomers know it is there because of the “wobbles” it causes in the movement of its giant neighbor.

From the extent of the wobbles, astronomers think the dark star in Cygnus X-1 must weigh from five to eight times as much as the Sun. This fact alone suggests that it is likely to be a black hole. But the X-rays offer still stronger evidence. Careful studies of the X-rays have revealed that they are almost certainly coming from a whirlpool of extremely hot gas. This gas, scientists believe, has been stripped away from the bright giant star by the gravitational pull of a nearby black hole. Just before it disappears down the black hole, the gas is heated to more than 18 million °F. At that superhigh temperature, it gives off an intense X-ray glow.

Into the Black Hole

To travel from a point in space and time A to another point in space and timeB, spaceship 1 takes an ordinary route around the Universe. Spaceship 2, though, takes a shortcut using a wormhole. If B lies farther back in time thanA, then the journey could only be made through the wormhole.


Even before scientists found signs of real black holes in the Universe, they had studied the mathematics of what black holes might be like inside. According to their theories, black holes may be like the entrances of tunnels that join different regions of space and time. These strange tunnels are called wormholes. At the end of a wormhole is an exit known as a white hole. By going into a black hole, traveling along its wormhole, and then coming out the white hole at the other end, a spacecraft might be able to leap across huge distances of space and millions of years in time.

But two British scientists, Stephen Hawking and Roger Penrose, pointed out some problems with this wonderful way to travel. For one thing, there seems to be an energy barrier inside a black hole. No normal object, such as a spacecraft, could pass through this barrier without being torn to bits. The two scientists identified a second major problem. It appears that the wormhole tunnel would instantly squeeze shut if a piece of matter tried to move along it.

However, in 1988, new results were published by researchers Michael Morris, Kip Thorne, and Ulvi Yurtsever at the California Institute of Technology. These showed that a wormhole might be kept open with the help of two round plates that carried a charge of electricity. The plates would be located on either side of the “throat” leading into the wormhole. Results from even more recent research have shown that objects entering a spinning black hole might also be able to travel through time.

Yet, just because something is possible in theory does not mean it will quickly, or ever, become fact. We are still not certain that black holes exist. The evidence for them, though, is strong. If they do exist, then the nearest one is likely to be many trillions of miles away. Cygnus X-1 is about 10,000 light-years from Earth. One light-year is the distance that light travels in a year, or about 6 trillion miles. Cygnus X-1, then, lies about 60 thousand trillion miles away!

It is possible that there are closer black holes to Earth that we have not yet found. If they are not members of binary systems, then they would be extremely hard to detect. Still, it would be surprising if there were a black hole similar to Cygnus X-1 that was closer than a few hundred light-years to the Sun. At such a distance, it would be very difficult to reach such an object. And it would be even harder to use it as a time machine.

Black Holes, Large and Small

Much larger black holes, weighing millions or even billions of times as much as the Sun, are thought to lie in the center of galaxies. Galaxies are huge collections of stars arranged in spiral, round, oval, or irregular shapes. We live in a galaxy called the Milky Way. To explain the unusual amount of energy coming from the middle of large galaxies, scientists have proposed the idea of “supermassive” black holes. But these would lie even farther from Earth than black holes that formed from neighboring stars.

There may also be mini back holes. These may be smaller than a pea but with the mass, or amount of matter, of a mountain. It is also possible that scientists will someday be able to create their own tiny black holes in the laboratory. They might do this by directing extremely intense, pure beams of light into a tiny pellet of matter. If enough energy could be focused onto the pellet at one time, it would collapse to form a black hole so small that it could only be seen under a microscope.

But there is a problem with this plan. Small black holes would tend to rip apart any object that was sent into them. This would happen because the pull of gravity on anything approaching a mini black hole would be much greater at the front of the object than at the back.

In the case of a very large, massive black hole, the difference in gravitational pull across an approaching object would be much less. The supermassive black holes that may occupy the center of some galaxies also appear to be the only kind that human beings might be able to enter and survive.

Beyond the Light Barrier


According to Einstein’s Special Theory of Relativity, no object can accelerate up to the speed of light. As an object goes faster, its mass increases. That makes it harder and harder to boost its speed further. To reach the speed of light, even a particle that started out with a tiny mass would require more energy than there is in the whole Universe.

Einstein’s theory, though, does not say that faster-than-light particles cannot exist. It only says that if there are such particles, known as tachyons, then they can never travel at or less than light speed.

If tachyons did turn out to be real, they would behave in a very strange way. They would travel backward in time! This is another prediction of Einstein’s theory. Any object that travels faster than light would seem to us to be moving into the past. As a result, a tachyon could be detected by an instrument before it was actually formed. On the practical side, tachyons might make possible an unusual kind of telephone. On this phone, calls could be sent into the past! So far, despite searches carried out by various groups of researchers, no real tachyon has yet been found.

The Prospect for Time Travel

Could you then build a time machine? With devices such as cameras and video recorders, it is already possible to review events from the past. Researchers are also making progress in learning how humans age and how the aging process might be slowed. Perhaps within 20 or 30 years, there will be methods to allow people to live longer. If so, they will see much more of the future.

Other forms of time travel will probably take longer to develop. It is unlikely that there will be any crew carrying spaceships that can fly close to the speed of light by the end of the twenty-first century. But such craft will be built. Then human beings who travel to the stars will go on journeys through time. They will leap hundreds, thousands, or even millions of years into the future during their own lifetimes.

Scientists today do not know if black holes will ever be used as a means to jump instantly into the remote past or future. The technical problems to be overcome, even if such journeys are possible, are among the most difficult imaginable. Yet the people who lived a century ago might have thought of human missions to the Moon in the same way.

Someday, in some form, the human race is likely to build a machine that can swiftly travel through time. Where that will lead us to, no one yet knows.

Space Time:Continuums And Curvature

Relativity views space-time as a continuum; that is, time becomes another dimension of space, making space four-dimensional. This is really common sense-we know that it takes time to move through the physical dimensions of space. (length, width, and heigth) Time is a property of space that is distinct from yet closely related to the other three. (Althought we know we can move through space in any direction, we can only move forward in time, at least until wormholes are discovered.)

Curvature of space-time can be more difficult to understand. Although the rubber sheet model gives a picture of how it happens, one cannot easily picture the so-called nothingness of space being curved or a non-physical property like time being warped. But relativity (a theory which has yet to be disproved) predicts this curvature and uses gravity as proof of it. In fact, relativity predicts singularities, points in space-time where the curvature reaches infinity. Singularities are the centers of black holes, points of gravity so strong that nothing, not even light, can escape.

According to relativity, the curvature of space-time is gravity, and this raises an intersting paradox: the amount of curvature is governed by the distribution of matter and energy in the univers, but this distribution is determined by the curvature of space-time. Thinking back to the rubber sheet model, this becomes an obvious truth. A large object, such as a shot put, would cause a large indentation that would cause a marble to roll in. Or, if an area of rubber sheet space contained only small objects, several marbles might roll together to form an area of ‘strong gravity’, which would in turn attract more objects.

Besides creating the all-important force of gravity, space-time curvature also makes a major dent (no pun intended) in one of our most common beliefs from geometry and family vacations: in curved space-time, a straight line is NOT always the shortest distance between two points. But that’s a different topic.

In order to move through the physical dimensions of space, one must also move through time. In this graph, time surrounds the axes, and although the lines could be extended so that we could move in any physical direction, we do not extend them because we do not know how to move backwards in time.

                                               

Black holea re probably the most researched and best known of the topics dealing with relativity. Their existence has been speculated for over 200 years, but has yet to be proven.

A black hole is a region of space where gravity is so strong that nothing, not even light, can escape. (According to relativity, nothing can travel faster than light, so this makes sense.)

But what would cause this strong of a gravitational force? According astronomer John Michell in 1783, it would have to be the collapse of a massive star. And today we know that these massive stars exist-neutron stars.

A neutron star is the final phase of a star more than two times as large as the sun. The sun would collapse into a white dwarf-a dense, earth-sized ball of gas that can collapse no further due to the outward pressure of electrons spinning at near the speed of light.

But in a large star, the gravitational force is so strong that the electrons are pulled into the atomic nucleus where they combine with protons to form neutrons. A neutron star is small and unchanged-only a few miles in diameter. Then one of two things can happen.

That ‘strong force’-the force that holds the atomic nucleus together can abruptly stop the implosion and cause the start to burst into a supernova. But if they star is more than two times the sun’s size, nothing can stop its collapse into a small, dense object that traps even light- a black hole.

How does aone picture this in the rubber sheet model? Imagine placing an object so massive on the sheet that it cause its indentation to pinch off. This would cause the rest of the sheet to angle down towards the hole, and smaller objects would roll in towards this huge ‘gravitational pull’.

Anatomy of a Black Hole…

Although black holes would seem the upitome of chaos, they have a definite structure, and it is even thought that the more matter and energy they pull in, the more ordered they become. (This distintly goes against Newton’s Laws of Physics, but who’s going to tell the black hole that?)

The outermost edge of a black hole is the event horizon, or Schwarzschild radius. It’s the point at which the star collapsed into a black hole, and its size is therefore proportional to the star’s mass.

That’s the only definite part of a black hole. It used to be also generally agreed that there is a singularity at the center of a black holes where the laws of physics break down, but recently, Stephen Hawking, the leading expert on black holes, has begun to suspect that this may not be true.

Although black holes have the same structure, they are not all alike. Size varies greatly among black holes, with smaller ones causing more distortion of space-time; space-time would have to wrap itself more tightly around a smaller one to close it off. (Think of tine, extremely dense object being dropped on the rubber sheet.)

The physical difference with the most impact, though, is whether it is a rotating or non-rotating black hole. A still black hole is just as was discribed: event horizon, that singularity. But a rotating black hole has two even horizons, and makes some major differences.

Inside the first event horizon, it is just like a non-rotating black hole (the rotation, by the way, is from the rotation of the star before it collapses): gravity pulling you in faster and faster. But when you hit the second event horizon, it’s like the eye of a storm: There is no singularity, and space-time seems to return to normal.

There is a problem, of course-there may be anti-gravity after the second event horizon, so you would be spit right back out. To where? Perhaps an alternate universe.

 

…And some other important schtuff

As was mentioned earlies, black holes are not known for sure to exist. But there may be one at the center of our galaxy, or in the binary system Cygnus X-1, 6000 light years from Earth.

Besides looking for the obvious area of ‘nothingness’ in space, there are other clues to the presence of one. In a binary system, one looks for accretion disks, a disk of gas that swirls into the suspected black hole from a neighboring star.

There is also the gravitational red shift. Longer light waves (red colors) have less energy. Photons of light will lose more and more energy as they try to escape the steadily stronger gravity of a black hole. The wavelengths lengthens until we must use radio and infrared telescopes to detect it, and then it either becomes to long to detect or it disappears.

The newest proof of black holes may be quasars-stars that radiate enough energy like an entire galaxy. These could be ‘white holes’, the opposite end of a black hole.

Black holes may have another way of being detected – Hawking Radiatin. Although nothing escapes from a black hole, Steven Hawking theorized that something must, because black holes have entropy. Anything with entropy must have a temperature, and anything with a temperature must emit radiation. The empty space around a black hole, he says, contains miniscule virtual particles that have positive and negative charges. Normally they combine to annhiliate each other. Sometimes the negative one will fall into the black hole, and the positively charged one will escape.

We have, been, plenty of proof that black holes exist. We just have yet to prove that they do exist. If the do, the all important question would be;

What happens when you fall into a black hole???

Good question. And there is two ways to look at it.

From the point of view of the person falling in, not much would change. You would feel fine, time would run normally, and life would be good. That is, until you began to be stretched apart by the difference in gravity between your head and feet. All parts of you body would be pulled towards the center of gravity, so you would be taffy before you reached the event horizon.

To the person watching you, this would not be the case. Say that you were sending singals back to the observer every second. To you, the singals would be sent out every second, but the closer you got the the event horizon, the longer they would take to reach the observer. The one sent out when you are at the event horizon can (ingnoring the fact that you would be dead) would never reach them. In fact, they would never see you reach the event horizon. Time at the event horizon is so slowed down according to the observers relative time, that you would seem to hang at the brink forever.

Black holes are still an unproven enigma, but their presence could lead to the discovery of an even more elusive theory-wormholes.

Parallel universes would seem to be the most unlikely prediction of relativity, but their proposal is just as fact-based as those dealing with black holes.

The idea of parallel universes was taken seriously after experiments with properties of light. Night exhibits wave-particle duality-it acts like both a particle and a wave. But even this odd characteristic did not account for the surprising results scientists noted in ‘double slit tests’. A beam of light would be shined at a screen through another screen with two slits in it. When both slits were open, it seemed as if an electron would pass through both at the same time; and with one open, some areas of the screen would get more light then when both were open. While some of this could be attributed to particle-wave duality, in some cases it seemed almost as though the possibilities of what the light could do was affecting the outcome.

The only way for this to happen is for all the possiblities to exist at once. This idea is the backbone of the parallel universe theory-that all the possibilities for every action exist as an alternate universe. At the moment when an outcome is needed, they can overlap, or one of the separate universes will bend its solution.

Because there are an infinite number of possibilities, there is an infinite number of parallel universes, and therefore, an infinite number of you. A parallel universe for you oversleeping this morning, losing your homework, wearing different clothes… it goes on. For every interaction, there is a myriad of possibilites.

This all seems very far-fetched from Einstein’s theory, but Einstein actually speculated and believed in parallel universes. He helped to discover the Einstein-Rosen  Bridge-the area at the singularity of a rotating black hole where one can cross into a parallel universe.

Which is really the heart of the problem-reaching the singularity of a rotating black hole. But you’ll have to read about black holes to find out why.

Myth of Strange Matter And Black Hole at LHC

The LHC, like other particle accelerators, recreates the natural phenomena of cosmic rays under controlled laboratory conditions, enabling them to be studied in more detail. Cosmic rays are particles produced in outer space, some of which are accelerated to energies far exceeding those of the LHC. The energy and the rate at which they reach the Earth’s atmosphere have been measured in experiments for some 70 years. Over the past billions of years, Nature has already generated on Earth as many collisions as about a million LHC experiments – and the planet still exists. Astronomers observe an enormous number of larger astronomical bodies throughout the Universe, all of which are also struck by cosmic rays. The Universe as a whole conducts more than 10 million million LHC-like experiments per second. The possibility of any dangerous consequences contradicts what astronomers see – stars and galaxies still exist.

Microscopic black holes

Microscopic black holes which are said to be formed at LHC and related dooms day myth is one of the most popularized myth. I can remember when news channels were highlighting those myths. Well, how this implication came to existence?

Nature forms black holes when certain stars, much larger than our Sun, collapse on themselves at the end of their lives. They concentrate a very large amount of matter in a very small space. Speculations about microscopic black holes at the LHC refer to particles produced in the collisions of pairs of protons, each of which has an energy comparable to that of a mosquito in flight. Astronomical black holes are much heavier than anything that could be produced at the LHC.

According to the well-established properties of gravity, described by Einstein’s relativity, it is impossible for microscopic black holes to be produced at the LHC. There are, however, some speculative theories that predict the production of such particles at the LHC. All these theories predict that these particles would disintegrate immediately. Black holes, therefore, would have no time to start accreting matter and to cause macroscopic effects.

Although theory predicts that microscopic black holes decay rapidly, even hypothetical stable black holes can be shown to be harmless by studying  the consequences of their production by cosmic rays.  Whilst collisions at the LHC differ from cosmic-ray collisions with astronomical bodies like the Earth in that new particles produced in LHC collisions tend to move more slowly than those produced by cosmic rays, one can still demonstrate their safety.  The specific reasons for this depend whether the black holes are electrically charged, or neutral. Many stable black holes would be expected to be electrically charged, since they are created by charged particles.  In this case they would interact with ordinary matter and be stopped while traversing the Earth or Sun, whether produced by cosmic rays or the LHC. The fact that the Earth and Sun are still here rules out the possibility that cosmic rays or the LHC could produce dangerous charged microscopic black holes. If stable microscopic black holes had no electric charge, their interactions with the Earth would be very weak. Those produced by cosmic rays would pass harmlessly through the Earth into space, whereas those produced by the LHC could remain on Earth. However, there are much larger and denser astronomical bodies than the Earth in the Universe. Black holes produced in cosmic-ray collisions with bodies such as neutron stars and white dwarf stars would be brought to rest. The continued existence of such dense bodies, as well as the Earth, rules out the possibility of the LHC producing any dangerous black holes.

Strangelets

Strangelet is the term given to a hypothetical microscopic lump of ‘strange matter’ containing almost equal numbers of particles called up, down and strange quarks. According to most theoretical work, strangelets should change to ordinary matter within a thousand-millionth of a second. But could strangelets coalesce with ordinary matter and change it to strange matter? This question was first raised before the start up of the Relativistic Heavy Ion Collider, RHIC, in 2000 in the United States. A study at the time showed that there was no cause for concern, and RHIC has now run for eight years, searching for strangelets without detecting any. At times, the LHC will run with beams of heavy nuclei, just as RHIC does. The LHC’s beams will have more energy than RHIC, but this makes it even less likely that strangelets could form. It is difficult for strange matter to stick together in the high temperatures produced by such colliders, rather as ice does not form in hot water. In addition, quarks will be more dilute at the LHC than at RHIC, making it more difficult to assemble strange matter. Strangelet production at the LHC is therefore less likely than at RHIC, and experience there has already validated the arguments that strangelets cannot be produced. 

Vacuum bubbles

There have been speculations that the Universe is not in its most stable configuration, and that perturbations caused by the LHC could tip it into a more stable state, called a vacuum bubble, in which we could not exist. If the LHC could do this, then so could cosmic-ray collisions. Since such vacuum bubbles have not been produced anywhere in the visible Universe, they will not be made by the LHC.

Magnetic monopoles

Magnetic monopoles are hypothetical particles with a single magnetic charge, either a north pole or a south pole. Some speculative theories suggest that, if they do exist, magnetic monopoles could cause protons to decay. These theories also say that such monopoles would be too heavy to be produced at the LHC. Nevertheless, if the magnetic monopoles were light enough to appear at the LHC, cosmic rays striking the Earth’s atmosphere would already be making them, and the Earth would very effectively stop and trap them. The continued existence of the Earth and other astronomical bodies therefore rules out dangerous proton-eating magnetic monopoles light enough to be produced at the LHC.

Other aspects of LHC safety:

Concern has recently been expressed that a ‘runaway fusion reaction’ might be created in the LHC carbon beam dump. The safety of the LHC beam dump had previously been reviewed by the relevant regulatory authorities of the CERN host states, France and Switzerland. The specific concerns expressed more recently have been addressed in a technical memorandum by Assmann et al. As they point out, fusion reactions can be maintained only in material compressed by some external pressure, such as that provided by gravity inside a star, a fission explosion in a thermonuclear device, a magnetic field in a Tokamak, or by continuing isotropic laser or particle beams in the case of inertial fusion. In the case of the LHC beam dump, it is struck once by the beam coming from a single direction. There is no countervailing pressure, so the dump material is not compressed, and no fusion is possible.

Concern has been expressed that a ‘runaway fusion reaction’ might be created in a nitrogen tank inside the LHC tunnel. There are no such nitrogen tanks. Moreover, the arguments in the previous paragraph prove that no fusion would be possible even if there were.

Finally, concern has also been expressed that the LHC beam might somehow trigger a ‘Bose-Nova’ in the liquid helium used to cool the LHC magnets. A study by Fairbairn and McElrath has clearly shown there is no possibility of the LHC beam triggering a fusion reaction in helium.

We recall that ‘Bose-Novae’ are known to be related to chemical reactions that release an infinitesimal amount of energy by nuclear standards. We also recall that helium is one of the most stable elements known, and that liquid helium has been used in many previous particle accelerators without mishap. The facts that helium is chemically inert and has no nuclear spin imply that no ‘Bose-Nova’ can be triggered in the superfluid helium used in the LHC.

Comments on the papers by Giddings and Mangano, and by LSAG

The papers by Giddings and Mangano and LSAG demonstrating the safety of the LHC have been studied, reviewed and endorsed by leading experts from the CERN Member States, Japan, Russia and the United States, working in astrophysics, cosmology, general relativity, mathematics, particle physics and risk analysis, including several Nobel Laureates in Physics. They all agree that the LHC is safe.

The paper by Giddings and Mangano has been peer-reviewed by anonymous experts in astrophysics and particle physics and published in the professional scientific journal Physical Review D. The American Physical Society chose to highlight this as one of the most significant papers it has published recently, commissioning a commentary by Prof. Peskin from the Stanford Linear Accelerator Laboratory in which he endorses its conclusions. The Executive Committee of the Division of Particles and Fields of the American Physical Society has issued a statement endorsing the LSAG report.

The LSAG report has been published by the UK Institute of Physics in its publication Journal of Physics G. The conclusions of the LSAG report were endorsed in a press release that announced this publication.

The conclusions of LSAG have also been endorsed by the Particle and Nuclear Physics Section (KET) of the German Physical Society. A translation into German of the complete LSAG report may be found on the KET website, as well as here. (A translation into French of the complete LSAG report is also available.)

Thus, the conclusion that LHC collisions are completely safe has been endorsed by the three respected professional societies of physicists that have reviewed it, which rank among the most highly respected professional societies in the world.

The overwhelming majority of physicists agree that microscopic black holes would be unstable, as predicted by basic principles of quantum mechanics. As discussed in the LSAG report, if microscopic black holes can be produced by the collisions of quarks and/or gluons inside protons, they must also be able to decay back into quarks and/or gluons. Moreover, quantum mechanics predicts specifically that they should decay via Hawking radiation.

Nevertheless, a few papers have suggested that microscopic black holes might be stable. The paper by Giddings and Mangano and the LSAG report analyzed very conservatively the hypothetical case of stable microscopic black holes and concluded that even in this case there would be no conceivable danger. Another analysis with similar conclusions has been documented by Dr. Koch, Prof. Bleicher and Prof. Stoecker of Frankfurt University and GSI, Darmstadt, who conclude:

“We discussed the logically possible black hole evolution paths. Then we discussed every single outcome of those paths and showed that none of the physically sensible paths can lead to a black hole disaster at the LHC.”

Professor Roessler (who has a medical degree and was formerly a chaos theorist in Tuebingen) also raised doubts on the existence of Hawking radiation. His ideas have been refuted by Profs. Nicolai (Director at the Max Planck Institute for Gravitational Physics – Albert-Einstein-Institut – in Potsdam) and Giulini, whose report (see here for the English translation, and here for further statements) point to his failure to understand general relativity and the Schwarzschild metric, and his reliance on an alternative theory of gravity that was disproven in 1915. Their verdict:

“[Roessler’s] argument is not valid; the argument is not self-consistent.”

The paper of Prof. Roessler has also been criticized by Prof. Bruhn of the Darmstadt University of Technology, who concludes that:

“Roessler’s misinterpretation of the Schwarzschild metric [renders] his further considerations … null and void. These are not papers that could be taken into account when problems of black holes are discussed.”

A hypothetical scenario for possibly dangerous metastable black holes has recently been proposed by Dr. Plaga. The conclusions of this work have been shown to be inconsistent in a second paper by Giddings and Mangano, where it is also stated that the safety of this class of metastable black hole scenarios is already established by their original work. Finally I can decern that such existing myths are nonexistent.

KOCH, B., BLEICHER, M., & STOCKER, H. (2009). Exclusion of black hole disaster scenarios at the LHC Physics Letters B, 672 (1), 71-76 DOI: 10.1016/j.physletb.2009.01.003

 
PANAGIOTOU, A., & KATSAS, P. (2007). Searching for Strange Quark Matter with the CMS/CASTOR Detector at the LHC Nuclear Physics A, 782 (1-4), 383-391 DOI: 10.1016/j.nuclphysa.2006.10.020

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